Subgroups — C₂×C₃×D₃×C₂₃⋊C₁₁ #22603471

Order 9108.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₂₃⋊C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₂₃⋊C₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₃×C₂₃⋊C₁₁	—	3	1	no	maximal
4	C₂×D₃×C₂₃⋊C₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₂₃⋊C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₂₃⋊C₁₁	—	2	1	no	—
7	C₂×C₃×C₂₃⋊C₁₁	—	3	2	no	—
8	C₂×C₃×C₂₃⋊C₁₁	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₂₃⋊C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
10	D₃×C₂₃⋊C₁₁	C₂×C₃	1	2	yes	direct product factor
11	C₂²×C₂₃⋊C₁₁	—	3	1	no	Hall
12	C₂×C₃×D₃×C₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
13	C₃×C₂₃⋊C₁₁	—	2	1	no	—
14	C₃×C₂₃⋊C₁₁	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₃×C₂₃⋊C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₂₃⋊C₁₁	—	3	2	no	—
17	C₂×C₂₃⋊C₁₁	C₃×D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₂₃	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×D₃×C₂₃	C₂×C₁₁	1	2	yes	complemented
20	C₂×C₃×D₃×C₁₁	—	23	1	no	maximal, Hall
21	C₂²×C₃×C₂₃	—	3	1	no	—
22	C₂×D₃×C₂₃	C₃×C₁₁	1	1	yes	characteristic, complemented
23	C₂₃⋊C₁₁	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
24	C₃²×C₂₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃²×C₁₁	—	23	1	no	—
26	C₃×D₃×C₁₁	—	23	2	no	—
27	C₂×C₃×C₂₃	—	2	1	no	—
28	C₂×C₃×C₂₃	—	3	2	no	—
29	C₂×C₃×C₂₃	D₃×C₁₁	1	1	yes	characteristic, complemented
30	C₂×C₃×C₂₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
31	D₃×C₂₃	C₂×C₃×C₁₁	1	2	yes	complemented
32	C₂²×C₃×C₁₁	—	69	1	no	—
33	C₂×D₃×C₁₁	—	23	1	no	—
34	C₃²×C₁₁	—	23	1	no	Hall
35	C₂²×C₂₃	—	3	1	no	Hall
36	C₃×C₂₃	—	2	1	no	—
37	C₃×C₂₃	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented
38	C₃×C₂₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented
39	C₂×C₃×C₁₁	—	23	1	no	—
40	C₂×C₃×C₁₁	—	23	1	no	—
41	C₂×C₃×C₁₁	—	46	1	no	—
42	C₂×C₃×C₁₁	—	69	2	no	—
43	D₃×C₁₁	—	23	2	no	—
44	C₂×C₂₃	—	3	2	no	—
45	C₂×C₂₃	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented
46	C₂²×C₁₁	—	69	1	no	Hall
47	C₂×C₃×D₃	C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor, Hall
48	C₃×C₁₁	—	23	1	no	—
49	C₃×C₁₁	—	23	1	no	—
50	C₃×C₁₁	—	46	1	no	—
51	C₂₃	C₂×C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₁₁	—	23	1	no	—
53	C₂×C₁₁	—	69	2	no	—
54	C₂×C₃²	C₂×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
55	C₃×D₃	C₂×C₂₃⋊C₁₁	1	2	yes	direct product factor
56	C₂²×C₃	—	3	1	no	—
57	C₂×D₃	C₃×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor
58	C₁₁	—	23	1	no	Sylow
59	C₃²	C₂²×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3	2	no	—
62	C₂×C₃	D₃×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor
63	C₂×C₃	C₂×C₃×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
64	D₃	C₂×C₃×C₂₃⋊C₁₁	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×D₃×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor
68	C₃	C₂²×C₃×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₂₃⋊C₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×C₂₃⋊C₁₁
commutator, hypocenter	C₃×C₂₃	C₂²×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₂₃	C₂×C₁₁
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₂₃⋊C₁₁	C₂	semidirect
2. C₃×D₃×C₂₃⋊C₁₁	C₂	direct (N × H)
4. C₂×D₃×C₂₃⋊C₁₁	C₃	direct (N × H)
5. C₃²×C₂₃⋊C₁₁	C₂²	semidirect
8. C₂×C₃×C₂₃⋊C₁₁	D₃	direct (N × H)
9. C₂×C₃×C₂₃⋊C₁₁	C₂×C₃	semidirect
10. D₃×C₂₃⋊C₁₁	C₂×C₃	direct (N × H)
12. C₂×C₃×D₃×C₂₃	C₁₁	semidirect
14. C₃×C₂₃⋊C₁₁	C₂×D₃	direct (N × H)
15. C₃×C₂₃⋊C₁₁	C₂²×C₃	semidirect
17. C₂×C₂₃⋊C₁₁	C₃×D₃	direct (N × H)
18. C₂×C₃²×C₂₃	C₂×C₁₁	semidirect
19. C₃×D₃×C₂₃	C₂×C₁₁	semidirect
22. C₂×D₃×C₂₃	C₃×C₁₁	semidirect
23. C₂₃⋊C₁₁	C₂×C₃×D₃	direct (N × H)
24. C₃²×C₂₃	C₂²×C₁₁	semidirect
29. C₂×C₃×C₂₃	D₃×C₁₁	semidirect
30. C₂×C₃×C₂₃	C₂×C₃×C₁₁	semidirect
31. D₃×C₂₃	C₂×C₃×C₁₁	semidirect
37. C₃×C₂₃	C₂×D₃×C₁₁	semidirect
38. C₃×C₂₃	C₂²×C₃×C₁₁	semidirect
45. C₂×C₂₃	C₃×D₃×C₁₁	semidirect
47. C₂×C₃×D₃	C₂₃⋊C₁₁	direct (N × H)
51. C₂₃	C₂×C₃×D₃×C₁₁	semidirect
54. C₂×C₃²	C₂×C₂₃⋊C₁₁	semidirect
55. C₃×D₃	C₂×C₂₃⋊C₁₁	direct (N × H)
57. C₂×D₃	C₃×C₂₃⋊C₁₁	direct (N × H)
59. C₃²	C₂²×C₂₃⋊C₁₁	semidirect
62. C₂×C₃	D₃×C₂₃⋊C₁₁	direct (N × H)
63. C₂×C₃	C₂×C₃×C₂₃⋊C₁₁	semidirect
64. D₃	C₂×C₃×C₂₃⋊C₁₁	direct (N × H)
67. C₃	C₂×D₃×C₂₃⋊C₁₁	direct (N × H)
68. C₃	C₂²×C₃×C₂₃⋊C₁₁	semidirect
70. C₂	C₃×D₃×C₂₃⋊C₁₁	direct (N × H)

Subgroups — C2×C3×D3×C23⋊C11 #22603471

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₃×C₂₃⋊C₁₁ #22603471