Subgroups — (C₃⋊D₃)⋊D₆₇₁ #37563549

Order 24156.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₀₁₃	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₃⋊D₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×D₆₇₁	—	3	2	no	maximal
4	C₃²×C₁₁×C₆₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₀₁₃	D₃	1	2	yes	complemented
6	D₃×C₁₁×C₆₁	—	3	2	no	—
7	D₃×C₁₁×C₆₁	—	6	1	no	—
8	C₃×D₆₇₁	—	3	2	no	—
9	C₂×D₆₇₁	—	9	1	no	Hall
10	(C₃⋊D₃)⋊D₆₁	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₆₁	—	2	1	no	—
12	C₃×C₁₁×C₆₁	C₂×D₃	1	2	yes	complemented
13	C₂×C₁₁×C₆₁	—	9	1	no	—
14	D₆₇₁	—	3	2	no	—
15	C₃⋊D₃×C₆₁	D₁₁	1	1	yes	characteristic, complemented
16	C₃×D₁₈₃	—	11	2	no	—
17	D₃×D₆₁	—	33	2	no	—
18	C₁₁×C₆₁	D₃²	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₆₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	(C₃⋊D₃)⋊D₁₁	—	61	1	no	maximal, Hall
21	D₁₈₃	—	11	2	no	—
22	C₃×D₆₁	—	33	2	no	—
23	D₃×C₆₁	—	3	2	no	—
24	D₃×C₆₁	—	6	1	no	—
25	C₂×D₆₁	—	99	1	no	Hall
26	C₁₁×C₃⋊D₃	D₆₁	1	1	yes	characteristic, complemented
27	C₃×D₃₃	—	61	2	no	—
28	C₃×C₆₁	—	2	1	no	—
29	C₃×C₆₁	D₃×D₁₁	1	2	yes	complemented
30	D₃×D₁₁	—	183	2	no	—
31	C₂×C₆₁	—	9	1	no	—
32	D₆₁	—	33	2	no	—
33	C₃²×C₁₁	C₂×D₆₁	1	1	yes	characteristic, complemented, Hall
34	D₃₃	—	61	2	no	—
35	C₃×D₁₁	—	183	2	no	—
36	D₃×C₁₁	—	3	2	no	—
37	D₃×C₁₁	—	6	1	no	—
38	C₆₁	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₁	—	549	1	no	Hall
40	D₃²	—	671	1	no	Hall
41	C₃×C₁₁	—	2	1	no	—
42	C₃×C₁₁	D₃×D₆₁	1	2	yes	complemented
43	C₂×C₁₁	—	9	1	no	—
44	D₁₁	—	183	2	no	—
45	C₃⋊D₃	D₆₇₁	1	1	yes	characteristic, complemented
46	C₃×D₃	—	671	2	no	—
47	C₂×D₃	—	2013	2	no	—
48	C₁₁	(C₃⋊D₃)⋊D₆₁	1	1	yes	characteristic, complemented, Sylow
49	C₃²	C₂×D₆₇₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	2013	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	671	2	no	—
54	C₂²	—	6039	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₆₇₁	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	2013	2	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. C₃×D₂₀₁₃	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₆₁	C₂	semidirect
4. C₃²×C₁₁×C₆₁	C₂²	semidirect
5. D₂₀₁₃	D₃	semidirect
12. C₃×C₁₁×C₆₁	C₂×D₃	semidirect
15. C₃⋊D₃×C₆₁	D₁₁	semidirect
18. C₁₁×C₆₁	D₃²	semidirect
19. C₃²×C₆₁	C₂×D₁₁	semidirect
26. C₁₁×C₃⋊D₃	D₆₁	semidirect
29. C₃×C₆₁	D₃×D₁₁	semidirect
33. C₃²×C₁₁	C₂×D₆₁	semidirect
38. C₆₁	(C₃⋊D₃)⋊D₁₁	semidirect
42. C₃×C₁₁	D₃×D₆₁	semidirect
45. C₃⋊D₃	D₆₇₁	semidirect
48. C₁₁	(C₃⋊D₃)⋊D₆₁	semidirect
49. C₃²	C₂×D₆₇₁	semidirect
56. C₃	D₃×D₆₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₂₀₁₃	2
C₁₁×C₃⋊D₃×C₆₁	2
D₃×D₆₇₁	3
(C₃⋊D₃)⋊D₆₁	11
(C₃⋊D₃)⋊D₁₁	61

Subgroups — (C3⋊D3)⋊D671 #37563549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₆₇₁ #37563549