Subgroups — C₂²×C₁₁×C₇₉⋊C₉ #44530862

Order 31284.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×C₇₉⋊C₉	C₂	direct (N × H)
3. C₁₁×C₇₉⋊C₉	C₂²	direct (N × H)
5. C₂²×C₁₁×C₇₉	C₉	semidirect
6. C₂²×C₇₉⋊C₉	C₁₁	direct (N × H)
8. C₂×C₁₁×C₇₉	C₂×C₉	semidirect
9. C₂×C₇₉⋊C₉	C₂×C₁₁	direct (N × H)
11. C₁₁×C₇₉	C₂²×C₉	semidirect
12. C₇₉⋊C₉	C₂²×C₁₁	direct (N × H)
15. C₂²×C₇₉	C₉×C₁₁	semidirect
18. C₂×C₇₉	C₂×C₉×C₁₁	semidirect
21. C₇₉	C₂²×C₉×C₁₁	semidirect
23. C₂²×C₁₁	C₇₉⋊C₉	direct (N × H)
26. C₂×C₁₁	C₂×C₇₉⋊C₉	direct (N × H)
29. C₁₁	C₂²×C₇₉⋊C₉	direct (N × H)
32. C₂²	C₁₁×C₇₉⋊C₉	direct (N × H)
34. C₂	C₂×C₁₁×C₇₉⋊C₉	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×C₁₁×C₇₉⋊C₉	2
C₂²×C₃×C₁₁×C₇₉	3
C₂²×C₇₉⋊C₉	11
C₂²×C₉×C₁₁	79

Subgroups — C22×C11×C79⋊C9 #44530862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₇₉⋊C₉ #44530862