Subgroups — Dic₄₈ #4450

Order 192.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₄	C₂	1	2	yes	maximal
2	C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	Q₆₄	—	3	1	no	maximal, Sylow
4	Dic₁₂	—	2	2	no	—
5	C₃×C₁₆	C₂²	1	1	yes	characteristic
6	Q₃₂	—	3	2	no	—
7	C₃₂	D₃	1	1	yes	characteristic
8	Dic₆	—	4	2	no	—
9	C₃×C₈	D₄	1	1	yes	characteristic
10	Q₁₆	—	6	2	no	—
11	C₁₆	C₂×D₃	1	1	yes	characteristic
12	C₃×C₄	D₈	1	1	yes	characteristic
13	Dic₃	—	8	2	no	—
14	Q₈	—	12	2	no	—
15	C₈	D₁₂	1	1	yes	characteristic
16	C₂×C₃	D₁₆	1	1	yes	characteristic
17	C₄	—	24	2	no	—
18	C₄	D₂₄	1	1	yes	characteristic
19	C₃	Q₆₄	1	1	yes	characteristic, complemented, Sylow
20	C₂	D₄₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₃	Q₆₄	semidirect

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