Subgroups — Dic₈₄₈ #16810464

Order 3392.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₂₄	C₂	1	2	yes	maximal
2	C₃₂×C₅₃	C₂	1	1	yes	maximal, characteristic
3	Dic₂₁₂	—	2	2	no	—
4	C₁₆×C₅₃	C₂²	1	1	yes	characteristic
5	Dic₁₀₆	—	4	2	no	—
6	C₈×C₅₃	D₄	1	1	yes	characteristic
7	C₄×C₅₃	D₈	1	1	yes	characteristic
8	Dic₅₃	—	8	2	no	—
9	C₂×C₅₃	D₁₆	1	1	yes	characteristic
10	Q₆₄	—	53	1	no	maximal, Sylow
11	C₅₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
12	Q₃₂	—	53	2	no	—
13	C₃₂	D₅₃	1	1	yes	characteristic
14	Q₁₆	—	106	2	no	—
15	C₁₆	C₂×D₅₃	1	1	yes	characteristic
16	Q₈	—	212	2	no	—
17	C₈	D₂₁₂	1	1	yes	characteristic
18	C₄	—	424	2	no	—
19	C₄	D₄₂₄	1	1	yes	characteristic
20	C₂	D₈₄₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₅₃	Q₆₄	semidirect

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