Subgroups — C₂×C₇×C₇⋊AGL(1,𝔽₁₁) #24924751

Order 10780.

104 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)	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₇×AGL(1,𝔽₁₁)	—	7	1	no	maximal
7	C₂×C₇²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₇×D₇₇	C₂×C₅	1	2	yes	complemented
9	C₂×C₅×C₇×D₇	—	11	1	no	maximal, Hall
10	C₂×C₇×C₁₁⋊C₅	—	2	3	no	—
11	C₂×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic, complemented
12	C₂×C₇×C₁₁⋊C₅	C₂×C₇	1	1	yes	characteristic, complemented
13	C₇⋊AGL(1,𝔽₁₁)	C₂×C₇	1	2	yes	direct product factor
14	C₇×AGL(1,𝔽₁₁)	—	7	2	no	—
15	C₇²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇²	—	11	1	no	—
17	C₅×C₇×D₇	—	11	2	no	—
18	C₇×C₁₁⋊C₅	—	2	3	no	—
19	C₇×C₁₁⋊C₅	C₂×D₇	1	1	yes	characteristic, complemented
20	C₇×C₁₁⋊C₅	C₂²×C₇	1	1	yes	characteristic, complemented
21	C₂×D₇₇	C₅×C₇	1	1	yes	characteristic, complemented
22	C₂×C₇×D₁₁	—	7	1	no	—
23	C₅×C₇²	—	11	1	no	Hall
24	C₂×AGL(1,𝔽₁₁)	—	7	1	no	Hall
25	C₂×C₇×D₇	—	11	1	no	Hall
26	C₂×C₇×C₁₁	—	2	3	no	—
27	C₂×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic, complemented
28	C₂×C₇×C₁₁	C₂×C₅×C₇	1	1	yes	characteristic, complemented
29	D₇₇	C₂×C₅×C₇	1	2	yes	complemented
30	C₇×D₁₁	—	7	2	no	—
31	C₂²×C₅×C₇	—	77	1	no	—
32	C₂×C₅×D₇	—	11	1	no	—
33	C₂×C₁₁⋊C₅	C₇×D₇	1	1	yes	characteristic, complemented
34	AGL(1,𝔽₁₁)	—	7	2	no	—
35	C₂×C₇²	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
36	C₇×D₇	—	11	2	no	—
37	C₇×C₁₁	—	2	3	no	—
38	C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic, complemented
39	C₇×C₁₁	C₂²×C₅×C₇	1	1	yes	characteristic, complemented
40	C₂×C₅×C₇	—	11	1	no	—
41	C₂×C₅×C₇	—	11	1	no	—
42	C₂×C₅×C₇	—	22	3	no	—
43	C₂×C₅×C₇	—	77	2	no	—
44	C₅×D₇	—	11	2	no	—
45	C₁₁⋊C₅	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Hall
46	C₇²	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₁₁	—	7	1	no	Hall
48	C₅×C₇	—	11	1	no	—
49	C₅×C₇	—	11	1	no	—
50	C₅×C₇	—	22	3	no	—
51	C₂²×C₇	—	77	1	no	—
52	C₂×D₇	—	11	1	no	—
53	C₂×C₁₁	C₅×C₇×D₇	1	1	yes	characteristic, complemented
54	D₁₁	—	7	2	no	—
55	C₂²×C₅	—	77	1	no	Hall
56	C₂×C₇	—	2	3	no	—
57	C₂×C₇	—	77	2	no	—
58	C₂×C₇	C₇×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
59	C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
60	D₇	—	11	2	no	—
61	C₁₁	C₂×C₅×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₅	—	11	1	no	—
63	C₂×C₅	—	77	2	no	—
64	C₇	—	2	3	no	—
65	C₇	C₂×C₇×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
66	C₇	C₂×C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
67	C₅	—	11	1	no	Sylow
68	C₂²	—	77	1	no	Sylow
69	C₂	—	77	2	no	—
70	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	C₇×C₁₁	C₂²×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₁	C₂×C₅
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂×C₇

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
5. C₂×C₇⋊AGL(1,𝔽₁₁)	C₇	direct (N × H)
7. C₂×C₇²×C₁₁	C₂×C₅	semidirect
8. C₇×D₇₇	C₂×C₅	semidirect
11. C₂×C₇×C₁₁⋊C₅	D₇	semidirect
12. C₂×C₇×C₁₁⋊C₅	C₂×C₇	semidirect
13. C₇⋊AGL(1,𝔽₁₁)	C₂×C₇	direct (N × H)
15. C₇²×C₁₁	C₂²×C₅	semidirect
19. C₇×C₁₁⋊C₅	C₂×D₇	semidirect
20. C₇×C₁₁⋊C₅	C₂²×C₇	semidirect
21. C₂×D₇₇	C₅×C₇	semidirect
27. C₂×C₇×C₁₁	C₅×D₇	semidirect
28. C₂×C₇×C₁₁	C₂×C₅×C₇	semidirect
29. D₇₇	C₂×C₅×C₇	semidirect
33. C₂×C₁₁⋊C₅	C₇×D₇	semidirect
35. C₂×C₇²	AGL(1,𝔽₁₁)	semidirect
38. C₇×C₁₁	C₂×C₅×D₇	semidirect
39. C₇×C₁₁	C₂²×C₅×C₇	semidirect
45. C₁₁⋊C₅	C₂×C₇×D₇	semidirect
46. C₇²	C₂×AGL(1,𝔽₁₁)	semidirect
53. C₂×C₁₁	C₅×C₇×D₇	semidirect
58. C₂×C₇	C₇×AGL(1,𝔽₁₁)	semidirect
59. C₂×C₇	C₇⋊AGL(1,𝔽₁₁)	direct (N × H)
61. C₁₁	C₂×C₅×C₇×D₇	semidirect
65. C₇	C₂×C₇×AGL(1,𝔽₁₁)	semidirect
66. C₇	C₂×C₇⋊AGL(1,𝔽₁₁)	direct (N × H)
70. C₂	C₇×C₇⋊AGL(1,𝔽₁₁)	direct (N × H)

Subgroups — C2×C7×C7⋊AGL(1,𝔽11) #24924751

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×C₇⋊AGL(1,𝔽₁₁) #24924751