Subgroups — D₃×C₃⋊AGL(1,𝔽₁₁) #14520439

Order 1980.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊AGL(1,𝔽₁₁))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊AGL(1,𝔽₁₁)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃⋊AGL(1,𝔽₁₁)	—	3	1	no	maximal
5	D₃×AGL(1,𝔽₁₁)	—	3	1	no	maximal
6	C₃²×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₃₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
8	C₂×C₃×C₁₁⋊C₅	—	3	1	no	—
9	C₃⋊AGL(1,𝔽₁₁)	—	3	1	no	—
10	C₃⋊AGL(1,𝔽₁₁)	—	3	1	no	—
11	C₃⋊AGL(1,𝔽₁₁)	—	6	1	no	—
12	C₃⋊AGL(1,𝔽₁₁)	D₃	1	1	yes	characteristic, direct product factor
13	D₃×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented
14	C₃×AGL(1,𝔽₁₁)	—	3	1	no	—
15	C₂×AGL(1,𝔽₁₁)	—	9	1	no	Hall
16	C₃⋊D₃₃	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×D₃₃	C₂×C₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
19	C₅×D₃²	—	11	1	no	maximal, Hall
20	C₃×C₁₁⋊C₅	—	2	1	no	—
21	C₃×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented
22	C₃×C₁₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented
23	C₂×D₃₃	—	3	1	no	—
24	D₃×D₁₁	—	3	1	no	—
25	C₂×C₁₁⋊C₅	—	3	1	no	—
26	AGL(1,𝔽₁₁)	—	3	1	no	—
27	AGL(1,𝔽₁₁)	—	9	1	no	—
28	C₃²×C₁₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
29	C₅×C₃⋊D₃	—	11	1	no	—
30	C₃×C₅×D₃	—	11	1	no	—
31	C₃×C₅×D₃	—	11	1	no	—
32	C₂×C₃×C₁₁	—	3	1	no	—
33	D₃₃	—	3	1	no	—
34	D₃₃	—	3	1	no	—
35	D₃₃	—	6	1	no	—
36	D₃₃	C₅×D₃	1	1	yes	characteristic, complemented
37	C₃×D₁₁	—	3	1	no	—
38	D₃×C₁₁	C₅×D₃	1	1	yes	characteristic, complemented
39	C₂×C₅×D₃	—	33	1	no	—
40	C₂×C₅×D₃	—	33	1	no	—
41	C₁₁⋊C₅	D₃²	1	1	yes	characteristic, complemented, Hall
42	C₃²×C₅	—	11	1	no	Hall
43	C₂×D₁₁	—	9	1	no	Hall
44	D₃²	—	11	1	no	Hall
45	C₃×C₁₁	—	2	1	no	—
46	C₃×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
47	C₃×C₁₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅	—	33	1	no	—
49	C₂×C₃×C₅	—	33	1	no	—
50	C₅×D₃	—	11	1	no	—
51	C₅×D₃	—	11	1	no	—
52	C₅×D₃	—	33	1	no	—
53	C₅×D₃	—	33	1	no	—
54	C₅×D₃	—	66	1	no	—
55	C₂×C₁₁	—	3	1	no	—
56	D₁₁	—	3	1	no	—
57	D₁₁	—	9	1	no	—
58	C₂²×C₅	—	99	1	no	Hall
59	C₃⋊D₃	—	11	1	no	—
60	C₃×D₃	—	11	1	no	—
61	C₃×D₃	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
62	C₃×C₅	—	11	1	no	—
63	C₃×C₅	—	11	1	no	—
64	C₃×C₅	—	22	1	no	—
65	C₂×D₃	—	33	1	no	—
66	C₂×D₃	—	33	1	no	—
67	C₁₁	C₅×D₃²	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₅	—	33	1	no	—
69	C₂×C₅	—	33	1	no	—
70	C₂×C₅	—	99	1	no	—
71	C₃²	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	33	1	no	—
74	D₃	—	11	1	no	—
75	D₃	—	33	1	no	—
76	D₃	—	33	1	no	—
77	D₃	—	66	1	no	—
78	D₃	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
79	C₅	—	11	1	no	Sylow
80	C₂²	—	99	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
83	C₃	C₂×C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	33	1	no	—
86	C₂	—	99	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₁	C₂²×C₅
LCS	G ▷ C₃²×C₁₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊AGL(1,𝔽₁₁))	C₂	semidirect
2. C₃×C₃⋊AGL(1,𝔽₁₁)	C₂	semidirect
3. C₃×D₃×C₁₁⋊C₅	C₂	semidirect
6. C₃²×C₁₁⋊C₅	C₂²	semidirect
7. D₃×D₃₃	C₅	semidirect
12. C₃⋊AGL(1,𝔽₁₁)	D₃	direct (N × H)
13. D₃×C₁₁⋊C₅	D₃	semidirect
16. C₃⋊D₃₃	C₂×C₅	semidirect
17. C₃×D₃₃	C₂×C₅	semidirect
18. C₃×D₃×C₁₁	C₂×C₅	semidirect
21. C₃×C₁₁⋊C₅	C₂×D₃	semidirect
22. C₃×C₁₁⋊C₅	C₂×D₃	semidirect
28. C₃²×C₁₁	C₂²×C₅	semidirect
36. D₃₃	C₅×D₃	semidirect
38. D₃×C₁₁	C₅×D₃	semidirect
41. C₁₁⋊C₅	D₃²	semidirect
46. C₃×C₁₁	C₂×C₅×D₃	semidirect
47. C₃×C₁₁	C₂×C₅×D₃	semidirect
61. C₃×D₃	AGL(1,𝔽₁₁)	semidirect
67. C₁₁	C₅×D₃²	semidirect
71. C₃²	C₂×AGL(1,𝔽₁₁)	semidirect
78. D₃	C₃⋊AGL(1,𝔽₁₁)	direct (N × H)
82. C₃	D₃×AGL(1,𝔽₁₁)	semidirect
83. C₃	C₂×C₃⋊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⋊(C₃⋊AGL(1,𝔽₁₁))	2
C₃×C₃⋊AGL(1,𝔽₁₁)	2
C₃×D₃×C₁₁⋊C₅	2
C₂×C₃⋊AGL(1,𝔽₁₁)	3
D₃×AGL(1,𝔽₁₁)	3
D₃×D₃₃	5
C₅×D₃²	11

Subgroups — D3×C3⋊AGL(1,𝔽11) #14520439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₃⋊AGL(1,𝔽₁₁) #14520439