Subgroups — #907

Order 96.

62 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	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
5	D₃×C₈	C₂	1	2	yes	maximal, complemented
6	#131	—	3	1	no	maximal, Sylow
7	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
8	#67	C₄	1	2	yes	—
9	D₁₂	C₄	1	1	yes	characteristic
10	C₄×D₃	C₂²	1	2	yes	—
11	Dic₆	C₄	1	1	yes	characteristic
12	C₃×C₈	C₂²	1	2	yes	—
13	C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₃⋊C₈	C₂²	1	1	yes	characteristic
15	#41	—	3	1	no	—
16	M₁₆	—	3	2	no	—
17	M₁₆	D₃	1	1	yes	characteristic, complemented
18	C₂×C₈	—	3	1	no	—
19	C₂×C₈	—	3	2	no	—
20	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
21	C₂×D₃	C₂×C₄	1	2	yes	—
22	C₃×C₄	C₂×C₄	1	1	yes	characteristic
23	C₃×C₄	C₂³	1	1	yes	characteristic
24	Dic₃	C₂×C₄	1	2	yes	—
25	Q₈	—	3	1	no	—
26	D₄	—	3	2	no	—
27	D₄	—	3	1	no	—
28	C₂×C₄	—	3	2	no	—
29	C₂×C₄	C₂×D₃	1	1	yes	characteristic
30	C₈	—	3	1	no	—
31	C₈	—	3	1	no	—
32	C₈	C₂×D₃	1	2	yes	—
33	C₂×C₃	—	2	1	no	—
34	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
35	D₃	—	2	2	no	—
36	C₂²	—	3	2	no	—
37	C₂²	C₄×D₃	1	1	yes	characteristic
38	C₄	—	3	2	no	—
39	C₄	C₄×D₃	1	1	yes	characteristic
40	C₄	C₂²×D₃	1	1	yes	characteristic
41	C₃	#131	1	1	yes	characteristic, complemented, Sylow
42	C₂	—	2	1	no	—
43	C₂	—	6	2	no	—
44	C₂	C₂×C₄×D₃	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.