Subgroups — C₄²×D₃ #871

Order 96.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃	C₂	1	3	yes	maximal
2	C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₃	C₂	1	3	yes	maximal, complemented
4	C₂×C₄²	—	3	1	no	maximal, Sylow
5	C₂²×D₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄	C₂²	1	3	yes	—
7	C₂×Dic₃	C₂²	1	3	yes	—
8	C₄×D₃	C₄	1	12	yes	direct product factor
9	C₂²×C₄	—	3	3	no	—
10	C₄²	—	3	3	no	—
11	C₄²	D₃	1	1	yes	characteristic, direct product factor
12	C₂²×C₃	C₂³	1	1	yes	characteristic
13	C₂×D₃	C₂×C₄	1	6	yes	—
14	C₃×C₄	C₂×C₄	1	6	yes	complemented
15	Dic₃	C₂×C₄	1	6	yes	complemented
16	C₂³	—	3	1	no	—
17	C₂×C₄	—	3	3	no	—
18	C₂×C₄	—	3	12	no	—
19	C₂×C₄	C₂×D₃	1	3	yes	—
20	C₂×C₃	C₂²×C₄	1	3	yes	—
21	D₃	C₄²	1	4	yes	direct product factor
22	C₂²	—	3	6	no	—
23	C₂²	C₂²×D₃	1	1	yes	characteristic
24	C₄	—	3	6	no	—
25	C₄	C₄×D₃	1	6	yes	direct product factor
26	C₃	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
27	C₂	—	3	4	no	—
28	C₂	C₂×C₄×D₃	1	3	yes	—

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.