Taxonomy of fish

es are a paraphyletic group and for this reason, the class Pisces seen in older reference works is no longer used in formal taxonomy. Traditional classification divides fish into three extant classes, and with extinct forms sometimes classified within those groups, sometimes as their own classes:
Fish account for more than half of vertebrate species. As of 2016, there are over 32,000 described species of bony fish, over 1,100 species of cartilaginous fish, and over 100 hagfish and lampreys. A third of these fall within the nine largest families; from largest to smallest, these are Cyprinidae, Gobiidae, Cichlidae, Characidae, Loricariidae, Balitoridae, Serranidae, Labridae, and Scorpaenidae. About 64 families are monotypic, containing only one species.

Class "Agnatha"
* Subclass Cyclostomata
* Subclass †"Ostracodermi"
Class Chondrichthyes
* Subclass Elasmobranchii
* Subclass Holocephali
Class †"Placodermi"
Class †"Acanthodii"
Superclass Osteichthyes
* Class Actinopterygii
* Clade Sarcopterygii

The above scheme is the one most commonly encountered in non-specialist and general works. Many of the above groups are paraphyletic, in that they have given rise to successive groups: Agnatha are ancestral to Placodermi, who again have given rise to Osteichthyes, as well as to Acanthodii, the ancestors of Chondrichthyes. With the arrival of phylogenetic nomenclature, the fishes has been split up into a more detailed scheme, with the following major groups:

Class Myxini
Class †Pteraspidomorphi
Class †Thelodonti
Class †Anaspida
Class Petromyzontida or Hyperoartia
* Family Petromyzontidae
Class †Conodonta
Class †Cephalaspidomorphi
* Clade †Galeaspida
* Clade †Pituriaspida
* Clade †Osteostraci
Infraphylum Gnathostomata
* Class †"Placodermi"
* Class Chondrichthyes
* Class †"Acanthodii"
* Superclass Osteichthyes
** Class Actinopterygii
*** Subclass Chondrostei
**** Order Acipenseriformes
**** Order Polypteriformes.
*** Subclass Neopterygii
**** Infraclass Holostei
**** Infraclass Teleostei
** Class Sarcopterygii
*** Subclass Actinistia
*** Subclass Dipnoi

† – indicates extinct taxon
Some palaeontologists contend that because Conodonta are chordates, they are primitive fish. For a fuller treatment of this taxonomy, see the vertebrate article.
The position of hagfish in the phylum Chordata is not settled. Phylogenetic research in 1998 and 1999 supported the idea that the hagfish and the lampreys form a natural group, the Cyclostomata, that is a sister group of the Gnathostomata.