Halecomorphi

Halecomorphi is a taxon of ray-finned bony fish in the clade Neopterygii. The only extant Halecomorph species are the bowfin and eyespot bowfin, but the group contains many extinct species in several families in the order Amiiformes, as well as the extinct orders Ionoscopiformes, Ophiopsiformes, Panxianichthyiformes, and Parasemionotiformes. The fossil record of halecomorphs goes back at least to the Early Triassic epoch.
The Halecomorphi exhibit a combination of ancestral features, such as most heavily mineralized scales, but also by more derived or "modern" features, particularly in the structure of the skull. Unique derived traits of the Halecomorphi include:

Unique jaw articulation in which the quadrate and symplectic participate in the joint.
Lengthened dorsal fins
Two biconcave vertebrae per segment in the posterior body region
Fan like arrangement of small bones in the tail.
Systematics and phylogeny

On the systematic position of the Halecomorphi, there are two competing hypotheses:

The Halecostomi hypothesis proposes Halecomorphi as the sister group of Teleostei, the major group of living neopterygians, rendering the Holostei paraphyletic.
The Holostei hypothesis proposes Halecomorphi as the sister group of Ginglymodi, the group which includes gars and their fossil relatives, rendering the Halecostomi paraphyletic.

The latter hypothesis is more widely accepted.
The following cladogram summarizes the evolutionary relationships of extinct and living orders of Halecomorphi.