Subgroups — C₄⋊AGL(1,𝔽₁₁) #89156

Order 440.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₁₁)	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
4	AGL(1,𝔽₁₁)	—	2	2	no	—
5	D₄₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₁⋊C₅	D₄	1	1	yes	characteristic, complemented, Hall
7	C₂×D₁₁	C₂×C₅	1	2	yes	complemented
8	C₄×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₄	—	11	1	no	maximal, Hall
10	C₂×C₁₁	C₂²×C₅	1	1	yes	characteristic
11	D₁₁	—	2	2	no	—
12	C₂²×C₅	—	11	2	no	—
13	C₄×C₅	—	22	1	no	—
14	C₁₁	C₅×D₄	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₅	—	22	2	no	—
16	C₂×C₅	—	22	1	no	—
17	D₄	—	11	1	no	Sylow
18	C₅	—	22	1	no	Sylow
19	C₂²	—	11	2	no	—
20	C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
21	C₂	—	22	2	no	—
22	C₂	C₂×AGL(1,𝔽₁₁)	1	1	yes	characteristic

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.