Subgroups — C₂²×C₄×D₃ #999

Order 96.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₃	C₂	1	12	yes	maximal, direct product factor
5	C₂³×C₄	—	3	1	no	maximal, Sylow
6	C₂³×C₃	C₂²	1	1	yes	characteristic
7	C₂²×D₃	C₄	1	8	yes	direct product factor
8	C₂²×D₃	C₂²	1	6	yes	—
9	C₂×C₃×C₄	C₂²	1	6	yes	complemented
10	C₂×Dic₃	C₂²	1	6	yes	complemented
11	C₄×D₃	C₂²	1	16	yes	direct product factor
12	C₂⁴	—	3	1	no	—
13	C₂²×C₄	—	3	1	no	—
14	C₂²×C₄	—	3	12	no	—
15	C₂²×C₄	D₃	1	1	yes	characteristic, direct product factor
16	C₂²×C₃	C₂×C₄	1	4	yes	complemented
17	C₂²×C₃	C₂³	1	3	yes	—
18	C₂×D₃	C₂×C₄	1	24	yes	direct product factor
19	C₂×D₃	C₂³	1	4	yes	—
20	C₃×C₄	C₂³	1	4	yes	complemented
21	Dic₃	C₂³	1	4	yes	complemented
22	C₂³	—	3	8	no	—
23	C₂³	—	3	6	no	—
24	C₂³	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄	—	3	6	no	—
26	C₂×C₄	—	3	16	no	—
27	C₂×C₄	C₂×D₃	1	6	yes	direct product factor
28	C₂×C₃	C₂²×C₄	1	6	yes	complemented
29	C₂×C₃	C₂⁴	1	1	yes	characteristic
30	D₃	C₂²×C₄	1	8	yes	direct product factor
31	C₂²	—	3	24	no	—
32	C₂²	—	3	4	no	—
33	C₂²	C₄×D₃	1	4	yes	direct product factor
34	C₂²	C₂²×D₃	1	3	yes	—
35	C₄	—	3	4	no	—
36	C₄	C₂²×D₃	1	4	yes	direct product factor
37	C₃	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
38	C₂	—	3	8	no	—
39	C₂	C₂×C₄×D₃	1	6	yes	direct product factor
40	C₂	C₂³×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.