Subgroups — C₂×C₇⋊(C₂₃⋊AGL(1,𝔽₁₁)) #47978430

Order 35420.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊(C₂₃⋊AGL(1,𝔽₁₁))	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₂₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇₇₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₃⋊AGL(1,𝔽₁₁)	—	7	1	no	maximal, Hall
6	D₁₇₇₁	C₂×C₅	1	2	yes	complemented
7	C₂×C₇×C₁₁×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
8	C₂×C₅×D₁₆₁	—	11	1	no	maximal, Hall
9	C₂₃⋊AGL(1,𝔽₁₁)	—	7	2	no	—
10	C₂×C₂₃×C₁₁⋊C₅	D₇	1	1	yes	characteristic, complemented
11	C₇×C₁₁×C₂₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₅×C₇×C₂₃	—	11	1	no	—
13	C₅×D₁₆₁	—	11	2	no	—
14	C₂×C₇⋊AGL(1,𝔽₁₁)	—	23	1	no	maximal, Hall
15	C₂₃×C₁₁⋊C₅	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	C₂×D₂₅₃	—	7	1	no	Hall
17	C₅×C₇×C₂₃	—	11	1	no	Hall
18	C₂×C₇×C₁₁⋊C₅	D₂₃	1	1	yes	characteristic, complemented
19	C₇⋊AGL(1,𝔽₁₁)	—	23	2	no	—
20	C₂×D₁₆₁	—	11	1	no	Hall
21	C₂×C₁₁×C₂₃	C₅×D₇	1	1	yes	characteristic, complemented
22	D₂₅₃	—	7	2	no	—
23	C₂×C₅×D₂₃	—	77	1	no	Hall
24	C₇×C₁₁⋊C₅	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₂₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
26	D₁₆₁	—	11	2	no	—
27	C₂×D₇₇	—	23	1	no	Hall
28	C₁₁×C₂₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₅×C₂₃	—	11	1	no	—
30	C₅×D₂₃	—	77	2	no	—
31	C₂×AGL(1,𝔽₁₁)	—	161	1	no	Hall
32	C₇×C₂₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
33	C₂×C₇×C₁₁	C₅×D₂₃	1	1	yes	characteristic, complemented
34	D₇₇	—	23	2	no	—
35	C₂×C₅×D₇	—	253	1	no	Hall
36	C₅×C₂₃	—	11	1	no	Hall
37	C₂×C₁₁⋊C₅	D₁₆₁	1	1	yes	characteristic, complemented
38	AGL(1,𝔽₁₁)	—	161	2	no	—
39	C₂×D₂₃	—	77	1	no	Hall
40	C₇×C₁₁	C₂×C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
41	C₂×C₅×C₇	—	11	1	no	—
42	C₅×D₇	—	253	2	no	—
43	C₁₁⋊C₅	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Hall
44	C₂×C₂₃	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
45	D₂₃	—	77	2	no	—
46	C₂×D₁₁	—	161	1	no	Hall
47	C₅×C₇	—	11	1	no	Hall
48	C₂×D₇	—	253	1	no	Hall
49	C₂₃	C₂×C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₁₁	C₅×D₁₆₁	1	1	yes	characteristic, complemented
51	D₁₁	—	161	2	no	—
52	C₂²×C₅	—	1771	1	no	Hall
53	C₂×C₇	C₂₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
54	D₇	—	253	2	no	—
55	C₁₁	C₂×C₅×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	11	1	no	—
57	C₂×C₅	—	1771	2	no	—
58	C₇	C₂×C₂₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
59	C₅	—	11	1	no	Sylow
60	C₂²	—	1771	1	no	Sylow
61	C₂	—	1771	2	no	—
62	C₂	C₇⋊(C₂₃⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊(C₂₃⋊AGL(1,𝔽₁₁))
commutator, cosocle, hypocenter	C₇×C₁₁×C₂₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₂₃	C₂×C₅
LCS	G ▷ C₇×C₁₁×C₂₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₇⋊(C₂₃⋊AGL(1,𝔽₁₁))	C₂	direct (N × H)
2. C₂×C₇×C₂₃×C₁₁⋊C₅	C₂	semidirect
3. C₇×C₂₃×C₁₁⋊C₅	C₂²	semidirect
4. C₂×D₁₇₇₁	C₅	semidirect
6. D₁₇₇₁	C₂×C₅	semidirect
7. C₂×C₇×C₁₁×C₂₃	C₂×C₅	semidirect
10. C₂×C₂₃×C₁₁⋊C₅	D₇	semidirect
11. C₇×C₁₁×C₂₃	C₂²×C₅	semidirect
15. C₂₃×C₁₁⋊C₅	C₂×D₇	semidirect
18. C₂×C₇×C₁₁⋊C₅	D₂₃	semidirect
21. C₂×C₁₁×C₂₃	C₅×D₇	semidirect
24. C₇×C₁₁⋊C₅	C₂×D₂₃	semidirect
25. C₂×C₇×C₂₃	AGL(1,𝔽₁₁)	semidirect
28. C₁₁×C₂₃	C₂×C₅×D₇	semidirect
32. C₇×C₂₃	C₂×AGL(1,𝔽₁₁)	semidirect
33. C₂×C₇×C₁₁	C₅×D₂₃	semidirect
37. C₂×C₁₁⋊C₅	D₁₆₁	semidirect
40. C₇×C₁₁	C₂×C₅×D₂₃	semidirect
43. C₁₁⋊C₅	C₂×D₁₆₁	semidirect
44. C₂×C₂₃	C₇⋊AGL(1,𝔽₁₁)	semidirect
49. C₂₃	C₂×C₇⋊AGL(1,𝔽₁₁)	semidirect
50. C₂×C₁₁	C₅×D₁₆₁	semidirect
53. C₂×C₇	C₂₃⋊AGL(1,𝔽₁₁)	semidirect
55. C₁₁	C₂×C₅×D₁₆₁	semidirect
58. C₇	C₂×C₂₃⋊AGL(1,𝔽₁₁)	semidirect
62. C₂	C₇⋊(C₂₃⋊AGL(1,𝔽₁₁))	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇⋊(C₂₃⋊AGL(1,𝔽₁₁))	2
C₂×C₇×C₂₃×C₁₁⋊C₅	2
C₂×D₁₇₇₁	5
C₂×C₂₃⋊AGL(1,𝔽₁₁)	7
C₂×C₅×D₁₆₁	11
C₂×C₇⋊AGL(1,𝔽₁₁)	23

Subgroups — C2×C7⋊(C23⋊AGL(1,𝔽11)) #47978430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇⋊(C₂₃⋊AGL(1,𝔽₁₁)) #47978430