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It may be unreasonable to call them sub human but I disagree with your reasoning. The etemology of the phrase sub human in English predates the Nazis by over 200 years. I would also venture that the direct translation of the Nazi term is under human.
I do think you would have a case for the Nazi reflection if someone chose to use the expression in English "under human" or "under man" (which I believe has pre Nazi KKK origins) then I would totally agree with you.
And somehow people vote for these sub-humans.