Subgroups — A₄⋊AGL(1,𝔽₁₁) #13050436

Order 1320.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊AGL(1,𝔽₁₁)	—	3	1	no	maximal, Hall
3	C₃⋊AGL(1,𝔽₁₁)	—	4	1	no	maximal
4	C₁₁⋊S₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂²×C₁₁⋊C₅	D₃	1	1	yes	characteristic, complemented
6	C₂×AGL(1,𝔽₁₁)	—	3	1	no	—
7	Dic₁₁⋊C₅	—	3	1	no	—
8	C₃×C₁₁⋊C₅	—	4	1	no	Hall
9	C₁₁×A₄	C₂×C₅	1	1	yes	characteristic, complemented
10	C₅×S₄	—	11	1	no	maximal, Hall
11	C₂×C₁₁⋊C₅	—	3	1	no	—
12	AGL(1,𝔽₁₁)	—	6	1	no	—
13	C₂²⋊D₁₁	—	3	1	no	Hall
14	D₃₃	—	4	1	no	—
15	C₅×A₄	—	11	1	no	—
16	C₁₁⋊C₅	S₄	1	1	yes	characteristic, complemented, Hall
17	C₂²×C₁₁	C₅×D₃	1	1	yes	characteristic, complemented
18	C₂×D₁₁	—	3	1	no	—
19	Dic₁₁	—	3	1	no	—
20	C₅×D₄	—	33	1	no	Hall
21	C₃×C₁₁	—	4	1	no	Hall
22	C₅×D₃	—	44	1	no	—
23	S₄	—	11	1	no	Hall
24	C₂×C₁₁	—	3	1	no	—
25	D₁₁	—	6	1	no	—
26	C₂²×C₅	—	11	1	no	—
27	C₂²×C₅	—	33	1	no	—
28	C₄×C₅	—	33	1	no	—
29	C₃×C₅	—	44	1	no	Hall
30	A₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
31	C₁₁	C₅×S₄	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₅	—	33	1	no	—
33	C₂×C₅	—	66	1	no	—
34	D₄	—	33	1	no	Sylow
35	D₃	—	44	1	no	—
36	C₅	—	11	1	no	Sylow
37	C₂²	—	33	1	no	—
38	C₂²	C₃⋊AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
39	C₄	—	33	1	no	—
40	C₃	—	4	1	no	Sylow
41	C₂	—	3	1	no	—
42	C₂	—	66	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₁₁×A₄	C₂×C₅
Fitting, socle	C₂²×C₁₁	C₅×D₃
LCS	G ▷ C₁₁×A₄
UCS	C₁

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

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