Subgroups — Dic₈₈ #66865

Order 352.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₄	C₂	1	2	yes	maximal
2	C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₂₂	—	2	2	no	—
4	C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₄×C₁₁	D₄	1	1	yes	characteristic
6	Dic₁₁	—	4	2	no	—
7	Q₃₂	—	11	1	no	maximal, Sylow
8	C₂×C₁₁	D₈	1	1	yes	characteristic
9	Q₁₆	—	11	2	no	—
10	C₁₆	D₁₁	1	1	yes	characteristic
11	C₁₁	Q₃₂	1	1	yes	characteristic, complemented, Sylow
12	Q₈	—	22	2	no	—
13	C₈	C₂×D₁₁	1	1	yes	characteristic
14	C₄	—	44	2	no	—
15	C₄	D₄₄	1	1	yes	characteristic
16	C₂	D₈₈	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
11. C₁₁	Q₃₂	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.