Arguments could (and will???) rage for ever on the subject.

Originally, the National Socialists opposed both capitalists and communists and claimed to be socialists but it was their version of what socialists were.

They were neither Conservatives or Socialists, they became/were fascists/authoritarianists.

What happened was like the Conservatives forming an alliance with ukip, then ukip ousting any Conservative "oposition" to the ukip nationalism ideology and becoming authoritarians..........