ASTEROCYATHIDAE Vologdin, 1956: Inner wall with simple pores.
RUDANULIDAE Debrenne, Rozanov, & Zhuravlev, 1989: Inner wall with bracts or scales.
SALAIROCYATHIDAE Zhuravleva, 1956: Inner wall with annuli.
CRASSICOSCINIDAE Debrenne, Rozanov, & Zhuravlev, 1988: Inner wall with noncommunicating canals.
KASYRICYATHOIDEA Zhuravleva, 1961: Outer wall with independent microporous sheath.
XESTECYATHIDAE Debrenne, Rozanov, & Zhuravlev, 1989: Inner wall with bracts or scales.
KASYRICYATHIDAE Zhuravleva, 1961: Inner wall with communicating canals.
MEMBRANACYATHIDAE Debrenne, Zhuravlev, & Kruse, 2002: Inner wall with microporous sheath.
ANAPTYCTOCYATHIDAE Debrenne, 1970: Inner wall with simple pores.
POLYCOSCINIDAE Debrenne, 1964: Inner wall with bracts or scales.
VERONICACYATHIDAE Debrenne, Zhuravlev, & Kruse, 2002: Inner wall with noncommunicating canals.
ZONACOSCINIDAE Debrenne, 1971: Inner wall with communicating canals.
TUMULOCOSCINIDAE Zhuravleva, 1960: Inner wall with simple pores.
ETHMOCOSCINIDAE Zhuravleva, 1957: Inner wall with noncommunicating canals.
GEYERICOSCINIDAE Debrenne & Zhuravlev, 2000: Inner wall with simple pores.
COSCINOPTYCTIDAE Debrenne, Rozanov, & Zhuravlev, 1989: Inner wall with bracts or scales.
JEBILETICOSCINIDAE Debrenne, Rozanov, & Zhuravlev, 1989: Inner wall with noncommunicating canals.
SYLVIACOSCINIDAE Debrenne, Rozanov, & Zhuravlev, 1989: Inner wall with simple pores.
SIGMOCOSCINIDAE R. Bedford & J. Bedford, 1939: Inner wall with annuli.
ROZANOVICYATHIDAE Korshunov, 1969: Inner wall with simple pores.
TATIJANAECYATHIDAE Korshunov, 1976: Inner wall with annuli.
POROCOSCINIDAE Debrenne, 1964: Inner wall with noncommunicating canals.
MOOTWINGEECYATHIDAE Kruse, 1982: Inner wall with bracts or scales.