tsk, tsk, Taz.
You've forgotten all the extinct mammals.
# 1 Subclass Prototheria
* 1.1 Infraclass Yinotheria
o 1.1.1 Order Monotremata
# 2 Subclass Allotheria
* 2.1 Order Multituberculata
o 2.1.1 Suborder "Plagiaulacida"
o 2.1.2 Suborder Cimolodonta
* 2.2 Order Triconodonta
* 2.3 Order Docodonta
# 3 Subclass Theria
* 3.1 Infraclass Pantotheria
o 3.1.1 Order Symmetrodonta
o 3.1.2 Order Pantotheria (Eupantotheria)
* 3.2 Infraclass Metatheria
o 3.2.1 Order Dasyuromorphia
o 3.2.2 Order Peramelemorphia
o 3.2.3 Order Diprotodontia
+ 3.2.3.1 Suborder Vombatiformes
+ 3.2.3.2 Suborder Phalangeriformes
+ 3.2.3.3 Suborder Macropodiformes
* 3.3 Infraclass Eutheria
o 3.3.1 Order Leptictida
o 3.3.2 Order Apatotheria
o 3.3.3 Order Pantolesta
o 3.3.4 Order Insectivora
+ 3.3.4.1 Suborder Erinaceomorpha
+ 3.3.4.2 Suborder Soricomorpha
o 3.3.5 Order Macroscelidea
o 3.3.6 Order Dermoptera
o 3.3.7 Order Chiroptera
o 3.3.8 Order Scandentia
o 3.3.9 Order Primates
+ 3.3.9.1 Suborder Strepsirrhini
+ 3.3.9.2 Suborder Haplorrhini
o 3.3.10 Order Anagalida
o 3.3.11 Order Lagomorpha
o 3.3.12 Order Rodentia
o 3.3.13 Order Condylarthra
o 3.3.14 Order Mesonychia
o 3.3.15 Order Litopterna
o 3.3.16 Order Notoungulata
+ 3.3.16.1 Suborder Notioprogonia
+ 3.3.16.2 Suborder Toxodontia
+ 3.3.16.3 Suborder Typotheria
+ 3.3.16.4 Suborder Hegetotheria
o 3.3.17 Order Astrapotheria
o 3.3.18 Order Xenungulata
o 3.3.19 Order Pyrotheria
o 3.3.20 Order Dinocerata
o 3.3.21 Order Pantodonta
o 3.3.22 Order Tillodontia
o 3.3.23 Order Taeniodonta
o 3.3.24 Order Arctostylopida
o 3.3.25 Order Embrithopoda
o 3.3.26 Order Creodonta
o 3.3.27 Order Carnivora
+ 3.3.27.1 Suborder Caniformia (Dog-like carnivores)
+ 3.3.27.2 Suborder Aeluroidea (Cat-like carnivores)
o 3.3.28 Order Xenarthra (Edentata)
+ 3.3.28.1 Suborder Vermilingua
+ 3.3.28.2 Suborder Tardigrada
+ 3.3.28.3 Suborder Cingulata
o 3.3.29 Order Pholidota
o 3.3.30 Order Tubulidentata
o 3.3.31 Order Bibymalagasia
o 3.3.32 Order Proboscidea
o 3.3.33 Order Hyracoidea
o 3.3.34 Order Desmostylia
o 3.3.35 Order Sirenia
o 3.3.36 Order Cetacea
+ 3.3.36.1 Suborder Archaeoceti
+ 3.3.36.2 Suborder Mysticeti
+ 3.3.36.3 Suborder Odontoceti
o 3.3.37 Order Perissodactyla
+ 3.3.37.1 Suborder Hippomorpha
+ 3.3.37.2 Suborder Ceratomorpha
o 3.3.38 Order Artiodactyla
+ 3.3.38.1 Suborder Suina
+ 3.3.38.2 Suborder Tylopoda
+ 3.3.38.3 Suborder Ruminantia
(From wiki)
And that's not counting all the individual species.
That list is too long to post.
More to come.