Subgroups — #14519051

Order 1944.

83 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×SU(3,𝔽₂)	C₃	1	1	yes	maximal, characteristic
2	#10620012	C₃	1	3	yes	maximal, complemented
3	#92283	—	4	1	no	maximal
4	C₃×#1088	—	3	1	no	—
5	#6910	—	4	1	no	Sylow
6	SU(3,𝔽₂)	C₃²	1	1	yes	characteristic
7	#6204	—	9	1	no	maximal
8	C₃×#272	A₄	1	1	yes	characteristic
9	D₃×3₋¹⁺²	—	12	1	no	—
10	#4176	—	4	3	no	—
11	#1088	—	3	1	no	—
12	C₃×3₋¹⁺²	—	4	1	no	—
13	C₃×3₋¹⁺²	—	8	1	no	—
14	C₃×H(3,𝔽₃)	SL(2,𝔽₃)	1	1	yes	characteristic
15	#731	—	4	3	no	—
16	#731	—	8	3	no	—
17	C₃²×Q₈	—	9	1	no	—
18	Q₈⋊C₉	—	9	3	no	—
19	C₃²×D₃	—	12	1	no	—
20	C₂×3₋¹⁺²	—	36	1	no	—
21	#272	C₃×A₄	1	1	yes	characteristic
22	D₃×C₉	—	12	3	no	—
23	C₃²×C₄	—	27	1	no	—
24	C₃³	—	4	1	no	—
25	3₋¹⁺²	—	8	3	no	—
26	3₋¹⁺²	—	12	1	no	—
27	3₋¹⁺²	—	24	1	no	—
28	3₋¹⁺²	—	24	1	no	—
29	3₋¹⁺²	—	24	1	no	—
30	H(3,𝔽₃)	—	8	1	no	—
31	H(3,𝔽₃)	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
32	C₃×C₉	—	4	3	no	—
33	C₃×C₉	—	24	1	no	—
34	C₃×Q₈	—	9	1	no	—
35	C₃×Q₈	—	27	1	no	—
36	C₂×C₃²	—	9	1	no	—
37	C₃×D₃	—	12	1	no	—
38	C₃×D₃	—	36	1	no	—
39	C₂×C₉	—	36	3	no	—
40	C₃×C₄	—	27	1	no	—
41	C₃×C₄	—	27	3	no	—
42	C₃²	—	4	1	no	—
43	C₃²	—	8	1	no	—
44	C₃²	—	36	1	no	—
45	C₃²	PSU(3,𝔽₂)⋊C₃	1	1	yes	characteristic
46	C₉	—	12	3	no	—
47	C₉	—	24	3	no	—
48	Q₈	—	9	1	no	Sylow
49	C₂×C₃	—	9	1	no	—
50	C₂×C₃	—	27	1	no	—
51	D₃	—	12	1	no	—
52	C₄	—	27	1	no	—
53	C₃	—	3	1	no	—
54	C₃	—	12	1	no	—
55	C₃	—	24	1	no	—
56	C₃	C₃×PSU(3,𝔽₂)⋊C₃	1	1	yes	characteristic
57	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, socle	C₃	C₃×PSU(3,𝔽₂)⋊C₃
commutator, cosocle, hypocenter	SU(3,𝔽₂)	C₃²
Fitting	C₃×H(3,𝔽₃)	SL(2,𝔽₃)
prime radical	C₃×#272	A₄
hypercenter	C₃²	PSU(3,𝔽₂)⋊C₃
LCS	G ▷ SU(3,𝔽₂)
UCS	C₁ ◁ C₃ ◁ C₃²

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

N	H ≅ G/N	type
2. #10620012	C₃	semidirect

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