Subgroups — C₁₁×Dic₇₁₁ #44530842

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	C₁₁×Dic₂₃₇	—	3	1	no	maximal
3	C₉×C₁₁×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₁×C₇₉	D₃	1	1	yes	characteristic
5	C₁₁×Dic₇₉	—	9	1	no	Hall
6	Dic₇₁₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₁×C₇₉	Dic₃	1	1	yes	characteristic
8	C₂×C₁₁×C₇₉	D₉	1	1	yes	characteristic
9	C₂×C₉×C₇₉	C₂×C₁₁	1	1	yes	characteristic
10	Dic₂₃₇	—	3	1	no	—
11	C₁₁×C₇₉	Dic₉	1	1	yes	characteristic, complemented, Hall
12	C₉×C₇₉	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇₉	D₃×C₁₁	1	1	yes	characteristic
14	C₁₁×Dic₉	—	79	1	no	maximal, Hall
15	Dic₇₉	—	9	1	no	Hall
16	C₃×C₇₉	C₁₁×Dic₃	1	1	yes	characteristic
17	C₂×C₉×C₁₁	D₇₉	1	1	yes	characteristic
18	C₂×C₇₉	C₁₁×D₉	1	1	yes	characteristic
19	C₁₁×Dic₃	—	237	1	no	—
20	C₉×C₁₁	Dic₇₉	1	1	yes	characteristic, complemented, Hall
21	C₇₉	C₁₁×Dic₉	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₁₁	D₂₃₇	1	1	yes	characteristic
23	C₄×C₁₁	—	711	1	no	Hall
24	Dic₉	—	79	1	no	Hall
25	C₃×C₁₁	Dic₂₃₇	1	1	yes	characteristic
26	C₂×C₁₁	D₇₁₁	1	1	yes	characteristic
27	C₂×C₉	C₁₁×D₇₉	1	1	yes	characteristic
28	Dic₃	—	237	1	no	—
29	C₁₁	Dic₇₁₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₉	C₁₁×Dic₇₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₁₁×D₂₃₇	1	1	yes	characteristic
32	C₄	—	711	1	no	Sylow
33	C₃	C₁₁×Dic₂₃₇	1	1	yes	characteristic
34	C₂	C₁₁×D₇₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₇₁₁
commutator, hypocenter	C₉×C₇₉	C₄×C₁₁
Frattini	C₂×C₃	C₁₁×D₂₃₇
Fitting	C₂×C₉×C₁₁×C₇₉	C₂
socle, prime radical	C₂×C₃×C₁₁×C₇₉	D₃
cosocle	C₂×C₉×C₇₉	C₂×C₁₁
LCS	G ▷ C₉×C₇₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₁×C₇₉	C₄	semidirect
6. Dic₇₁₁	C₁₁	direct (N × H)
11. C₁₁×C₇₉	Dic₉	semidirect
12. C₉×C₇₉	C₄×C₁₁	semidirect
20. C₉×C₁₁	Dic₇₉	semidirect
21. C₇₉	C₁₁×Dic₉	semidirect
29. C₁₁	Dic₇₁₁	direct (N × H)
30. C₉	C₁₁×Dic₇₉	semidirect

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
C₁₁×Dic₂₃₇	3
Dic₇₁₁	11
C₁₁×Dic₉	79

Subgroups — C11×Dic711 #44530842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×Dic₇₁₁ #44530842