No, lol. Socialism is far left, while nazism is far right.
It's an ironic name. The name implies both Socialism and Fascism.
It was called the National Socialist party to lure communist workers in Germany before WWII to be a part of the "Volkisch", a paramilitary group that fought the communists in World War I.
Communism = Equality
Marxism = Social Equality
Nationalism = "What you earn is what you own".
Socialism = "What I earn is what you also own".
National Socialism = "What I earn is what you own, but only if you are like me, and we have a person to represent us as one person".
Fascism = "What I earn is what we own together as one government".