Subgroups — C₂×D₃×Q₈ #1005

Order 96.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×Q₈	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₃	C₂	1	3	yes	maximal
4	C₂×Dic₆	C₂	1	3	yes	maximal, complemented
5	C₂²×Q₈	—	3	1	no	maximal, Sylow
6	C₂²×D₃	C₂²	1	1	yes	characteristic
7	C₃×Q₈	C₂²	1	4	yes	complemented
8	C₂×C₃×C₄	C₂²	1	3	yes	—
9	C₂×Dic₃	C₂²	1	3	yes	—
10	C₄×D₃	C₂²	1	12	yes	—
11	Dic₆	C₂²	1	12	yes	complemented
12	C₂×Q₈	—	3	8	no	—
13	C₂×Q₈	—	3	3	no	—
14	C₂×Q₈	D₃	1	1	yes	characteristic, direct product factor
15	C₂²×C₄	—	3	3	no	—
16	C₂²×C₃	C₂³	1	1	yes	characteristic
17	C₂×D₃	Q₈	1	4	yes	direct product factor
18	C₂×D₃	C₂³	1	2	yes	—
19	C₃×C₄	C₂³	1	6	yes	—
20	Dic₃	C₂³	1	6	yes	—
21	C₂³	—	3	1	no	—
22	Q₈	—	3	12	no	—
23	Q₈	C₂×D₃	1	4	yes	direct product factor
24	C₂×C₄	—	3	3	no	—
25	C₂×C₄	—	3	12	no	—
26	C₂×C₄	C₂×D₃	1	3	yes	—
27	C₂×C₃	C₂×Q₈	1	2	yes	complemented
28	C₂×C₃	C₂⁴	1	1	yes	characteristic
29	D₃	C₂×Q₈	1	4	yes	direct product factor
30	C₂²	—	3	4	no	—
31	C₂²	—	3	2	no	—
32	C₂²	C₂²×D₃	1	1	yes	characteristic
33	C₄	—	3	6	no	—
34	C₄	C₂²×D₃	1	6	yes	—
35	C₃	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	3	4	no	—
37	C₂	D₃×Q₈	1	2	yes	direct product factor
38	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.