Here is a picture from 1927 at Miami University of a group with the letters "HIM"
The letters were an acronym for The H I M (Happy Independent Maidens) Club, an organization of non-fraternity women. This was a precursor to GDI.
According to the MU website:
"Each pledge wore "a blue stocking on one leg and tan one on the other, a high heel and a low heel, dress on backwards and hair in pigtails with blue and tan ribbons in the end." H I M stands for Happily Independent Maidens."