You can be from the authoritarian right, or indeed, the countercultural left. Hitler was an extreme version of the former. It's worth noting the Nazis purged the "Strasserite" more socialist elements of the party in 1933.
This is what Joseph Bendersky says about them: The Nazis claimed that communism was dangerous to the well-being of nations because of its intention to dissolve private property, its support of class war, its aggression against the middle class, its hostility towards small businessmen, and its atheism. Nazism rejected class-based socialism and economic egalatarianism, instead favouring a stratified economy with social classes based on merit and talent, retaining private property and the creation of national solidarity that transcends class distinctions.