Subgroups — Dic₉₂₄₃ #49149366

Order 36972.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₃×C₇₉	C₂	1	1	yes	maximal, characteristic
2	Dic₃₀₈₁	—	3	1	no	maximal
3	C₉×C₁₃×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃×C₇₉	D₃	1	1	yes	characteristic
5	Dic₁₀₂₇	—	9	1	no	Hall
6	C₃×C₁₃×C₇₉	Dic₃	1	1	yes	characteristic
7	Dic₇₁₁	—	13	1	no	maximal, Hall
8	C₂×C₁₃×C₇₉	D₉	1	1	yes	characteristic
9	C₂×C₉×C₇₉	D₁₃	1	1	yes	characteristic
10	C₁₃×C₇₉	Dic₉	1	1	yes	characteristic, complemented, Hall
11	Dic₂₃₇	—	39	1	no	—
12	C₉×C₇₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇₉	D₃₉	1	1	yes	characteristic
14	Dic₁₁₇	—	79	1	no	maximal, Hall
15	Dic₇₉	—	117	1	no	Hall
16	C₃×C₇₉	Dic₃₉	1	1	yes	characteristic
17	C₂×C₉×C₁₃	D₇₉	1	1	yes	characteristic
18	C₂×C₇₉	D₁₁₇	1	1	yes	characteristic
19	Dic₃₉	—	237	1	no	—
20	C₉×C₁₃	Dic₇₉	1	1	yes	characteristic, complemented, Hall
21	C₇₉	Dic₁₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₁₃	D₂₃₇	1	1	yes	characteristic
23	Dic₁₃	—	711	1	no	Hall
24	C₃×C₁₃	Dic₂₃₇	1	1	yes	characteristic
25	Dic₉	—	1027	1	no	Hall
26	C₂×C₁₃	D₇₁₁	1	1	yes	characteristic
27	C₂×C₉	D₁₀₂₇	1	1	yes	characteristic
28	C₁₃	Dic₇₁₁	1	1	yes	characteristic, complemented, Sylow
29	Dic₃	—	3081	1	no	—
30	C₉	Dic₁₀₂₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₃₀₈₁	1	1	yes	characteristic
32	C₄	—	9243	1	no	Sylow
33	C₃	Dic₃₀₈₁	1	1	yes	characteristic
34	C₂	D₉₂₄₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₉₂₄₃
commutator, hypocenter	C₉×C₁₃×C₇₉	C₄
Frattini	C₂×C₃	D₃₀₈₁
Fitting, cosocle	C₂×C₉×C₁₃×C₇₉	C₂
socle, prime radical	C₂×C₃×C₁₃×C₇₉	D₃
LCS	G ▷ C₉×C₁₃×C₇₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₃×C₇₉	C₄	semidirect
10. C₁₃×C₇₉	Dic₉	semidirect
12. C₉×C₇₉	Dic₁₃	semidirect
20. C₉×C₁₃	Dic₇₉	semidirect
21. C₇₉	Dic₁₁₇	semidirect
28. C₁₃	Dic₇₁₁	semidirect
30. C₉	Dic₁₀₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₃×C₇₉	2
Dic₃₀₈₁	3
Dic₇₁₁	13
Dic₁₁₇	79

Subgroups — Dic9243 #49149366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₉₂₄₃ #49149366