Clade †Pterosauria Owen 1842 [Andres & Padian 2020] see Order Pterosauria Kaup, 1834
   Clade †Macronychoptera Unwin 2003 [Andres 2021]
     Clade †Novialoidea Kellner 2003 [Andres 2021]
       Clade †Breviquartossa Unwin 2003 [Andres 2021]
         Clade †Pterodactylomorpha Andres, Clark & Xu 2014 [Andres 2021] see Suborder Pterodactylomorpha Schaller, 2007
           Clade †Monofenestrata Lü, Unwin, Jin, Liu & Ji 2010 [Andres 2021]
             Clade †Pterodactyliformes Andres, Clark & Xu 2014 [Andres 2021]
               Clade †Caelicodracones Andres, Clark & Xu 2014 [Andres 2021] see Clade Caelidracones Unwin 2003
                 Clade †Anurognathidae Kuhn 1937 [Andres 2021] see Family Anurognathidae Nopcsa, 1928
                   Clade †Batrachognathinae Kellner, Wang, Tischlinger, Campos, Hone & Xi 2009 [Andres 2021] see Subfamily Batrachognathinae Kellner, Wang, Tischlinger, Campos, Hone & Xi, 2009
                     Genus †Luopterus Hone, 2020