The Nazi Economist of the early to mid thirties (schacht) was a capitalist who advocated a relatively free market combined with some regulation. Many of his projected ideas were not unlike what goes on now. Nazi germany was involved in the economy, but that doesn't make the nation socialist. It was, as I said, an authoritarian mixed economy. It had socialist elements, but it also had capitalist elements. Much of the businesses were privately owned--but not all. There was regulation--but the property was largely in the hands of private investors and owners. That is very unsocialist. Now, if one takes into consideration the historical context, we know that the Nazis largely purged much of the Socialist groups and backing of their party by the late thirties.
Now, in socialist nations, it is supposed to be a "will of the people" and "workers revolution." Hitler directly crushed this attempt at worker-freedom and did many very, again, unsocialist things. For example, in the German industrial worker leagu, "Workers lost their right to strike and the ability to organize into unions. Now, at the same time, the Nazis replaced these with contradictory policies in the DAF. The essential gist of the movement is such: Worker freedom is replaced by totalitarian control over the worker, yet the worker is kept entertained and happy via Kraft Durch Freude. Meanwhile, while some professed this was good for the worker, it also greatly benefited the private industries.
Now, the agriculture market was, perhaps, the most heavily socalistic element of the Third Reich, because it was completely dominated by the government. Prices were set, wages were fixed, and much of the land and property was State owned and operated.
At the same time, however, "Inside Hitler's Germany" claims that "German [private] business in general was happy to go along with thes new regime. The Nazis smashed organized labour, left-wing revolution, and resotred order. In return, German big business was expected to help finance the Nazis."
Hitler also commented in a meeting with jubilant business leaders that, "Private enterprise cannot be maintained in the age of democraacy; it is conceivable only if the people have an idea of sound authority and personality." Further, Hitler promised "to eliminate Marxism, [...] [which] appealed to the industrialists [...] such as Krupp, United Steel, and I.G.Farben
There existed both a private and a public sector in Germany, and many policies were logically contradictory. The only thing consistant in Germany was the use of authoritarianism, however.