Were Nazis Socialist?

I have been reading that they weren’t actually socialists, but haven’t been convinced either way, so what better way to solve this than to go to a debate sub and hear everyone’s opinion?

I understand they did implement socialist policies like increased benefits, creating jobs by increasing the state, restricting wages so more people had a job, free daycare (state raised), nationalized healthcare, etc.

The only arguments I can find that they weren’t socialists seem to be either axiomatic or that it wasn’t some specific person’s idealized socialism.

There are many definitions of socialism, but I believe the original is something like:

any of various egalitarian economic and political theories or movements advocating collective or governmental ownership and administration of the means of production and distribution of goods

Specifics like abolition of private property seem to be added on later and apply to just a specific type of socialism, which doesn’t reflect every type of socialism.