Yes and No.
They definitely combine elements of socialism, but I can give you a source from a pro-slavery Southerner who spoke of slavery as the ultimate form of socialism. It doesn't mean that the person who wrote that is a 'leftist.'
As much as I don't like saying it (mainly because I've said the same as you before) the Nazis main base of support was the 'right.' The conservatives of Germany were in favor of returning to an authoritarian government and ending the Weimar experiment. THe Nazis eventually turned on everyone, including the small businesspeople they pledged to protect against the encroachments of big "Jewish" industry and banking.
But if one judges a movement by where it gets its support, Nazi allies(those that foolishly thought they could exploit its nationalism an anti-bolshevism) it is a right-wing movement. It is not Burkean conservative, of course, but it ain't really left wing.
That is not to say, however, that there aren't new splinters and revisionings of the National Socialist ideology that look much more left-wing than the past. These 'spectra' change over time.
Nation of Islam would also qualify as 'right-wing' or a 'conservative' movement, though they'd probably not think of themselves as such.
I think of any ideology that expands the scope of government as leftist, no matter what the ultimate goal is. By that definition, there are lots of big spenders in the GOP controlled Congress that qualify.
I guess I'm just a right wing extremist! lol