Kenetic Kups, is absolutely, 100% right.
Corporatism is defined "the control of a state or organization by large interest groups."
Corporatism by it's definition is inherently a collectivist ideology, that is, it prioritizes groups of people's interests versus individualist views. It was developed in the 19th century as a "third" way between classic liberalism (laissez-faire) and marxism, and is far-far closer to Syndicalism. "According to corporatist theory , workers and employers would be organized into industrial and professional corporations serving as organs of political representation and controlling to a large extent the persons and activities within their jurisdiction." This is done for the greater good of societies. In layman's terms, think of it rather than individual workers, professionals, companies, etc having some sort of say in the political decision making, it's an entire industry that represents a certain sector; say farmers, or miners, or manufacturers.
It was largely adopted by Fascist Italy, and Nazi Germany, and still adopted by European countries post WW2. However, Nazi Germany generally converted the focus of their economy more and more into war-production. Privatization was a means for the Nazis to finance the war-effort.
But they were anti-consumerist not because of the Jews. They were anti-consumerist because the Nazis wanted to, and did, convert the majority of industries from developing consumer goods, to military goods. Consumerism demands industries focus on consumer goods which went against the goals of Nazi Germany's military rearmament.
They were cool with private enterpries – as long as the goal of the enterprise matched that of the State – i.e. if you decide to open up a Shtrudel shop, they would come and say "nein", but if you decide to open up a tank-parts factory or convert your shtrudel shop into a tank parts factory, then you get subsidies, tax breaks, etc.
The reason I asked "how do you define socialism" is that it's a broad economic ideology, and if we are to generalize all those variants of the ideology under a single concept is prioritization of the collection rather than the individual, then Nazis would fit under that umbrella, as they were still, in many ways, collectivist. Indeed Nazis wanted to redefine traditional socialism from Marxist bent of international socialism and class conflict with the idea that all of German society should replace their personal interests to the "common good", which tended to reflect collectivization.