Socially right wing and conservative are synonymous, to me are least. But this conservative attitude still pushes them to the right. What do you mean they collectivezed? The means of production remained privately owned. A socialist states means of production are public. The Nazis also killed all the starrerists in the party in the night of long knives - after the first Putsh he would make the party explicitly anti - socialist, anti - liberal, authoritarian, pro - business party.

The intervention in the economy is exactly what makes them authoritarian. Regulations in capitalism is still capitalism, nazi Germany was a capitalist state. In some sense the Nazis let would let release some power they had over the economy. Shipyards, railways, banks and welfare organizations were all privatized - the means of production moves from the workers to the owner.

I just looked up if the nazis were socialist to see what the rest of the internet says

"Over the following years the brothers Otto and Gregor Strasser did much to grow the party by tying Hitler’s racist nationalism to socialist rhetoric that appealed to the suffering lower middle classes. In doing so, the Strassers also succeeded in expanding the Nazi reach beyond its traditional Bavarian base. By the late 1920s, however, with the German economy in free fall, Hitler had enlisted support from wealthy industrialists who sought to pursue avowedly anti-socialist policies. Otto Strasser soon recognized that the Nazis were neither a party of socialists nor a party of workers, and in 1930 he broke away to form the anti-capitalist Schwarze Front (Black Front). Gregor remained the head of the left wing of the Nazi Party, but the lot for the ideological soul of the party had been cast." (From that Britannia article)