Subgroups — (C₇⋊D₇)⋊AGL(1,𝔽₁₁) #24924746

Order 10780.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₇⋊AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, complemented
3	C₇²×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	(C₇⋊D₇)⋊D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	D₇×AGL(1,𝔽₁₁)	—	7	2	no	maximal
6	C₁₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇×D₇₇	C₂×C₅	1	2	yes	complemented
8	C₅×D₇²	—	11	1	no	maximal, Hall
9	C₇⋊AGL(1,𝔽₁₁)	D₇	1	2	yes	complemented
10	D₇×C₁₁⋊C₅	—	7	2	no	—
11	D₇×C₁₁⋊C₅	—	14	3	no	—
12	C₇×AGL(1,𝔽₁₁)	—	7	2	no	—
13	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₇⋊D₇	—	11	1	no	—
15	C₅×C₇×D₇	—	11	2	no	—
16	C₇×C₁₁⋊C₅	—	2	3	no	—
17	C₇×C₁₁⋊C₅	C₂×D₇	1	2	yes	complemented
18	D₇×D₁₁	—	7	2	no	—
19	C₅×C₇²	—	11	1	no	Hall
20	C₂×AGL(1,𝔽₁₁)	—	49	1	no	Hall
21	D₇²	—	11	1	no	Hall
22	D₇₇	C₅×D₇	1	2	yes	complemented
23	C₇×D₁₁	—	7	2	no	—
24	C₁₁×D₇	—	7	2	no	—
25	C₁₁×D₇	—	14	3	no	—
26	C₂×C₅×D₇	—	77	2	no	—
27	C₂×C₁₁⋊C₅	—	49	1	no	—
28	AGL(1,𝔽₁₁)	—	7	2	no	—
29	C₇⋊D₇	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
30	C₇×D₇	—	11	2	no	—
31	C₇×C₁₁	—	2	3	no	—
32	C₇×C₁₁	C₂×C₅×D₇	1	2	yes	complemented
33	C₂×C₅×C₇	—	77	2	no	—
34	C₅×D₇	—	11	2	no	—
35	C₅×D₇	—	77	2	no	—
36	C₅×D₇	—	154	3	no	—
37	C₁₁⋊C₅	D₇²	1	1	yes	characteristic, complemented, Hall
38	C₇²	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₁₁	—	49	1	no	Hall
40	C₅×C₇	—	11	2	no	—
41	C₅×C₇	—	22	3	no	—
42	C₂×D₇	—	77	2	no	—
43	C₂×C₁₁	—	49	1	no	—
44	D₁₁	—	7	2	no	—
45	C₂²×C₅	—	539	1	no	Hall
46	C₂×C₇	—	77	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	11	2	no	—
49	D₇	—	14	3	no	—
50	C₁₁	C₅×D₇²	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₅	—	539	1	no	—
52	C₂×C₅	—	77	2	no	—
53	C₇	—	2	3	no	—
54	C₇	D₇×AGL(1,𝔽₁₁)	1	2	yes	complemented
55	C₅	—	11	1	no	Sylow
56	C₂²	—	539	1	no	Sylow
57	C₂	—	49	1	no	—
58	C₂	—	77	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₁	C₂²×C₅
LCS	G ▷ C₇²×C₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₁⋊C₅×C₇⋊D₇	C₂	semidirect
2. C₇×C₇⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₇²×C₁₁⋊C₅	C₂²	semidirect
4. (C₇⋊D₇)⋊D₁₁	C₅	semidirect
6. C₁₁×C₇⋊D₇	C₂×C₅	semidirect
7. C₇×D₇₇	C₂×C₅	semidirect
9. C₇⋊AGL(1,𝔽₁₁)	D₇	semidirect
13. C₇²×C₁₁	C₂²×C₅	semidirect
17. C₇×C₁₁⋊C₅	C₂×D₇	semidirect
22. D₇₇	C₅×D₇	semidirect
29. C₇⋊D₇	AGL(1,𝔽₁₁)	semidirect
32. C₇×C₁₁	C₂×C₅×D₇	semidirect
37. C₁₁⋊C₅	D₇²	semidirect
38. C₇²	C₂×AGL(1,𝔽₁₁)	semidirect
50. C₁₁	C₅×D₇²	semidirect
54. C₇	D₇×AGL(1,𝔽₁₁)	semidirect

Subgroups — (C7⋊D7)⋊AGL(1,𝔽11) #24924746

Conjugacy classes of subgroups

Complements

Subgroups — (C₇⋊D₇)⋊AGL(1,𝔽₁₁) #24924746