Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Stauraxonaria Afanasieva & Amon, 2005
       Order Lobatiradiata Afanasieva & Amon, 2005
         Family †Hagiastridae Riedel, 1971
           01 Genus †Archaeohagiastrum Baumgartner, 1984
           02 Genus †Crucella Pessagno, 1971
           03 Genus †Hagiastrum Haeckel, 1881
           04 Genus †Higumastra Baumgartner, 1980
           05 Genus †Orbiculiforma Pessagno, 1973
           06 Genus †Paratriassoastrum Kozur & Mostler, 1981
           07 Genus †Pentaporobrachia Kozur & Mostler, 1981
           08 Genus †Pseudocrucella Baumgartner, 1980
           09 Genus †Pseudohagiastrum Pessagno, 1979
           10 Genus †Pseudohigumastra Yang, 1993
           11 Genus †Saldorfus Pessagno, Blome & Hull, 1993
           12 Genus †Savaryella Jud, 1994
           13 Genus †Sophia Whalen & Carter, 1998, nom. illeg.
           14 Genus †Tetraditryma Baumgartner, 1980
           15 Genus †Tetraporobrachia Kozur & Mostler, 1979
           16 Genus †Tetratrabs Baumgartner, 1980
           17 Genus †Udalia Whalen & Carter, 1998