Subgroups — C₂×C₄×D₃ #233

Order 48.

54 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	C₄×D₃	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄	—	3	1	no	maximal, Sylow
6	C₂²×C₃	C₂²	1	1	yes	characteristic
7	C₂×D₃	C₄	1	4	yes	direct product factor
8	C₂×D₃	C₂²	1	2	yes	—
9	C₃×C₄	C₂²	1	2	yes	complemented
10	Dic₃	C₂²	1	2	yes	complemented
11	C₂³	—	3	1	no	—
12	C₂×C₄	—	3	1	no	—
13	C₂×C₄	—	3	4	no	—
14	C₂×C₄	D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃	C₂×C₄	1	2	yes	complemented
16	C₂×C₃	C₂³	1	1	yes	characteristic
17	D₃	C₂×C₄	1	4	yes	direct product factor
18	C₂²	—	3	4	no	—
19	C₂²	—	3	2	no	—
20	C₂²	C₂×D₃	1	1	yes	characteristic
21	C₄	—	3	2	no	—
22	C₄	C₂×D₃	1	2	yes	direct product factor
23	C₃	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂	—	3	4	no	—
25	C₂	C₄×D₃	1	2	yes	direct product factor
26	C₂	C₂²×D₃	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.