Subgroups — C₂×Dic₁₂ #905

Order 96.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₁₂	C₂	1	4	yes	maximal, direct product factor
4	C₂×Q₁₆	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×Dic₃	—	2	2	no	—
7	Dic₆	—	2	2	no	—
8	Dic₆	C₂²	1	4	yes	—
9	C₃×C₈	C₂²	1	2	yes	—
10	C₂×Q₈	—	3	2	no	—
11	Q₁₆	—	3	4	no	—
12	C₂×C₈	D₃	1	1	yes	characteristic
13	C₂²×C₃	D₄	1	1	yes	characteristic
14	C₃×C₄	D₄	1	1	yes	characteristic
15	C₃×C₄	C₂³	1	1	yes	characteristic
16	Dic₃	—	2	4	no	—
17	Q₈	—	3	4	no	—
18	Q₈	—	6	2	no	—
19	C₂×C₄	—	6	2	no	—
20	C₂×C₄	C₂×D₃	1	1	yes	characteristic
21	C₈	C₂×D₃	1	2	yes	—
22	C₂×C₃	Q₁₆	1	2	yes	complemented
23	C₂×C₃	C₂×D₄	1	1	yes	characteristic
24	C₂²	D₁₂	1	1	yes	characteristic
25	C₄	—	6	4	no	—
26	C₄	D₁₂	1	1	yes	characteristic
27	C₄	C₂²×D₃	1	1	yes	characteristic
28	C₃	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂	Dic₁₂	1	2	yes	direct product factor
30	C₂	C₂×D₁₂	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.