Subgroups — C₂²⋊AGL(1,𝔽₁₁) #89158

Order 440.

32 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	1	yes	maximal, characteristic, complemented
3	Dic₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁⋊C₅	—	2	1	no	—
5	C₂×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
6	AGL(1,𝔽₁₁)	—	2	1	no	—
7	C₂²⋊D₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
8	C₁₁⋊C₅	D₄	1	1	yes	characteristic, complemented, Hall
9	C₂²×C₁₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₂×D₁₁	C₂×C₅	1	1	yes	characteristic, complemented
11	Dic₁₁	C₂×C₅	1	1	yes	characteristic, complemented
12	C₅×D₄	—	11	1	no	maximal, Hall
13	C₂×C₁₁	—	2	1	no	—
14	C₂×C₁₁	C₂²×C₅	1	1	yes	characteristic
15	D₁₁	—	2	1	no	—
16	C₂²×C₅	—	11	1	no	—
17	C₂²×C₅	—	11	1	no	—
18	C₄×C₅	—	11	1	no	—
19	C₁₁	C₅×D₄	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₅	—	11	1	no	—
21	C₂×C₅	—	22	1	no	—
22	C₂×C₅	—	22	1	no	—
23	D₄	—	11	1	no	Sylow
24	C₅	—	11	1	no	Sylow
25	C₂²	—	11	1	no	—
26	C₂²	AGL(1,𝔽₁₁)	1	1	yes	characteristic, complemented
27	C₄	—	11	1	no	—
28	C₂	—	2	1	no	—
29	C₂	—	22	1	no	—
30	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.