Subgroups — C₂×C₇⋊(C₇⋊AGL(1,𝔽₁₁)) #24924753

Order 10780.

200 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, complemented
2	C₇⋊(C₇⋊AGL(1,𝔽₁₁))	C₂	1	2	yes	maximal, direct product factor
3	C₇²×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇⋊D₇₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₇⋊AGL(1,𝔽₁₁)	—	7	8	no	maximal
6	C₂×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
7	C₇⋊D₇₇	C₂×C₅	1	2	yes	complemented
8	C₂×C₅×C₇⋊D₇	—	11	1	no	maximal, Hall
9	C₂×C₇×C₁₁⋊C₅	D₇	1	8	yes	complemented
10	C₇⋊AGL(1,𝔽₁₁)	—	7	16	no	—
11	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇²	—	11	1	no	—
13	C₅×C₇⋊D₇	—	11	2	no	—
14	C₇×C₁₁⋊C₅	C₂×D₇	1	8	yes	complemented
15	C₂×D₇₇	—	7	8	no	—
16	C₅×C₇²	—	11	1	no	Hall
17	C₂×AGL(1,𝔽₁₁)	—	49	1	no	Hall
18	C₂×C₇⋊D₇	—	11	1	no	Hall
19	C₂×C₇×C₁₁	C₅×D₇	1	8	yes	complemented
20	D₇₇	—	7	16	no	—
21	C₂×C₅×D₇	—	77	8	no	—
22	C₂×C₁₁⋊C₅	C₇⋊D₇	1	1	yes	characteristic, complemented
23	AGL(1,𝔽₁₁)	—	49	2	no	—
24	C₂×C₇²	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
25	C₇⋊D₇	—	11	2	no	—
26	C₇×C₁₁	C₂×C₅×D₇	1	8	yes	complemented
27	C₂×C₅×C₇	—	11	8	no	—
28	C₅×D₇	—	77	16	no	—
29	C₁₁⋊C₅	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
30	C₇²	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₁	—	49	1	no	Hall
32	C₅×C₇	—	11	8	no	—
33	C₂×D₇	—	77	8	no	—
34	C₂×C₁₁	C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
35	D₁₁	—	49	2	no	—
36	C₂²×C₅	—	539	1	no	Hall
37	C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	1	8	yes	complemented
38	D₇	—	77	16	no	—
39	C₁₁	C₂×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₅	—	11	1	no	—
41	C₂×C₅	—	539	2	no	—
42	C₇	C₂×C₇⋊AGL(1,𝔽₁₁)	1	8	yes	complemented
43	C₅	—	11	1	no	Sylow
44	C₂²	—	539	1	no	Sylow
45	C₂	—	539	2	no	—
46	C₂	C₇⋊(C₇⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊(C₇⋊AGL(1,𝔽₁₁))
commutator, cosocle, hypocenter	C₇²×C₁₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₁	C₂×C₅
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×C₁₁⋊C₅	C₂	semidirect
2. C₇⋊(C₇⋊AGL(1,𝔽₁₁))	C₂	direct (N × H)
3. C₇²×C₁₁⋊C₅	C₂²	semidirect
4. C₂×C₇⋊D₇₇	C₅	semidirect
6. C₂×C₇²×C₁₁	C₂×C₅	semidirect
7. C₇⋊D₇₇	C₂×C₅	semidirect
9. C₂×C₇×C₁₁⋊C₅	D₇	semidirect
11. C₇²×C₁₁	C₂²×C₅	semidirect
14. C₇×C₁₁⋊C₅	C₂×D₇	semidirect
19. C₂×C₇×C₁₁	C₅×D₇	semidirect
22. C₂×C₁₁⋊C₅	C₇⋊D₇	semidirect
24. C₂×C₇²	AGL(1,𝔽₁₁)	semidirect
26. C₇×C₁₁	C₂×C₅×D₇	semidirect
29. C₁₁⋊C₅	C₂×C₇⋊D₇	semidirect
30. C₇²	C₂×AGL(1,𝔽₁₁)	semidirect
34. C₂×C₁₁	C₅×C₇⋊D₇	semidirect
37. C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	semidirect
39. C₁₁	C₂×C₅×C₇⋊D₇	semidirect
42. C₇	C₂×C₇⋊AGL(1,𝔽₁₁)	semidirect
46. C₂	C₇⋊(C₇⋊AGL(1,𝔽₁₁))	direct (N × H)

Subgroups — C2×C7⋊(C7⋊AGL(1,𝔽11)) #24924753

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇⋊(C₇⋊AGL(1,𝔽₁₁)) #24924753