Subgroups — C₂×C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))) #38788123

Order 25740.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁)))	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	—	3	4	no	maximal
4	C₃²×C₁₃×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₄₂₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	—	3	8	no	—
7	C₂×C₃×C₁₃×C₁₁⋊C₅	D₃	1	4	yes	complemented
8	C₂×C₁₃⋊AGL(1,𝔽₁₁)	—	9	1	no	Hall
9	C₃⋊D₄₂₉	C₂×C₅	1	2	yes	complemented
10	C₂×C₃²×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₃⋊D₃₉	—	11	1	no	maximal, Hall
12	C₃×C₁₃×C₁₁⋊C₅	C₂×D₃	1	4	yes	complemented
13	C₂×C₃⋊(C₃⋊AGL(1,𝔽₁₁))	—	13	1	no	maximal, Hall
14	C₂×D₄₂₉	—	3	4	no	—
15	C₂×C₁₃×C₁₁⋊C₅	C₃⋊D₃	1	1	yes	characteristic, complemented
16	C₁₃⋊AGL(1,𝔽₁₁)	—	9	2	no	—
17	C₃²×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₃	—	11	1	no	—
19	C₅×C₃⋊D₃₉	—	11	2	no	—
20	C₂×C₃²×C₁₁⋊C₅	D₁₃	1	1	yes	characteristic, complemented
21	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	—	13	2	no	—
22	C₂×C₃×C₁₁×C₁₃	C₅×D₃	1	4	yes	complemented
23	D₄₂₉	—	3	8	no	—
24	C₂×C₅×D₃₉	—	33	4	no	—
25	C₁₃×C₁₁⋊C₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃⋊AGL(1,𝔽₁₁)	—	39	4	no	—
27	C₃²×C₅×C₁₃	—	11	1	no	Hall
28	C₂×D₁₄₃	—	9	1	no	Hall
29	C₃²×C₁₁⋊C₅	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃⋊D₃₉	—	11	1	no	Hall
31	C₃×C₁₁×C₁₃	C₂×C₅×D₃	1	4	yes	complemented
32	C₂×C₃⋊D₃₃	—	13	1	no	Hall
33	C₂×C₃×C₅×C₁₃	—	11	4	no	—
34	C₅×D₃₉	—	33	8	no	—
35	C₂×C₃×C₁₁⋊C₅	D₃₉	1	4	yes	complemented
36	C₃⋊AGL(1,𝔽₁₁)	—	39	8	no	—
37	C₂×C₁₁×C₁₃	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
38	D₁₄₃	—	9	2	no	—
39	C₂×C₅×D₁₃	—	99	1	no	Hall
40	C₂×C₃²×C₁₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
41	C₃⋊D₃₉	—	11	2	no	—
42	C₂×AGL(1,𝔽₁₁)	—	117	1	no	Hall
43	C₂×C₃²×C₁₁	C₅×D₁₃	1	1	yes	characteristic, complemented
44	C₃⋊D₃₃	—	13	2	no	—
45	C₃×C₅×C₁₃	—	11	4	no	—
46	C₂×C₅×C₃⋊D₃	—	143	1	no	Hall
47	C₃×C₁₁⋊C₅	C₂×D₃₉	1	4	yes	complemented
48	C₂×D₃₉	—	33	4	no	—
49	C₁₁×C₁₃	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
50	C₂×D₃₃	—	39	4	no	—
51	C₂×C₅×C₁₃	—	11	1	no	—
52	C₅×D₁₃	—	99	2	no	—
53	C₃²×C₁₃	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Hall
54	C₂×C₁₁⋊C₅	C₃⋊D₃₉	1	1	yes	characteristic, complemented
55	AGL(1,𝔽₁₁)	—	117	2	no	—
56	C₃²×C₁₁	C₂×C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃²×C₅	—	11	1	no	—
58	C₅×C₃⋊D₃	—	143	2	no	—
59	C₂×C₃×C₁₃	C₃⋊AGL(1,𝔽₁₁)	1	4	yes	complemented
60	D₃₉	—	33	8	no	—
61	C₂×C₃×C₁₁	C₅×D₃₉	1	4	yes	complemented
62	D₃₃	—	39	8	no	—
63	C₅×C₁₃	—	11	1	no	Hall
64	C₂×C₅×D₃	—	429	4	no	—
65	C₁₁⋊C₅	C₂×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Hall
66	C₂×D₁₃	—	99	1	no	Hall
67	C₃²×C₅	—	11	1	no	Hall
68	C₂×D₁₁	—	117	1	no	Hall
69	C₃×C₁₃	C₂×C₃⋊AGL(1,𝔽₁₁)	1	4	yes	complemented
70	C₂×C₃⋊D₃	—	143	1	no	Hall
71	C₃×C₁₁	C₂×C₅×D₃₉	1	4	yes	complemented
72	C₂×C₃×C₅	—	11	4	no	—
73	C₅×D₃	—	429	8	no	—
74	C₂×C₁₃	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, complemented
75	D₁₃	—	99	2	no	—
76	C₂×C₁₁	C₅×C₃⋊D₃₉	1	1	yes	characteristic, complemented
77	D₁₁	—	117	2	no	—
78	C₂²×C₅	—	1287	1	no	Hall
79	C₂×C₃²	C₁₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
80	C₃⋊D₃	—	143	2	no	—
81	C₃×C₅	—	11	4	no	—
82	C₁₃	C₂×C₃⋊(C₃⋊AGL(1,𝔽₁₁))	1	1	yes	characteristic, complemented, Sylow
83	C₂×D₃	—	429	4	no	—
84	C₁₁	C₂×C₅×C₃⋊D₃₉	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	1287	2	no	—
86	C₂×C₅	—	11	1	no	—
87	C₃²	C₂×C₁₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	1	4	yes	complemented
89	D₃	—	429	8	no	—
90	C₅	—	11	1	no	Sylow
91	C₂²	—	1287	1	no	Sylow
92	C₃	C₂×C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	1	4	yes	complemented
93	C₂	—	1287	2	no	—
94	C₂	C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁)))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁)))
commutator, cosocle, hypocenter	C₃²×C₁₁×C₁₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₁₃	C₂×C₅
LCS	G ▷ C₃²×C₁₁×C₁₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₁₃×C₁₁⋊C₅	C₂	semidirect
2. C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁)))	C₂	direct (N × H)
4. C₃²×C₁₃×C₁₁⋊C₅	C₂²	semidirect
5. C₂×C₃⋊D₄₂₉	C₅	semidirect
7. C₂×C₃×C₁₃×C₁₁⋊C₅	D₃	semidirect
9. C₃⋊D₄₂₉	C₂×C₅	semidirect
10. C₂×C₃²×C₁₁×C₁₃	C₂×C₅	semidirect
12. C₃×C₁₃×C₁₁⋊C₅	C₂×D₃	semidirect
15. C₂×C₁₃×C₁₁⋊C₅	C₃⋊D₃	semidirect
17. C₃²×C₁₁×C₁₃	C₂²×C₅	semidirect
20. C₂×C₃²×C₁₁⋊C₅	D₁₃	semidirect
22. C₂×C₃×C₁₁×C₁₃	C₅×D₃	semidirect
25. C₁₃×C₁₁⋊C₅	C₂×C₃⋊D₃	semidirect
29. C₃²×C₁₁⋊C₅	C₂×D₁₃	semidirect
31. C₃×C₁₁×C₁₃	C₂×C₅×D₃	semidirect
35. C₂×C₃×C₁₁⋊C₅	D₃₉	semidirect
37. C₂×C₁₁×C₁₃	C₅×C₃⋊D₃	semidirect
40. C₂×C₃²×C₁₃	AGL(1,𝔽₁₁)	semidirect
43. C₂×C₃²×C₁₁	C₅×D₁₃	semidirect
47. C₃×C₁₁⋊C₅	C₂×D₃₉	semidirect
49. C₁₁×C₁₃	C₂×C₅×C₃⋊D₃	semidirect
53. C₃²×C₁₃	C₂×AGL(1,𝔽₁₁)	semidirect
54. C₂×C₁₁⋊C₅	C₃⋊D₃₉	semidirect
56. C₃²×C₁₁	C₂×C₅×D₁₃	semidirect
59. C₂×C₃×C₁₃	C₃⋊AGL(1,𝔽₁₁)	semidirect
61. C₂×C₃×C₁₁	C₅×D₃₉	semidirect
65. C₁₁⋊C₅	C₂×C₃⋊D₃₉	semidirect
69. C₃×C₁₃	C₂×C₃⋊AGL(1,𝔽₁₁)	semidirect
71. C₃×C₁₁	C₂×C₅×D₃₉	semidirect
74. C₂×C₁₃	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	semidirect
76. C₂×C₁₁	C₅×C₃⋊D₃₉	semidirect
79. C₂×C₃²	C₁₃⋊AGL(1,𝔽₁₁)	semidirect
82. C₁₃	C₂×C₃⋊(C₃⋊AGL(1,𝔽₁₁))	semidirect
84. C₁₁	C₂×C₅×C₃⋊D₃₉	semidirect
87. C₃²	C₂×C₁₃⋊AGL(1,𝔽₁₁)	semidirect
88. C₂×C₃	C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	semidirect
92. C₃	C₂×C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	semidirect
94. C₂	C₃⋊(C₃⋊(C₁₃⋊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
C₂×C₃²×C₁₃×C₁₁⋊C₅	2
C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁)))	2
C₂×C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))	3
C₂×C₃⋊D₄₂₉	5
C₂×C₅×C₃⋊D₃₉	11
C₂×C₃⋊(C₃⋊AGL(1,𝔽₁₁))	13

Subgroups — C2×C3⋊(C3⋊(C13⋊AGL(1,𝔽11))) #38788123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(C₃⋊(C₁₃⋊AGL(1,𝔽₁₁))) #38788123