DICTYOCYATHOIDEA Taylor, 1910: Outer wall simple, either rudimentary (of marginal intervallar elements only) or basic (of marginal intervallar elements with additional linking lintels) and segmented tabulae.
ARCHAEOCYATHOIDEA Hinde, 1889: Outer wall concentrically porous.
METACYATHOIDEA R. Bedford & W. R. Bedford, 1934: Outer wall compound.
NAIMARKCYATHOIDEA Wrona & Zhuravlev, 1996: Outer wall pustular.
WARRIOOTACYATHOIDEA Debrenne & Zhuravlev, 1992: Outer wall with canals.
BELTANACYATHOIDEA Debrenne, 1974: Outer wall with subdivided canals.
TABELLAECYATHOIDEA Fonin, 1963: Outer wall tabellar.