Subgroups — Dic₈₇₁₅ #46852829

Order 34860.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₇×C₈₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₉₀₅	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₈₃	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₇₄₃	—	5	1	no	maximal, Hall
5	C₂×C₅×C₇×C₈₃	D₃	1	1	yes	characteristic
6	Dic₁₂₄₅	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇×C₈₃	D₅	1	1	yes	characteristic
8	C₅×C₇×C₈₃	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₅×C₈₃	D₇	1	1	yes	characteristic
10	Dic₅₈₁	—	15	1	no	Hall
11	C₃×C₇×C₈₃	Dic₅	1	1	yes	characteristic, complemented, Hall
12	Dic₄₁₅	—	21	1	no	Hall
13	C₃×C₅×C₈₃	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₈₃	D₁₅	1	1	yes	characteristic
15	Dic₂₄₉	—	35	1	no	Hall
16	C₂×C₅×C₈₃	D₂₁	1	1	yes	characteristic
17	C₇×C₈₃	Dic₁₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₈₃	D₃₅	1	1	yes	characteristic
19	Dic₁₀₅	—	83	1	no	maximal, Hall
20	C₅×C₈₃	Dic₂₁	1	1	yes	characteristic, complemented, Hall
21	Dic₈₃	—	105	1	no	Hall
22	C₃×C₈₃	Dic₃₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₅×C₇	D₈₃	1	1	yes	characteristic
24	C₂×C₈₃	D₁₀₅	1	1	yes	characteristic
25	Dic₃₅	—	249	1	no	Hall
26	C₃×C₅×C₇	Dic₈₃	1	1	yes	characteristic, complemented, Hall
27	Dic₂₁	—	415	1	no	Hall
28	C₈₃	Dic₁₀₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₅×C₇	D₂₄₉	1	1	yes	characteristic
30	Dic₁₅	—	581	1	no	Hall
31	C₂×C₃×C₇	D₄₁₅	1	1	yes	characteristic
32	C₅×C₇	Dic₂₄₉	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₅	D₅₈₁	1	1	yes	characteristic
34	Dic₇	—	1245	1	no	Hall
35	C₃×C₇	Dic₄₁₅	1	1	yes	characteristic, complemented, Hall
36	Dic₅	—	1743	1	no	Hall
37	C₃×C₅	Dic₅₈₁	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	D₁₂₄₅	1	1	yes	characteristic
39	Dic₃	—	2905	1	no	Hall
40	C₂×C₅	D₁₇₄₃	1	1	yes	characteristic
41	C₇	Dic₁₂₄₅	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	D₂₉₀₅	1	1	yes	characteristic
43	C₅	Dic₁₇₄₃	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	8715	1	no	Sylow
45	C₃	Dic₂₉₀₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	D₈₇₁₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₇₁₅
commutator, hypocenter	C₃×C₅×C₇×C₈₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₅×C₇×C₈₃	C₂
LCS	G ▷ C₃×C₅×C₇×C₈₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₈₃	C₄	semidirect
8. C₅×C₇×C₈₃	Dic₃	semidirect
11. C₃×C₇×C₈₃	Dic₅	semidirect
13. C₃×C₅×C₈₃	Dic₇	semidirect
17. C₇×C₈₃	Dic₁₅	semidirect
20. C₅×C₈₃	Dic₂₁	semidirect
22. C₃×C₈₃	Dic₃₅	semidirect
26. C₃×C₅×C₇	Dic₈₃	semidirect
28. C₈₃	Dic₁₀₅	semidirect
32. C₅×C₇	Dic₂₄₉	semidirect
35. C₃×C₇	Dic₄₁₅	semidirect
37. C₃×C₅	Dic₅₈₁	semidirect
41. C₇	Dic₁₂₄₅	semidirect
43. C₅	Dic₁₇₄₃	semidirect
45. C₃	Dic₂₉₀₅	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×C₇×C₈₃	2
Dic₂₉₀₅	3
Dic₁₇₄₃	5
Dic₁₂₄₅	7
Dic₁₀₅	83

Subgroups — Dic8715 #46852829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₈₇₁₅ #46852829