The basis of the claim that Nazi Germany was capitalist was the fact that most industries in Nazi Germany appeared to be left in private hands.
What Mises identified was that private ownership of the means of production existed in name only under the Nazis and that the actual substance of ownership of the means of production resided in the German government. For it was the German government and not the nominal private owners that exercised all of the substantive powers of ownership: it, not the nominal private owners, decided what was to be produced, in what quantity, by what methods, and to whom it was to be distributed, as well as what prices would be charged and what wages would be paid, and what dividends or other income the nominal private owners would be permitted to receive. The position of the alleged private owners, Mises showed, was reduced essentially to that of government pensioners.
De facto government ownership of the means of production, as Mises termed it, was logically implied by such fundamental collectivist principles embraced by the Nazis as that the common good comes before the private good and the individual exists as a means to the ends of the State. If the individual is a means to the ends of the State, so too, of course, is his property. Just as he is owned by the State, his property is also owned by the State.
But what specifically established de facto socialism in Nazi Germany was the introduction of price and wage controls in 1936. These were imposed in response to the inflation of the money supply carried out by the regime from the time of its coming to power in early 1933. The Nazi regime inflated the money supply as the means of financing the vast increase in government spending required by its programs of public works, subsidies, and rearmament. The price and wage controls were imposed in response to the rise in prices that began to result from the inflation.