Subgroups — C₂×C₉×C₁₁×D₇₉ #44530869

Order 31284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₁	D₇₉
commutator, hypocenter	C₇₉	C₂²×C₉×C₁₁
Frattini	C₃	C₂×C₃×C₁₁×D₇₉
Fitting	C₂×C₉×C₁₁×C₇₉	C₂
socle	C₂×C₃×C₁₁×C₇₉	C₂×C₃
prime radical	C₂×C₃×C₁₁×D₇₉	C₃
cosocle	C₃×C₇₉	C₂²×C₃×C₁₁
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₂×C₉×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₁×D₇₉	C₂	direct (N × H)
2. C₂×C₉×C₁₁×C₇₉	C₂	semidirect
4. C₉×C₁₁×C₇₉	C₂²	semidirect
7. C₂×C₁₁×D₇₉	C₉	direct (N × H)
8. C₂×C₉×D₇₉	C₁₁	direct (N × H)
10. C₂×C₁₁×C₇₉	C₂×C₉	semidirect
11. C₁₁×D₇₉	C₂×C₉	direct (N × H)
12. C₂×C₉×C₇₉	C₂×C₁₁	semidirect
13. C₉×D₇₉	C₂×C₁₁	direct (N × H)
15. C₁₁×C₇₉	C₂²×C₉	semidirect
16. C₉×C₇₉	C₂²×C₁₁	semidirect
20. C₂×D₇₉	C₉×C₁₁	direct (N × H)
23. C₂×C₉×C₁₁	D₇₉	direct (N × H)
24. C₂×C₇₉	C₂×C₉×C₁₁	semidirect
25. D₇₉	C₂×C₉×C₁₁	direct (N × H)
27. C₉×C₁₁	C₂×D₇₉	direct (N × H)
28. C₇₉	C₂²×C₉×C₁₁	semidirect
35. C₂×C₁₁	C₉×D₇₉	direct (N × H)
37. C₂×C₉	C₁₁×D₇₉	direct (N × H)
39. C₁₁	C₂×C₉×D₇₉	direct (N × H)
40. C₉	C₂×C₁₁×D₇₉	direct (N × H)
46. C₂	C₉×C₁₁×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×C₁₁×D₇₉	2
C₂×C₉×C₁₁×C₇₉	2
C₂×C₃×C₁₁×D₇₉	3
C₂×C₉×D₇₉	11
C₂²×C₉×C₁₁	79

Subgroups — C2×C9×C11×D79 #44530869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₁×D₇₉ #44530869