Subgroups — Dic₄₀₆₄ #30636948

Order 16256.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀₃₂	C₂	1	2	yes	maximal
2	C₆₄×C₁₂₇	C₂	1	1	yes	maximal, characteristic
3	Dic₁₀₁₆	—	2	2	no	—
4	C₃₂×C₁₂₇	C₂²	1	1	yes	characteristic
5	Dic₅₀₈	—	4	2	no	—
6	C₁₆×C₁₂₇	D₄	1	1	yes	characteristic
7	Dic₂₅₄	—	8	2	no	—
8	C₈×C₁₂₇	D₈	1	1	yes	characteristic
9	C₄×C₁₂₇	D₁₆	1	1	yes	characteristic
10	Dic₁₂₇	—	16	2	no	—
11	C₂×C₁₂₇	D₃₂	1	1	yes	characteristic
12	Q₁₂₈	—	127	1	no	maximal, Sylow
13	C₁₂₇	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
14	Q₆₄	—	127	2	no	—
15	C₆₄	D₁₂₇	1	1	yes	characteristic
16	Q₃₂	—	254	2	no	—
17	C₃₂	C₂×D₁₂₇	1	1	yes	characteristic
18	Q₁₆	—	508	2	no	—
19	C₁₆	D₅₀₈	1	1	yes	characteristic
20	Q₈	—	1016	2	no	—
21	C₈	D₁₀₁₆	1	1	yes	characteristic
22	C₄	—	2032	2	no	—
23	C₄	D₂₀₃₂	1	1	yes	characteristic
24	C₂	D₄₀₆₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. C₁₂₇	Q₁₂₈	semidirect

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