Subgroups — #877

Order 96.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	#217	C₂	1	1	yes	maximal, characteristic
4	Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₃	C₂	1	2	yes	maximal, complemented
6	#117	—	3	1	no	maximal, Sylow
7	C₂³×C₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄	C₂²	1	2	yes	—
9	C₂×Dic₃	C₄	1	4	yes	complemented
10	C₂×Dic₃	C₂²	1	2	yes	—
11	C₂×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄	—	3	1	no	—
14	C₄⋊C₄	—	3	2	no	—
15	C₂²⋊C₄	—	3	1	no	—
16	C₂²⋊C₄	D₃	1	1	yes	characteristic
17	C₄²	—	3	2	no	—
18	C₂²×C₃	—	2	2	no	—
19	C₂²×C₃	C₂×C₄	1	2	yes	—
20	C₂²×C₃	C₂³	1	1	yes	characteristic
21	C₃×C₄	—	2	2	no	—
22	Dic₃	—	2	2	no	—
23	Dic₃	C₂×C₄	1	2	yes	—
24	Dic₃	C₂×C₄	1	2	yes	—
25	C₂³	C₂×D₃	1	1	yes	characteristic
26	C₂×C₄	—	3	4	no	—
27	C₂×C₄	—	3	1	no	—
28	C₂×C₄	—	3	1	no	—
29	C₂×C₄	—	3	2	no	—
30	C₂×C₄	C₂×D₃	1	2	yes	—
31	C₂×C₃	—	2	2	no	—
32	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₃	#41	1	2	yes	—
34	C₂²	—	2	2	no	—
35	C₂²	C₄×D₃	1	2	yes	—
36	C₂²	C₂²×D₃	1	1	yes	characteristic
37	C₄	—	2	2	no	—
38	C₄	—	3	2	no	—
39	C₄	—	3	2	no	—
40	C₄	—	6	2	no	—
41	C₃	#117	1	1	yes	characteristic, complemented, Sylow
42	C₂	—	2	2	no	—
43	C₂	C₂×C₄×D₃	1	1	yes	characteristic
44	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.