Subgroups — Dic₃₀₀₈ #26104196

Order 12032.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₅₀₄	C₂	1	2	yes	maximal
2	C₄₇×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	Dic₇₅₂	—	2	2	no	—
4	C₄₇×C₆₄	C₂²	1	1	yes	characteristic
5	Dic₃₇₆	—	4	2	no	—
6	C₃₂×C₄₇	D₄	1	1	yes	characteristic
7	Dic₁₈₈	—	8	2	no	—
8	C₁₆×C₄₇	D₈	1	1	yes	characteristic
9	Dic₉₄	—	16	2	no	—
10	C₈×C₄₇	D₁₆	1	1	yes	characteristic
11	Q₂₅₆	—	47	1	no	maximal, Sylow
12	C₄×C₄₇	D₃₂	1	1	yes	characteristic
13	Dic₄₇	—	32	2	no	—
14	Q₁₂₈	—	47	2	no	—
15	C₁₂₈	D₄₇	1	1	yes	characteristic
16	C₂×C₄₇	D₆₄	1	1	yes	characteristic
17	Q₆₄	—	94	2	no	—
18	C₆₄	C₂×D₄₇	1	1	yes	characteristic
19	C₄₇	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
20	Q₃₂	—	188	2	no	—
21	C₃₂	D₁₈₈	1	1	yes	characteristic
22	Q₁₆	—	376	2	no	—
23	C₁₆	D₃₇₆	1	1	yes	characteristic
24	Q₈	—	752	2	no	—
25	C₈	D₇₅₂	1	1	yes	characteristic
26	C₄	—	1504	2	no	—
27	C₄	D₁₅₀₄	1	1	yes	characteristic
28	C₂	D₃₀₀₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₄₇	Q₂₅₆	semidirect

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