Subgroups — Q₈×D₂₀₁₁ #44565632

Order 32176.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₀₂₂	C₂	1	3	yes	maximal, complemented
2	C₄×D₂₀₁₁	C₂	1	3	yes	maximal
3	Q₈×C₂₀₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₀₁₁	C₂²	1	1	yes	characteristic
5	C₄×C₂₀₁₁	C₂²	1	3	yes	—
6	Dic₂₀₁₁	C₂²	1	3	yes	—
7	C₂×C₂₀₁₁	C₂³	1	1	yes	characteristic
8	D₂₀₁₁	Q₈	1	2	yes	direct product factor
9	C₂₀₁₁	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
10	C₂×Q₈	—	2011	1	no	maximal, Sylow
11	Q₈	—	2011	3	no	—
12	Q₈	D₂₀₁₁	1	1	yes	characteristic, direct product factor
13	C₂×C₄	—	2011	3	no	—
14	C₂²	—	2011	1	no	—
15	C₄	—	2011	3	no	—
16	C₄	C₂×D₂₀₁₁	1	3	yes	—
17	C₂	—	2011	2	no	—
18	C₂	C₂²×D₂₀₁₁	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.