Subgroups — C₁₁⋊D₉₇₉ #36340596

Order 21538.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₉₇₉	—	11	12	no	maximal
3	C₁₁×C₈₉	D₁₁	1	12	yes	complemented
4	C₁₁⋊D₁₁	—	89	1	no	maximal, Hall
5	D₈₉	—	121	1	no	Hall
6	C₁₁²	D₈₉	1	1	yes	characteristic, complemented, Sylow
7	C₈₉	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
8	D₁₁	—	979	12	no	—
9	C₁₁	D₉₇₉	1	12	yes	complemented
10	C₂	—	10769	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²×C₈₉	C₂
LCS	G ▷ C₁₁²×C₈₉
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.