Subgroups — C₁₁×D₇×C₆₇⋊C₃ #44526264

Order 30954.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×C₆₇⋊C₃	—	7	1	no	maximal, Hall
5	D₇×C₆₇⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₁×C₆₇⋊C₃	D₇	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₁₁×C₆₇	—	7	1	no	Hall
8	C₇×C₆₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
9	D₇×C₆₇	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×C₆₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₆₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×D₇	—	67	1	no	maximal, Hall
13	C₂×C₆₇⋊C₃	—	7	1	no	Hall
14	C₃×C₇×C₁₁	—	67	1	no	Hall
15	C₆₇⋊C₃	C₁₁×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₁₁×D₇	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₇	—	7	1	no	Hall
18	C₇×C₁₁	C₂×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₆₇	C₃×C₁₁×D₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃×C₁₁	—	469	1	no	Hall
21	C₃×D₇	—	67	1	no	Hall
22	C₃×C₁₁	—	67	1	no	Hall
23	C₂×C₁₁	—	7	1	no	Hall
24	C₃×C₇	—	67	1	no	Hall
25	D₇	C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁	D₇×C₆₇⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₂×C₁₁×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	469	1	no	Hall
29	C₃	—	67	1	no	Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₇×C₆₇⋊C₃
commutator, cosocle, hypocenter	C₇×C₆₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×C₆₇⋊C₃	C₂	semidirect
2. C₁₁×D₇×C₆₇	C₃	semidirect
3. C₇×C₁₁×C₆₇	C₂×C₃	semidirect
5. D₇×C₆₇⋊C₃	C₁₁	direct (N × H)
6. C₁₁×C₆₇⋊C₃	D₇	direct (N × H)
8. C₇×C₆₇⋊C₃	C₂×C₁₁	semidirect
9. D₇×C₆₇	C₃×C₁₁	semidirect
10. C₁₁×C₆₇	C₃×D₇	semidirect
11. C₇×C₆₇	C₂×C₃×C₁₁	semidirect
15. C₆₇⋊C₃	C₁₁×D₇	direct (N × H)
16. C₁₁×D₇	C₆₇⋊C₃	direct (N × H)
18. C₇×C₁₁	C₂×C₆₇⋊C₃	semidirect
19. C₆₇	C₃×C₁₁×D₇	semidirect
25. D₇	C₁₁×C₆₇⋊C₃	direct (N × H)
26. C₁₁	D₇×C₆₇⋊C₃	direct (N × H)
27. C₇	C₂×C₁₁×C₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁×C₆₇⋊C₃	2
C₁₁×D₇×C₆₇	3
C₂×C₁₁×C₆₇⋊C₃	7
D₇×C₆₇⋊C₃	11
C₃×C₁₁×D₇	67

Subgroups — C11×D7×C67⋊C3 #44526264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₇×C₆₇⋊C₃ #44526264