Calyptratae

Superregnum: Eukaryota
Cladus: Unikonta
Cladus: Opisthokonta
Cladus: Holozoa
Regnum: Animalia
Subregnum: Eumetazoa
Cladus: Bilateria
Cladus: Nephrozoa
Cladus: Protostomia
Cladus: Ecdysozoa
Cladus: Panarthropoda
Phylum: Arthropoda
Subphylum: Hexapoda
Classis: Insecta
Cladus: Dicondylia
Subclassis: Pterygota
Cladus: Metapterygota
Infraclassis: Neoptera
Cladus: Eumetabola
Cladus: Endopterygota
Superordo: Panorpida
Cladus: Antliophora
Ordo: Diptera
Subordo: Brachycera
Infraordo: Muscomorpha
Sectio: Schizophora
Subsectio: Calyptratae
Superfamiliae (3): Hippoboscoidea - Muscoidea - Oestroidea
Overview of familiae (12-13)

Anthomyiidae - Calliphoridae - Fanniidae - Glossinidae - Hippoboscidae - Muscidae - Mystacinobiidae - Nycteribiidae - Oestridae - Rhinophoridae - Sarcophagidae - Scathophagidae - Tachinidae

Note:

Correct name may be Calyptratae
References

Kutty, S.N.; Pape, T.; Wiegmann, B.M.; Meier, R. 2010: Molecular phylogeny of the Calyptratae (Diptera: Cyclorrhapha) with an emphasis on the superfamily Oestroidea and the position of Mystacinobiidae and McAlpine's fly. Systematic entomology, 35(4): 614–635. DOI: 10.1111/j.1365-3113.2010.00536.x
Nirmala, X.; Hypša, V.; Žurovec, M. 2001: Molecular phylogeny of Calyptratae (Diptera: Brachycera): the evolution of 18S and 16S ribosomal rDNAs in higher dipterans and their use in phylogenetic inference. Insect molecular biology, 10(5): 475–485. DOI: 10.1046/j.0962-1075.2001.00286.x
Pollock, J.N. 2010: Bot flies (Insecta: Oestridae, part) and Glossinidae-Hippoboscidae derive from basal Ephydroidea, not Calyptratae. Journal of natural history, 44: 1929–1952. DOI: 10.1080/00222931003764071

Calyptratae is a subsection of Schizophora in the insect order Diptera, commonly referred to as the calyptrate muscoids (or simply calyptrates). It consists of those flies which possess a calypter that covers the halteres, among which are some of the most familiar of all flies, such as the house fly.

About 18,000 described species are in this group, or about 12% of all the flies yet described.[1]
Subsection

Superfamily Muscoidea

Anthomyiidae - cabbage flies
Fanniidae
Muscidae - house flies
Scathophagidae - dung flies

Superfamily Oestroidea

Calliphoridae
Mystacinobiidae
Oestridae
Rhinophoridae
Sarcophagidae
Tachinidae
Ulurumyiidae[2]

Superfamily Hippoboscoidea

Glossinidae
Hippoboscidae
Nycteribiidae
Streblidae

The Mormotomyiidae belong to the Ephydroidea and not to Hippoboscoidea as previously construed.[3] The Streblidae are probably not monophyletic.[4]
References

Kutty, Sujatha Narayanan; Pape, Thomas; Wiegmann, Brian M.; Meier, Rudolf (2010). "Molecular phylogeny of the Calyptratae (Diptera: Cyclorrhapha) with an emphasis on the superfamily Oestroidea and the position of Mystacinobiidae and Mc Alpines fly". Systematic Entomology. 35 (4): 614–635. doi:10.1111/j.1365-3113.2010.00536.x.
Michelsen, Verner; Pape, Thomas (2017). "Ulurumyiidae – a new family of calyptrate flies (Diptera)". Systematic Entomology. 42 (4): 826–836.
Kirk-Spriggs, A.H., Kotrba, M. & Copeland, R.S. 2011. Further details of the morphology of the enigmatic African fly Mormotomyia hirsuta Austen (Diptera: Mormotomyiidae). African Invertebrates 52 (1): 145-165."Archived copy". Archived from the original on 2011-10-04. Retrieved 2011-10-04.
Petersen, Frederik Torp; Meier, Rudolf; Kutty, Sujatha Narayanan & Wiegmann, Brian M. (2007): The phylogeny and evolution of host choice in the Hippoboscoidea (Diptera) as reconstructed using four molecular markers. Mol. Phylogenet. Evol. 45(1): 111–122. doi:10.1016/j.ympev.2007.04.023 (HTML abstract)