Subgroups — #936

Order 96.

76 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	C₂×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#217	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#124	—	3	1	no	maximal, Sylow
6	C₂³×C₃	C₂²	1	2	yes	—
7	C₃×D₄	—	2	2	no	—
8	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
9	C₂×Dic₃	C₂²	1	2	yes	—
10	C₂×Dic₃	C₂²	1	2	yes	—
11	Dic₆	—	2	2	no	—
12	C₂×Q₈	—	3	1	no	—
13	C₂×D₄	D₃	1	1	yes	characteristic
14	C₂²⋊C₄	—	3	4	no	—
15	C₄²	—	3	1	no	—
16	C₂²×C₃	—	2	2	no	—
17	C₂²×C₃	—	2	4	no	—
18	C₂²×C₃	C₂³	1	1	yes	characteristic
19	C₃×C₄	D₄	1	2	yes	—
20	Dic₃	—	2	2	no	—
21	Dic₃	—	2	2	no	—
22	C₂³	C₂×D₃	1	2	yes	—
23	Q₈	—	6	2	no	—
24	D₄	—	2	2	no	—
25	C₂×C₄	—	3	2	no	—
26	C₂×C₄	—	3	2	no	—
27	C₂×C₄	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃	—	4	2	no	—
29	C₂×C₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃	#41	1	2	yes	—
31	C₂²	—	2	4	no	—
32	C₂²	—	2	2	no	—
33	C₂²	C₂²×D₃	1	1	yes	characteristic
34	C₄	—	6	2	no	—
35	C₄	—	6	2	no	—
36	C₄	#67	1	2	yes	—
37	C₃	#124	1	1	yes	characteristic, complemented, Sylow
38	C₂	—	4	2	no	—
39	C₂	#237	1	2	yes	—
40	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.