Subgroups — SU(3,𝔽₂)⋊C₉ #14517898

Order 1944.

73 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	#272⋊C₉	—	4	1	no	maximal
3	C₃×#1088	—	3	1	no	—
4	H(3,𝔽₃)⋊C₉	—	4	1	no	Sylow
5	SU(3,𝔽₂)	C₉	1	1	yes	characteristic, complemented
6	C₃×Q₈⋊C₉	—	9	1	no	maximal
7	C₃×#272	A₄	1	1	yes	characteristic
8	C₃×D₃×C₉	—	12	1	no	—
9	#1088	—	3	1	no	—
10	C₃×H(3,𝔽₃)	SL(2,𝔽₃)	1	1	yes	characteristic
11	C₃²×C₉	—	4	1	no	—
12	C₃²⋊C₉	—	8	1	no	—
13	C₃²×Q₈	—	9	1	no	—
14	Q₈⋊C₉	—	9	3	no	—
15	C₃²×D₃	—	12	1	no	—
16	C₂×C₃×C₉	—	36	1	no	—
17	#272	C₂²⋊C₉	1	1	yes	characteristic
18	D₃×C₉	—	12	3	no	—
19	C₃²×C₄	—	27	1	no	—
20	C₃³	—	4	1	no	—
21	H(3,𝔽₃)	—	8	1	no	—
22	H(3,𝔽₃)	Q₈⋊C₉	1	1	yes	characteristic, complemented
23	C₃×C₉	—	12	1	no	—
24	C₃×C₉	—	12	3	no	—
25	C₃×C₉	—	24	1	no	—
26	C₃×Q₈	—	9	1	no	—
27	C₃×Q₈	—	9	1	no	—
28	C₃×Q₈	—	9	1	no	—
29	C₃×Q₈	—	9	1	no	—
30	C₂×C₃²	—	9	1	no	—
31	C₃×D₃	—	12	1	no	—
32	C₃×D₃	—	12	1	no	—
33	C₃×D₃	—	12	1	no	—
34	C₃×D₃	—	12	1	no	—
35	C₂×C₉	—	36	3	no	—
36	C₃×C₄	—	27	1	no	—
37	C₃×C₄	—	27	1	no	—
38	C₃×C₄	—	27	1	no	—
39	C₃×C₄	—	27	1	no	—
40	C₃²	—	4	1	no	—
41	C₃²	—	8	1	no	—
42	C₃²	—	12	1	no	—
43	C₃²	—	12	1	no	—
44	C₃²	—	12	1	no	—
45	C₃²	PSU(3,𝔽₂)⋊C₃	1	1	yes	characteristic
46	C₉	—	12	3	no	—
47	C₉	—	72	1	no	—
48	Q₈	—	9	1	no	Sylow
49	C₂×C₃	—	9	1	no	—
50	C₂×C₃	—	9	1	no	—
51	C₂×C₃	—	9	1	no	—
52	C₂×C₃	—	9	1	no	—
53	D₃	—	12	1	no	—
54	C₄	—	27	1	no	—
55	C₃	—	12	1	no	—
56	C₃	—	24	1	no	—
57	C₃	#10620012	1	1	yes	characteristic
58	C₃	#10620013	1	1	yes	characteristic
59	C₃	GU(3,𝔽₂)	1	1	yes	characteristic
60	C₃	PSU(3,𝔽₂)⋊C₉	1	1	yes	characteristic
61	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, socle, hypercenter	C₃²	PSU(3,𝔽₂)⋊C₃
commutator, hypocenter	SU(3,𝔽₂)	C₉
Fitting	C₃×H(3,𝔽₃)	SL(2,𝔽₃)
prime radical	C₃×#272	A₄
cosocle	C₃×SU(3,𝔽₂)	C₃
LCS	G ▷ SU(3,𝔽₂)
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
5. SU(3,𝔽₂)	C₉	semidirect
22. H(3,𝔽₃)	Q₈⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×SU(3,𝔽₂)	3
#272⋊C₉	4
C₃×Q₈⋊C₉	9

Subgroups — SU(3,𝔽2)⋊C9 #14517898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SU(3,𝔽₂)⋊C₉ #14517898