Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Nassellaria Ehrenberg, 1847
       Order Cyrtidinata Haeckel, 1862
         Superfamily Amphipyndacioidea Riedel, 1967
           Family †Canoptidae Pessagno, 1979
             1 Genus †Canoptum Pessagno, 1979
             2 Genus †Cinguloturris Dumitrica, 1982
             3 Genus †Globolaxtorum Carter, 1993
             4 Genus †Laxtorum Blome, 1984
             5 Genus †Neocanoptum Zhang, 1990
             6 Genus †Relanus Pessagno & Whalen, 1982