If you think there's a hard definition of socialism that Hitler clearly falls outside of, I'm pretty sure you're wrong. They blamed rich people for all the ills of society (Jewish people for them); they believed in the state running the economy through "corporatism"; they believed in a disarmed population that relies on the state for planning and protection; and they were willing to sacrifice millions of their populace to get there. It sounds a lot like most incarnations of socialism.