Subgroups — C₁₁×D₁₂₂₁ #41001764

Order 26862.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₄₀₇	—	3	1	no	maximal, Hall
3	C₁₁²×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₁₂₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₁₁×D₁₁₁	—	11	1	no	maximal
6	C₃×C₁₁×C₃₇	—	2	5	no	—
7	C₃×C₁₁×C₃₇	D₁₁	1	1	yes	characteristic, complemented
8	C₃×C₁₁×C₃₇	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₄₀₇	—	3	1	no	—
10	C₁₁×D₃₇	—	33	1	no	—
11	C₁₁×D₃₃	—	37	1	no	maximal, Hall
12	C₁₁×C₃₇	—	2	5	no	—
13	C₁₁×C₃₇	D₃×C₁₁	1	1	yes	characteristic, complemented
14	C₁₁×C₃₇	D₃₃	1	1	yes	characteristic, complemented
15	C₃×C₁₁²	D₃₇	1	1	yes	characteristic, complemented, Hall
16	C₁₁×D₁₁	—	111	1	no	Hall
17	D₁₁₁	—	11	1	no	Hall
18	C₁₁²	D₁₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₃₇	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₃₇	—	33	1	no	Hall
21	D₃₃	—	37	1	no	—
22	D₃×C₁₁	—	407	1	no	—
23	C₃₇	C₁₁×D₃₃	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₁	—	2	5	no	—
25	C₃×C₁₁	C₁₁×D₃₇	1	1	yes	characteristic, complemented
26	C₃×C₁₁	D₄₀₇	1	1	yes	characteristic, complemented
27	C₂×C₁₁	—	1221	1	no	—
28	D₁₁	—	111	1	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	C₁₁×D₁₁₁	1	1	yes	characteristic, complemented
31	C₁₁	D₁₂₂₁	1	1	yes	characteristic, direct product factor
32	D₃	—	407	1	no	Hall
33	C₃	C₁₁×D₄₀₇	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	1221	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	D₁₂₂₁
commutator, cosocle, hypocenter	C₃×C₁₁×C₃₇	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₃₇	C₂
LCS	G ▷ C₃×C₁₁×C₃₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁²×C₃₇	C₂	semidirect
3. C₁₁²×C₃₇	D₃	semidirect
4. D₁₂₂₁	C₁₁	direct (N × H)
7. C₃×C₁₁×C₃₇	D₁₁	semidirect
8. C₃×C₁₁×C₃₇	C₂×C₁₁	semidirect
13. C₁₁×C₃₇	D₃×C₁₁	semidirect
14. C₁₁×C₃₇	D₃₃	semidirect
15. C₃×C₁₁²	D₃₇	semidirect
18. C₁₁²	D₁₁₁	semidirect
19. C₃×C₃₇	C₁₁×D₁₁	semidirect
23. C₃₇	C₁₁×D₃₃	semidirect
25. C₃×C₁₁	C₁₁×D₃₇	semidirect
26. C₃×C₁₁	D₄₀₇	semidirect
30. C₁₁	C₁₁×D₁₁₁	semidirect
31. C₁₁	D₁₂₂₁	direct (N × H)
33. C₃	C₁₁×D₄₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₁²×C₃₇	2
C₁₁×D₄₀₇	3
D₁₂₂₁	11
C₁₁×D₁₁₁	11
C₁₁×D₃₃	37

Subgroups — C11×D1221 #41001764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×D₁₂₂₁ #41001764