Finite Group Databasebeta

← C₁₁×D₁₁×C₈₉ #36340593

Subgroups — C₁₁×D₁₁×C₈₉ #36340593

Order 21538.

26 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	C₂×C₁₁×C₈₉	—	11	1	no	maximal
3	D₁₁×C₈₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor
4	C₁₁×C₈₉	—	2	5	no	—
5	C₁₁×C₈₉	D₁₁	1	1	yes	characteristic, direct product factor
6	C₁₁×C₈₉	C₂×C₁₁	1	1	yes	characteristic, complemented
7	C₁₁×D₁₁	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₈₉	—	11	1	no	Hall
9	C₁₁²	C₂×C₈₉	1	1	yes	characteristic, complemented, Sylow
10	C₈₉	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₂×C₁₁	—	11	1	no	—
12	D₁₁	C₁₁×C₈₉	1	1	yes	characteristic, direct product factor
13	C₁₁	—	2	5	no	—
14	C₁₁	D₁₁×C₈₉	1	1	yes	characteristic, direct product factor
15	C₁₁	C₂×C₁₁×C₈₉	1	1	yes	characteristic, complemented
16	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₈₉	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₁₁×C₈₉
Frattini	C₁	G
Fitting, socle	C₁₁²×C₈₉	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₁₁×C₈₉

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₈₉	C₂	semidirect
3. D₁₁×C₈₉	C₁₁	direct (N × H)
5. C₁₁×C₈₉	D₁₁	direct (N × H)
6. C₁₁×C₈₉	C₂×C₁₁	semidirect
7. C₁₁×D₁₁	C₈₉	direct (N × H)
9. C₁₁²	C₂×C₈₉	semidirect
10. C₈₉	C₁₁×D₁₁	direct (N × H)
12. D₁₁	C₁₁×C₈₉	direct (N × H)
14. C₁₁	D₁₁×C₈₉	direct (N × H)
15. C₁₁	C₂×C₁₁×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₁²×C₈₉	2
C₂×C₁₁×C₈₉	11
D₁₁×C₈₉	11
C₁₁×D₁₁	89