Subgroups — #235

Order 48.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#67	C₂	1	2	yes	maximal, complemented
3	D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₃	C₂	1	2	yes	maximal, complemented
5	Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#41	—	3	1	no	maximal, Sylow
7	C₂²×C₃	C₂²	1	1	yes	characteristic
8	C₂×D₃	C₂²	1	2	yes	—
9	C₃×C₄	C₂²	1	1	yes	characteristic
10	C₃×C₄	C₂²	1	1	yes	characteristic
11	Dic₃	C₂²	1	2	yes	—
12	Q₈	—	3	1	no	—
13	D₄	—	3	2	no	—
14	D₄	—	3	1	no	—
15	C₂×C₄	—	3	2	no	—
16	C₂×C₄	D₃	1	1	yes	characteristic, complemented
17	C₂×C₃	—	2	1	no	—
18	C₂×C₃	C₂³	1	1	yes	characteristic
19	D₃	—	2	2	no	—
20	C₂²	—	3	2	no	—
21	C₂²	C₂×D₃	1	1	yes	characteristic
22	C₄	—	3	2	no	—
23	C₄	C₂×D₃	1	1	yes	characteristic
24	C₄	C₂×D₃	1	1	yes	characteristic
25	C₃	#41	1	1	yes	characteristic, complemented, Sylow
26	C₂	—	2	1	no	—
27	C₂	—	6	2	no	—
28	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.