Subgroups — SL(2,𝔽₃)⋊C₈ #4624

Order 192.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	Q₈⋊C₈	—	3	1	no	maximal, Sylow
3	C₂×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
4	C₂×C₃⋊C₈	—	4	1	no	maximal
5	C₄×Q₈	D₃	1	1	yes	characteristic
6	C₄⋊C₈	—	3	1	no	—
7	C₄×C₈	—	3	1	no	—
8	C₂×C₃×C₄	—	4	1	no	—
9	SL(2,𝔽₃)	C₈	1	1	yes	characteristic, complemented
10	C₃⋊C₈	—	4	2	no	—
11	C₂×Q₈	Dic₃	1	1	yes	characteristic
12	C₂×C₈	—	6	1	no	—
13	C₂×C₈	—	6	1	no	—
14	C₄⋊C₄	—	3	1	no	—
15	C₄²	—	3	1	no	—
16	C₂²×C₃	—	4	1	no	—
17	C₃×C₄	—	4	1	no	—
18	C₃×C₄	—	4	1	no	—
19	Q₈	—	3	1	no	—
20	Q₈	C₃⋊C₈	1	1	yes	characteristic, complemented
21	C₂×C₄	—	3	1	no	—
22	C₂×C₄	—	3	1	no	—
23	C₂×C₄	S₄	1	1	yes	characteristic
24	C₈	—	6	2	no	—
25	C₈	—	12	1	no	—
26	C₂×C₃	—	4	1	no	—
27	C₂×C₃	—	4	1	no	—
28	C₂×C₃	—	4	1	no	—
29	C₂²	SL(2,ℤ/4)	1	1	yes	characteristic
30	C₄	—	3	1	no	—
31	C₄	—	3	1	no	—
32	C₄	—	6	1	no	—
33	C₄	#226	1	1	yes	characteristic
34	C₄	GL(2,𝔽₃)	1	1	yes	characteristic
35	C₃	—	4	1	no	Sylow
36	C₂	A₄⋊C₈	1	1	yes	characteristic
37	C₂	#859	1	1	yes	characteristic
38	C₂	GU(2,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	S₄
commutator, hypocenter	SL(2,𝔽₃)	C₈
Fitting	C₄×Q₈	D₃
socle	C₂²	SL(2,ℤ/4)
prime radical	C₂×SL(2,𝔽₃)	C₄
cosocle	C₄×SL(2,𝔽₃)	C₂
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
9. SL(2,𝔽₃)	C₈	semidirect
20. Q₈	C₃⋊C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.