Subgroups — D₄₈ #799

Order 96.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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