Subgroups — #887

Order 96.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	Dic₃⋊C₄	C₂	1	2	yes	maximal
4	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₄×Dic₃	C₂	1	2	yes	maximal
6	C₄×Q₈	—	3	1	no	maximal, Sylow
7	C₂×C₃×C₄	C₂²	1	2	yes	—
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×Dic₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₃	C₂²	1	2	yes	—
11	C₂×Dic₃	C₂²	1	1	yes	characteristic
12	Dic₆	C₄	1	4	yes	complemented
13	C₂×Q₈	—	3	1	no	—
14	C₄⋊C₄	—	3	2	no	—
15	C₄⋊C₄	D₃	1	1	yes	characteristic
16	C₄²	—	3	2	no	—
17	C₄²	—	3	1	no	—
18	C₂²×C₃	C₂³	1	1	yes	characteristic
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	C₂×C₄	1	2	yes	—
21	Dic₃	—	2	1	no	—
22	Dic₃	C₂×C₄	1	4	yes	—
23	Dic₃	Q₈	1	2	yes	complemented
24	Q₈	—	3	4	no	—
25	C₂×C₄	—	3	1	no	—
26	C₂×C₄	—	3	2	no	—
27	C₂×C₄	—	3	1	no	—
28	C₂×C₄	C₂×D₃	1	2	yes	—
29	C₂×C₄	C₂×D₃	1	1	yes	characteristic
30	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₃	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃	#41	1	1	yes	characteristic
33	C₂²	C₂²×D₃	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	3	4	no	—
36	C₄	—	3	2	no	—
37	C₄	—	6	1	no	—
38	C₄	C₄×D₃	1	2	yes	—
39	C₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
40	C₂	C₂×C₄×D₃	1	1	yes	characteristic
41	C₂	#237	1	1	yes	characteristic
42	C₂	D₃×Q₈	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.