Subgroups — C₂²×D₁₂ #1000

Order 96.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₂	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₄	—	3	1	no	maximal, Sylow
5	C₂³×C₃	C₂²	1	1	yes	characteristic
6	C₂²×D₃	—	2	8	no	—
7	C₂²×D₃	C₂²	1	12	yes	complemented
8	C₂×C₃×C₄	C₂²	1	6	yes	complemented
9	D₁₂	C₂²	1	16	yes	direct product factor
10	C₂⁴	—	3	2	no	—
11	C₂×D₄	—	3	12	no	—
12	C₂²×C₄	D₃	1	1	yes	characteristic, complemented
13	C₂²×C₃	D₄	1	4	yes	complemented
14	C₂²×C₃	C₂³	1	3	yes	—
15	C₂×D₃	—	2	24	no	—
16	C₂×D₃	C₂³	1	8	yes	complemented
17	C₃×C₄	C₂³	1	4	yes	complemented
18	C₂³	—	3	12	no	—
19	C₂³	—	6	8	no	—
20	C₂³	C₂×D₃	1	1	yes	characteristic
21	D₄	—	3	16	no	—
22	C₂×C₄	C₂×D₃	1	6	yes	complemented
23	C₂×C₃	C₂×D₄	1	6	yes	complemented
24	C₂×C₃	C₂⁴	1	1	yes	characteristic
25	D₃	—	2	8	no	—
26	C₂²	—	3	8	no	—
27	C₂²	—	6	24	no	—
28	C₂²	D₁₂	1	4	yes	direct product factor
29	C₂²	C₂²×D₃	1	3	yes	—
30	C₄	C₂²×D₃	1	4	yes	complemented
31	C₃	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
32	C₂	—	6	8	no	—
33	C₂	C₂×D₁₂	1	6	yes	direct product factor
34	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.