Subgroups — #815

Order 96.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#97	—	3	1	no	maximal, Sylow
5	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂×Dic₃	C₄	1	2	yes	—
7	C₃×C₈	C₄	1	2	yes	complemented
8	C₃⋊C₈	C₄	1	2	yes	complemented
9	C₂×C₈	—	3	1	no	—
10	C₂×C₈	D₃	1	1	yes	characteristic
11	C₄²	—	3	1	no	—
12	C₂²×C₃	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄	C₂×C₄	1	1	yes	characteristic
15	Dic₃	—	2	2	no	—
16	C₂×C₄	—	3	2	no	—
17	C₂×C₄	C₂×D₃	1	1	yes	characteristic
18	C₈	—	3	2	no	—
19	C₈	Dic₃	1	2	yes	complemented
20	C₂×C₃	C₄²	1	1	yes	characteristic
21	C₂×C₃	M₁₆	1	2	yes	—
22	C₂²	C₄×D₃	1	1	yes	characteristic
23	C₄	—	6	2	no	—
24	C₄	C₄×D₃	1	1	yes	characteristic
25	C₄	C₂×Dic₃	1	1	yes	characteristic
26	C₃	#97	1	1	yes	characteristic, complemented, Sylow
27	C₂	ΓL(1,𝔽₂₅)	1	2	yes	—
28	C₂	C₄×Dic₃	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.