Subgroups — C₂×D₁₁×C₆₇⋊C₁₁ #44569839

Order 32428.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₆₇⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₁×C₆₇⋊C₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₁₁×C₆₇⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁×C₆₇	C₁₁	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₆₇⋊C₁₁	—	11	1	no	maximal
6	C₂×C₁₁×C₆₇	C₂×C₁₁	1	1	yes	characteristic, complemented
7	D₁₁×C₆₇	C₂×C₁₁	1	2	yes	complemented
8	C₂×C₆₇⋊C₁₁	—	2	5	no	—
9	C₂×C₆₇⋊C₁₁	—	11	2	no	—
10	C₂×C₆₇⋊C₁₁	D₁₁	1	1	yes	characteristic, direct product factor
11	C₁₁×C₆₇	C₂²×C₁₁	1	1	yes	characteristic, complemented
12	C₆₇⋊C₁₁	—	2	5	no	—
13	C₆₇⋊C₁₁	C₂×D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×C₁₁×D₁₁	—	67	1	no	maximal, Hall
15	C₂²×C₆₇	—	11	1	no	Hall
16	C₂×C₁₁²	—	67	1	no	—
17	C₁₁×D₁₁	—	67	2	no	—
18	C₂×C₆₇	—	11	2	no	—
19	C₂×C₆₇	C₁₁×D₁₁	1	1	yes	characteristic, complemented
20	C₁₁²	—	67	1	no	Sylow
21	C₆₇	C₂×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂²×C₁₁	—	737	1	no	—
23	C₂×D₁₁	C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor
24	C₂×C₁₁	—	67	1	no	—
25	C₂×C₁₁	—	134	5	no	—
26	C₂×C₁₁	—	737	2	no	—
27	C₂×C₁₁	C₂×C₆₇⋊C₁₁	1	1	yes	characteristic, complemented
28	D₁₁	C₂×C₆₇⋊C₁₁	1	2	yes	direct product factor
29	C₁₁	—	67	1	no	—
30	C₁₁	—	134	5	no	—
31	C₁₁	C₂²×C₆₇⋊C₁₁	1	1	yes	characteristic, complemented
32	C₂²	—	11	1	no	Sylow
33	C₂	—	11	2	no	—
34	C₂	D₁₁×C₆₇⋊C₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₁×C₆₇⋊C₁₁
commutator, cosocle, hypocenter	C₁₁×C₆₇	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₆₇	C₂×C₁₁
LCS	G ▷ C₁₁×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×C₆₇⋊C₁₁	C₂	semidirect
2. D₁₁×C₆₇⋊C₁₁	C₂	direct (N × H)
3. C₁₁×C₆₇⋊C₁₁	C₂²	semidirect
4. C₂×D₁₁×C₆₇	C₁₁	semidirect
6. C₂×C₁₁×C₆₇	C₂×C₁₁	semidirect
7. D₁₁×C₆₇	C₂×C₁₁	semidirect
10. C₂×C₆₇⋊C₁₁	D₁₁	direct (N × H)
11. C₁₁×C₆₇	C₂²×C₁₁	semidirect
13. C₆₇⋊C₁₁	C₂×D₁₁	direct (N × H)
19. C₂×C₆₇	C₁₁×D₁₁	semidirect
21. C₆₇	C₂×C₁₁×D₁₁	semidirect
23. C₂×D₁₁	C₆₇⋊C₁₁	direct (N × H)
27. C₂×C₁₁	C₂×C₆₇⋊C₁₁	semidirect
28. D₁₁	C₂×C₆₇⋊C₁₁	direct (N × H)
31. C₁₁	C₂²×C₆₇⋊C₁₁	semidirect
34. C₂	D₁₁×C₆₇⋊C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₆₇⋊C₁₁	2
D₁₁×C₆₇⋊C₁₁	2
C₂×D₁₁×C₆₇	11
C₂²×C₆₇⋊C₁₁	11
C₂×C₁₁×D₁₁	67

Subgroups — C2×D11×C67⋊C11 #44569839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁×C₆₇⋊C₁₁ #44569839