Subgroups — (C₃⋊D₃)⋊D₇₃₇ #40997706

Order 26532.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₂₁₁	C₂	1	2	yes	maximal, complemented
2	C₁₁×C₃⋊D₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×D₇₃₇	—	3	2	no	maximal
4	C₃²×C₁₁×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₂₂₁₁	D₃	1	2	yes	complemented
6	D₃×C₁₁×C₆₇	—	3	2	no	—
7	D₃×C₁₁×C₆₇	—	6	1	no	—
8	C₃×D₇₃₇	—	3	2	no	—
9	C₂×D₇₃₇	—	9	1	no	Hall
10	(C₃⋊D₃)⋊D₆₇	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₆₇	—	2	1	no	—
12	C₃×C₁₁×C₆₇	C₂×D₃	1	2	yes	complemented
13	C₂×C₁₁×C₆₇	—	9	1	no	—
14	D₇₃₇	—	3	2	no	—
15	C₃⋊D₃×C₆₇	D₁₁	1	1	yes	characteristic, complemented
16	C₃×D₂₀₁	—	11	2	no	—
17	D₃×D₆₇	—	33	2	no	—
18	C₁₁×C₆₇	D₃²	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₆₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
20	D₂₀₁	—	11	2	no	—
21	C₃×D₆₇	—	33	2	no	—
22	D₃×C₆₇	—	3	2	no	—
23	D₃×C₆₇	—	6	1	no	—
24	(C₃⋊D₃)⋊D₁₁	—	67	1	no	maximal, Hall
25	C₂×D₆₇	—	99	1	no	Hall
26	C₃×C₆₇	—	2	1	no	—
27	C₃×C₆₇	D₃×D₁₁	1	2	yes	complemented
28	C₁₁×C₃⋊D₃	D₆₇	1	1	yes	characteristic, complemented
29	C₃×D₃₃	—	67	2	no	—
30	C₂×C₆₇	—	9	1	no	—
31	D₆₇	—	33	2	no	—
32	D₃×D₁₁	—	201	2	no	—
33	C₃²×C₁₁	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
34	C₆₇	(C₃⋊D₃)⋊D₁₁	1	1	yes	characteristic, complemented, Sylow
35	D₃₃	—	67	2	no	—
36	C₃×D₁₁	—	201	2	no	—
37	D₃×C₁₁	—	3	2	no	—
38	D₃×C₁₁	—	6	1	no	—
39	C₂×D₁₁	—	603	1	no	Hall
40	D₃²	—	737	1	no	Hall
41	C₃×C₁₁	—	2	1	no	—
42	C₃×C₁₁	D₃×D₆₇	1	2	yes	complemented
43	C₂×C₁₁	—	9	1	no	—
44	D₁₁	—	201	2	no	—
45	C₃⋊D₃	D₇₃₇	1	1	yes	characteristic, complemented
46	C₃×D₃	—	737	2	no	—
47	C₂×D₃	—	2211	2	no	—
48	C₁₁	(C₃⋊D₃)⋊D₆₇	1	1	yes	characteristic, complemented, Sylow
49	C₃²	C₂×D₇₃₇	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	2211	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	—	737	2	no	—
54	C₂²	—	6633	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₃×D₇₃₇	1	2	yes	complemented
57	C₂	—	9	1	no	—
58	C₂	—	2211	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁×C₆₇	C₂²
LCS	G ▷ C₃²×C₁₁×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₂₁₁	C₂	semidirect
2. C₁₁×C₃⋊D₃×C₆₇	C₂	semidirect
4. C₃²×C₁₁×C₆₇	C₂²	semidirect
5. D₂₂₁₁	D₃	semidirect
12. C₃×C₁₁×C₆₇	C₂×D₃	semidirect
15. C₃⋊D₃×C₆₇	D₁₁	semidirect
18. C₁₁×C₆₇	D₃²	semidirect
19. C₃²×C₆₇	C₂×D₁₁	semidirect
27. C₃×C₆₇	D₃×D₁₁	semidirect
28. C₁₁×C₃⋊D₃	D₆₇	semidirect
33. C₃²×C₁₁	C₂×D₆₇	semidirect
34. C₆₇	(C₃⋊D₃)⋊D₁₁	semidirect
42. C₃×C₁₁	D₃×D₆₇	semidirect
45. C₃⋊D₃	D₇₃₇	semidirect
48. C₁₁	(C₃⋊D₃)⋊D₆₇	semidirect
49. C₃²	C₂×D₇₃₇	semidirect
56. C₃	D₃×D₇₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₂₂₁₁	2
C₁₁×C₃⋊D₃×C₆₇	2
D₃×D₇₃₇	3
(C₃⋊D₃)⋊D₆₇	11
(C₃⋊D₃)⋊D₁₁	67

Subgroups — (C3⋊D3)⋊D737 #40997706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊D₇₃₇ #40997706