Hitler was not actually a socialist. Yes, the party name (English translation) was the National Socialist German Workers' Party, and even Mussolini's fascism definition overlapped socialism. But in practice, both Mussolini and Hitler hated communists and their focus was on purity and national identity. Communist socialism was class-based. Both fascists and communists hated liberal capitalism.

Hyper-nationalism is a property of conservatives, including defining their nation based on it's religious, racial, ethnic history. This is, more or less, what Hitler and Mussolini promoted, with Hitler focused more on racial national purity and using Christian religious institutions. Socialism isn't nationalistic and more about economic classes, subverted today as social classes by race and other identity groups, and replacing economic privilege with social privilege, incorrectly via identity group. Both have their totalitarians and built in bigotry. Liberal democracy beats both.