Nope. The Nazis used the term socialism when it pleased them but they were as right wing as they come. This is an interested article about the common misconception https://www.snopes.com/news/2017/09/05/were-nazis-socialists/
The problem is all of this discussion is talking past each in an attempt to stick people with "icky" labels. Right and left as originally conceived in the French Revolution have almost nothing to do with right or left now. These are just bats to beat people with. When someone on the left says the Nazis are "right wing" despite sharing almost no views with the "right wing" in any modern country they are just trying to use labels to fight. Its the same from the right in trying to say the Nazis were socialists. Sure they were socialists (Snopes is great for debunking internet rumors but have no intellectual heft for thoughtfully discussing serious history) but almost nothing like the modern left of socialist democracies. Its just stupid labels all the way around. But thinking beyond labels is hard.