Subgroups — Dic₁₅₀₄ #20241606

Order 6016.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₅₂	C₂	1	2	yes	maximal
2	C₄₇×C₆₄	C₂	1	1	yes	maximal, characteristic
3	Dic₃₇₆	—	2	2	no	—
4	C₃₂×C₄₇	C₂²	1	1	yes	characteristic
5	Dic₁₈₈	—	4	2	no	—
6	C₁₆×C₄₇	D₄	1	1	yes	characteristic
7	Dic₉₄	—	8	2	no	—
8	C₈×C₄₇	D₈	1	1	yes	characteristic
9	C₄×C₄₇	D₁₆	1	1	yes	characteristic
10	Dic₄₇	—	16	2	no	—
11	Q₁₂₈	—	47	1	no	maximal, Sylow
12	C₂×C₄₇	D₃₂	1	1	yes	characteristic
13	Q₆₄	—	47	2	no	—
14	C₆₄	D₄₇	1	1	yes	characteristic
15	C₄₇	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
16	Q₃₂	—	94	2	no	—
17	C₃₂	C₂×D₄₇	1	1	yes	characteristic
18	Q₁₆	—	188	2	no	—
19	C₁₆	D₁₈₈	1	1	yes	characteristic
20	Q₈	—	376	2	no	—
21	C₈	D₃₇₆	1	1	yes	characteristic
22	C₄	—	752	2	no	—
23	C₄	D₇₅₂	1	1	yes	characteristic
24	C₂	D₁₅₀₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₄₇	Q₁₂₈	semidirect