Subgroups — C₇×C₇⋊(Dic₁₁⋊C₅) #24924726

Order 10780.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×Dic₇₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₇⋊(Dic₁₁⋊C₅)	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×Dic₁₁⋊C₅	—	7	1	no	maximal
6	C₂×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic
7	C₅×C₇×Dic₇	—	11	1	no	maximal, Hall
8	C₂×C₇×C₁₁⋊C₅	—	2	3	no	—
9	C₂×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic
10	C₂×C₇×C₁₁⋊C₅	C₂×C₇	1	1	yes	characteristic
11	C₇²×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	—	11	1	no	—
13	C₇×C₁₁⋊C₅	—	2	3	no	—
14	C₇×C₁₁⋊C₅	Dic₇	1	1	yes	characteristic, complemented
15	C₇×C₁₁⋊C₅	C₄×C₇	1	1	yes	characteristic, complemented
16	Dic₇₇	C₅×C₇	1	1	yes	characteristic, complemented
17	C₇×Dic₁₁	—	7	1	no	—
18	C₅×C₇²	—	11	1	no	Hall
19	Dic₁₁⋊C₅	—	7	1	no	Hall
20	C₇×Dic₇	—	11	1	no	Hall
21	C₂×C₇×C₁₁	—	2	3	no	—
22	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
23	C₂×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic
24	C₄×C₅×C₇	—	77	1	no	—
25	C₅×Dic₇	—	11	1	no	—
26	C₂×C₁₁⋊C₅	C₇×D₇	1	1	yes	characteristic
27	C₂×C₇²	AGL(1,𝔽₁₁)	1	1	yes	characteristic
28	C₇×C₁₁	—	2	3	no	—
29	C₇×C₁₁	C₅×Dic₇	1	1	yes	characteristic, complemented
30	C₇×C₁₁	C₄×C₅×C₇	1	1	yes	characteristic, complemented
31	C₂×C₅×C₇	—	11	1	no	—
32	C₂×C₅×C₇	—	11	1	no	—
33	C₂×C₅×C₇	—	22	3	no	—
34	C₁₁⋊C₅	C₇×Dic₇	1	1	yes	characteristic, complemented, Hall
35	C₇²	Dic₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
36	Dic₁₁	—	7	1	no	Hall
37	C₅×C₇	—	11	1	no	—
38	C₅×C₇	—	11	1	no	—
39	C₅×C₇	—	22	3	no	—
40	C₄×C₇	—	77	1	no	—
41	Dic₇	—	11	1	no	—
42	C₂×C₁₁	C₅×C₇×D₇	1	1	yes	characteristic
43	C₄×C₅	—	77	1	no	Hall
44	C₂×C₇	—	2	3	no	—
45	C₂×C₇	C₇×AGL(1,𝔽₁₁)	1	1	yes	characteristic
46	C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
47	C₁₁	C₅×C₇×Dic₇	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅	—	11	1	no	—
49	C₇	—	2	3	no	—
50	C₇	C₇×Dic₁₁⋊C₅	1	1	yes	characteristic, complemented
51	C₇	C₇⋊(Dic₁₁⋊C₅)	1	1	yes	characteristic, direct product factor
52	C₅	—	11	1	no	Sylow
53	C₄	—	77	1	no	Sylow
54	C₂	C₇×C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	C₇⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₇×C₁₁	C₄×C₅×C₇
Frattini	C₂	C₇×C₇⋊AGL(1,𝔽₁₁)
Fitting, socle	C₂×C₇²×C₁₁	C₂×C₅
prime radical	C₂×C₇²×C₁₁⋊C₅	C₂
cosocle	C₂×C₇×C₁₁	C₂×C₅×C₇
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
2. C₇²×C₁₁⋊C₅	C₄	semidirect
3. C₇×Dic₇₇	C₅	semidirect
4. C₇⋊(Dic₁₁⋊C₅)	C₇	direct (N × H)
11. C₇²×C₁₁	C₄×C₅	semidirect
14. C₇×C₁₁⋊C₅	Dic₇	semidirect
15. C₇×C₁₁⋊C₅	C₄×C₇	semidirect
16. Dic₇₇	C₅×C₇	semidirect
29. C₇×C₁₁	C₅×Dic₇	semidirect
30. C₇×C₁₁	C₄×C₅×C₇	semidirect
34. C₁₁⋊C₅	C₇×Dic₇	semidirect
35. C₇²	Dic₁₁⋊C₅	semidirect
47. C₁₁	C₅×C₇×Dic₇	semidirect
50. C₇	C₇×Dic₁₁⋊C₅	semidirect
51. C₇	C₇⋊(Dic₁₁⋊C₅)	direct (N × H)

Subgroups — C7×C7⋊(Dic11⋊C5) #24924726

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₇⋊(Dic₁₁⋊C₅) #24924726