Subgroups — C₃⋊(SL(2,𝔽₃)⋊C₈) #10590110

Order 576.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	SL(2,𝔽₃)⋊C₈	—	3	3	no	maximal
3	#4535	—	3	1	no	maximal
4	C₂×C₃×SL(2,𝔽₃)	C₄	1	1	yes	characteristic
5	C₂×C₃⋊(C₃⋊C₈)	—	4	1	no	maximal
6	C₃×C₄×Q₈	D₃	1	1	yes	characteristic
7	C₄×SL(2,𝔽₃)	D₃	1	3	yes	—
8	C₄⋊(C₃⋊C₈)	—	3	1	no	—
9	C₄×C₃⋊C₈	—	3	1	no	—
10	C₂×C₃²×C₄	—	4	1	no	—
11	C₃×SL(2,𝔽₃)	C₈	1	1	yes	characteristic, complemented
12	C₃⋊(C₃⋊C₈)	—	4	2	no	—
13	Q₈⋊C₈	—	9	1	no	Sylow
14	C₂×C₃×Q₈	Dic₃	1	1	yes	characteristic
15	C₂×SL(2,𝔽₃)	Dic₃	1	3	yes	—
16	C₃×C₄⋊C₄	—	3	1	no	—
17	C₃×C₄²	—	3	1	no	—
18	C₂×C₃⋊C₈	—	6	1	no	—
19	C₂×C₃⋊C₈	—	6	1	no	—
20	C₂×C₃⋊C₈	—	12	3	no	—
21	C₂²×C₃²	—	4	1	no	—
22	C₃²×C₄	—	4	1	no	—
23	C₃²×C₄	—	4	1	no	—
24	C₄×Q₈	C₃⋊D₃	1	1	yes	characteristic
25	C₄⋊C₈	—	9	1	no	—
26	C₄×C₈	—	9	1	no	—
27	C₃×Q₈	—	3	1	no	—
28	C₃×Q₈	C₃⋊C₈	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄	—	3	1	no	—
30	C₂×C₃×C₄	—	3	1	no	—
31	C₂×C₃×C₄	—	4	3	no	—
32	C₂×C₃×C₄	S₄	1	1	yes	characteristic
33	SL(2,𝔽₃)	C₃⋊C₈	1	3	yes	complemented
34	C₃⋊C₈	—	6	2	no	—
35	C₃⋊C₈	—	12	6	no	—
36	C₃⋊C₈	—	12	1	no	—
37	C₂×C₃²	—	4	1	no	—
38	C₂×C₃²	—	4	1	no	—
39	C₂×C₃²	—	4	1	no	—
40	C₂×Q₈	C₃⋊Dic₃	1	1	yes	characteristic
41	C₂×C₈	—	18	1	no	—
42	C₂×C₈	—	18	1	no	—
43	C₄⋊C₄	—	3	1	no	—
44	C₄²	—	3	1	no	—
45	C₂²×C₃	—	4	3	no	—
46	C₂²×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
47	C₃×C₄	—	3	1	no	—
48	C₃×C₄	—	3	1	no	—
49	C₃×C₄	—	4	3	no	—
50	C₃×C₄	—	4	3	no	—
51	C₃×C₄	—	6	1	no	—
52	C₃×C₄	#226	1	1	yes	characteristic
53	C₃×C₄	GL(2,𝔽₃)	1	1	yes	characteristic
54	C₃²	—	4	1	no	Sylow
55	Q₈	—	3	1	no	—
56	Q₈	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic, complemented
57	C₂×C₄	—	3	1	no	—
58	C₂×C₄	—	3	1	no	—
59	C₂×C₄	C₃⋊S₄	1	1	yes	characteristic
60	C₈	—	18	2	no	—
61	C₈	—	36	1	no	—
62	C₂×C₃	—	4	3	no	—
63	C₂×C₃	—	4	3	no	—
64	C₂×C₃	—	4	3	no	—
65	C₂×C₃	A₄⋊C₈	1	1	yes	characteristic
66	C₂×C₃	#859	1	1	yes	characteristic
67	C₂×C₃	GU(2,𝔽₃)	1	1	yes	characteristic
68	C₂²	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic
69	C₄	—	3	1	no	—
70	C₄	—	3	1	no	—
71	C₄	—	6	1	no	—
72	C₄	C₃⋊#226	1	1	yes	characteristic
73	C₄	C₃⋊GL(2,𝔽₃)	1	1	yes	characteristic
74	C₃	—	4	3	no	—
75	C₃	SL(2,𝔽₃)⋊C₈	1	1	yes	characteristic, complemented
76	C₂	C₃⋊(A₄⋊C₈)	1	1	yes	characteristic
77	C₂	C₃⋊#859	1	1	yes	characteristic
78	C₂	C₃⋊GU(2,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	C₃⋊S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₈
Fitting	C₃×C₄×Q₈	D₃
socle	C₂²×C₃	SL(2,ℤ/4)
prime radical	C₂×C₃×SL(2,𝔽₃)	C₄
cosocle	C₃×C₄×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
11. C₃×SL(2,𝔽₃)	C₈	semidirect
28. C₃×Q₈	C₃⋊C₈	semidirect
33. SL(2,𝔽₃)	C₃⋊C₈	semidirect
56. Q₈	C₃⋊(C₃⋊C₈)	semidirect
75. C₃	SL(2,𝔽₃)⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×SL(2,𝔽₃)	2
SL(2,𝔽₃)⋊C₈	3
#4535	3
C₂×C₃⋊(C₃⋊C₈)	4

Subgroups — C3⋊(SL(2,𝔽3)⋊C8) #10590110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(SL(2,𝔽₃)⋊C₈) #10590110