Nazism in relation to other concepts

Nazi sacred symbol – the swastika or gamma cross
The Nazi symbol is the right-facing swastika.

Nazism and religion
The relationship between Nazism and mysticism is one that has provoked both curiosity and controversy over the years, as has the relationship between Nazism and Christianity.
Hitler and other Nazi leaders clearly made use of both Christian and Pagan symbolism and emotion in propagandizing the Germanic public, and it remains a matter of controversy whether Hitler believed himself a Christian, a heathen, or something else entirely. Some historians have typified Hitler as a Satanist or occultist, whereas other writers have utilized Nazism's occasional outward use of Christian doctrine, regardless of what its inner-party mythology may have been. The existence of a Ministry of Church Affairs, instituted in 1935 and headed by Hanns Kerrl, was hardly recognized by ideologists such as Rosenberg and by other political decision-makers.
The nature of the Nazi Party's relations with the Catholic Church is also complicated. Many Catholic priests and leaders vociferously opposed Nazism on the grounds of its incompatibility with Christian morals. Pope Pius XI issued the encyclical Mit brennender Sorge (1937) condemning Nazi ideology. Like political dissenters, many priests were sent to the concentration camps for their opposition, including the parson of Berlin Cathedral Bernhard Lichtenberg. (Some of these were Poles persecuted for their nationality.) Hitler was never excommunicated by the Catholic Church.
Nonetheless, since the 1960s it has been claimed by some that the Church hierarchy headed by Pope Pius XII remained largely silent in the face of Nazism, and allegations of the Pope's complicity are today commonplace; see for example John Cornwell's book Hitler's Pope: The Secret History of Pius XII (although many works have since been published defending Pius's wartime record, e.g. Ralph McInerny's The Defamation of Pius XII.)
As Nazism continued to rule Germany, to many people it became a kind of religion in and of itself, sometimes called Esoteric Hitlerism, and sometimes associated with Ásatrú.

Nazism and fascism
The term Nazism is often used interchangeably with fascism, but this usage is controversial. Some use the word Fascism (spelled with a capital F), only to describe Italian Fascism, while generic fascism (spelled with a small f) may include many different movements, in many different countries.
Nazism and Italian Fascism both employed a similar style of propaganda, including military parades and uniforms, and the Roman salute. The ideologies of both ostensibly included an extreme nationalism and a rebirth of their own nation to some former, past state of national greatness. Both movements, when in power, also put in place totalitarian governments that pursued wars of expansion.
There were also many important differences between the two movements. For example, racism was central to Nazism but of less significance in Italian Fascism. Fascist Italy did not adopt anti-semitism until it followed Hitler's example.

Nazism and socialism
Because Nazism is an abbreviation for "National Socialism", and Nazi leaders sometimes described their ideology as a form of socialism, some people believe that Nazism was a form of socialism, or that there are similarities between Nazism and socialism. It has also been argued that the Nazi use of economic intervention, including central planning and some limited public ownership, is indicative of socialism.
Nazi leaders were opposed to the Marxist idea of class conflict and opposed the idea that capitalism should be abolished and that workers should control the means of production. For those who consider class conflict and the abolition of capitalism as essential components of socialist progress, these factors alone are sufficient to categorize "National Socialism" as non-socialist.
Nazi leaders made statements describing their views as socialist, while at the same time opposing the idea of class conflict espoused by the Social Democrats (SPD) and Communists (KPD). Established socialist movements did not view the Nazis as socialists and argued that the Nazis were thinly disguised reactionaries. Historians such as Ian Kershaw also note the links between the Nazis and the German political and economic establishment and the significance of the Night of the Long Knives in which Hitler purged what were at the time seen as "leftist" elements in the Nazi Party and how this was done at the urging of the military and conservatives.
Many of the traditional center and right political parties of the Weimar Republic accused the Nazis of being socialists citing planks in the Nazis' party program which called for nationalization of trusts and other socialist measures. However, the German National People's Party (DNVP), the most important party on the mainstream right, usually treated the Nazis as a respected potential member of coalition cabinet.
The Nazis came to power through an alliance with some conservative factions, though also experienced opposition from some others. Franz von Papen, a conservative former German Chancellor and former member of the Catholic Centre Party supported Hitler for the position of Chancellor. Events during the Papen chancellorship led to the Enabling Act which gave the Nazis dictatorial powers, passed with the support of conservative and centrist deputies in the Reichstag, over the opposition of Social Democrats and Communists. Other conservatives opposed Hitler, notably Chancellor Kurt von Schleicher, who attempted to construct a center-right-led "cross front" that united anti-Hitler factions on the right and center-left in the Reichstag. Schleicher, having been forced from the Chancellorship by Papen, was assassinated by the Nazis on the Night of the Long Knives.
When the Nazis were still an opposition party some leaders, particularly Gregor Strasser, espoused anti-big business stances and advocated the idea of the Nazis as a workers' party. In spite of this, most workers continued to vote for the SPD or the KPD as late as the March 1933 elections held shortly after Hitler's appointment as chancellor.
Ideologically fascism and Nazism reject the most important aspects of Marxist theory. For instance, Hitler did not exalt the working class over the capitalist class as Marx prescribed. In his book Mein Kampf, Hitler wrote 'the suspicion was whispered in German Nationalist circles that we also were merely another variety of Marxism, perhaps even Marxists suitably disguised, or better still, Socialists... We used to roar with laughter at these silly faint-hearted bourgeoisie and their efforts to puzzle out our origin, our intentions and our aims. ' Hitler despised Karl Marx as a Jew and condemned communism and Marxism as a Judeo-Bolshevist conspiracy pledging to block its rise in Germany arguing that the nation's downfall was due to Marxism and its Jewish influence. These actions prompted some prominent conservatives and capitalists to fund and support the Nazis because they saw them as a bulwark against Bolshevism.
There were ideological shades of opinion within the Nazi Party, particularly before their seizure of power in 1933, but a central tenet of the party was always the leader principle or Führerprinzip. The Nazi Party did not have party congresses in which policy was deliberated upon and concessions made to different factions. What mattered most was what the leader, Adolf Hitler, thought and decreed. Those who held opinions which were at variance with Hitler's either learned to keep quiet or were purged, particularly after 1933. Although this is in some respects comparable to the behavior of certain Communist dictatorships such as that of Stalin in the Soviet Union or Mao Zedong in China, it also presents a strong contrast to the collective leadership exercised in other Communist parties, more so to the more democratic organization of most European socialist parties.
In power, the Nazis jettisoned practically all of the socialistic aspects of their program, and worked with big business, frequently at the expense of both small business and the working classes. Gregor Strasser was murdered, as was Ernst Röhm while Otto Strasser was purged from the party. Independent trade unions were outlawed, as were strikes. In place of the unions, the Nazis created the German Labour Front (Deutschen Arbeitsfront (DAF)). The Nazis took other symbolic steps to co-opt the working classes' support, such as the introduction of May Day as a national holiday in 1933. These were described by socialists as superficial moves designed to win the allegiance of workers rather than grant them any material concessions at the expense of capital.
Industries and trusts were not nationalised, with the exception of private rail lines (nationalised in the late 1930s to meet military contingencies). The only private holdings that were expropriated were those belonging to Jews. These holdings were then sold or awarded to businessmen who supported the Nazis and satisifed their ethnic and racial policies. Military production and even film production remained in the hands of private industries whilst serving the Nazi government, and many private companies flourished during the Nazi period. The Nazis never interfered with the profits made by such large German firms as Krupp, Siemens AG, and IG Farben. Efforts were made to coordinate business's actions with the needs of the state, particularly with regard to rearmament, and the Nazis established some state-owned concerns such as Volkswagen. But these were functions of the new German expansionism rather than an implementation of socialist measures. Germany had moved to a war economy, and similar measures occurred in the western democracies during the First World War, and again once the Second World War had begun.
The Nazis engaged in an extensive public works program including the construction of the Autobahn system. As with the expropriation of rail lines, however, the Autobahn system was created with the purpose of facilitating military transport, and government investment in transport systems is common in almost all nations. Similarly, all political movements that have formed governments have used economic intervention of some form or another. The suggestion that economic intervention is left-wing ignores the tradition of intervention practiced by monarchies and oligarchies in Europe before the eighteenth century, and the intervention, including protectionism, subsidies and anti-trade union laws, practiced by right-wing parties in government in Europe and North America during the eighteenth, nineteenth and twentieth centuries.
Since the fall of the Nazi regime, many theorists have argued that there are similarities between the government of Nazi Germany and that of Stalin's Soviet Union. In most cases, this has not taken the form of arguing that the Nazis were socialist, but arguing that both Nazism and Stalinism are forms of totalitarianism. This view was advanced most famously by Hannah Arendt in The Origins of Totalitarianism. However, most socialists argue that Stalin's system was not a truly socialist one, since it did not meet certain requirements that they see as essential for socialism - requirements such as a functional democracy, for example.
For more information see the article on Totalitarianism

Nazism and race
All forms of socialism focus on economic relationships as central in shaping society. In contrast, as can be seen in Mein Kampf, the central doctrine of Nazism is racism and the struggle between peoples. Nazis see the society divided not according to social classes, but according to races and peoples.
Nazis claimed to scientifically measure a strict hierarchy among races; at the top was the Caucasian or ("Aryan") race (minus the Slavs, who were seen as below Aryan), then lesser races. At the bottom of this hierarchy were "parasitic" races, especially the Jews, which were perceived to be dangerous to society. Nazi theory said that because the nation was the expression of the race, the greatness of a race could be evaluated according to a race's ability and desire to acquire a large homeland. German accomplishments in science, weaponry, philosophy and art were interpreted as scientific evidence to support Nazi racist claims.
Primo Levi suggested another difference between socialism and Nazism: while both had their idea of what kind of parasitic classes or races society ought to be rid of, he saw the former to determine them by a social position (which people may change within their life), while the latter assign a place given by birth. In his view, revolutionary communists would accept one may be born the son of a wealthy capitalist to be acceptable as a productive member of society; according to Nazis, one born a Jew is a born parasite who must be disposed of. A counterexample may be found in Maoism in China, where at times during the Cultural Revolution the relatives of a "capitalist", even generations removed, were beaten, killed, or, at best, sent to a reeducation camp. Collective punishment is another way of describing this phenomenon. In support of Levi's contention, however, the Chinese Communists have had some members with "bourgeois" social origin, some of whom, such as Soong Ching-ling, achieved prominent positions in the People's Republic of China. Similarly there were a number of prominent Bolsheviks who came from wealthy backgrounds and were accepted in the movement despite this