Subgroups — C₉×Dic₈₆₉ #44530840

Order 31284.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₈₆₉	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₁×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₇₉	C₂×C₃	1	1	yes	characteristic
5	Dic₈₆₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×Dic₇₉	—	11	1	no	maximal, Hall
7	C₃×C₁₁×C₇₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₁₁×C₇₉	C₂×C₉	1	1	yes	characteristic
9	C₂×C₉×C₇₉	D₁₁	1	1	yes	characteristic
10	C₃×Dic₇₉	—	11	1	no	—
11	C₁₁×C₇₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₉×C₇₉	Dic₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇₉	C₃×D₁₁	1	1	yes	characteristic
14	C₉×Dic₁₁	—	79	1	no	maximal, Hall
15	Dic₇₉	—	11	1	no	Hall
16	C₃×C₇₉	C₃×Dic₁₁	1	1	yes	characteristic
17	C₂×C₉×C₁₁	D₇₉	1	1	yes	characteristic
18	C₂×C₇₉	C₉×D₁₁	1	1	yes	characteristic
19	C₃×Dic₁₁	—	79	1	no	—
20	C₉×C₁₁	Dic₇₉	1	1	yes	characteristic, complemented, Hall
21	C₇₉	C₉×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₁₁	C₃×D₇₉	1	1	yes	characteristic
23	Dic₁₁	—	79	1	no	Hall
24	C₄×C₉	—	869	1	no	Hall
25	C₃×C₁₁	C₃×Dic₇₉	1	1	yes	characteristic
26	C₂×C₁₁	C₉×D₇₉	1	1	yes	characteristic
27	C₂×C₉	D₈₆₉	1	1	yes	characteristic
28	C₃×C₄	—	869	1	no	—
29	C₁₁	C₉×Dic₇₉	1	1	yes	characteristic, complemented, Sylow
30	C₉	Dic₈₆₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×D₈₆₉	1	1	yes	characteristic
32	C₄	—	869	1	no	Sylow
33	C₃	C₃×Dic₈₆₉	1	1	yes	characteristic
34	C₂	C₉×D₈₆₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	D₈₆₉
commutator, hypocenter	C₁₁×C₇₉	C₄×C₉
Frattini	C₂×C₃	C₃×D₈₆₉
Fitting	C₂×C₉×C₁₁×C₇₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₁₁×C₇₉	C₂×C₃
LCS	G ▷ C₁₁×C₇₉
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₁×C₇₉	C₄	semidirect
5. Dic₈₆₉	C₉	direct (N × H)
11. C₁₁×C₇₉	C₄×C₉	semidirect
12. C₉×C₇₉	Dic₁₁	semidirect
20. C₉×C₁₁	Dic₇₉	semidirect
21. C₇₉	C₉×Dic₁₁	semidirect
29. C₁₁	C₉×Dic₇₉	semidirect
30. C₉	Dic₈₆₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₁×C₇₉	2
C₃×Dic₈₆₉	3
C₉×Dic₇₉	11
C₉×Dic₁₁	79

Subgroups — C9×Dic869 #44530840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₈₆₉ #44530840