Nazism is about power, corruption, and "might makes right". Trying to define it in terms of traditional political systems is not easy, because it does not fit very well into them. Italian fascism and Nazism were both overt power grabs, designed to appeal to the most gullible ideologues on both sides of the political spectrum, united in their zeal for nationalism and subservience to the State. In practice, the Nazis and Fascists were rather unconcerned with right vs left, as long as they were able to maintain absolute power. In that way, one might call them centrist, though that's a somewhat misleading term for Nazism and Fascism. Hitler himself was centrist on many issues, far right on others. While nationalism is a traditionally right-wing concern, Nazi economic policy was influenced by Keynesian theory. In short, they borrowed whatever elements from the left and right they thought would guarantee them absolute power. They persecuted socialists, communists, and trade unionists, as well as social liberals, gays, and modernists. They hated everyone, but they hated Jews and the far left most of all. It's tempting to call them conservative, but they really don't fit into such tidy little categories. Nazism and Fascism are designed to grab absolute power, not address political theory.