Subgroups — C₉×Dic₁₁×C₇₉ #44530839

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×Dic₁₁×C₇₉	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	Dic₁₁×C₇₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₉×C₇₉	—	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×C₄×C₇₉	—	11	1	no	—
11	C₁₁×C₇₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
12	C₉×C₇₉	Dic₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇₉	C₃×D₁₁	1	1	yes	characteristic
14	C₉×Dic₁₁	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₄×C₇₉	—	11	1	no	Hall
16	C₃×C₇₉	C₃×Dic₁₁	1	1	yes	characteristic
17	C₂×C₉×C₁₁	C₂×C₇₉	1	1	yes	characteristic
18	C₂×C₇₉	C₉×D₁₁	1	1	yes	characteristic
19	C₃×Dic₁₁	C₃×C₇₉	1	1	yes	characteristic
20	C₉×C₁₁	C₄×C₇₉	1	1	yes	characteristic, complemented, Hall
21	C₇₉	C₉×Dic₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃×C₁₁	C₂×C₃×C₇₉	1	1	yes	characteristic
23	Dic₁₁	C₉×C₇₉	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₉	—	11	1	no	Hall
25	C₃×C₁₁	C₃×C₄×C₇₉	1	1	yes	characteristic
26	C₂×C₁₁	C₂×C₉×C₇₉	1	1	yes	characteristic
27	C₂×C₉	D₁₁×C₇₉	1	1	yes	characteristic
28	C₃×C₄	—	11	1	no	—
29	C₁₁	C₄×C₉×C₇₉	1	1	yes	characteristic, complemented, Sylow
30	C₉	Dic₁₁×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×D₁₁×C₇₉	1	1	yes	characteristic
32	C₄	—	11	1	no	Sylow
33	C₃	C₃×Dic₁₁×C₇₉	1	1	yes	characteristic
34	C₂	C₉×D₁₁×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉×C₇₉	D₁₁
commutator, hypocenter	C₁₁	C₄×C₉×C₇₉
Frattini	C₂×C₃	C₃×D₁₁×C₇₉
Fitting	C₂×C₉×C₁₁×C₇₉	C₂
socle, prime radical	C₂×C₃×C₁₁×C₇₉	C₂×C₃
cosocle	C₂×C₃×C₁₁	C₂×C₃×C₇₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₉×C₇₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₁×C₇₉	C₄	semidirect
5. Dic₁₁×C₇₉	C₉	direct (N × H)
11. C₁₁×C₇₉	C₄×C₉	semidirect
12. C₉×C₇₉	Dic₁₁	direct (N × H)
14. C₉×Dic₁₁	C₇₉	direct (N × H)
20. C₉×C₁₁	C₄×C₇₉	semidirect
21. C₇₉	C₉×Dic₁₁	direct (N × H)
23. Dic₁₁	C₉×C₇₉	direct (N × H)
29. C₁₁	C₄×C₉×C₇₉	semidirect
30. C₉	Dic₁₁×C₇₉	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×Dic₁₁×C₇₉	3
C₄×C₉×C₇₉	11
C₉×Dic₁₁	79

Subgroups — C9×Dic11×C79 #44530839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₁₁×C₇₉ #44530839