Subgroups — Dic₂₀₃₂ #22549717

Order 8128.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₀₁₆	C₂	1	2	yes	maximal
2	C₃₂×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	Dic₅₀₈	—	2	2	no	—
4	C₁₆×C₁₂₇	C₂²	1	1	yes	characteristic
5	Dic₂₅₄	—	4	2	no	—
6	C₈×C₁₂₇	D₄	1	1	yes	characteristic
7	C₄×C₁₂₇	D₈	1	1	yes	characteristic
8	Dic₁₂₇	—	8	2	no	—
9	C₂×C₁₂₇	D₁₆	1	1	yes	characteristic
10	C₁₂₇	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	127	1	no	maximal, Sylow
12	Q₃₂	—	127	2	no	—
13	C₃₂	D₁₂₇	1	1	yes	characteristic
14	Q₁₆	—	254	2	no	—
15	C₁₆	C₂×D₁₂₇	1	1	yes	characteristic
16	Q₈	—	508	2	no	—
17	C₈	D₅₀₈	1	1	yes	characteristic
18	C₄	—	1016	2	no	—
19	C₄	D₁₀₁₆	1	1	yes	characteristic
20	C₂	D₂₀₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₁₂₇	Q₆₄	semidirect