Subgroups — Dic₁₆₄₈ #20267632

Order 6592.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₈₂₄	C₂	1	2	yes	maximal
2	C₃₂×C₁₀₃	C₂	1	1	yes	maximal, characteristic
3	Dic₄₁₂	—	2	2	no	—
4	C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
5	Dic₂₀₆	—	4	2	no	—
6	C₈×C₁₀₃	D₄	1	1	yes	characteristic
7	C₄×C₁₀₃	D₈	1	1	yes	characteristic
8	Dic₁₀₃	—	8	2	no	—
9	C₂×C₁₀₃	D₁₆	1	1	yes	characteristic
10	C₁₀₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
11	Q₆₄	—	103	1	no	maximal, Sylow
12	Q₃₂	—	103	2	no	—
13	C₃₂	D₁₀₃	1	1	yes	characteristic
14	Q₁₆	—	206	2	no	—
15	C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
16	Q₈	—	412	2	no	—
17	C₈	D₄₁₂	1	1	yes	characteristic
18	C₄	—	824	2	no	—
19	C₄	D₈₂₄	1	1	yes	characteristic
20	C₂	D₁₆₄₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
10. C₁₀₃	Q₆₄	semidirect