For years it has been parroted by those in the mainstream media that Nazism is a right-wing ideology. Much in the same way, that the KKK is somehow a right-wing group. Of course, neither of these is true, and you can bet that if the mainstream media is pushing a narrative, it is false and self-serving towards their socialist agenda. So lets define the three main ideologies.
Democracy/Republic and Capitalism:
Our system of governing here in the U.S. is a Republic. A Republic goes beyond a democracy in that the Republic enshrines the idea that the People have ultimate control over themselves, but not ultimate control over others. The sovereign rights of the individual hold supreme over the rights of the majority. Capitalism fits in well with a Republic because the individual has the power over his own earnings to spend it where and how he wishes.
Socialism is a form of collectivist government where the sovereign rights of the individual must give way to the collective rights/needs of the majority. This centralized model of governing leaves out the rights of the individual and the governing entities reign complete control. In Europe there are countries that have a mix of Socialism and Capitalism, and it tends to almost work. Why almost? Because you still have centralized power where the citizens wield little power over their governing entity. Taxes are generally 50% or higher in these countries, and if you do not like it, too bad. As with all these collectivist ideologies, they are ultimately bastions of corruption because of their centralized power and lack of individual rights.
Communism, another collectivist ideology, this ideology goes a step than Socialism in that no individual may own property. This further divides the chasm between the sovereign person and their ability to live a fruitful life.
Nazism is more a mix of the above, but still giving dictatorial leadership, along with an elite class, all the power over the citizens. Again, collectivist, these three are the failed attempts for government to strip individuals of their God given rights.