Subgroups — C₂²×AGL(1,𝔽₁₁) #89189

Order 440.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,𝔽₁₁)	C₂	1	6	yes	maximal, direct product factor
3	C₂×C₁₁⋊C₅	C₂²	1	3	yes	complemented
4	AGL(1,𝔽₁₁)	C₂²	1	4	yes	direct product factor
5	C₂²×D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₁⋊C₅	C₂³	1	1	yes	characteristic, complemented, Hall
7	C₂²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
8	C₂×D₁₁	C₂×C₅	1	6	yes	complemented
9	C₂³×C₅	—	11	1	no	maximal, Hall
10	C₂×C₁₁	C₂²×C₅	1	3	yes	complemented
11	D₁₁	C₂²×C₅	1	4	yes	complemented
12	C₂²×C₅	—	11	6	no	—
13	C₂²×C₅	—	11	1	no	—
14	C₁₁	C₂³×C₅	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅	—	11	4	no	—
16	C₂×C₅	—	11	3	no	—
17	C₂³	—	11	1	no	Sylow
18	C₅	—	11	1	no	Sylow
19	C₂²	—	11	6	no	—
20	C₂²	AGL(1,𝔽₁₁)	1	1	yes	characteristic, direct product factor
21	C₂	—	11	4	no	—
22	C₂	C₂×AGL(1,𝔽₁₁)	1	3	yes	direct product factor

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

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.