Subgroups — #940

Order 96.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#67	C₂	1	4	yes	maximal, complemented
3	C₂×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#127	—	3	1	no	maximal, Sylow
6	C₂³×C₃	C₂²	1	2	yes	—
7	C₂²×D₃	C₂²	1	2	yes	—
8	C₃×D₄	—	2	2	no	—
9	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
10	#67	—	2	8	no	—
11	C₂×Dic₃	C₂²	1	2	yes	—
12	D₁₂	—	2	2	no	—
13	C₂×D₄	—	3	4	no	—
14	C₂×D₄	—	3	1	no	—
15	C₂×D₄	D₃	1	1	yes	characteristic, complemented
16	C₄²	—	3	1	no	—
17	C₂²×C₃	—	2	4	no	—
18	C₂²×C₃	—	2	2	no	—
19	C₂²×C₃	C₂³	1	1	yes	characteristic
20	C₂×D₃	—	2	2	no	—
21	C₂×D₃	—	2	4	no	—
22	C₃×C₄	D₄	1	2	yes	complemented
23	Dic₃	D₄	1	4	yes	complemented
24	C₂³	—	3	2	no	—
25	C₂³	C₂×D₃	1	2	yes	—
26	D₄	—	2	2	no	—
27	D₄	—	6	8	no	—
28	D₄	—	6	2	no	—
29	C₂×C₄	—	3	2	no	—
30	C₂×C₄	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃	—	4	2	no	—
32	C₂×C₃	C₂×D₄	1	2	yes	—
33	C₂×C₃	C₂×D₄	1	1	yes	characteristic
34	D₃	—	4	2	no	—
35	C₂²	—	2	4	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	6	4	no	—
38	C₂²	—	6	2	no	—
39	C₂²	C₂²×D₃	1	1	yes	characteristic
40	C₄	—	3	4	no	—
41	C₄	#67	1	2	yes	complemented
42	C₃	#127	1	1	yes	characteristic, complemented, Sylow
43	C₂	—	4	2	no	—
44	C₂	—	12	2	no	—
45	C₂	D₃×D₄	1	2	yes	—
46	C₂	C₂×#67	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.