Subgroups — C₃⋊(C₇⋊Dic₃₈₅) #44568516

Order 32340.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₇⋊Dic₃₈₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇²×C₁₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₇⋊Dic₇₇)	—	5	1	no	maximal, Hall
5	C₂×C₅×C₇²×C₁₁	D₃	1	1	yes	characteristic
6	Dic₁₁₅₅	—	7	8	no	maximal
7	C₂×C₃×C₇²×C₁₁	D₅	1	1	yes	characteristic
8	C₃⋊(C₇⋊Dic₃₅)	—	11	1	no	maximal, Hall
9	C₅×C₇²×C₁₁	Dic₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅×C₇×C₁₁	D₇	1	8	yes	—
11	C₇⋊Dic₇₇	—	15	1	no	Hall
12	C₃×C₇²×C₁₁	Dic₅	1	1	yes	characteristic, complemented, Hall
13	Dic₃₈₅	—	21	8	no	—
14	C₂×C₃×C₅×C₇²	D₁₁	1	1	yes	characteristic
15	C₃×C₅×C₇×C₁₁	Dic₇	1	8	yes	complemented
16	C₂×C₇²×C₁₁	D₁₅	1	1	yes	characteristic
17	C₇⋊Dic₃₅	—	33	1	no	Hall
18	Dic₂₃₁	—	35	8	no	—
19	C₂×C₅×C₇×C₁₁	D₂₁	1	8	yes	—
20	C₃×C₅×C₇²	Dic₁₁	1	1	yes	characteristic, complemented, Hall
21	Dic₁₆₅	—	49	1	no	Hall
22	C₃⋊(C₇⋊Dic₇)	—	55	1	no	Hall
23	C₇²×C₁₁	Dic₁₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₇²	D₃₃	1	1	yes	characteristic
25	C₂×C₃×C₇×C₁₁	D₃₅	1	8	yes	—
26	Dic₁₀₅	—	77	8	no	—
27	C₅×C₇×C₁₁	Dic₂₁	1	8	yes	complemented
28	C₂×C₃×C₅×C₁₁	C₇⋊D₇	1	1	yes	characteristic
29	Dic₇₇	—	105	8	no	—
30	C₂×C₃×C₇²	D₅₅	1	1	yes	characteristic
31	C₅×C₇²	Dic₃₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	Dic₃₅	1	8	yes	complemented
33	Dic₅₅	—	147	1	no	Hall
34	C₂×C₃×C₅×C₇	D₇₇	1	8	yes	—
35	C₇⋊Dic₇	—	165	1	no	Hall
36	C₃×C₅×C₁₁	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₁	D₁₀₅	1	8	yes	—
38	C₃×C₇²	Dic₅₅	1	1	yes	characteristic, complemented, Hall
39	Dic₃₅	—	231	8	no	—
40	Dic₃₃	—	245	1	no	Hall
41	C₂×C₅×C₁₁	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic
42	C₃×C₅×C₇	Dic₇₇	1	8	yes	complemented
43	C₂×C₇²	D₁₆₅	1	1	yes	characteristic
44	Dic₂₁	—	385	8	no	—
45	C₇×C₁₁	Dic₁₀₅	1	8	yes	complemented
46	C₂×C₅×C₇	D₂₃₁	1	8	yes	—
47	C₂×C₃×C₁₁	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic
48	Dic₁₅	—	539	1	no	Hall
49	C₅×C₁₁	C₃⋊(C₇⋊Dic₇)	1	1	yes	characteristic, complemented, Hall
50	C₇²	Dic₁₆₅	1	1	yes	characteristic, complemented, Sylow
51	Dic₁₁	—	735	1	no	Hall
52	C₂×C₃×C₇	D₃₈₅	1	8	yes	—
53	C₅×C₇	Dic₂₃₁	1	8	yes	complemented
54	C₃×C₁₁	C₇⋊Dic₃₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	C₇⋊D₇₇	1	1	yes	characteristic
56	Dic₇	—	1155	8	no	—
57	C₂×C₁₁	C₃⋊(C₅⋊(C₇⋊D₇))	1	1	yes	characteristic
58	C₃×C₇	Dic₃₈₅	1	8	yes	complemented
59	Dic₅	—	1617	1	no	Hall
60	C₃×C₅	C₇⋊Dic₇₇	1	1	yes	characteristic, complemented, Hall
61	C₂×C₇	D₁₁₅₅	1	8	yes	—
62	Dic₃	—	2695	1	no	Hall
63	C₁₁	C₃⋊(C₇⋊Dic₃₅)	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	C₃⋊(C₇⋊D₇₇)	1	1	yes	characteristic
65	C₇	Dic₁₁₅₅	1	8	yes	complemented
66	C₂×C₃	C₅⋊(C₇⋊D₇₇)	1	1	yes	characteristic
67	C₅	C₃⋊(C₇⋊Dic₇₇)	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	8085	1	no	Sylow
69	C₃	C₇⋊Dic₃₈₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	C₃⋊(C₅⋊(C₇⋊D₇₇))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₅⋊(C₇⋊D₇₇))
commutator, hypocenter	C₃×C₅×C₇²×C₁₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₇²×C₁₁	C₂
LCS	G ▷ C₃×C₅×C₇²×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇²×C₁₁	C₄	semidirect
9. C₅×C₇²×C₁₁	Dic₃	semidirect
12. C₃×C₇²×C₁₁	Dic₅	semidirect
15. C₃×C₅×C₇×C₁₁	Dic₇	semidirect
20. C₃×C₅×C₇²	Dic₁₁	semidirect
23. C₇²×C₁₁	Dic₁₅	semidirect
27. C₅×C₇×C₁₁	Dic₂₁	semidirect
31. C₅×C₇²	Dic₃₃	semidirect
32. C₃×C₇×C₁₁	Dic₃₅	semidirect
36. C₃×C₅×C₁₁	C₇⋊Dic₇	semidirect
38. C₃×C₇²	Dic₅₅	semidirect
42. C₃×C₅×C₇	Dic₇₇	semidirect
45. C₇×C₁₁	Dic₁₀₅	semidirect
49. C₅×C₁₁	C₃⋊(C₇⋊Dic₇)	semidirect
50. C₇²	Dic₁₆₅	semidirect
53. C₅×C₇	Dic₂₃₁	semidirect
54. C₃×C₁₁	C₇⋊Dic₃₅	semidirect
58. C₃×C₇	Dic₃₈₅	semidirect
60. C₃×C₅	C₇⋊Dic₇₇	semidirect
63. C₁₁	C₃⋊(C₇⋊Dic₃₅)	semidirect
65. C₇	Dic₁₁₅₅	semidirect
67. C₅	C₃⋊(C₇⋊Dic₇₇)	semidirect
69. C₃	C₇⋊Dic₃₈₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₇²×C₁₁	2
C₇⋊Dic₃₈₅	3
C₃⋊(C₇⋊Dic₇₇)	5
Dic₁₁₅₅	7
C₃⋊(C₇⋊Dic₃₅)	11

Subgroups — C3⋊(C7⋊Dic385) #44568516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊Dic₃₈₅) #44568516