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 Archipilioidea Haeckel, 1881
           Family Archipiliidae Haeckel, 1881
             Subfamily Clathromitrinae Petrushevskaya, 1971
               01 Genus Archiscenium Haeckel, 1881
               02 Genus Clathromitra Haeckel, 1881
               03 Genus †Corythomelissa Campbell, 1951
               04 Genus Euscenarium Haeckel, 1887
               05 Genus Euscenium Haeckel, 1887
               06 Genus Halicalyptra Ehrenberg, 1847
               07 Genus Phaenocalpis Haeckel, 1887
               08 Genus Phaenoscenium Haeckel, 1887
               09 Genus †Spongomelissa Haeckel, 1887
               10 Genus Tripocalpis Haeckel, 1881
               11 Genus †Tripodiscinus Haeckel, 1887
               12 Genus Tripodisculus Haeckel, 1887
               13 Genus †Tripophaenoscenium Campbell & Clark, 1944
               14 Genus Vicillata Afanasieva & Amon, 2005, nom. null. see Genus Verticillata Popofsky, 1913