Subgroups — C₂×D₂₄ #903

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₈	—	3	1	no	maximal, Sylow
5	C₂²×D₃	—	2	2	no	—
6	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
7	D₁₂	—	2	2	no	—
8	D₁₂	C₂²	1	4	yes	complemented
9	C₃×C₈	C₂²	1	2	yes	complemented
10	C₂×D₄	—	3	2	no	—
11	D₈	—	3	4	no	—
12	C₂×C₈	D₃	1	1	yes	characteristic, complemented
13	C₂²×C₃	D₄	1	1	yes	characteristic
14	C₂×D₃	—	2	4	no	—
15	C₂×D₃	—	4	4	no	—
16	C₃×C₄	D₄	1	1	yes	characteristic
17	C₃×C₄	C₂³	1	1	yes	characteristic
18	C₂³	—	6	2	no	—
19	D₄	—	3	4	no	—
20	D₄	—	6	2	no	—
21	C₂×C₄	C₂×D₃	1	1	yes	characteristic
22	C₈	C₂×D₃	1	2	yes	complemented
23	C₂×C₃	D₈	1	2	yes	complemented
24	C₂×C₃	C₂×D₄	1	1	yes	characteristic
25	D₃	—	4	4	no	—
26	C₂²	—	6	4	no	—
27	C₂²	—	12	4	no	—
28	C₂²	D₁₂	1	1	yes	characteristic
29	C₄	D₁₂	1	1	yes	characteristic
30	C₄	C₂²×D₃	1	1	yes	characteristic
31	C₃	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
32	C₂	—	12	4	no	—
33	C₂	D₂₄	1	2	yes	direct product factor
34	C₂	C₂×D₁₂	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.