For researchers or the curious, here is a list of all fraternal organizations that have existed in the United States, by initials. In case you have found a medal or sword with unknown initials on it in grandpa's attic chest or on a tombstone.
Go here, Secret Society. Fraternal Organizations, Abbreviations, Slogans, Mottoes, a Complete List.
I'm not sure how complete it is. They list my favorite, the International Order of Hoo Hoo, but by a shortened name. It's official name is the International Concatenenated Order of Hoo Hoo, Incorporated. But interesting for collectors and geneologists.