Subgroups — C₂×AGL(1,𝔽₁₁)×#4294 #49178331

Order 37620.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,𝔽₁₁)×#4294	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁⋊C₅×#4294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₉×AGL(1,𝔽₁₁)	C₃	1	1	yes	maximal, characteristic
4	C₁₁⋊C₅×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁×#4294	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃×C₁₉×AGL(1,𝔽₁₁)	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₁₉×C₁₁⋊C₅	C₂×C₃	1	1	yes	characteristic
8	C₂×C₁₉×AGL(1,𝔽₁₁)	C₉	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₁×#4294	C₂×C₅	1	1	yes	characteristic, complemented
10	D₁₁×#4294	C₂×C₅	1	2	yes	complemented
11	C₂²×C₅×#4294	—	11	1	no	maximal, Hall
12	C₃×C₁₉×C₁₁⋊C₅	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×C₁₉×D₁₁	C₃×C₅	1	1	yes	characteristic
14	C₁₉×AGL(1,𝔽₁₁)	C₂×C₉	1	2	yes	complemented
15	C₂×C₁₉×C₁₁⋊C₅	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×C₉×AGL(1,𝔽₁₁)	—	19	1	no	maximal, Hall
17	C₁₁×#4294	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×#4294	—	11	2	no	—
19	C₂×C₅×#4294	—	11	1	no	—
20	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₁₉×D₁₁	C₂×C₃×C₅	1	2	yes	—
22	C₂²×C₃×C₅×C₁₉	—	11	1	no	—
23	C₁₉×C₁₁⋊C₅	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₉×C₁₁⋊C₅	—	19	1	no	—
25	C₉×AGL(1,𝔽₁₁)	—	19	2	no	—
26	C₅×#4294	—	11	1	no	Hall
27	C₂×C₁₉×D₁₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂²×#4294	—	11	1	no	Hall
29	C₂×C₃×AGL(1,𝔽₁₁)	C₁₉⋊C₃	1	1	yes	characteristic
30	C₃×C₁₁×C₁₉	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₉	—	11	2	no	—
32	C₂×C₃×C₅×C₁₉	—	11	1	no	—
33	C₉×C₁₁⋊C₅	—	19	1	no	Hall
34	C₂×C₁₁×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented
35	C₁₉×D₁₁	C₂×C₅×C₉	1	2	yes	complemented
36	C₂×C₉×D₁₁	—	19	1	no	Hall
37	C₂²×C₅×C₁₉	—	11	1	no	Hall
38	C₂×#4294	—	11	2	no	—
39	C₂×#4294	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₁₁⋊C₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic
41	C₃×AGL(1,𝔽₁₁)	C₂×C₁₉⋊C₃	1	2	yes	—
42	C₃×C₅×C₁₉	—	11	1	no	—
43	C₂²×C₃×C₁₉	—	11	1	no	—
44	C₂×AGL(1,𝔽₁₁)	#4294	1	1	yes	characteristic, direct product factor, Hall
45	C₁₁×C₁₉	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
46	C₂×C₉×C₁₁	—	19	1	no	—
47	C₉×D₁₁	—	19	2	no	—
48	C₂×C₅×C₁₉	—	11	2	no	—
49	C₂×C₅×C₁₉	—	11	1	no	—
50	C₂²×C₅×C₉	—	209	1	no	Hall
51	#4294	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor, Hall
52	C₃×C₁₁⋊C₅	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
53	C₂×C₃×D₁₁	C₅×C₁₉⋊C₃	1	1	yes	characteristic
54	C₂×C₃×C₁₉	—	11	2	no	—
55	C₂×C₃×C₁₉	C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
56	C₂×C₁₁⋊C₅	C₂×#4294	1	1	yes	characteristic, complemented
57	AGL(1,𝔽₁₁)	C₂×#4294	1	2	yes	direct product factor
58	C₉×C₁₁	—	19	1	no	Hall
59	C₅×C₁₉	—	11	1	no	Hall
60	C₂×C₅×C₉	—	209	1	no	—
61	C₂×C₅×C₉	—	209	2	no	—
62	C₂²×C₁₉	—	11	1	no	Hall
63	C₂×C₃×C₁₁	C₂×C₅×C₁₉⋊C₃	1	1	yes	characteristic
64	C₃×D₁₁	C₂×C₅×C₁₉⋊C₃	1	2	yes	—
65	C₂²×C₃×C₅	—	11	1	no	—
66	C₃×C₁₉	C₂×C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
67	C₁₁⋊C₅	C₂²×#4294	1	1	yes	characteristic, complemented, Hall
68	C₅×C₉	—	209	1	no	Hall
69	C₂×D₁₁	C₅×#4294	1	1	yes	characteristic, complemented, Hall
70	C₂×C₁₉	—	11	2	no	—
71	C₂×C₁₉	C₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
72	C₂²×C₉	—	209	1	no	Hall
73	C₃×C₁₁	C₂²×C₅×C₁₉⋊C₃	1	1	yes	characteristic
74	C₂×C₃×C₅	—	11	2	no	—
75	C₂×C₃×C₅	—	11	1	no	—
76	C₂×C₁₁	C₂×C₅×#4294	1	1	yes	characteristic, complemented
77	D₁₁	C₂×C₅×#4294	1	2	yes	complemented
78	C₂²×C₅	—	11	1	no	Hall
79	C₁₉	C₂×C₉×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
80	C₂×C₉	—	19	1	no	—
81	C₂×C₉	—	209	2	no	—
82	C₃×C₅	—	11	1	no	—
83	C₂²×C₃	—	11	1	no	—
84	C₁₁	C₂²×C₅×#4294	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	2	no	—
86	C₂×C₅	—	11	1	no	—
87	C₉	—	19	1	no	Sylow
88	C₂×C₃	—	11	2	no	—
89	C₂×C₃	C₁₉⋊C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
90	C₅	—	11	1	no	Sylow
91	C₂²	—	11	1	no	Sylow
92	C₃	C₂×C₁₉⋊C₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic
93	C₂	—	11	2	no	—
94	C₂	AGL(1,𝔽₁₁)×#4294	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₉⋊C₃×AGL(1,𝔽₁₁)
commutator, hypocenter	C₁₁×C₁₉	C₂²×C₅×C₉
Frattini	C₃	C₂×C₁₉⋊C₃×AGL(1,𝔽₁₁)
Fitting, socle	C₂×C₃×C₁₁×C₁₉	C₂×C₃×C₅
prime radical	C₂×C₃×C₁₉×AGL(1,𝔽₁₁)	C₃
cosocle	C₃×C₁₁×C₁₉	C₂²×C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. AGL(1,𝔽₁₁)×#4294	C₂	direct (N × H)
2. C₂×C₁₁⋊C₅×#4294	C₂	semidirect
4. C₁₁⋊C₅×#4294	C₂²	semidirect
5. C₂×D₁₁×#4294	C₅	semidirect
8. C₂×C₁₉×AGL(1,𝔽₁₁)	C₉	semidirect
9. C₂×C₁₁×#4294	C₂×C₅	semidirect
10. D₁₁×#4294	C₂×C₅	semidirect
14. C₁₉×AGL(1,𝔽₁₁)	C₂×C₉	semidirect
15. C₂×C₁₉×C₁₁⋊C₅	C₂×C₉	semidirect
17. C₁₁×#4294	C₂²×C₅	semidirect
23. C₁₉×C₁₁⋊C₅	C₂²×C₉	semidirect
27. C₂×C₁₉×D₁₁	C₅×C₉	semidirect
34. C₂×C₁₁×C₁₉	C₂×C₅×C₉	semidirect
35. C₁₉×D₁₁	C₂×C₅×C₉	semidirect
39. C₂×#4294	AGL(1,𝔽₁₁)	direct (N × H)
44. C₂×AGL(1,𝔽₁₁)	#4294	direct (N × H)
45. C₁₁×C₁₉	C₂²×C₅×C₉	semidirect
51. #4294	C₂×AGL(1,𝔽₁₁)	direct (N × H)
56. C₂×C₁₁⋊C₅	C₂×#4294	semidirect
57. AGL(1,𝔽₁₁)	C₂×#4294	direct (N × H)
67. C₁₁⋊C₅	C₂²×#4294	semidirect
69. C₂×D₁₁	C₅×#4294	semidirect
71. C₂×C₁₉	C₉×AGL(1,𝔽₁₁)	semidirect
76. C₂×C₁₁	C₂×C₅×#4294	semidirect
77. D₁₁	C₂×C₅×#4294	semidirect
79. C₁₉	C₂×C₉×AGL(1,𝔽₁₁)	semidirect
84. C₁₁	C₂²×C₅×#4294	semidirect
94. C₂	AGL(1,𝔽₁₁)×#4294	direct (N × H)

Maximal subgroups

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

subgroup	index
AGL(1,𝔽₁₁)×#4294	2
C₂×C₁₁⋊C₅×#4294	2
C₂×C₃×C₁₉×AGL(1,𝔽₁₁)	3
C₂×D₁₁×#4294	5
C₂²×C₅×#4294	11
C₂×C₉×AGL(1,𝔽₁₁)	19

Subgroups — C2×AGL(1,𝔽11)×#4294 #49178331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×AGL(1,𝔽₁₁)×#4294 #49178331