Yes. In fact the concentration camps were started (by Göring and the Luftwaffe) specifically for Communists, not Jews. They were also specifically started for people who were suspected of being an enemy of the state but without proof; under Göring’s law, the arrested had to be informed within 48 hours of the reason for their arrest, but they did not have the right to legal counsel or even a trial. Essentially the concentration camps began when the standards for which people could be arrested were so lowered that there was no longer enough space in all of the prisons of Germany, Austria, and their occupied lands.
The Star of David (actually two yellow triangles) worn by the Jews and the pink triangle worn by homosexuals are the two most famous badges today, but there were many others.
Just a very few:
They were amazingly detailed: there were particular badges for Jews who were also communists, or homosexuals who were also biracial, or- you name it. These things were amazingly bureaucratic.
There was a major difference between concentration camps and death camps. Neither were fun or even humanely run places, but a concentration camp was essentially a big prison camp. Death was common due to disease (when you cram 200 people into one room without running water or ventilation disease spreads quickly), malnutrition, overwork, and shootings/executions, but the primary purpose was to house prisoners (often for use as slave labor in the war effort), not to kill them. The death camps- Bierkenau (the sister camp that adjoined Auschwitz), Sobibor, Treblinka, and others- were either specifically built for or evolved into places where large numbers of people could be killed and their bodies disposed of as quickly as possible. These were “the showers” (where the nozzles were not even connected to plumbing) and incinerators and crematoriums (into which- especially by the end of the war- many prisoners were thrown while still alive, sometimes as punishment and sometimes as expedience). When trains arrived at Auschwitz-Bierkenau those who seemed healthy enough to work for the war effort, twins, perhaps “special cases” (those who had once been in the German military or celebrities or who had some kind of friend) would be sent to Auschwitz, where your odds of survival were slim but they did exist. The rest- the old, children, the weak, the sick, the handicapped, etc.- were automatically sent to Bierkenau, where the only people who had any chance of surviving the night were the Sonderkommando (inmates who went through the clothing of/shaved the heads of/removed and ‘processed’ the remains of the arrivees who were sent there).
There are MOUNTAINS of testimony as to the exact running of the concentration camps and death camps from former guards, officers, and attorneys. The Nazis themselves damned near documented it in triplicate or better. To date I am not aware of one Jew who was imprisoned by the Nazis who has ever come forward and said “Ah, the concentration camps weren’t so bad, the stuff about the showers and the ovens… pffft, made up”, and with as many hundreds of thousands of survivors of the camps who are still alive today there is absolutely no humanly conceivable way the story wouldn’t have broken many many many times.