This is sometimes difficult to nail down, because even Hitler contradicted himself, sometimes appealing to the right wing, but most often to the left wing workers: he was a politician first and foremost. https://en.wikiquote.org/wiki/Adolf_Hitler
“ To put it quite clearly: we have an economic programme. Point №13 in that programme demands the nationalisation of all public companies, in other words socialisation, or what is known here as socialism. … the basic principle of my Party’s economic programme should be made perfectly clear and that is the principle of authority… the good of the community takes priority over that of the individual. But the State should retain control; every owner should feel himself to be an agent of the State; it is his duty not to misuse his possessions to the detriment of the State or the interests of his fellow countrymen. That is the overriding point. The Third Reich will always retain the right to control property owners. If you say that the bourgeoisie is tearing its hair over the question of private property, that does not affect me in the least. Does the bourgeoisie expect some consideration from me?… Today’s bourgeoisie is rotten to the core; it has no ideals any more; all it wants to do is earn money and so it does me what damage it can. The bourgeois press does me damage too and would like to consign me and my movement to the devil.”
‘Socialism as the final concept of duty, the ethical duty of work, not just for oneself but also for one’s fellow man’s sake, and above all the principle: Common good before own good, a struggle against all parasitism and especially against easy and unearned income. And we were aware that in this fight we can rely on no one but our own people. We are convinced that socialism in the right sense will only be possible in nations and races that are Aryan, and there in the first place we hope for our own people and are convinced that socialism is inseparable from nationalism.
Why We Are Anti-Semites,” August 15, 1920 speech in Munich at the Hofbräuhaus. Speech also known as “Why Are We Anti-Semites?”’
Socialism with Nationalism and racism added = National Socialism.
There are thousands of Nazi policies that are socialist in intent: they introduced old age pensions, unemployment benefits, National work schemes including the construction of Autobahns and the People’s Car company (Volkswagen) to give jobs to German unemployed. They were anti-Capitalist, but allowed existing owners to retain paper ownership of their businesses as long as they were controlled absolutely by the Party.
Socialism is “a political and economic theory of social organization which advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.” Socialism of the German Nazi type insisted on State Control of the means of production, distribution, and exchange not necessarily the ownership of same. It gives the party absolute control of a centrally planned economy, without requiring actual Nationalision of every business. The planned economy of the Nazis was Socialist is intent and in practise.
If it walks like a Socialist, talks like a Socialist, and screws up the economy like a Socialist, then it is probably a Socialist. German Socialism was deeply racist and unlike Soviet Socialism was not Internationalist, but Nationalist. It was a Socialism for Germans only: other races could not be citizens of the Reich, but was still Socialism. Socialists are always totalitarian, given the chance, and the Nazis were absolute totalitarians, just like the Soviets. A Russian living under Stalin’s Terror would have been living in a slavery indistinguishable from a German living under Hitler’s Reich.