Subgroups — (C₁₁⋊C₅)⋊Q₈ #89154

Order 440.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	Dic₁₁⋊C₅	C₂	1	2	yes	maximal
3	C₂×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
4	Dic₂₂	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₁⋊C₅	Q₈	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₁	C₂×C₅	1	1	yes	characteristic
7	Dic₁₁	C₂×C₅	1	2	yes	—
8	C₅×Q₈	—	11	1	no	maximal, Hall
9	C₂×C₁₁	C₂²×C₅	1	1	yes	characteristic
10	C₄×C₅	—	11	2	no	—
11	C₄×C₅	—	22	1	no	—
12	C₁₁	C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₅	—	22	1	no	—
14	Q₈	—	11	1	no	Sylow
15	C₅	—	22	1	no	Sylow
16	C₄	—	11	2	no	—
17	C₄	AGL(1,𝔽₁₁)	1	1	yes	characteristic
18	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.