Subgroups — C₄×SL(2,𝔽₃) #862

Order 96.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂×C₃×C₄	—	4	1	no	maximal
4	SL(2,𝔽₃)	C₄	1	1	yes	characteristic, direct product factor
5	C₂×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₄⋊C₄	—	3	1	no	—
7	C₄²	—	3	1	no	—
8	C₂²×C₃	—	4	1	no	—
9	C₃×C₄	—	4	2	no	—
10	Q₈	—	3	1	no	—
11	Q₈	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂×C₄	—	3	1	no	—
13	C₂×C₄	—	3	1	no	—
14	C₂×C₄	A₄	1	1	yes	characteristic
15	C₂×C₃	—	4	1	no	—
16	C₂×C₃	—	4	1	no	—
17	C₂×C₃	—	4	1	no	—
18	C₂²	C₂×A₄	1	1	yes	characteristic
19	C₄	—	3	1	no	—
20	C₄	—	3	1	no	—
21	C₄	—	6	1	no	—
22	C₄	SL(2,𝔽₃)	1	2	yes	direct product factor
23	C₃	—	4	1	no	Sylow
24	C₂	C₄×A₄	1	1	yes	characteristic
25	C₂	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
26	C₂	#41⋊C₃	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.