Definitions are not absolute facts; they are conventions. I define the left as committed to the ideal of equality. I define the right as committed to some form of inequality, be it of income, race, religion or nation.
By these definitions the Nazi movement is solidly on the right. It believed in the superiority of German Gentiles. It considered Jews, Gypsies, and Slavs to be sub humans.
Most rich Germans supported the Nazis, albeit reluctantly. They knew that if the Nazis took power they would remain rich. If the Communists took power their wealth would be confiscated.