Subgroups — C₂×C₁₁⋊C₅×D₁₆₇ #49145083

Order 36740.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×D₁₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁⋊C₅×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₅×C₁₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₁₆₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₁×C₁₆₇	C₂×C₅	1	1	yes	characteristic, complemented
6	C₁₁×D₁₆₇	C₂×C₅	1	2	yes	complemented
7	C₂×C₅×D₁₆₇	—	11	1	no	maximal, Hall
8	C₁₁×C₁₆₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₁₆₇	—	11	1	no	—
10	C₅×D₁₆₇	—	11	2	no	—
11	C₅×C₁₆₇	—	11	1	no	Hall
12	C₂×D₁₆₇	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₁₆₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
14	D₁₆₇	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
15	C₂²×C₁₁⋊C₅	—	167	1	no	maximal, Hall
16	C₁₆₇	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₁⋊C₅	—	167	2	no	—
18	C₂×C₁₁⋊C₅	D₁₆₇	1	1	yes	characteristic, direct product factor
19	C₁₁⋊C₅	C₂×D₁₆₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₁₁	—	167	1	no	Hall
21	C₂×C₁₁	—	167	2	no	—
22	C₂×C₁₁	C₅×D₁₆₇	1	1	yes	characteristic, complemented
23	C₂²×C₅	—	1837	1	no	Hall
24	C₁₁	C₂×C₅×D₁₆₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	11	1	no	—
26	C₂×C₅	—	1837	2	no	—
27	C₅	—	11	1	no	Sylow
28	C₂²	—	167	1	no	Sylow
29	C₂	—	167	2	no	—
30	C₂	C₁₁⋊C₅×D₁₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₁⋊C₅×D₁₆₇
commutator, cosocle, hypocenter	C₁₁×C₁₆₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₁₆₇	C₂×C₅
LCS	G ▷ C₁₁×C₁₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×D₁₆₇	C₂	direct (N × H)
2. C₂×C₁₁⋊C₅×C₁₆₇	C₂	semidirect
3. C₁₁⋊C₅×C₁₆₇	C₂²	semidirect
4. C₂×C₁₁×D₁₆₇	C₅	semidirect
5. C₂×C₁₁×C₁₆₇	C₂×C₅	semidirect
6. C₁₁×D₁₆₇	C₂×C₅	semidirect
8. C₁₁×C₁₆₇	C₂²×C₅	semidirect
12. C₂×D₁₆₇	C₁₁⋊C₅	direct (N × H)
13. C₂×C₁₆₇	C₂×C₁₁⋊C₅	semidirect
14. D₁₆₇	C₂×C₁₁⋊C₅	direct (N × H)
16. C₁₆₇	C₂²×C₁₁⋊C₅	semidirect
18. C₂×C₁₁⋊C₅	D₁₆₇	direct (N × H)
19. C₁₁⋊C₅	C₂×D₁₆₇	direct (N × H)
22. C₂×C₁₁	C₅×D₁₆₇	semidirect
24. C₁₁	C₂×C₅×D₁₆₇	semidirect
30. C₂	C₁₁⋊C₅×D₁₆₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁⋊C₅×D₁₆₇	2
C₂×C₁₁⋊C₅×C₁₆₇	2
C₂×C₁₁×D₁₆₇	5
C₂×C₅×D₁₆₇	11
C₂²×C₁₁⋊C₅	167

Subgroups — C2×C11⋊C5×D167 #49145083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁⋊C₅×D₁₆₇ #49145083