"All associations with rituals and signs of recognition not made public are not criminal, nor condemnable. Only those which, behind a veil of secrecy commit crimes and formulate plans against their fellows, the legally established state, or any lawfully existing institution. Such societies are the enemies of mankind." (Reynolds and Sjodahl, Commentary on the Book of Mormon, vol. 6, p. 131)
If we are to correctly identify secret combinations, we must know what constitutes a secret combination. Ether 8 instructs us that:
For a more comprehensive list, see commentary for Helaman 6:18.