Subgroups — #909

Order 96.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#235	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₂	C₂	1	2	yes	maximal, complemented
5	#204	C₂	1	2	yes	maximal, complemented
6	#137	—	3	1	no	maximal, Sylow
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	#67	—	2	1	no	—
9	C₂×Dic₃	—	2	1	no	—
10	D₁₂	C₂²	1	1	yes	characteristic
11	C₄×D₃	—	2	1	no	—
12	Dic₆	—	2	1	no	—
13	Dic₆	C₂²	1	2	yes	—
14	Dic₆	C₂²	1	1	yes	characteristic
15	C₃×C₈	C₂²	1	2	yes	—
16	#41	—	3	1	no	—
17	C₂×Q₈	—	3	1	no	—
18	Q₁₆	—	3	2	no	—
19	SD₁₆	—	3	2	no	—
20	M₁₆	D₃	1	1	yes	characteristic, complemented
21	C₂²×C₃	D₄	1	1	yes	characteristic
22	C₂×D₃	—	2	1	no	—
23	C₃×C₄	D₄	1	1	yes	characteristic
24	C₃×C₄	C₂³	1	1	yes	characteristic
25	Dic₃	—	2	2	no	—
26	Dic₃	—	2	1	no	—
27	Q₈	—	3	2	no	—
28	Q₈	—	3	1	no	—
29	Q₈	—	6	1	no	—
30	D₄	—	3	1	no	—
31	D₄	—	6	1	no	—
32	C₂×C₄	—	6	1	no	—
33	C₂×C₄	—	6	1	no	—
34	C₂×C₄	C₂×D₃	1	1	yes	characteristic
35	C₈	C₂×D₃	1	2	yes	—
36	C₂×C₃	—	2	1	no	—
37	C₂×C₃	C₂×D₄	1	1	yes	characteristic
38	D₃	—	4	1	no	—
39	C₂²	—	6	1	no	—
40	C₂²	D₁₂	1	1	yes	characteristic
41	C₄	—	6	1	no	—
42	C₄	—	6	2	no	—
43	C₄	D₁₂	1	1	yes	characteristic
44	C₄	C₂²×D₃	1	1	yes	characteristic
45	C₃	#137	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	2	1	no	—
47	C₂	—	12	1	no	—
48	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.