Subgroups — #825

Order 96.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#235	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#104	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	#67	—	2	1	no	—
7	C₂×Dic₃	—	2	1	no	—
8	D₁₂	C₄	1	1	yes	characteristic, complemented
9	C₄×D₃	—	2	1	no	—
10	Dic₆	C₄	1	1	yes	characteristic, complemented
11	C₃×C₈	—	2	1	no	—
12	#41	—	3	1	no	—
13	M₁₆	D₃	1	1	yes	characteristic, complemented
14	C₄²	—	3	1	no	—
15	C₂²×C₃	D₄	1	1	yes	characteristic
16	C₂×D₃	—	2	1	no	—
17	C₃×C₄	C₂×C₄	1	1	yes	characteristic
18	C₃×C₄	D₄	1	1	yes	characteristic
19	Dic₃	—	2	2	no	—
20	Dic₃	—	2	1	no	—
21	Q₈	—	3	1	no	—
22	D₄	—	3	1	no	—
23	D₄	—	6	1	no	—
24	C₂×C₄	—	6	1	no	—
25	C₂×C₄	—	6	1	no	—
26	C₂×C₄	C₂×D₃	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₂×C₃	—	2	1	no	—
29	C₂×C₃	C₂²⋊C₄	1	1	yes	characteristic
30	D₃	—	4	1	no	—
31	C₂²	—	6	1	no	—
32	C₂²	D₁₂	1	1	yes	characteristic
33	C₄	—	6	2	no	—
34	C₄	—	6	1	no	—
35	C₄	C₄×D₃	1	1	yes	characteristic
36	C₄	#67	1	1	yes	characteristic
37	C₃	#104	1	1	yes	characteristic, complemented, Sylow
38	C₂	—	2	1	no	—
39	C₂	—	12	1	no	—
40	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.