Subgroups — D₁₁×C₃⋊D₁₈₃ #37563555

Order 24156.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₁₁×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₁₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₀₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×D₁₈₃	—	3	4	no	maximal
5	C₃²×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₀₁₃	—	3	4	no	—
7	C₁₁×D₁₈₃	—	3	4	no	—
8	C₃×D₁₁×C₆₁	D₃	1	4	yes	complemented
9	D₁₁×D₆₁	—	9	1	no	Hall
10	C₂×C₃⋊D₁₈₃	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₆₁	C₂×D₃	1	4	yes	complemented
12	D₆₇₁	—	9	1	no	—
13	C₁₁×D₆₁	—	9	1	no	—
14	D₁₁×C₆₁	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₂×C₃²×C₆₁	—	11	1	no	—
16	C₃⋊D₁₈₃	—	11	1	no	—
17	C₃⋊D₁₈₃	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×D₁₈₃	—	33	4	no	—
19	C₁₁×C₆₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₆₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₃⋊D₃×D₁₁	—	61	1	no	maximal, Hall
22	C₂×C₃×C₆₁	—	11	4	no	—
23	D₁₈₃	—	3	4	no	—
24	D₁₈₃	—	33	4	no	—
25	C₂×D₆₁	—	99	1	no	Hall
26	C₃⋊D₃₃	—	61	1	no	—
27	C₁₁×C₃⋊D₃	—	61	1	no	—
28	C₃²×D₁₁	D₆₁	1	1	yes	characteristic, complemented
29	C₃×C₆₁	D₃×D₁₁	1	4	yes	complemented
30	D₃×D₁₁	—	183	4	no	—
31	C₂×C₆₁	—	11	1	no	—
32	D₆₁	—	9	1	no	—
33	D₆₁	—	99	1	no	—
34	C₃²×C₁₁	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
35	D₃₃	—	183	4	no	—
36	C₃×D₁₁	D₁₈₃	1	4	yes	complemented
37	D₃×C₁₁	—	183	4	no	—
38	C₆₁	C₃⋊D₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₁	—	549	1	no	Hall
40	C₂×C₃⋊D₃	—	671	1	no	Hall
41	C₃×C₁₁	C₂×D₁₈₃	1	4	yes	complemented
42	C₂×C₁₁	—	549	1	no	—
43	D₁₁	—	549	1	no	—
44	D₁₁	C₃⋊D₁₈₃	1	1	yes	characteristic, direct product factor
45	C₂×C₃²	—	11	1	no	—
46	C₃⋊D₃	—	61	1	no	—
47	C₃⋊D₃	—	671	1	no	—
48	C₂×D₃	—	2013	4	no	—
49	C₁₁	C₂×C₃⋊D₁₈₃	1	1	yes	characteristic, complemented, Sylow
50	C₃²	D₁₁×D₆₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	11	4	no	—
52	D₃	—	183	4	no	—
53	D₃	—	2013	4	no	—
54	C₂²	—	6039	1	no	Sylow
55	C₃	D₁₁×D₁₈₃	1	4	yes	complemented
56	C₂	—	11	1	no	—
57	C₂	—	549	1	no	—
58	C₂	—	6039	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃²×D₁₁×C₆₁	C₂	semidirect
2. C₁₁×C₃⋊D₁₈₃	C₂	semidirect
3. C₃⋊D₂₀₁₃	C₂	semidirect
5. C₃²×C₁₁×C₆₁	C₂²	semidirect
8. C₃×D₁₁×C₆₁	D₃	semidirect
11. C₃×C₁₁×C₆₁	C₂×D₃	semidirect
14. D₁₁×C₆₁	C₃⋊D₃	semidirect
17. C₃⋊D₁₈₃	D₁₁	direct (N × H)
19. C₁₁×C₆₁	C₂×C₃⋊D₃	semidirect
20. C₃²×C₆₁	C₂×D₁₁	semidirect
28. C₃²×D₁₁	D₆₁	semidirect
29. C₃×C₆₁	D₃×D₁₁	semidirect
34. C₃²×C₁₁	C₂×D₆₁	semidirect
36. C₃×D₁₁	D₁₈₃	semidirect
38. C₆₁	C₃⋊D₃×D₁₁	semidirect
41. C₃×C₁₁	C₂×D₁₈₃	semidirect
44. D₁₁	C₃⋊D₁₈₃	direct (N × H)
49. C₁₁	C₂×C₃⋊D₁₈₃	semidirect
50. C₃²	D₁₁×D₆₁	semidirect
55. C₃	D₁₁×D₁₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₁₁×C₆₁	2
C₁₁×C₃⋊D₁₈₃	2
C₃⋊D₂₀₁₃	2
D₁₁×D₁₈₃	3
C₂×C₃⋊D₁₈₃	11
C₃⋊D₃×D₁₁	61

Subgroups — D11×C3⋊D183 #37563555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×C₃⋊D₁₈₃ #37563555