Subgroups — #806

Order 96.

52 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	C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#217	C₂	1	1	yes	maximal, characteristic, complemented
4	#99	—	3	1	no	maximal, Sylow
5	C₂³×C₃	C₂²	1	1	yes	characteristic
6	C₂²×D₃	C₄	1	1	yes	characteristic, complemented
7	C₂×C₃×C₄	—	2	1	no	—
8	#67	—	2	1	no	—
9	#67	—	2	1	no	—
10	C₂×Dic₃	—	2	1	no	—
11	C₂×Dic₃	C₄	1	1	yes	characteristic, complemented
12	C₂×D₄	—	3	1	no	—
13	C₂²⋊C₄	—	3	1	no	—
14	C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
15	C₂²×C₃	—	4	1	no	—
16	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₃	D₄	1	1	yes	characteristic
18	C₂²×C₃	D₄	1	1	yes	characteristic
19	C₂×D₃	—	2	1	no	—
20	C₂×D₃	—	4	1	no	—
21	C₃×C₄	—	4	1	no	—
22	Dic₃	—	2	1	no	—
23	Dic₃	—	4	1	no	—
24	C₂³	—	3	1	no	—
25	C₂³	C₂×D₃	1	1	yes	characteristic
26	D₄	—	6	1	no	—
27	D₄	—	6	1	no	—
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	3	1	no	—
30	C₂×C₄	—	6	1	no	—
31	C₂×C₃	—	2	1	no	—
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	—	2	1	no	—
34	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
35	D₃	—	4	1	no	—
36	C₂²	—	4	1	no	—
37	C₂²	—	6	1	no	—
38	C₂²	—	12	1	no	—
39	C₂²	C₄×D₃	1	1	yes	characteristic
40	C₂²	D₁₂	1	1	yes	characteristic
41	C₂²	#67	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	—	6	1	no	—
44	C₄	—	12	1	no	—
45	C₃	#99	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	2	1	no	—
47	C₂	—	2	1	no	—
48	C₂	—	2	1	no	—
49	C₂	—	12	1	no	—
50	C₂	(C₂×D₃)⋊C₄	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.