Subgroups — #834

Order 96.

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