There was certainly “socialists” in the Nazi movement, namely Goebbels and Ernst Rhoem, who advocated a complete government takeover of German industry. This was one of the reasons he was eliminated, because he scared off the German industrialists, who Hitler needed to build the war machine.
What’s interesting is to contemplate what would have become of the industrialists, once they were no longer needed.
Of course it’s all more complicated, always is.
Merely saying socialist is in their name so they’re socialists, is inaccurate and lazy.