Subgroups — Dic₈₀₈₅ #44568317

Order 32340.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₉₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₄₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₆₁₇	—	5	1	no	maximal, Hall
5	C₂×C₅×C₁₁×C₄₉	D₃	1	1	yes	characteristic
6	Dic₁₁₅₅	—	7	1	no	maximal
7	C₂×C₃×C₁₁×C₄₉	D₅	1	1	yes	characteristic
8	Dic₇₃₅	—	11	1	no	maximal, Hall
9	C₅×C₁₁×C₄₉	Dic₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₅×C₇×C₁₁	D₇	1	1	yes	characteristic
11	Dic₅₃₉	—	15	1	no	Hall
12	C₃×C₁₁×C₄₉	Dic₅	1	1	yes	characteristic, complemented, Hall
13	Dic₃₈₅	—	21	1	no	—
14	C₂×C₃×C₅×C₄₉	D₁₁	1	1	yes	characteristic
15	C₃×C₅×C₇×C₁₁	Dic₇	1	1	yes	characteristic
16	C₂×C₁₁×C₄₉	D₁₅	1	1	yes	characteristic
17	Dic₂₄₅	—	33	1	no	Hall
18	Dic₂₃₁	—	35	1	no	—
19	C₂×C₅×C₇×C₁₁	D₂₁	1	1	yes	characteristic
20	C₃×C₅×C₄₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
21	Dic₁₆₅	—	49	1	no	Hall
22	Dic₁₄₇	—	55	1	no	Hall
23	C₁₁×C₄₉	Dic₁₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅×C₄₉	D₃₃	1	1	yes	characteristic
25	C₂×C₃×C₇×C₁₁	D₃₅	1	1	yes	characteristic
26	Dic₁₀₅	—	77	1	no	—
27	C₅×C₇×C₁₁	Dic₂₁	1	1	yes	characteristic
28	C₂×C₃×C₅×C₁₁	D₄₉	1	1	yes	characteristic
29	Dic₇₇	—	105	1	no	—
30	C₂×C₃×C₄₉	D₅₅	1	1	yes	characteristic
31	C₅×C₄₉	Dic₃₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	Dic₃₅	1	1	yes	characteristic
33	Dic₅₅	—	147	1	no	Hall
34	C₂×C₃×C₅×C₇	D₇₇	1	1	yes	characteristic
35	Dic₄₉	—	165	1	no	Hall
36	C₃×C₅×C₁₁	Dic₄₉	1	1	yes	characteristic, complemented, Hall
37	C₂×C₇×C₁₁	D₁₀₅	1	1	yes	characteristic
38	C₃×C₄₉	Dic₅₅	1	1	yes	characteristic, complemented, Hall
39	Dic₃₅	—	231	1	no	—
40	Dic₃₃	—	245	1	no	Hall
41	C₂×C₅×C₁₁	D₁₄₇	1	1	yes	characteristic
42	C₃×C₅×C₇	Dic₇₇	1	1	yes	characteristic
43	C₂×C₄₉	D₁₆₅	1	1	yes	characteristic
44	Dic₂₁	—	385	1	no	—
45	C₇×C₁₁	Dic₁₀₅	1	1	yes	characteristic
46	C₂×C₅×C₇	D₂₃₁	1	1	yes	characteristic
47	C₂×C₃×C₁₁	D₂₄₅	1	1	yes	characteristic
48	Dic₁₅	—	539	1	no	Hall
49	C₅×C₁₁	Dic₁₄₇	1	1	yes	characteristic, complemented, Hall
50	C₄₉	Dic₁₆₅	1	1	yes	characteristic, complemented, Sylow
51	Dic₁₁	—	735	1	no	Hall
52	C₂×C₃×C₇	D₃₈₅	1	1	yes	characteristic
53	C₅×C₇	Dic₂₃₁	1	1	yes	characteristic
54	C₃×C₁₁	Dic₂₄₅	1	1	yes	characteristic, complemented, Hall
55	C₂×C₃×C₅	D₅₃₉	1	1	yes	characteristic
56	Dic₇	—	1155	1	no	—
57	C₂×C₁₁	D₇₃₅	1	1	yes	characteristic
58	C₃×C₇	Dic₃₈₅	1	1	yes	characteristic
59	Dic₅	—	1617	1	no	Hall
60	C₃×C₅	Dic₅₃₉	1	1	yes	characteristic, complemented, Hall
61	C₂×C₇	D₁₁₅₅	1	1	yes	characteristic
62	Dic₃	—	2695	1	no	Hall
63	C₁₁	Dic₇₃₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	D₁₆₁₇	1	1	yes	characteristic
65	C₇	Dic₁₁₅₅	1	1	yes	characteristic
66	C₂×C₃	D₂₆₉₅	1	1	yes	characteristic
67	C₅	Dic₁₆₁₇	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	8085	1	no	Sylow
69	C₃	Dic₂₆₉₅	1	1	yes	characteristic, complemented, Sylow
70	C₂	D₈₀₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₈₀₈₅
commutator, hypocenter	C₃×C₅×C₁₁×C₄₉	C₄
Frattini	C₂×C₇	D₁₁₅₅
Fitting, cosocle	C₂×C₃×C₅×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₃×C₅×C₇×C₁₁	D₇
LCS	G ▷ C₃×C₅×C₁₁×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₄₉	C₄	semidirect
9. C₅×C₁₁×C₄₉	Dic₃	semidirect
12. C₃×C₁₁×C₄₉	Dic₅	semidirect
20. C₃×C₅×C₄₉	Dic₁₁	semidirect
23. C₁₁×C₄₉	Dic₁₅	semidirect
31. C₅×C₄₉	Dic₃₃	semidirect
36. C₃×C₅×C₁₁	Dic₄₉	semidirect
38. C₃×C₄₉	Dic₅₅	semidirect
49. C₅×C₁₁	Dic₁₄₇	semidirect
50. C₄₉	Dic₁₆₅	semidirect
54. C₃×C₁₁	Dic₂₄₅	semidirect
60. C₃×C₅	Dic₅₃₉	semidirect
63. C₁₁	Dic₇₃₅	semidirect
67. C₅	Dic₁₆₁₇	semidirect
69. C₃	Dic₂₆₉₅	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×C₁₁×C₄₉	2
Dic₂₆₉₅	3
Dic₁₆₁₇	5
Dic₁₁₅₅	7
Dic₇₃₅	11

Subgroups — Dic8085 #44568317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₈₀₈₅ #44568317