Subgroups — #886

Order 96.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
6	#123	—	3	1	no	maximal, Sylow
7	C₂³×C₃	C₂²	1	1	yes	characteristic
8	C₂²×D₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄	C₂²	1	2	yes	—
10	#67	—	2	2	no	—
11	C₂×Dic₃	—	2	2	no	—
12	C₂×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₃	C₂²	1	2	yes	—
14	C₂×D₄	—	3	1	no	—
15	C₂²×C₄	—	3	1	no	—
16	C₄⋊C₄	—	3	2	no	—
17	C₂²⋊C₄	—	3	2	no	—
18	C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
19	C₂²×C₃	—	2	2	no	—
20	C₂²×C₃	D₄	1	2	yes	—
21	C₂²×C₃	C₂³	1	1	yes	characteristic
22	C₂×D₃	—	2	1	no	—
23	C₂×D₃	—	2	2	no	—
24	C₃×C₄	—	2	2	no	—
25	Dic₃	—	2	2	no	—
26	Dic₃	—	2	1	no	—
27	C₂³	—	3	1	no	—
28	C₂³	C₂×D₃	1	1	yes	characteristic
29	D₄	—	6	2	no	—
30	C₂×C₄	—	3	2	no	—
31	C₂×C₄	—	3	1	no	—
32	C₂×C₄	—	6	2	no	—
33	C₂×C₄	C₂×D₃	1	2	yes	—
34	C₂×C₃	—	2	2	no	—
35	C₂×C₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₃	#41	1	2	yes	—
37	D₃	—	4	1	no	—
38	C₂²	—	2	2	no	—
39	C₂²	—	6	1	no	—
40	C₂²	—	6	2	no	—
41	C₂²	D₁₂	1	2	yes	—
42	C₂²	C₂²×D₃	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	6	2	no	—
45	C₄	—	6	1	no	—
46	C₃	#123	1	1	yes	characteristic, complemented, Sylow
47	C₂	—	2	2	no	—
48	C₂	—	12	1	no	—
49	C₂	C₂×D₁₂	1	1	yes	characteristic
50	C₂	#237	1	2	yes	—

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.