Subgroups — C₂³×C₄⋊AGL(1,𝔽₁₁) #72248869

Order 3520.

2724 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, complemented
2	C₂³×C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊AGL(1,𝔽₁₁)	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
5	C₂³×AGL(1,𝔽₁₁)	—	2	16	no	—
6	C₂³×AGL(1,𝔽₁₁)	C₂²	1	28	yes	complemented
7	C₂²×C₄×C₁₁⋊C₅	C₂²	1	14	yes	complemented
8	C₂×C₄⋊AGL(1,𝔽₁₁)	C₂²	1	112	yes	direct product factor
9	C₂³×D₄₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
10	C₂³×C₁₁⋊C₅	D₄	1	8	yes	complemented
11	C₂³×C₁₁⋊C₅	C₂³	1	7	yes	—
12	C₂²×AGL(1,𝔽₁₁)	—	2	112	no	—
13	C₂²×AGL(1,𝔽₁₁)	C₂³	1	56	yes	complemented
14	C₂×C₄×C₁₁⋊C₅	C₂³	1	28	yes	complemented
15	C₄⋊AGL(1,𝔽₁₁)	C₂³	1	64	yes	direct product factor
16	C₂⁴×D₁₁	C₂×C₅	1	2	yes	complemented
17	C₂³×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
18	C₂²×D₄₄	C₂×C₅	1	28	yes	complemented
19	C₂³×C₅×D₄	—	11	1	no	maximal, Hall
20	C₂²×C₁₁⋊C₅	C₂×D₄	1	28	yes	complemented
21	C₂²×C₁₁⋊C₅	C₂⁴	1	7	yes	—
22	C₂×AGL(1,𝔽₁₁)	—	2	112	no	—
23	C₂×AGL(1,𝔽₁₁)	C₂⁴	1	16	yes	complemented
24	C₄×C₁₁⋊C₅	C₂⁴	1	8	yes	complemented
25	C₂⁴×C₁₁	C₂²×C₅	1	1	yes	characteristic
26	C₂³×D₁₁	—	2	16	no	—
27	C₂³×D₁₁	C₂²×C₅	1	28	yes	complemented
28	C₂²×C₄×C₁₁	C₂²×C₅	1	14	yes	complemented
29	C₂×D₄₄	C₂²×C₅	1	112	yes	complemented
30	C₂⁵×C₅	—	11	2	no	—
31	C₂²×C₅×D₄	—	11	28	no	—
32	C₂³×C₄×C₅	—	11	1	no	—
33	C₂×C₁₁⋊C₅	C₂²×D₄	1	14	yes	complemented
34	C₂×C₁₁⋊C₅	C₂⁵	1	1	yes	characteristic
35	AGL(1,𝔽₁₁)	—	2	16	no	—
36	C₂³×C₁₁	C₅×D₄	1	8	yes	complemented
37	C₂³×C₁₁	C₂³×C₅	1	7	yes	—
38	C₂²×D₁₁	—	2	112	no	—
39	C₂²×D₁₁	C₂³×C₅	1	56	yes	complemented
40	C₂×C₄×C₁₁	C₂³×C₅	1	28	yes	complemented
41	D₄₄	C₂³×C₅	1	64	yes	complemented
42	C₂⁴×C₅	—	11	28	no	—
43	C₂⁴×C₅	—	11	1	no	—
44	C₂⁴×C₅	—	22	16	no	—
45	C₂×C₅×D₄	—	11	112	no	—
46	C₂²×C₄×C₅	—	11	14	no	—
47	C₂³×D₄	—	11	1	no	Sylow
48	C₁₁⋊C₅	C₂³×D₄	1	1	yes	characteristic, complemented, Hall
49	C₂²×C₁₁	C₂×C₅×D₄	1	28	yes	complemented
50	C₂²×C₁₁	C₂⁴×C₅	1	7	yes	—
51	C₂×D₁₁	—	2	112	no	—
52	C₂×D₁₁	C₂⁴×C₅	1	16	yes	complemented
53	C₄×C₁₁	C₂⁴×C₅	1	8	yes	complemented
54	C₂³×C₅	—	11	56	no	—
55	C₂³×C₅	—	11	8	no	—
56	C₂³×C₅	—	11	7	no	—
57	C₂³×C₅	—	22	112	no	—
58	C₅×D₄	—	11	64	no	—
59	C₂×C₄×C₅	—	11	28	no	—
60	C₂⁵	—	11	2	no	—
61	C₂²×D₄	—	11	28	no	—
62	C₂³×C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
63	C₂×C₁₁	C₂²×C₅×D₄	1	14	yes	complemented
64	C₂×C₁₁	C₂⁵×C₅	1	1	yes	characteristic
65	D₁₁	—	2	16	no	—
66	C₂²×C₅	—	11	16	no	—
67	C₂²×C₅	—	11	28	no	—
68	C₂²×C₅	—	11	7	no	—
69	C₂²×C₅	—	22	112	no	—
70	C₄×C₅	—	11	8	no	—
71	C₂⁴	—	11	28	no	—
72	C₂⁴	—	22	16	no	—
73	C₂⁴	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic
74	C₂×D₄	—	11	112	no	—
75	C₂²×C₄	C₂×AGL(1,𝔽₁₁)	1	14	yes	complemented
76	C₁₁	C₂³×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
77	C₂×C₅	—	11	14	no	—
78	C₂×C₅	—	11	1	no	—
79	C₂×C₅	—	22	16	no	—
80	C₂³	—	11	56	no	—
81	C₂³	—	22	112	no	—
82	C₂³	C₄⋊AGL(1,𝔽₁₁)	1	8	yes	direct product factor
83	C₂³	C₂²×AGL(1,𝔽₁₁)	1	7	yes	—
84	D₄	—	11	64	no	—
85	C₂×C₄	C₂²×AGL(1,𝔽₁₁)	1	28	yes	complemented
86	C₅	—	11	1	no	Sylow
87	C₂²	—	11	16	no	—
88	C₂²	—	22	112	no	—
89	C₂²	C₂×C₄⋊AGL(1,𝔽₁₁)	1	28	yes	direct product factor
90	C₂²	C₂³×AGL(1,𝔽₁₁)	1	7	yes	—
91	C₄	C₂³×AGL(1,𝔽₁₁)	1	8	yes	complemented
92	C₂	—	22	16	no	—
93	C₂	C₂²×C₄⋊AGL(1,𝔽₁₁)	1	14	yes	direct product factor
94	C₂	C₂⁴×AGL(1,𝔽₁₁)	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×AGL(1,𝔽₁₁)
commutator, cosocle	C₂×C₁₁	C₂⁵×C₅
Frattini	C₂	C₂⁴×AGL(1,𝔽₁₁)
Fitting	C₂³×C₄×C₁₁	C₂×C₅
socle	C₂⁴×C₁₁	C₂²×C₅
hypercenter	C₂³×C₄	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₂³×C₅×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×AGL(1,𝔽₁₁)	C₂	semidirect
2. C₂³×C₄×C₁₁⋊C₅	C₂	semidirect
3. C₂²×C₄⋊AGL(1,𝔽₁₁)	C₂	direct (N × H)
6. C₂³×AGL(1,𝔽₁₁)	C₂²	semidirect
7. C₂²×C₄×C₁₁⋊C₅	C₂²	semidirect
8. C₂×C₄⋊AGL(1,𝔽₁₁)	C₂²	direct (N × H)
9. C₂³×D₄₄	C₅	semidirect
10. C₂³×C₁₁⋊C₅	D₄	semidirect
13. C₂²×AGL(1,𝔽₁₁)	C₂³	semidirect
14. C₂×C₄×C₁₁⋊C₅	C₂³	semidirect
15. C₄⋊AGL(1,𝔽₁₁)	C₂³	direct (N × H)
16. C₂⁴×D₁₁	C₂×C₅	semidirect
17. C₂³×C₄×C₁₁	C₂×C₅	semidirect
18. C₂²×D₄₄	C₂×C₅	semidirect
20. C₂²×C₁₁⋊C₅	C₂×D₄	semidirect
23. C₂×AGL(1,𝔽₁₁)	C₂⁴	semidirect
24. C₄×C₁₁⋊C₅	C₂⁴	semidirect
27. C₂³×D₁₁	C₂²×C₅	semidirect
28. C₂²×C₄×C₁₁	C₂²×C₅	semidirect
29. C₂×D₄₄	C₂²×C₅	semidirect
33. C₂×C₁₁⋊C₅	C₂²×D₄	semidirect
36. C₂³×C₁₁	C₅×D₄	semidirect
39. C₂²×D₁₁	C₂³×C₅	semidirect
40. C₂×C₄×C₁₁	C₂³×C₅	semidirect
41. D₄₄	C₂³×C₅	semidirect
48. C₁₁⋊C₅	C₂³×D₄	semidirect
49. C₂²×C₁₁	C₂×C₅×D₄	semidirect
52. C₂×D₁₁	C₂⁴×C₅	semidirect
53. C₄×C₁₁	C₂⁴×C₅	semidirect
62. C₂³×C₄	AGL(1,𝔽₁₁)	semidirect
63. C₂×C₁₁	C₂²×C₅×D₄	semidirect
75. C₂²×C₄	C₂×AGL(1,𝔽₁₁)	semidirect
76. C₁₁	C₂³×C₅×D₄	semidirect
82. C₂³	C₄⋊AGL(1,𝔽₁₁)	direct (N × H)
85. C₂×C₄	C₂²×AGL(1,𝔽₁₁)	semidirect
89. C₂²	C₂×C₄⋊AGL(1,𝔽₁₁)	direct (N × H)
91. C₄	C₂³×AGL(1,𝔽₁₁)	semidirect
93. C₂	C₂²×C₄⋊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
C₂⁴×AGL(1,𝔽₁₁)	2
C₂³×C₄×C₁₁⋊C₅	2
C₂²×C₄⋊AGL(1,𝔽₁₁)	2
C₂³×D₄₄	5
C₂³×C₅×D₄	11

Subgroups — C23×C4⋊AGL(1,𝔽11) #72248869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄⋊AGL(1,𝔽₁₁) #72248869