Subgroups — D₈₉² #44540040

Order 31684.

108 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, complemented
2	C₈₉×D₈₉	C₂	1	2	yes	maximal, complemented
3	C₈₉²	C₂²	1	1	yes	characteristic, complemented, Sylow
4	C₂×D₈₉	—	89	2	no	maximal
5	C₂×C₈₉	—	89	2	no	—
6	D₈₉	—	89	2	no	—
7	D₈₉	—	178	44	no	—
8	D₈₉	D₈₉	1	2	yes	direct product factor
9	C₈₉	—	2	44	no	—
10	C₈₉	C₂×D₈₉	1	2	yes	complemented
11	C₂²	—	7921	1	no	Sylow
12	C₂	—	89	2	no	—
13	C₂	—	7921	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₈₉²	C₂²
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.