gestapo were right wing as was the Nazis
The Secret State Police (aka. Geheime Staatspolizei) was a typical Omnipotent Government outfit - no wingery here, just action - and these have to be eliminated with extreme prejudice, and I mean literally by cracking heads including those of the suave politicians that propose them, and in the early days of their making. Alas, this never happens, because "terrorists" are those that act or refuse to obey.
As for the left-wing/right-wing thing (ultimately a sterile exercise as one has to look at the actions, real or proposed, through the smokescreen of politically vapid promised of "better times" instead of using tired old labels arranged on a 1-dimensional strip by the masters of thought control) we read in War Revisionism, Fascism, and the CIA:
As you will recall from history, both Germany and Italy respectively became unified nations in the latter part of the 19th century. The ideas of Marx and communism constituted an international movement advocating violence and force to eliminate private property and capitalism. Another international movement was socialism which also attacked property and individualism yet many socialists stated that socialism could be established through democracy rather than force by expanding the number of eligible voters. After World War I, communism became a severe threat to take over Italy. Mussolini was a dedicated socialist and journalist who supported fascism as a national rather than an international movement to fight international communism and socialism. He advocated force and war as the method to combat the violence of communism. There was no racism connected to fascism in Italy. (....)
One of the 20th century’s most astute intellectuals in political theory was Erik von Kuehenelt-Leddihn who agrees completely with me and Jonah Goldberg on placing fascism on the left. He covers this in his book entitled Leftism Revisited. In chapter four of that book entitled “Right and Left”, he points out that in Germany after World War I the National Socialist (or Nazis) were, seated on the far right of the Reichstag or Assembly because on the left side of the assembly were the internationalists who were the communists and the socialists. The conservatives and monarchists were national movements and were seated on the right. Since Nazism or fascism was a national movement in Germany rather than international, they were seated on the right with the conservatives. He explains this is how fascism became to be placed on the right rather than the left in political dialogue.