The laughing hyena (Crocuta crocuta) is a ‘CatDog’

Traditionally
hyenas, like Crocuta crocuta (spotted or laughing hyaena, Kaup 1828, Erxleben 1777; up to 160 cm in length, Pliocene, 10 mya to present; Figs. 1,2), have been nested with palm civets, like Nandinia, and mongooses, like Herpestes. I hate to keep doing this, but adding Crocuta to the large reptile tree (LRT) nests this hyena rather strongly between dogs, like Canis (Fig. 3) and cats, like the African lion, Panthera leo (African lion, Linneaus 1758; up to 250 cm in length (sans tail), Pliocene, 10 mya to present; Fig. 4). So the hyena is something of a CatDog (see way below, Fig. 5). It is not a basal member of the Carnivora.

And it’s easy to see why hyenas nest with dogs.
There is even a clade of widely recognized dog-like hyenas among fossil taxa. Wikipedia reports, “Although phylogenetically they are closer to felines and viverrids, hyenas are behaviourally and morphologically similar to canines in several aspects” So most workers consider this convergent evolution. Having examined the characters in detail, I call this nothing but rather typical evolution and sisterhood. There are only a few traits that separate the three sisters.

From the  website of the
IUCN Hyaena Specialist Group “Although extant hyenas are rather dog-like in many aspects of their appearance, the family Hyaenidae actually belongs to the Carnivore suborder Feliformia, which also contains cats, mongooses, civets, and allies.”

Contra that hypothesis of relationships,
the LRT nests civets, mongooses, moles, raccoons, seals and allies as basal carnivores. Cats, dogs and  hyenas nest as derived carnivores and sisters to the extinct taxa, Miacis and Hyopsodus.

Perhaps more reasons to distrust DNA studies
The IUCN website notes: “Fossil data suggest that members of the family Hyaenidae last shared a common ancestor with their Feliform sister taxon in the Oligocene, around 25 million years ago (MYA) (Werdelin & Solounias 1991), and recent molecular data suggest this divergence occurred even earlier, approximately 29 MYA (Koepfli et al. 2006). The molecular data further suggest that the sister group to the Hyaenidae is a Feliform clade containing the mongooses (family Herpestidae) and the fossa (genus Cryptoprocta), a small, civet-like Malagasy carnivore that was assigned to the family Viverridae until quite recently (Yoder et al. 2003).”

Sisters to the dog-cat split, Miacis and Hyopsodus, 
were found in Late Paleocene to Late Eocene strata. So phylogenetic bracketing pushes the cat-dog + hyena split back to that era.

The cartoon
CatDog is a animated television character (Fig. 5) with two heads that in no way resembles the extant hyena. As you might imagine, they often want to go their separate ways and this leads to frustration and fun.

While we’re on the subject of hyenas…
Proteles crostata (aardwolf; Fig. 6; Sparrman 1783; extant), is in the same family as hyenas, according to Wikipedia. And it is, in a way… except the LRT nests this long-legged termite-eater closer to Canis than Crocuta.

And this footnote:
The weasel or stoat (Mustela erminea; Linneaus 1758) nests basal to all six above named taxa in the LRT, derived from a sister to the raccoon (Procyon).

References
Erxleben J 1777. Systema regni animalis.
Kaup JJ 1828. Über Hyaena, Uromastix, Basiliscus, Corthaeolus, Acontias. Isis 21, columns 1144–1150.
Linnaeus C von 1758. Systema naturæ per regna tria naturæ, secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis. Tomus I. Editio decima, reformata.
Sparman A 1783. 

wiki/Canis
wiki/Carnivora
wiki/Crocuta
wiki/Hyena
wiki/Panthera
wiki/Aardwolf