Subgroups — C₉×D₁₁×D₇₉ #44530853

Order 31284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₈₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₁₁×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₁×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₁×D₇₉	C₃	1	1	yes	maximal, characteristic
5	C₉×C₁₁×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₈₆₉	C₂×C₃	1	1	yes	characteristic
7	C₃×D₁₁×C₇₉	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₁×D₇₉	C₂×C₃	1	1	yes	characteristic
9	D₁₁×D₇₉	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₉×D₇₉	—	11	1	no	maximal, Hall
11	C₃×C₁₁×C₇₉	C₂²×C₃	1	1	yes	characteristic
12	D₈₆₉	C₂×C₉	1	1	yes	characteristic, complemented
13	C₁₁×D₇₉	C₂×C₉	1	1	yes	characteristic, complemented
14	D₁₁×C₇₉	C₂×C₉	1	1	yes	characteristic, complemented
15	C₂×C₉×C₇₉	—	11	1	no	—
16	C₉×D₇₉	—	11	1	no	—
17	C₉×D₇₉	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×C₃×D₇₉	—	11	1	no	—
19	C₁₁×C₇₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
20	C₉×C₇₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₇₉	—	11	1	no	—
22	C₃×D₇₉	—	11	1	no	—
23	C₃×D₇₉	C₃×D₁₁	1	1	yes	characteristic
24	C₂×C₉×D₁₁	—	79	1	no	maximal, Hall
25	C₂×D₇₉	—	11	1	no	Hall
26	C₃×C₇₉	C₂×C₃×D₁₁	1	1	yes	characteristic
27	C₂×C₉×C₁₁	—	79	1	no	—
28	C₉×D₁₁	—	79	1	no	—
29	C₉×D₁₁	D₇₉	1	1	yes	characteristic, direct product factor
30	C₂×C₇₉	—	11	1	no	—
31	D₇₉	—	11	1	no	—
32	D₇₉	C₉×D₁₁	1	1	yes	characteristic, direct product factor
33	C₂×C₃×D₁₁	—	79	1	no	—
34	C₉×C₁₁	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
35	C₇₉	C₂×C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃×C₁₁	—	79	1	no	—
37	C₃×D₁₁	—	79	1	no	—
38	C₃×D₁₁	C₃×D₇₉	1	1	yes	characteristic
39	C₂×D₁₁	—	79	1	no	Hall
40	C₂²×C₉	—	869	1	no	Hall
41	C₃×C₁₁	C₂×C₃×D₇₉	1	1	yes	characteristic
42	C₂×C₁₁	—	79	1	no	—
43	D₁₁	—	79	1	no	—
44	D₁₁	C₉×D₇₉	1	1	yes	characteristic, direct product factor
45	C₂×C₉	—	11	1	no	—
46	C₂×C₉	—	79	1	no	—
47	C₂×C₉	—	869	1	no	—
48	C₂²×C₃	—	869	1	no	—
49	C₁₁	C₂×C₉×D₇₉	1	1	yes	characteristic, complemented, Sylow
50	C₉	D₁₁×D₇₉	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	11	1	no	—
52	C₂×C₃	—	79	1	no	—
53	C₂×C₃	—	869	1	no	—
54	C₂²	—	869	1	no	Sylow
55	C₃	C₃×D₁₁×D₇₉	1	1	yes	characteristic
56	C₂	—	11	1	no	—
57	C₂	—	79	1	no	—
58	C₂	—	869	1	no	—

	subgroup	G/H
center, hypercenter	C₉	D₁₁×D₇₉
commutator, hypocenter	C₁₁×C₇₉	C₂²×C₉
Frattini	C₃	C₃×D₁₁×D₇₉
Fitting	C₉×C₁₁×C₇₉	C₂²
socle, cosocle	C₃×C₁₁×C₇₉	C₂²×C₃
prime radical	C₃×D₁₁×D₇₉	C₃
LCS	G ▷ C₁₁×C₇₉
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₈₆₉	C₂	semidirect
2. C₉×D₁₁×C₇₉	C₂	semidirect
3. C₉×C₁₁×D₇₉	C₂	semidirect
5. C₉×C₁₁×C₇₉	C₂²	semidirect
9. D₁₁×D₇₉	C₉	direct (N × H)
12. D₈₆₉	C₂×C₉	semidirect
13. C₁₁×D₇₉	C₂×C₉	semidirect
14. D₁₁×C₇₉	C₂×C₉	semidirect
17. C₉×D₇₉	D₁₁	direct (N × H)
19. C₁₁×C₇₉	C₂²×C₉	semidirect
20. C₉×C₇₉	C₂×D₁₁	semidirect
29. C₉×D₁₁	D₇₉	direct (N × H)
32. D₇₉	C₉×D₁₁	direct (N × H)
34. C₉×C₁₁	C₂×D₇₉	semidirect
35. C₇₉	C₂×C₉×D₁₁	semidirect
44. D₁₁	C₉×D₇₉	direct (N × H)
49. C₁₁	C₂×C₉×D₇₉	semidirect
50. C₉	D₁₁×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₈₆₉	2
C₉×D₁₁×C₇₉	2
C₉×C₁₁×D₇₉	2
C₃×D₁₁×D₇₉	3
C₂×C₉×D₇₉	11
C₂×C₉×D₁₁	79

Subgroups — C9×D11×D79 #44530853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₁₁×D₇₉ #44530853