Subgroups — Dic₈₄₁₅ #46777849

Order 33660.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic
2	Dic₂₈₀₅	—	3	1	no	maximal
3	C₅×C₉×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₆₈₃	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₁₁×C₁₇	D₃	1	1	yes	characteristic
6	Dic₉₃₅	—	9	1	no	Hall
7	C₂×C₉×C₁₁×C₁₇	D₅	1	1	yes	characteristic
8	Dic₇₆₅	—	11	1	no	maximal, Hall
9	C₃×C₅×C₁₁×C₁₇	Dic₃	1	1	yes	characteristic
10	Dic₅₆₁	—	15	1	no	—
11	Dic₄₉₅	—	17	1	no	maximal, Hall
12	C₂×C₅×C₁₁×C₁₇	D₉	1	1	yes	characteristic
13	C₉×C₁₁×C₁₇	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₉×C₁₇	D₁₁	1	1	yes	characteristic
15	C₂×C₃×C₁₁×C₁₇	D₁₅	1	1	yes	characteristic
16	Dic₂₅₅	—	33	1	no	—
17	C₂×C₅×C₉×C₁₁	D₁₇	1	1	yes	characteristic
18	C₅×C₁₁×C₁₇	Dic₉	1	1	yes	characteristic, complemented, Hall
19	C₅×C₉×C₁₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
20	Dic₁₈₇	—	45	1	no	Hall
21	Dic₁₆₅	—	51	1	no	—
22	Dic₁₅₃	—	55	1	no	Hall
23	C₃×C₁₁×C₁₇	Dic₁₅	1	1	yes	characteristic
24	C₂×C₃×C₅×C₁₇	D₃₃	1	1	yes	characteristic
25	C₅×C₉×C₁₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
26	Dic₉₉	—	85	1	no	Hall
27	C₂×C₁₁×C₁₇	D₄₅	1	1	yes	characteristic
28	Dic₈₅	—	99	1	no	Hall
29	C₂×C₃×C₅×C₁₁	D₅₁	1	1	yes	characteristic
30	C₂×C₉×C₁₇	D₅₅	1	1	yes	characteristic
31	C₃×C₅×C₁₇	Dic₃₃	1	1	yes	characteristic
32	Dic₅₅	—	153	1	no	Hall
33	Dic₅₁	—	165	1	no	—
34	C₂×C₉×C₁₁	D₈₅	1	1	yes	characteristic
35	C₁₁×C₁₇	Dic₄₅	1	1	yes	characteristic, complemented, Hall
36	Dic₄₅	—	187	1	no	Hall
37	C₂×C₅×C₁₇	D₉₉	1	1	yes	characteristic
38	C₃×C₅×C₁₁	Dic₅₁	1	1	yes	characteristic
39	C₉×C₁₇	Dic₅₅	1	1	yes	characteristic, complemented, Hall
40	Dic₃₃	—	255	1	no	—
41	C₂×C₅×C₁₁	D₁₅₃	1	1	yes	characteristic
42	C₂×C₃×C₁₇	D₁₆₅	1	1	yes	characteristic
43	C₉×C₁₁	Dic₈₅	1	1	yes	characteristic, complemented, Hall
44	C₂×C₅×C₉	D₁₈₇	1	1	yes	characteristic
45	C₅×C₁₇	Dic₉₉	1	1	yes	characteristic, complemented, Hall
46	Dic₁₇	—	495	1	no	Hall
47	C₂×C₃×C₁₁	D₂₅₅	1	1	yes	characteristic
48	Dic₁₅	—	561	1	no	—
49	C₅×C₁₁	Dic₁₅₃	1	1	yes	characteristic, complemented, Hall
50	C₃×C₁₇	Dic₁₆₅	1	1	yes	characteristic
51	C₅×C₉	Dic₁₈₇	1	1	yes	characteristic, complemented, Hall
52	Dic₁₁	—	765	1	no	Hall
53	Dic₉	—	935	1	no	Hall
54	C₂×C₁₇	D₄₉₅	1	1	yes	characteristic
55	C₃×C₁₁	Dic₂₅₅	1	1	yes	characteristic
56	C₂×C₃×C₅	D₅₆₁	1	1	yes	characteristic
57	C₂×C₁₁	D₇₆₅	1	1	yes	characteristic
58	Dic₅	—	1683	1	no	Hall
59	C₂×C₉	D₉₃₅	1	1	yes	characteristic
60	C₁₇	Dic₄₉₅	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	Dic₅₆₁	1	1	yes	characteristic
62	Dic₃	—	2805	1	no	—
63	C₁₁	Dic₇₆₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₅	D₁₆₈₃	1	1	yes	characteristic
65	C₉	Dic₉₃₅	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	D₂₈₀₅	1	1	yes	characteristic
67	C₅	Dic₁₆₈₃	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	8415	1	no	Sylow
69	C₃	Dic₂₈₀₅	1	1	yes	characteristic
70	C₂	D₈₄₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₈₄₁₅
commutator, hypocenter	C₅×C₉×C₁₁×C₁₇	C₄
Frattini	C₂×C₃	D₂₈₀₅
Fitting, cosocle	C₂×C₅×C₉×C₁₁×C₁₇	C₂
socle, prime radical	C₂×C₃×C₅×C₁₁×C₁₇	D₃
LCS	G ▷ C₅×C₉×C₁₁×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₅×C₉×C₁₁×C₁₇	C₄	semidirect
13. C₉×C₁₁×C₁₇	Dic₅	semidirect
18. C₅×C₁₁×C₁₇	Dic₉	semidirect
19. C₅×C₉×C₁₇	Dic₁₁	semidirect
25. C₅×C₉×C₁₁	Dic₁₇	semidirect
35. C₁₁×C₁₇	Dic₄₅	semidirect
39. C₉×C₁₇	Dic₅₅	semidirect
43. C₉×C₁₁	Dic₈₅	semidirect
45. C₅×C₁₇	Dic₉₉	semidirect
49. C₅×C₁₁	Dic₁₅₃	semidirect
51. C₅×C₉	Dic₁₈₇	semidirect
60. C₁₇	Dic₄₉₅	semidirect
63. C₁₁	Dic₇₆₅	semidirect
65. C₉	Dic₉₃₅	semidirect
67. C₅	Dic₁₆₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×C₁₁×C₁₇	2
Dic₂₈₀₅	3
Dic₁₆₈₃	5
Dic₇₆₅	11
Dic₄₉₅	17

Subgroups — Dic8415 #46777849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₈₄₁₅ #46777849