Sturmhauptführer was a Nazi Party paramilitary rank used by both the Sturmabteilung and the SS. It was the equivalent of a Hauptmann in the German Army. This is the equivalent of Captain (O-3) in western militaries.
The rank was first created in 1928 as an SA rank and was bestowed upon those SA officers who were company commanders of SA units. The rank translates as “Storm Head Leader” and can trace its origins to the German Shock Troops of the First World War, who were typically organized into Storm Trooper Companies under an officer ranked Lieutenant or Captain.
As an SS rank, Sturmhauptführer was established in 1930 as a senior rank to that of Sturmführer. Sturmhauptführer was initially considered as more of a senior Lieutenant, but after 1932 the rank was rated above that of Obersturmführer and became the equivalent of a Captain. The insignia for the rank was also modifed to denote the higher status.
In 1934, after the Night of the Long Knives, the SS changed the name of Sturmhauptführer to Hauptsturmführer. This was due in large part to separate the SS rank system from the SA, now considered two completely separate organizations. Sturmhauptführer remained an SA rank until 1945.
Source: Wikipedia; Picture courtesy of: U.S. National Archives