Subgroups — C₂×C₉×C₁₇⋊AGL(1,𝔽₁₁) #46777871

Order 33660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₇⋊AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₇×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₇⋊AGL(1,𝔽₁₁)	C₃	1	1	yes	maximal, characteristic
4	C₉×C₁₇×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₁₈₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃×C₁₇⋊AGL(1,𝔽₁₁)	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₁₇×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
8	C₂×C₁₇⋊AGL(1,𝔽₁₁)	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×D₁₈₇	C₂×C₅	1	2	yes	complemented
10	C₂×C₉×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₉×D₁₇	—	11	1	no	maximal, Hall
12	C₃×C₁₇×C₁₁⋊C₅	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×D₁₈₇	C₃×C₅	1	1	yes	characteristic
14	C₂×C₉×AGL(1,𝔽₁₁)	—	17	1	no	maximal, Hall
15	C₂×C₁₇×C₁₁⋊C₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₁₇⋊AGL(1,𝔽₁₁)	C₂×C₉	1	2	yes	direct product factor
17	C₉×C₁₁×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₇	—	11	1	no	—
19	C₅×C₉×D₁₇	—	11	2	no	—
20	C₂×C₃×C₁₁×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×D₁₈₇	C₂×C₃×C₅	1	2	yes	—
22	C₂×C₃×C₅×D₁₇	—	11	1	no	—
23	C₂×C₉×C₁₁⋊C₅	D₁₇	1	1	yes	characteristic, complemented
24	C₉×AGL(1,𝔽₁₁)	—	17	2	no	—
25	C₁₇×C₁₁⋊C₅	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₅×C₉×C₁₇	—	11	1	no	Hall
27	C₂×D₁₈₇	C₅×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×AGL(1,𝔽₁₁)	—	17	1	no	—
29	C₂×C₉×D₁₇	—	11	1	no	Hall
30	C₃×C₁₁×C₁₇	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₇	—	11	1	no	—
32	C₃×C₅×D₁₇	—	11	2	no	—
33	C₉×C₁₁⋊C₅	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₉×D₁₁	—	17	1	no	Hall
35	C₂×C₁₁×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented
36	D₁₈₇	C₂×C₅×C₉	1	2	yes	complemented
37	C₂×C₅×D₁₇	—	11	1	no	Hall
38	C₂×C₃×C₁₁⋊C₅	C₃×D₁₇	1	1	yes	characteristic
39	C₃×AGL(1,𝔽₁₁)	—	17	2	no	—
40	C₂×C₉×C₁₇	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
41	C₉×D₁₇	—	11	2	no	—
42	C₃×C₅×C₁₇	—	11	1	no	—
43	C₂×AGL(1,𝔽₁₁)	—	17	1	no	Hall
44	C₂×C₃×D₁₇	—	11	1	no	—
45	C₂×C₉×C₁₁	C₅×D₁₇	1	1	yes	characteristic, complemented
46	C₉×D₁₁	—	17	2	no	—
47	C₁₁×C₁₇	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅×C₉	—	187	1	no	Hall
49	C₂×C₅×C₁₇	—	11	1	no	—
50	C₅×D₁₇	—	11	2	no	—
51	C₃×C₁₁⋊C₅	C₂×C₃×D₁₇	1	1	yes	characteristic
52	C₉×C₁₇	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×D₁₁	—	17	1	no	—
54	C₂×C₁₁⋊C₅	C₉×D₁₇	1	1	yes	characteristic, complemented
55	AGL(1,𝔽₁₁)	—	17	2	no	—
56	C₂×C₃×C₁₇	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
57	C₃×D₁₇	—	11	2	no	—
58	C₉×C₁₁	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₅×C₉	—	11	1	no	—
60	C₂×C₅×C₉	—	187	2	no	—
61	C₅×C₁₇	—	11	1	no	Hall
62	C₂×D₁₇	—	11	1	no	Hall
63	C₂×C₃×C₁₁	C₃×C₅×D₁₇	1	1	yes	characteristic
64	C₃×D₁₁	—	17	2	no	—
65	C₂²×C₃×C₅	—	187	1	no	—
66	C₁₁⋊C₅	C₂×C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
67	C₃×C₁₇	C₂×C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
68	C₅×C₉	—	11	1	no	Hall
69	C₂×D₁₁	—	17	1	no	Hall
70	C₂²×C₉	—	187	1	no	Hall
71	C₂×C₁₇	C₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
72	D₁₇	—	11	2	no	—
73	C₃×C₁₁	C₂×C₃×C₅×D₁₇	1	1	yes	characteristic
74	C₂×C₃×C₅	—	11	1	no	—
75	C₂×C₃×C₅	—	187	2	no	—
76	C₂×C₁₁	C₅×C₉×D₁₇	1	1	yes	characteristic, complemented
77	D₁₁	—	17	2	no	—
78	C₂²×C₅	—	187	1	no	Hall
79	C₂×C₉	—	187	2	no	—
80	C₂×C₉	C₁₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
81	C₁₇	C₂×C₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
82	C₃×C₅	—	11	1	no	—
83	C₂²×C₃	—	187	1	no	—
84	C₁₁	C₂×C₅×C₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	1	no	—
86	C₂×C₅	—	187	2	no	—
87	C₉	C₂×C₁₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	187	2	no	—
89	C₂×C₃	C₃×C₁₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
90	C₅	—	11	1	no	Sylow
91	C₂²	—	187	1	no	Sylow
92	C₃	C₂×C₃×C₁₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
93	C₂	—	187	2	no	—
94	C₂	C₉×C₁₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	C₁₇⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁×C₁₇	C₂²×C₅×C₉
Frattini	C₃	C₂×C₃×C₁₇⋊AGL(1,𝔽₁₁)
Fitting	C₂×C₉×C₁₁×C₁₇	C₂×C₅
socle	C₂×C₃×C₁₁×C₁₇	C₂×C₃×C₅
prime radical	C₂×C₃×C₁₇⋊AGL(1,𝔽₁₁)	C₃
cosocle	C₃×C₁₁×C₁₇	C₂²×C₃×C₅
LCS	G ▷ C₁₁×C₁₇
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₁₇⋊AGL(1,𝔽₁₁)	C₂	direct (N × H)
2. C₂×C₉×C₁₇×C₁₁⋊C₅	C₂	semidirect
4. C₉×C₁₇×C₁₁⋊C₅	C₂²	semidirect
5. C₂×C₉×D₁₈₇	C₅	semidirect
8. C₂×C₁₇⋊AGL(1,𝔽₁₁)	C₉	direct (N × H)
9. C₉×D₁₈₇	C₂×C₅	semidirect
10. C₂×C₉×C₁₁×C₁₇	C₂×C₅	semidirect
15. C₂×C₁₇×C₁₁⋊C₅	C₂×C₉	semidirect
16. C₁₇⋊AGL(1,𝔽₁₁)	C₂×C₉	direct (N × H)
17. C₉×C₁₁×C₁₇	C₂²×C₅	semidirect
23. C₂×C₉×C₁₁⋊C₅	D₁₇	semidirect
25. C₁₇×C₁₁⋊C₅	C₂²×C₉	semidirect
27. C₂×D₁₈₇	C₅×C₉	semidirect
33. C₉×C₁₁⋊C₅	C₂×D₁₇	semidirect
35. C₂×C₁₁×C₁₇	C₂×C₅×C₉	semidirect
36. D₁₈₇	C₂×C₅×C₉	semidirect
40. C₂×C₉×C₁₇	AGL(1,𝔽₁₁)	semidirect
45. C₂×C₉×C₁₁	C₅×D₁₇	semidirect
47. C₁₁×C₁₇	C₂²×C₅×C₉	semidirect
52. C₉×C₁₇	C₂×AGL(1,𝔽₁₁)	semidirect
54. C₂×C₁₁⋊C₅	C₉×D₁₇	semidirect
58. C₉×C₁₁	C₂×C₅×D₁₇	semidirect
66. C₁₁⋊C₅	C₂×C₉×D₁₇	semidirect
71. C₂×C₁₇	C₉×AGL(1,𝔽₁₁)	semidirect
76. C₂×C₁₁	C₅×C₉×D₁₇	semidirect
80. C₂×C₉	C₁₇⋊AGL(1,𝔽₁₁)	direct (N × H)
81. C₁₇	C₂×C₉×AGL(1,𝔽₁₁)	semidirect
84. C₁₁	C₂×C₅×C₉×D₁₇	semidirect
87. C₉	C₂×C₁₇⋊AGL(1,𝔽₁₁)	direct (N × H)
94. C₂	C₉×C₁₇⋊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
C₉×C₁₇⋊AGL(1,𝔽₁₁)	2
C₂×C₉×C₁₇×C₁₁⋊C₅	2
C₂×C₃×C₁₇⋊AGL(1,𝔽₁₁)	3
C₂×C₉×D₁₈₇	5
C₂×C₅×C₉×D₁₇	11
C₂×C₉×AGL(1,𝔽₁₁)	17

Subgroups — C2×C9×C17⋊AGL(1,𝔽11) #46777871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₇⋊AGL(1,𝔽₁₁) #46777871