Were the Nazis socialists? No, not in any meaningful way, and certainly not after 1934. Hitler allied himself with leaders of German conservative and nationalist movements, and in January 1933 German President Paul von Hindenburg appointed him chancellor. Hitlers Third Reich had been born, and it was entirely fascist in character
Facism is an extremely statist ideology as well.
Giving the goverment or supreme leader more authority over the individual and his free will is the complete opposite of capitalism.
Facism and socialism are very close ideologies.
The major difference is that the enemy in socialism is found in class instead of race.
I don't agree that racism is a critical component of fascism. If you remove both the race and class elements from both, what you are left with is totalitarianism. That is the important part that ENABLES the racism and classism.