Hey Mike,
It's generally filed under extreme right wing as Nazism was (and is) a fascist movement. It's pretty significant that among the enemies of the Nazis politically were labor unions and Communists (the Communists especially were targeted for violence). The attachment of the term 'socialism' is kinda spurious, as the word held a different connotation before social democrats and modern socialists became more prominent. I file it away with the fact that 'terrorism' was considered a positive force when the term was originally employed. To my knowledge, Nazism was never considered a left-wing political movement (though there certainly has been a modern effort to redefine it as such in the US), and I'm reasonably knowledgeable on the subject (though I don't have a publication to point to).
In response to the whole 'mistake not to take out right-wing opposition,' Hitler wasn't really fond of opposition as a rule. He simply did not tolerate it, so he would probably have regarded as a mistake the failure to take out the kindergartener who asked him a math question he couldn't answer.
That said, the traditional left-right spectrum is a bit wonky when it comes to authoritarian movements (in my opinion), and so it'd be more useful probably to think of it as a two dimensional plane rather than a flat line. Both left and right sides have folks who tend authoritarian (in extreme terms, these would be Communists/Stalinists and Fascists/Neo-Nazis) and folks who tend more anarchist (the extremes would be sovereign citizens and anarchists). The "Nolan Chart" shows this reasonably well, though I don't think I buy into the idea that populism is inherently totalitarian (which the chart indicates).
Anyway, for further research, maybe take a look at Hitler's War Aims by Norman Rich or even some of the links provided by the Wikipedia article on the subject of Fascism and Nazism (I know citing Wikipedia is pretty weak, but the links tend to be fairly good sources).
Best,
Cronkam
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