Sarcopterygii or the lobe-finned fishes (coelacanths and lungfishes) were usually classified as either a class or a subclass of Osteichthyes based on the traditional Linnaean classification. The group are grouped together based on several characteristics, such as the presence of fleshy, lobed, paired fins, which are joined to the body by a single bone. This is in contrasts to the other bony fish group Actinopterygii which have lepidotrichia, or ray-fins made of bony rods. Regardless the two bony fish groups were classified in Osteichthyes for a while and as a whole were seen as the sister group to the tetrapods (mammals, birds and reptiles, and amphibians).
The extensive fossil record and numerous morphological and molecular studies have shown, however, that lungfish and some fossil lobe-finned fish are more closely related to tetrapods than they are to coelacanths; as a result tetrapods are nested within Sarcopterygii. This abides to cladistics in that in order for a clade to be monophyletic, it must have an ancestral species and all descendants of that common ancestor based on shared characteristics. As such mammals, birds and reptiles, and amphibians are highly derived lobe-finned fish despite looking nothing like the standard sarcopterygian anatomically speaking.
Below is shows the taxonomy of the class Sarcopterygii at the ordinal level. While this does reflect the evolutionary relationships within the group, it also retains the rankings seen in the Linnaean classification as suggested by some scientists. The evolutionary sequences are based from current phylogenetic work on the various subclades.
Class Sarcopterygii (Romer, 1955)
Subclass Actinistia (Cope, 1871)
Order Coelacanthiformes (Berg, 1937)
Subclass Rhipidistia (Cope, 1871)
Infraclass Dipnoi (Müller, 1844)
Order Ceratodontiformes (Berg, 1940)
Order Lepidosireniformes (Müller, 1844)
Infraclass Tetrapoda (Goodrich, 1930)
Parvclass Lissamphibia (Haeckel, 1866)
Order Apoda (Oppel, 1811)
Order Urodela (Duméril, 1806)
Order Anura (Duméril, 1806)
Parvclass Sauria (Macartney, 1802)
Cohort Lepidosauria (Haeckel, 1866)
Order Rhynchocephalia (Günther, 1867)
Order Squamata (Oppel, 1811)
Cohort Testudinata (Klein, 1760)
Order Testudines (Batsch, 1788)
Cohort Archosauria (Cope, 1869)
Order Crocodylia (Owen, 1842)
Subcohort Aves (Linnaeus, 1758)
Infracohort Palaeognathae (Pycraft, 1900)
Order Struthioniformes (Latham, 1790)
Order Rheiformes (Forbes, 1884)
Order Tinamiformes (Huxley, 1872)
†Order Dinornithiformes (Bonaparte, 1853)
†Order Aepyornithiformes (Newton, 1884)
Order Apterygiformes (Haeckel, 1866)
Order Casuariiformes (Sclater 1880)
Infracohort Neognathae (Pycraft, 1900)
Section Galloanserae (Sclater, 1880)
Order Anseriformes (Wagler, 1831)
Order Galliformes (Temminck, 1820)
Section Neoaves (Sibley et al., 1988)
Subsection Columbaves (Prum et al., 2015)
Order Musophagiformes (Seebohm, 1890)
Order Cuculiformes (Wagler, 1830)
Order Otidiformes (Wagler, 1830)
Order Columbiformes (Latham, 1790)
Order Pteroclidiformes (Huxley, 1868)
Order Mesitornithiformes (Wetmore, 1960)
Subsection Inopinaves (Prum et al., 2015)
Order Opisthocomiformes (L'Herminier, 1837)
Division Strisores (Baird, 1858)
Order Steatornithiformes (Sharpe, 1891)
Order Nyctibiiformes (Sharpe, 1891)
Order Caprimulgiformes (Ridgway, 1881)
Order Podargiformes (Sharpe, 1891)
Order Aegotheliformes (Simonetta, 1967)
Order Apodiformes (Peters, 1940)
Division Aequorlitornithes (Prum et al., 2015)
Subdivision Gruae (Bonaparte, 1854)
Order Gruiformes (Bonaparte, 1854)
Order Charadriiformes (Huxley, 1867)
Order Phoenicopteriformes (Fürbringer, 1888)
Order Podicipediformes (Fürbringer, 1888)
Subdivision Ardeae (Wagler, 1830)
Order Phaethontiformes (Sharpe, 1891)
Order Eurypygiformes (Fürbringer, 1888)
Order Gaviiformes (Wetmore & Miller, 1926)
Order Sphenisciformes (Sharpe, 1891)
Order Procellariiformes (Fürbringer, 1888)
Order Ciconiiformes (Bonaparte, 1854)
Order Suliformes (Sharpe, 1891)
Order Pelecaniformes (Sharpe, 1891)
Division Telluraves (Yuri et al., 2013)
Subdivision Afroaves (Ericson, 2012)
Order Cathartiformes (Coues, 1884)
Order Accipitriformes (Vieillot, 1816)
Order Strigiformes (Wagler, 1830)
Order Coliiformes (Murie, 1872)
Order Leptosomiformes (Sharpe, 1991)
Order Trogoniformes (AOU, 1886)
Order Bucerotiformes (Fürbringer, 1888)
Order Coraciiformes (Forbes, 1884)
Order Piciformes (Meyer & Wolf, 1810)
Subdivision Australaves (Ericson, 2012)
Order Cariamiformes (Fürbringer, 1888)
Order Falconiformes (Sharpe, 1874)
Order Psittaciformes (Wagler, 1830)
Order Passeriformes (Linnaeus, 1758)
Parvclass Mammalia (Linnaeus, 1758)
Order Monotremata (Bonaparte, 1837)
Supercohort Theria (Parker & Haswell, 1897)
Cohort Marsupialia (Illiger, 1811)
Order Didelphimorphia (Gill, 1872)
Order Paucituberculata (Trouessart, 1898)
Subcohort Australidelphia (Szalay, 1982)
Order Microbiotheria (Ameghino, 1889)
Order Diprotodontia (Owen, 1866)
Order Notoryctemorphia (Kirsch, 1977)
Order Dasyuromorphia (Gill, 1872)
Order Peramelemorphia (Ameghino, 1889)
Cohort Placentalia (Owen, 1837)
Subcohort Atlantogenata (Waddell, Okada & Hasegawa, 1999)
Infracohort Xenarthra (Cope, 1889)
Order Cingulata (Illiger, 1811)
Order Pilosa (Flower, 1883)
Infracohort Afrotheria (Stanhope et al., 1998)
Order Afrosoricida (Stanhope et al., 1998)
Order Macroscelidea (Butler, 1956)
Order Tubulidentata (Huxley, 1872)
Order Hyracoidea (Huxley, 1869)
Order Sirenia (Illiger, 1811)
Order Proboscidea (Illiger, 1810)
Subcohort Boreoeutheria (Springer & de Jong, 2001)
Infracohort Laurasiatheria (Waddell, Okada & Hasegawa, 1999)
Order Lipotyphla (Haeckel, 1866)
Order Chiroptera (Blumenbach, 1779)
Order Pholidota (Weber, 1904)
Order Carnivora (Bowdich, 1821)
Order Perissodactyla (Owen, 1848)
Order Artiodactyla (Owen, 1848)
Infracohort Euarchontoglires (Murphy et al., 2001)
Order Lagomorpha (Brandt, 1855)
Order Rodentia (Bowdich, 1821)
Order Scandentia (Wagner, 1855)
Order Dermoptera (Illiger, 1811)
Order Primates (Linnaeus, 1758)
