What are all of the clades of the magnorder Boreoeutheria?

Answer 1

Very briefly, Boreoeutheria are divided into two extant principal clades: Euarchontoglires and Laurasiatheria.

Euarchontoglires include in turn, Archonta and Glires.

The extant orders constituting Archonta are Scandentia (tree-shrews), Primates (lemurs etc., monkeys and people) and Dermoptera (colugos).

Glires include orders Lagomorpha (hares, rabbits) and Rodentia (porcupines, cavies, squirrels, beavers, rats, mice, gerbils, etc.).

Laurasiatheria include: Eulipotyphla and Scrotifera.

(Eulipotyphla are a depleted version of Lipotyphla which in turn was a remnant of the old Insectivora. Eulipotyphla were subsequently split into Soricomorpha (shrews) and Erinaceomorpha (hedgehogs & gymnures) but then recombined by those who accept that erinaceomorphs are nested within soricomorphs). So order, Eulipotyphla, is what we call them.

Scrotifera include order, Chiroptera (bats) and Fereuungulata. (Yes, there's a syllabic division between the two 'U's!)

Fereuungulata contain: Ferae - order, Pholidota (pangolins which have been estranged from anteaters) and order, Carnivora (cats, hyenas, dogs, bears, weasels, raccoons, seals, etc.) Now the ungulates probably form a single clade alongside Ferae and are called, Ungulata, or maybe Euungulata (proper ungulates unlike those imposters, the elephants and relatives which have been shunted elsewhere). If Ferae turn out to be nested within ungulates then the (Eu)ungulate clade would no longer stand.

We now arrive among ungulates. Two major groups: order, Perissodactyla (horses, tapirs, rhinos) and what seems to be fairly universally referred to these days as Cetartiodactyla.

Cetartiodactyla include the even-toed ungulates (camels, pigs, hippos, giraffes, antelopes, cattle, sheep, goats, deer) traditionally referred to order, Artiodactyla, but the so-called order, Cetacea (whales), is now considered as a prodigal child returned to the artiodactyl home, as the common cetacean ancestor appears to be rooted somewhere near the hippopotamus branch.

Work is still in progress, and will continue for a while yet, as individual researchers ride their personal hobby horses in progressively similar directions. Taxonomists furthermore are a fertile source of opinions.

As for including extinct taxa, like (just one example) the various prehistoric South American ungulate-type groups, that is another game within another level of mystery.