Class Actinopoda Calkins, 1902 see Parvkingdom Actinopoda Calkins, 1902
   Subclass Radiolaria Müller, 1858 see Phylum Actinopoda Calkins, 1902
     Superorder Polycystina Ehrenberg, 1838 see Class Polycystinea Ehrenberg, 1838
       Order Spumellaria Ehrenberg, 1875 see Class Spumellaria Ehrenberg, 1875
         Superfamily Pyloniacea Haeckel, 1881 see Superfamily Pylonioidea Haeckel, 1881
           Subsuperfamily Dactyliosphaerilae Squinabol, 1904 see Superfamily Dactyliosphaeroidea Squinabol, 1904
             Family †Hagiastridae Riedel, 1971
               01 Genus †Archaeohagiastrum Baumgartner, 1984
               02 Genus †Crucella Pessagno, 1971
               03 Genus †Hagiastrumᵀ Haeckel, 1881
               04 Genus †Higumastra Baumgartner, 1980
               05 Genus †Orbiculiforma Pessagno, 1973
               06 ?Genus †Paratriassoastrum Kozur & Mostler, 1981
               07 Genus †Pseudocrucella Baumgartner, 1980
               08 Genus †Pseudohagiastrum Pessagno, 1979
               09 Genus †Pseudohigumastra Yang, 1993
               10 ?Genus †Savaryella Jud, 1994
               11 Genus †Sophia Whalen & Carter, 1998, nom. illeg.
               12 Genus †Tetraditryma Baumgartner, 1980
               13 Genus †Tetraporobrachia Kozur & Mostler, 1979
               14 Genus †Tetratrabs Baumgartner, 1980
               15 Genus †Udalia Whalen & Carter, 1998