Subgroups — D₃²×C₁₁×C₆₁ #37563540

Order 24156.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₁×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₃⋊D₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₁₁×C₆₁	—	3	2	no	maximal
4	C₃²×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₁₁×C₆₁	—	3	2	no	—
6	D₃×C₁₁×C₆₁	—	6	1	no	—
7	D₃×C₁₁×C₆₁	D₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁×C₆₁	—	3	2	no	—
9	C₂²×C₁₁×C₆₁	—	9	1	no	Hall
10	D₃²×C₆₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₁×C₆₁	—	2	1	no	—
12	C₃×C₁₁×C₆₁	C₂×D₃	1	2	yes	complemented
13	C₂×C₁₁×C₆₁	—	3	2	no	—
14	C₂×C₁₁×C₆₁	—	9	1	no	—
15	C₃⋊D₃×C₆₁	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×D₃×C₆₁	C₂×C₁₁	1	2	yes	complemented
17	C₂×D₃×C₆₁	—	3	2	no	—
18	C₁₁×C₆₁	D₃²	1	1	yes	characteristic, direct product factor, Hall
19	C₃²×C₆₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
20	D₃²×C₁₁	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₆₁	—	3	2	no	—
22	D₃×C₆₁	—	3	2	no	—
23	D₃×C₆₁	—	6	1	no	—
24	D₃×C₆₁	D₃×C₁₁	1	2	yes	direct product factor
25	C₂²×C₆₁	—	9	1	no	Hall
26	C₁₁×C₃⋊D₃	C₂×C₆₁	1	1	yes	characteristic, complemented
27	C₃×D₃×C₁₁	C₂×C₆₁	1	2	yes	complemented
28	C₃×C₆₁	—	2	1	no	—
29	C₃×C₆₁	C₂×D₃×C₁₁	1	2	yes	complemented
30	C₂×D₃×C₁₁	—	3	2	no	—
31	C₂×C₆₁	—	3	2	no	—
32	C₂×C₆₁	—	9	1	no	—
33	C₃²×C₁₁	C₂²×C₆₁	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃×C₁₁	—	3	2	no	—
35	D₃×C₁₁	—	3	2	no	—
36	D₃×C₁₁	—	6	1	no	—
37	D₃×C₁₁	D₃×C₆₁	1	2	yes	direct product factor
38	C₆₁	D₃²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²×C₁₁	—	9	1	no	Hall
40	D₃²	C₁₁×C₆₁	1	1	yes	characteristic, direct product factor, Hall
41	C₃×C₁₁	—	2	1	no	—
42	C₃×C₁₁	C₂×D₃×C₆₁	1	2	yes	complemented
43	C₂×C₁₁	—	3	2	no	—
44	C₂×C₁₁	—	9	1	no	—
45	C₃⋊D₃	C₂×C₁₁×C₆₁	1	1	yes	characteristic, complemented
46	C₃×D₃	C₂×C₁₁×C₆₁	1	2	yes	complemented
47	C₂×D₃	—	3	2	no	—
48	C₁₁	D₃²×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
49	C₃²	C₂²×C₁₁×C₆₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	3	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	D₃×C₁₁×C₆₁	1	2	yes	direct product factor
54	C₂²	—	9	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	C₂×D₃×C₁₁×C₆₁	1	2	yes	complemented
57	C₂	—	3	2	no	—
58	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₆₁	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₁₁×C₆₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₆₁	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₁×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₁×C₆₁	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₆₁	C₂	semidirect
4. C₃²×C₁₁×C₆₁	C₂²	semidirect
7. D₃×C₁₁×C₆₁	D₃	direct (N × H)
10. D₃²×C₆₁	C₁₁	direct (N × H)
12. C₃×C₁₁×C₆₁	C₂×D₃	semidirect
15. C₃⋊D₃×C₆₁	C₂×C₁₁	semidirect
16. C₃×D₃×C₆₁	C₂×C₁₁	semidirect
18. C₁₁×C₆₁	D₃²	direct (N × H)
19. C₃²×C₆₁	C₂²×C₁₁	semidirect
20. D₃²×C₁₁	C₆₁	direct (N × H)
24. D₃×C₆₁	D₃×C₁₁	direct (N × H)
26. C₁₁×C₃⋊D₃	C₂×C₆₁	semidirect
27. C₃×D₃×C₁₁	C₂×C₆₁	semidirect
29. C₃×C₆₁	C₂×D₃×C₁₁	semidirect
33. C₃²×C₁₁	C₂²×C₆₁	semidirect
37. D₃×C₁₁	D₃×C₆₁	direct (N × H)
38. C₆₁	D₃²×C₁₁	direct (N × H)
40. D₃²	C₁₁×C₆₁	direct (N × H)
42. C₃×C₁₁	C₂×D₃×C₆₁	semidirect
45. C₃⋊D₃	C₂×C₁₁×C₆₁	semidirect
46. C₃×D₃	C₂×C₁₁×C₆₁	semidirect
48. C₁₁	D₃²×C₆₁	direct (N × H)
49. C₃²	C₂²×C₁₁×C₆₁	semidirect
53. D₃	D₃×C₁₁×C₆₁	direct (N × H)
56. C₃	C₂×D₃×C₁₁×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₁₁×C₆₁	2
C₁₁×C₃⋊D₃×C₆₁	2
C₂×D₃×C₁₁×C₆₁	3
D₃²×C₆₁	11
D₃²×C₁₁	61

Subgroups — D32×C11×C61 #37563540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃²×C₁₁×C₆₁ #37563540