Subgroups — C₂×C₃⋊(C₄₉⋊AGL(1,𝔽₁₁)) #44568366

Order 32340.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₄₉⋊AGL(1,𝔽₁₁))	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₄₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₉⋊AGL(1,𝔽₁₁)	—	3	1	no	maximal, Hall
4	C₃×C₄₉×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₆₁₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₄₉×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented
7	C₄₉⋊AGL(1,𝔽₁₁)	—	3	2	no	—
8	C₂×C₃⋊(C₇⋊AGL(1,𝔽₁₁))	—	7	1	no	maximal
9	D₁₆₁₇	C₂×C₅	1	2	yes	complemented
10	C₂×C₃×C₁₁×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×D₁₄₇	—	11	1	no	maximal, Hall
12	C₄₉×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃⋊(C₇⋊AGL(1,𝔽₁₁))	—	7	2	no	—
14	C₂×C₃×C₇×C₁₁⋊C₅	D₇	1	1	yes	characteristic
15	C₂×D₅₃₉	—	3	1	no	Hall
16	C₃×C₁₁×C₄₉	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₇⋊AGL(1,𝔽₁₁)	—	21	1	no	—
18	C₂×C₃×C₅×C₄₉	—	11	1	no	—
19	C₅×D₁₄₇	—	11	2	no	—
20	C₃×C₇×C₁₁⋊C₅	C₂×D₇	1	1	yes	characteristic
21	C₂×C₁₁×C₄₉	C₅×D₃	1	1	yes	characteristic, complemented
22	D₅₃₉	—	3	2	no	—
23	C₂×C₅×D₄₉	—	33	1	no	Hall
24	C₂×D₂₃₁	—	7	1	no	—
25	C₂×C₇×C₁₁⋊C₅	D₂₁	1	1	yes	characteristic
26	C₇⋊AGL(1,𝔽₁₁)	—	21	2	no	—
27	C₃×C₅×C₄₉	—	11	1	no	Hall
28	C₂×C₃⋊AGL(1,𝔽₁₁)	—	49	1	no	Hall
29	C₂×D₁₄₇	—	11	1	no	Hall
30	C₁₁×C₄₉	C₂×C₅×D₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅×C₄₉	—	11	1	no	—
32	C₅×D₄₉	—	33	2	no	—
33	C₂×C₃×C₇×C₁₁	C₅×D₇	1	1	yes	characteristic
34	D₂₃₁	—	7	2	no	—
35	C₂×C₅×D₂₁	—	77	1	no	—
36	C₇×C₁₁⋊C₅	C₂×D₂₁	1	1	yes	characteristic
37	C₂×C₃×C₁₁⋊C₅	D₄₉	1	1	yes	characteristic, complemented
38	C₃⋊AGL(1,𝔽₁₁)	—	49	2	no	—
39	C₂×D₇₇	—	21	1	no	—
40	C₂×C₃×C₄₉	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
41	D₁₄₇	—	11	2	no	—
42	C₅×C₄₉	—	11	1	no	Hall
43	C₃×C₇×C₁₁	C₂×C₅×D₇	1	1	yes	characteristic
44	C₂×AGL(1,𝔽₁₁)	—	147	1	no	Hall
45	C₂×C₃×C₅×C₇	—	11	1	no	—
46	C₅×D₂₁	—	77	2	no	—
47	C₂×D₄₉	—	33	1	no	Hall
48	C₃×C₁₁⋊C₅	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
49	C₂×C₇×C₁₁	C₅×D₂₁	1	1	yes	characteristic
50	D₇₇	—	21	2	no	—
51	C₃×C₄₉	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
52	C₂×C₅×D₇	—	231	1	no	—
53	C₂×D₃₃	—	49	1	no	Hall
54	C₂×C₁₁⋊C₅	D₁₄₇	1	1	yes	characteristic, complemented
55	AGL(1,𝔽₁₁)	—	147	2	no	—
56	C₃×C₅×C₇	—	11	1	no	—
57	C₂×C₄₉	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
58	D₄₉	—	33	2	no	—
59	C₂×D₂₁	—	77	1	no	—
60	C₇×C₁₁	C₂×C₅×D₂₁	1	1	yes	characteristic
61	C₂×C₅×C₇	—	11	1	no	—
62	C₅×D₇	—	231	2	no	—
63	C₂×C₃×C₁₁	C₅×D₄₉	1	1	yes	characteristic, complemented
64	D₃₃	—	49	2	no	—
65	C₂×C₅×D₃	—	539	1	no	Hall
66	C₁₁⋊C₅	C₂×D₁₄₇	1	1	yes	characteristic, complemented, Hall
67	C₄₉	C₂×C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
68	C₂×D₁₁	—	147	1	no	Hall
69	C₂×C₃×C₇	C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
70	D₂₁	—	77	2	no	—
71	C₅×C₇	—	11	1	no	—
72	C₃×C₁₁	C₂×C₅×D₄₉	1	1	yes	characteristic, complemented, Hall
73	C₂×C₃×C₅	—	11	1	no	—
74	C₅×D₃	—	539	2	no	—
75	C₂×D₇	—	231	1	no	—
76	C₂×C₁₁	C₅×D₁₄₇	1	1	yes	characteristic, complemented
77	D₁₁	—	147	2	no	—
78	C₃×C₇	C₂×C₇⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic
79	C₂²×C₅	—	1617	1	no	Hall
80	C₃×C₅	—	11	1	no	Hall
81	C₂×C₇	C₃⋊(C₇⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic
82	D₇	—	231	2	no	—
83	C₂×D₃	—	539	1	no	Hall
84	C₁₁	C₂×C₅×D₁₄₇	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	1	no	—
86	C₂×C₅	—	1617	2	no	—
87	C₇	C₂×C₃⋊(C₇⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic
88	C₂×C₃	C₄₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
89	D₃	—	539	2	no	—
90	C₅	—	11	1	no	Sylow
91	C₂²	—	1617	1	no	Sylow
92	C₃	C₂×C₄₉⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
93	C₂	—	1617	2	no	—
94	C₂	C₃⋊(C₄₉⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₄₉⋊AGL(1,𝔽₁₁))
commutator, cosocle, hypocenter	C₃×C₁₁×C₄₉	C₂²×C₅
Frattini	C₇	C₂×C₃⋊(C₇⋊AGL(1,𝔽₁₁))
Fitting	C₂×C₃×C₁₁×C₄₉	C₂×C₅
socle	C₂×C₃×C₇×C₁₁	C₅×D₇
LCS	G ▷ C₃×C₁₁×C₄₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₄₉⋊AGL(1,𝔽₁₁))	C₂	direct (N × H)
2. C₂×C₃×C₄₉×C₁₁⋊C₅	C₂	semidirect
4. C₃×C₄₉×C₁₁⋊C₅	C₂²	semidirect
5. C₂×D₁₆₁₇	C₅	semidirect
6. C₂×C₄₉×C₁₁⋊C₅	D₃	semidirect
9. D₁₆₁₇	C₂×C₅	semidirect
10. C₂×C₃×C₁₁×C₄₉	C₂×C₅	semidirect
12. C₄₉×C₁₁⋊C₅	C₂×D₃	semidirect
16. C₃×C₁₁×C₄₉	C₂²×C₅	semidirect
21. C₂×C₁₁×C₄₉	C₅×D₃	semidirect
30. C₁₁×C₄₉	C₂×C₅×D₃	semidirect
37. C₂×C₃×C₁₁⋊C₅	D₄₉	semidirect
40. C₂×C₃×C₄₉	AGL(1,𝔽₁₁)	semidirect
48. C₃×C₁₁⋊C₅	C₂×D₄₉	semidirect
51. C₃×C₄₉	C₂×AGL(1,𝔽₁₁)	semidirect
54. C₂×C₁₁⋊C₅	D₁₄₇	semidirect
57. C₂×C₄₉	C₃⋊AGL(1,𝔽₁₁)	semidirect
63. C₂×C₃×C₁₁	C₅×D₄₉	semidirect
66. C₁₁⋊C₅	C₂×D₁₄₇	semidirect
67. C₄₉	C₂×C₃⋊AGL(1,𝔽₁₁)	semidirect
72. C₃×C₁₁	C₂×C₅×D₄₉	semidirect
76. C₂×C₁₁	C₅×D₁₄₇	semidirect
84. C₁₁	C₂×C₅×D₁₄₇	semidirect
88. C₂×C₃	C₄₉⋊AGL(1,𝔽₁₁)	semidirect
92. C₃	C₂×C₄₉⋊AGL(1,𝔽₁₁)	semidirect
94. C₂	C₃⋊(C₄₉⋊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
C₃⋊(C₄₉⋊AGL(1,𝔽₁₁))	2
C₂×C₃×C₄₉×C₁₁⋊C₅	2
C₂×C₄₉⋊AGL(1,𝔽₁₁)	3
C₂×D₁₆₁₇	5
C₂×C₃⋊(C₇⋊AGL(1,𝔽₁₁))	7
C₂×C₅×D₁₄₇	11

Subgroups — C2×C3⋊(C49⋊AGL(1,𝔽11)) #44568366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₄₉⋊AGL(1,𝔽₁₁)) #44568366