Subgroups — C₁₁×C₁₁⋊(D₃₇⋊C₃) #41001749

Order 26862.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₄₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₁⋊(D₃₇⋊C₃)	C₁₁	1	1	yes	maximal, characteristic, direct product factor
5	C₁₁×D₃₇⋊C₃	—	11	1	no	maximal
6	C₁₁×C₃₇⋊C₃	—	2	5	no	—
7	C₁₁×C₃₇⋊C₃	D₁₁	1	1	yes	characteristic, complemented
8	C₁₁×C₃₇⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented
9	D₄₀₇	C₃×C₁₁	1	1	yes	characteristic, complemented
10	C₁₁×D₃₇	—	11	1	no	—
11	C₃×C₁₁×D₁₁	—	37	1	no	maximal, Hall
12	C₁₁×C₃₇	—	2	5	no	—
13	C₁₁×C₃₇	C₃×D₁₁	1	1	yes	characteristic, complemented
14	C₁₁×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
15	C₃×C₁₁²	—	37	1	no	Hall
16	C₁₁×D₁₁	—	111	1	no	Hall
17	D₃₇⋊C₃	—	11	1	no	Hall
18	C₁₁²	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃₇⋊C₃	C₁₁×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₃₇	—	11	1	no	Hall
21	C₂×C₃×C₁₁	—	407	1	no	—
22	C₃×D₁₁	—	37	1	no	—
23	C₃₇	C₃×C₁₁×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₁₁	—	37	1	no	—
25	C₃×C₁₁	—	37	1	no	—
26	C₃×C₁₁	—	74	5	no	—
27	C₂×C₁₁	—	1221	1	no	—
28	D₁₁	—	111	1	no	—
29	C₁₁	—	2	5	no	—
30	C₁₁	C₁₁×D₃₇⋊C₃	1	1	yes	characteristic, complemented
31	C₁₁	C₁₁⋊(D₃₇⋊C₃)	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	407	1	no	Hall
33	C₃	—	37	1	no	Sylow
34	C₂	—	1221	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₁₁⋊(D₃₇⋊C₃)
commutator, cosocle, hypocenter	C₁₁×C₃₇	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁²×C₃₇	C₂×C₃
LCS	G ▷ C₁₁×C₃₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁²×C₃₇⋊C₃	C₂	semidirect
2. C₁₁×D₄₀₇	C₃	semidirect
3. C₁₁²×C₃₇	C₂×C₃	semidirect
4. C₁₁⋊(D₃₇⋊C₃)	C₁₁	direct (N × H)
7. C₁₁×C₃₇⋊C₃	D₁₁	semidirect
8. C₁₁×C₃₇⋊C₃	C₂×C₁₁	semidirect
9. D₄₀₇	C₃×C₁₁	semidirect
13. C₁₁×C₃₇	C₃×D₁₁	semidirect
14. C₁₁×C₃₇	C₂×C₃×C₁₁	semidirect
18. C₁₁²	D₃₇⋊C₃	semidirect
19. C₃₇⋊C₃	C₁₁×D₁₁	semidirect
23. C₃₇	C₃×C₁₁×D₁₁	semidirect
30. C₁₁	C₁₁×D₃₇⋊C₃	semidirect
31. C₁₁	C₁₁⋊(D₃₇⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁²×C₃₇⋊C₃	2
C₁₁×D₄₀₇	3
C₁₁⋊(D₃₇⋊C₃)	11
C₁₁×D₃₇⋊C₃	11
C₃×C₁₁×D₁₁	37

Subgroups — C11×C11⋊(D37⋊C3) #41001749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₁⋊(D₃₇⋊C₃) #41001749