Subgroups — C₁₁×C₃⋊D₃×D₆₁ #37563551

Order 24156.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₁×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₃⋊D₁₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₁×D₆₁	—	3	4	no	maximal
5	C₃²×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₁×D₁₈₃	—	3	4	no	—
7	D₃×C₁₁×C₆₁	—	3	4	no	—
8	C₃×C₁₁×D₆₁	D₃	1	4	yes	complemented
9	C₂×C₁₁×D₆₁	—	9	1	no	Hall
10	C₃⋊D₃×D₆₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₁×C₆₁	C₂×D₃	1	4	yes	complemented
12	C₂×C₁₁×C₆₁	—	9	1	no	—
13	C₁₁×D₆₁	—	9	1	no	—
14	C₁₁×D₆₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃⋊D₁₈₃	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃⋊D₃×C₆₁	C₂×C₁₁	1	1	yes	characteristic, complemented
17	C₃²×D₆₁	C₂×C₁₁	1	1	yes	characteristic, complemented
18	D₃×D₆₁	—	3	4	no	—
19	C₁₁×C₆₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₆₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₁×C₃⋊D₃	—	61	1	no	maximal, Hall
22	D₁₈₃	—	3	4	no	—
23	C₃×D₆₁	D₃×C₁₁	1	4	yes	complemented
24	D₃×C₆₁	—	3	4	no	—
25	C₂×D₆₁	—	9	1	no	Hall
26	C₂×C₃²×C₁₁	—	61	1	no	—
27	C₁₁×C₃⋊D₃	—	61	1	no	—
28	C₁₁×C₃⋊D₃	D₆₁	1	1	yes	characteristic, direct product factor
29	C₃×C₆₁	C₂×D₃×C₁₁	1	4	yes	complemented
30	C₂×D₃×C₁₁	—	183	4	no	—
31	C₂×C₆₁	—	9	1	no	—
32	D₆₁	—	9	1	no	—
33	D₆₁	C₁₁×C₃⋊D₃	1	1	yes	characteristic, direct product factor
34	C₃²×C₁₁	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₁₁	—	61	4	no	—
36	D₃×C₁₁	—	3	4	no	—
37	D₃×C₁₁	—	183	4	no	—
38	C₆₁	C₂×C₁₁×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₁₁	—	549	1	no	Hall
40	C₂×C₃⋊D₃	—	61	1	no	Hall
41	C₃×C₁₁	D₃×D₆₁	1	4	yes	complemented
42	C₂×C₁₁	—	9	1	no	—
43	C₂×C₁₁	—	549	1	no	—
44	C₂×C₁₁	—	61	1	no	—
45	C₂×C₃²	—	61	1	no	—
46	C₃⋊D₃	—	61	1	no	—
47	C₃⋊D₃	C₁₁×D₆₁	1	1	yes	characteristic, direct product factor
48	C₂×D₃	—	183	4	no	—
49	C₁₁	C₃⋊D₃×D₆₁	1	1	yes	characteristic, direct product factor, Sylow
50	C₃²	C₂×C₁₁×D₆₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	61	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	183	4	no	—
54	C₂²	—	549	1	no	Sylow
55	C₃	D₃×C₁₁×D₆₁	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	549	1	no	—
58	C₂	—	61	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	C₃⋊D₃×D₆₁
commutator, cosocle, hypocenter	C₃²×C₆₁	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₆₁	C₂²
LCS	G ▷ C₃²×C₆₁
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₁×D₆₁	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₆₁	C₂	semidirect
3. C₁₁×C₃⋊D₁₈₃	C₂	semidirect
5. C₃²×C₁₁×C₆₁	C₂²	semidirect
8. C₃×C₁₁×D₆₁	D₃	semidirect
10. C₃⋊D₃×D₆₁	C₁₁	direct (N × H)
11. C₃×C₁₁×C₆₁	C₂×D₃	semidirect
14. C₁₁×D₆₁	C₃⋊D₃	direct (N × H)
15. C₃⋊D₁₈₃	C₂×C₁₁	semidirect
16. C₃⋊D₃×C₆₁	C₂×C₁₁	semidirect
17. C₃²×D₆₁	C₂×C₁₁	semidirect
19. C₁₁×C₆₁	C₂×C₃⋊D₃	semidirect
20. C₃²×C₆₁	C₂²×C₁₁	semidirect
23. C₃×D₆₁	D₃×C₁₁	semidirect
28. C₁₁×C₃⋊D₃	D₆₁	direct (N × H)
29. C₃×C₆₁	C₂×D₃×C₁₁	semidirect
33. D₆₁	C₁₁×C₃⋊D₃	direct (N × H)
34. C₃²×C₁₁	C₂×D₆₁	semidirect
38. C₆₁	C₂×C₁₁×C₃⋊D₃	semidirect
41. C₃×C₁₁	D₃×D₆₁	semidirect
47. C₃⋊D₃	C₁₁×D₆₁	direct (N × H)
49. C₁₁	C₃⋊D₃×D₆₁	direct (N × H)
50. C₃²	C₂×C₁₁×D₆₁	semidirect
55. C₃	D₃×C₁₁×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₁₁×D₆₁	2
C₁₁×C₃⋊D₃×C₆₁	2
C₁₁×C₃⋊D₁₈₃	2
D₃×C₁₁×D₆₁	3
C₃⋊D₃×D₆₁	11
C₂×C₁₁×C₃⋊D₃	61

Subgroups — C11×C3⋊D3×D61 #37563551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃⋊D₃×D₆₁ #37563551