Subgroups — (C₂×D₃)⋊C₄ #212

Order 48.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₄	—	3	1	no	maximal, Sylow
5	C₂²×C₃	C₂²	1	1	yes	characteristic
6	C₂×D₃	—	2	1	no	—
7	C₂×D₃	—	2	1	no	—
8	C₂×D₃	C₄	1	2	yes	complemented
9	C₃×C₄	—	2	1	no	—
10	Dic₃	—	2	1	no	—
11	C₂³	—	3	1	no	—
12	C₂×C₄	—	3	1	no	—
13	C₂×C₄	D₃	1	1	yes	characteristic, complemented
14	C₂×C₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃	D₄	1	1	yes	characteristic
16	C₂×C₃	D₄	1	1	yes	characteristic
17	D₃	—	2	2	no	—
18	C₂²	—	3	2	no	—
19	C₂²	—	6	1	no	—
20	C₂²	—	6	1	no	—
21	C₂²	C₂×D₃	1	1	yes	characteristic
22	C₄	—	2	1	no	—
23	C₄	—	6	1	no	—
24	C₃	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	6	2	no	—
26	C₂	C₄×D₃	1	1	yes	characteristic
27	C₂	D₁₂	1	1	yes	characteristic
28	C₂	#67	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.