Subgroups — #44540039

Order 31684.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉²	C₄	1	1	yes	characteristic, complemented, Sylow
3	#67063	—	89	1	no	maximal
4	Dic₈₉	—	89	1	no	maximal
5	C₂×C₈₉	—	89	1	no	—
6	D₈₉	D₈₉	1	1	yes	characteristic
7	C₈₉	—	4	22	no	—
8	C₈₉	Dic₈₉	1	1	yes	characteristic, complemented
9	C₈₉	#67063	1	1	yes	characteristic, complemented
10	C₄	—	7921	1	no	Sylow
11	C₂	—	89	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₈₉²	C₄
prime radical, cosocle	C₈₉×D₈₉	C₂
LCS	G ▷ C₈₉²
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.