Subgroups — C₃⋊#859 #63755

Order 288.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	#859	—	3	3	no	maximal
3	#835	—	3	1	no	maximal
4	C₂×C₃⋊Dic₃	—	4	1	no	maximal
5	C₃×SL(2,𝔽₃)	C₄	1	1	yes	characteristic, complemented
6	C₂×C₃×Q₈	D₃	1	1	yes	characteristic
7	C₂×SL(2,𝔽₃)	D₃	1	3	yes	—
8	C₄⋊Dic₃	—	3	1	no	—
9	C₂×C₃⋊C₈	—	3	1	no	—
10	C₂²×C₃²	—	4	1	no	—
11	C₃⋊Dic₃	—	4	2	no	—
12	#103	—	9	1	no	Sylow
13	C₃×Q₈	—	3	1	no	—
14	C₃×Q₈	Dic₃	1	1	yes	characteristic, complemented
15	C₂×C₃×C₄	—	3	1	no	—
16	C₂×Dic₃	—	6	1	no	—
17	C₂×Dic₃	—	12	3	no	—
18	SL(2,𝔽₃)	Dic₃	1	3	yes	complemented
19	C₃⋊C₈	—	6	1	no	—
20	C₂×C₃²	—	4	1	no	—
21	C₂×C₃²	—	4	1	no	—
22	C₂×C₃²	—	4	1	no	—
23	C₂×Q₈	C₃⋊D₃	1	1	yes	characteristic
24	C₂×C₈	—	9	1	no	—
25	C₄⋊C₄	—	9	1	no	—
26	C₂²×C₃	—	4	3	no	—
27	C₂²×C₃	S₄	1	1	yes	characteristic
28	C₃×C₄	—	3	1	no	—
29	C₃×C₄	—	3	1	no	—
30	Dic₃	—	12	6	no	—
31	Dic₃	—	12	1	no	—
32	C₃²	—	4	1	no	Sylow
33	Q₈	—	3	1	no	—
34	Q₈	C₃⋊Dic₃	1	1	yes	characteristic, complemented
35	C₂×C₄	—	3	1	no	—
36	C₂×C₄	—	18	1	no	—
37	C₈	—	18	1	no	—
38	C₂×C₃	—	4	3	no	—
39	C₂×C₃	—	4	3	no	—
40	C₂×C₃	—	4	3	no	—
41	C₂×C₃	#226	1	1	yes	characteristic
42	C₂×C₃	GL(2,𝔽₃)	1	1	yes	characteristic
43	C₂×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
44	C₂²	C₃⋊S₄	1	1	yes	characteristic
45	C₄	—	3	1	no	—
46	C₄	—	3	1	no	—
47	C₄	—	36	1	no	—
48	C₃	—	4	3	no	—
49	C₃	#859	1	1	yes	characteristic, complemented
50	C₂	C₃⋊#226	1	1	yes	characteristic
51	C₂	C₃⋊GL(2,𝔽₃)	1	1	yes	characteristic
52	C₂	C₃⋊SL(2,ℤ/4)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₃×SL(2,𝔽₃)	C₄	semidirect
14. C₃×Q₈	Dic₃	semidirect
18. SL(2,𝔽₃)	Dic₃	semidirect
34. Q₈	C₃⋊Dic₃	semidirect
49. C₃	#859	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×SL(2,𝔽₃)	2
#859	3
#835	3
C₂×C₃⋊Dic₃	4

Subgroups — C3⋊#859 #63755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#859 #63755