Subgroups — AGL(1,𝔽₁₁)×D₈₇ #34062339

Order 19140.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₂₉⋊AGL(1,𝔽₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁⋊C₅×D₈₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂₉×AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₉×AGL(1,𝔽₁₁)	—	3	1	no	maximal, Hall
5	C₃×C₂₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₁×D₈₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂₉⋊AGL(1,𝔽₁₁)	—	3	1	no	—
8	C₂₉×AGL(1,𝔽₁₁)	D₃	1	1	yes	characteristic, complemented
9	C₁₁⋊C₅×D₂₉	—	3	1	no	—
10	D₉₅₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₁₁×D₈₇	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₁₁×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₅×D₈₇	—	11	1	no	maximal, Hall
14	C₂₉×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₁×D₂₉	—	3	1	no	Hall
16	C₃×C₁₁×C₂₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₂₉	—	11	1	no	—
18	C₅×D₈₇	—	11	1	no	—
19	C₅×D₈₇	—	11	1	no	—
20	D₃×AGL(1,𝔽₁₁)	—	29	1	no	maximal, Hall
21	D₃₁₉	—	3	1	no	—
22	C₁₁×D₂₉	—	3	1	no	—
23	D₁₁×C₂₉	C₅×D₃	1	1	yes	characteristic, complemented
24	C₂×C₅×D₂₉	—	33	1	no	Hall
25	C₃×C₅×C₂₉	—	11	1	no	Hall
26	C₂×D₈₇	—	55	1	no	Hall
27	C₃⋊AGL(1,𝔽₁₁)	—	29	1	no	—
28	D₃×C₁₁⋊C₅	—	29	1	no	—
29	C₃×AGL(1,𝔽₁₁)	D₂₉	1	1	yes	characteristic, complemented
30	C₁₁×C₂₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₂₉	—	11	1	no	—
32	C₅×D₂₉	—	33	1	no	—
33	C₅×D₂₉	—	33	1	no	—
34	C₂×AGL(1,𝔽₁₁)	—	87	1	no	Hall
35	C₂×C₃×C₂₉	—	55	1	no	—
36	D₈₇	—	11	1	no	—
37	D₈₇	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
38	C₃×C₁₁⋊C₅	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
39	C₅×C₂₉	—	11	1	no	Hall
40	D₃×D₁₁	—	29	1	no	Hall
41	C₂×D₂₉	—	165	1	no	Hall
42	C₂×C₁₁⋊C₅	—	87	1	no	—
43	AGL(1,𝔽₁₁)	—	87	1	no	—
44	AGL(1,𝔽₁₁)	D₈₇	1	1	yes	characteristic, direct product factor
45	C₃×C₂₉	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
46	D₃₃	—	29	1	no	—
47	C₃×D₁₁	C₅×D₂₉	1	1	yes	characteristic, complemented
48	D₃×C₁₁	—	29	1	no	—
49	C₂×C₅×D₃	—	319	1	no	Hall
50	C₂×C₂₉	—	55	1	no	—
51	D₂₉	—	3	1	no	—
52	D₂₉	—	165	1	no	—
53	C₁₁⋊C₅	C₂×D₈₇	1	1	yes	characteristic, complemented, Hall
54	C₂×D₁₁	—	87	1	no	Hall
55	C₃×C₁₁	C₂×C₅×D₂₉	1	1	yes	characteristic, complemented, Hall
56	C₂×C₃×C₅	—	11	1	no	—
57	C₅×D₃	—	319	1	no	—
58	C₅×D₃	—	319	1	no	—
59	C₂₉	D₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₁₁	—	87	1	no	—
61	D₁₁	—	87	1	no	—
62	D₁₁	C₅×D₈₇	1	1	yes	characteristic, complemented
63	C₂²×C₅	—	957	1	no	Hall
64	C₃×C₅	—	11	1	no	Hall
65	C₂×D₃	—	1595	1	no	Hall
66	C₁₁	C₂×C₅×D₈₇	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	11	1	no	—
68	C₂×C₅	—	957	1	no	—
69	C₂×C₅	—	957	1	no	—
70	C₂×C₃	—	55	1	no	—
71	D₃	—	29	1	no	—
72	D₃	—	1595	1	no	—
73	C₅	—	11	1	no	Sylow
74	C₂²	—	4785	1	no	Sylow
75	C₃	D₂₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	55	1	no	—
77	C₂	—	87	1	no	—
78	C₂	—	4785	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₂₉	C₂²×C₅
LCS	G ▷ C₃×C₁₁×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₂₉⋊AGL(1,𝔽₁₁))	C₂	semidirect
2. C₁₁⋊C₅×D₈₇	C₂	semidirect
3. C₃×C₂₉×AGL(1,𝔽₁₁)	C₂	semidirect
5. C₃×C₂₉×C₁₁⋊C₅	C₂²	semidirect
6. D₁₁×D₈₇	C₅	semidirect
8. C₂₉×AGL(1,𝔽₁₁)	D₃	semidirect
10. D₉₅₇	C₂×C₅	semidirect
11. C₁₁×D₈₇	C₂×C₅	semidirect
12. C₃×D₁₁×C₂₉	C₂×C₅	semidirect
14. C₂₉×C₁₁⋊C₅	C₂×D₃	semidirect
16. C₃×C₁₁×C₂₉	C₂²×C₅	semidirect
23. D₁₁×C₂₉	C₅×D₃	semidirect
29. C₃×AGL(1,𝔽₁₁)	D₂₉	semidirect
30. C₁₁×C₂₉	C₂×C₅×D₃	semidirect
37. D₈₇	AGL(1,𝔽₁₁)	direct (N × H)
38. C₃×C₁₁⋊C₅	C₂×D₂₉	semidirect
44. AGL(1,𝔽₁₁)	D₈₇	direct (N × H)
45. C₃×C₂₉	C₂×AGL(1,𝔽₁₁)	semidirect
47. C₃×D₁₁	C₅×D₂₉	semidirect
53. C₁₁⋊C₅	C₂×D₈₇	semidirect
55. C₃×C₁₁	C₂×C₅×D₂₉	semidirect
59. C₂₉	D₃×AGL(1,𝔽₁₁)	semidirect
62. D₁₁	C₅×D₈₇	semidirect
66. C₁₁	C₂×C₅×D₈₇	semidirect
75. C₃	D₂₉×AGL(1,𝔽₁₁)	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₂₉⋊AGL(1,𝔽₁₁))	2
C₁₁⋊C₅×D₈₇	2
C₃×C₂₉×AGL(1,𝔽₁₁)	2
D₂₉×AGL(1,𝔽₁₁)	3
D₁₁×D₈₇	5
C₂×C₅×D₈₇	11
D₃×AGL(1,𝔽₁₁)	29

Subgroups — AGL(1,𝔽11)×D87 #34062339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₁₁)×D₈₇ #34062339