Subgroups — #13090676

Order 1458.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624571	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊AGL(1,ℤ/9)	—	3	4	no	maximal
3	#92197	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×3₋¹⁺²	D₃	1	4	yes	—
5	#6855	—	2	4	no	—
6	#6855	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃²×C₃⋊D₃	—	9	1	no	—
8	C₃⋊AGL(1,ℤ/9)	—	3	12	no	—
9	C₃×C₃⋊D₉	—	3	4	no	—
10	C₃×AGL(1,ℤ/9)	—	9	12	no	—
11	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
12	C₃×3₋¹⁺²	—	3	12	no	—
13	C₃×3₋¹⁺²	—	3	12	no	—
14	C₃×3₋¹⁺²	—	6	12	no	—
15	C₃²×C₉	—	2	4	no	—
16	C₃²×C₉	C₃×D₃	1	4	yes	—
17	C₃×C₃⋊D₃	—	9	3	no	—
18	C₃×C₃⋊D₃	—	9	1	no	—
19	C₃²×D₃	—	27	4	no	—
20	C₃⋊D₉	—	3	4	no	—
21	AGL(1,ℤ/9)	—	9	36	no	—
22	C₃×D₉	—	9	12	no	—
23	C₃³	—	3	4	no	—
24	C₃³	—	6	4	no	—
25	C₃³	#272	1	3	yes	—
26	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
27	3₋¹⁺²	—	3	36	no	—
28	3₋¹⁺²	—	6	36	no	—
29	C₃×C₉	—	2	12	no	—
30	C₃×C₉	—	3	4	no	—
31	C₃×C₉	—	6	4	no	—
32	C₃×C₉	—	6	4	no	—
33	C₃×C₉	—	6	4	no	—
34	C₃×C₉	—	6	4	no	—
35	C₃×C₉	AGL(1,ℤ/9)	1	12	yes	complemented
36	C₂×C₃²	—	81	1	no	—
37	C₃⋊D₃	—	9	1	no	—
38	C₃×D₃	—	27	12	no	—
39	C₃×D₃	—	27	4	no	—
40	D₉	—	9	12	no	—
41	C₃²	—	2	4	no	—
42	C₃²	—	3	12	no	—
43	C₃²	—	9	1	no	—
44	C₃²	—	18	4	no	—
45	C₃²	C₃×#272	1	1	yes	characteristic
46	C₃²	C₃⋊AGL(1,ℤ/9)	1	4	yes	—
47	C₉	—	3	12	no	—
48	C₉	—	6	12	no	—
49	C₂×C₃	—	81	3	no	—
50	C₂×C₃	—	81	1	no	—
51	D₃	—	27	4	no	—
52	C₃	—	2	4	no	—
53	C₃	—	9	3	no	—
54	C₃	#92302	1	4	yes	—
55	C₃	#92314	1	1	yes	characteristic
56	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#92314
commutator, cosocle, hypocenter	#6855	C₂×C₃
Frattini, socle	C₃³	C₃×C₃⋊D₃
Fitting	#10624571	C₂
LCS	G ▷ #6855
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624571	C₂	semidirect
3. #92197	C₃	semidirect
6. #6855	C₂×C₃	semidirect
35. C₃×C₉	AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
#10624571	2
C₃×C₃⋊AGL(1,ℤ/9)	3
#92197	3