Subgroups — D₃×D₄ #236

Order 48.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃	C₂	1	2	yes	maximal, complemented
2	C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#67	C₂	1	2	yes	maximal, complemented
4	D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄	—	3	1	no	maximal, Sylow
7	C₂²×C₃	C₂²	1	2	yes	complemented
8	C₂×D₃	—	2	4	no	—
9	C₂×D₃	C₂²	1	1	yes	characteristic
10	C₂×D₃	C₂²	1	2	yes	complemented
11	C₃×C₄	C₂²	1	1	yes	characteristic, complemented
12	Dic₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³	—	3	2	no	—
14	D₄	—	3	2	no	—
15	D₄	—	3	1	no	—
16	D₄	D₃	1	1	yes	characteristic, direct product factor
17	C₂×C₄	—	3	1	no	—
18	C₂×C₃	—	2	2	no	—
19	C₂×C₃	C₂³	1	1	yes	characteristic
20	D₃	—	2	2	no	—
21	D₃	D₄	1	2	yes	direct product factor
22	C₂²	—	3	1	no	—
23	C₂²	—	3	2	no	—
24	C₂²	—	6	4	no	—
25	C₂²	C₂×D₃	1	2	yes	complemented
26	C₄	—	3	1	no	—
27	C₄	C₂×D₃	1	1	yes	characteristic, complemented
28	C₃	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	2	2	no	—
30	C₂	—	3	2	no	—
31	C₂	—	6	2	no	—
32	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.