@James ... I find it fallacious to assume that the right side of the political spectrum is economically laissez-faire. There is a swathe of so-called conservatives that can't keep their hands off of the economy right now and for many years. As much as militancy and equity mean to the right side of the spectrum, there is no argument at all suggesting that they want to play the game of small government. Likewise, there is hardly an argument saying that they don't want control over the economy. They don't wish to nationalize it, only to delegate that control elsewhere - rarely, though, to the people. I don't know of a government that actually practices a hands-off approach economically other than industrial giants for a very, very brief period of time (brief because it didn't go so great).
Yes, though, Hitler nationalized, no doubt about that. That is a leftist ideal. He also held that if you aren't doing good for the state (and we all know what that truly meant to him), then the state murders you - that is economic authoritarianism, among other far worse things. However, the left is supposed to value equality, wherein those that cannot help themselves receive the help that they need, and Hitler was not at all in favor of that. The moderate-to-somewhat-far left is also supposed to value a free society according to conventional standards (not that the right isn't, but they do so differently), which Hitler also didn't do, obviously. He was nativist and xenophobic - two things that the left typically does not support. The NSDAP had a racial hierarchy, a political hierarchy, a socioeconomic hierarchy, a religious hierarchy, and a general caste system, which is a tenet of the far-right. That is not unrelated to the economy, as much as simpleminded economists like to believe. And, lastly, Hitler was blatantly militaristic. Like, he was the most militaristic ever. That is the crown jewel of the right.
Besides this, pretty much every German political party of the mid-20th century was, by your standard, leftist economically. There were welfare systems, infrastructure developments, a very low unemployment rate, etc etc. These were German things, not NSDAP things. The way that the Nazis messed things up so much was, oh, I don't know, imprisoning countless millions of people for slaughter and attempting to take over the goddamn world.
As an aside, the Nazis defined themselves as far-right, possibly to separate themselves from the communists to their east, and as much as they did not believe in self-determination, I do, so if they want to be far-right, by gods, I'll give them a chance to be far-right. Anything that keeps them far, far away from me.
tl;dr - laissez-faire doesn't exist, all German political parties in the 20th century, NSDAP included, were leftist by today's standards economically, Hitler's mustache from the statue in Berlin is kept in Moscow, which is to the far right of Germany. Ergo, far right.