Subgroups — D₃×D₈ #910

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×D₄	C₂	1	2	yes	maximal, complemented
2	C₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#213	C₂	1	2	yes	maximal, complemented
4	D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₈	—	3	1	no	maximal, Sylow
7	C₂²×D₃	—	2	2	no	—
8	C₃×D₄	C₂²	1	2	yes	complemented
9	#67	—	2	2	no	—
10	D₁₂	C₂²	1	2	yes	complemented
11	C₄×D₃	C₂²	1	1	yes	characteristic
12	C₃×C₈	C₂²	1	1	yes	characteristic, complemented
13	C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₄	—	3	2	no	—
15	D₈	—	3	2	no	—
16	D₈	—	3	1	no	—
17	D₈	D₃	1	1	yes	characteristic, direct product factor
18	C₂×C₈	—	3	1	no	—
19	C₂²×C₃	—	2	2	no	—
20	C₂×D₃	—	2	2	no	—
21	C₂×D₃	—	4	4	no	—
22	C₂×D₃	D₄	1	1	yes	characteristic
23	C₃×C₄	C₂³	1	1	yes	characteristic
24	Dic₃	D₄	1	1	yes	characteristic
25	C₂³	—	6	2	no	—
26	D₄	—	3	2	no	—
27	D₄	—	6	2	no	—
28	D₄	C₂×D₃	1	2	yes	complemented
29	C₂×C₄	—	3	1	no	—
30	C₈	—	3	1	no	—
31	C₈	C₂×D₃	1	1	yes	characteristic, complemented
32	C₂×C₃	—	4	2	no	—
33	C₂×C₃	C₂×D₄	1	1	yes	characteristic
34	D₃	—	4	2	no	—
35	D₃	D₈	1	2	yes	direct product factor
36	C₂²	—	2	2	no	—
37	C₂²	—	3	1	no	—
38	C₂²	—	6	2	no	—
39	C₂²	—	12	4	no	—
40	C₄	—	3	1	no	—
41	C₄	C₂²×D₃	1	1	yes	characteristic
42	C₃	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
43	C₂	—	3	2	no	—
44	C₂	—	4	2	no	—
45	C₂	—	12	2	no	—
46	C₂	D₃×D₄	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.