Subgroups — #13090774

Order 1458.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624617	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#92302	C₃	1	1	yes	maximal, characteristic
3	#92259	—	3	1	no	maximal
4	#92165	C₃	1	3	yes	maximal, complemented
5	#6891	D₃	1	1	yes	characteristic
6	#6891	C₂×C₃	1	1	yes	characteristic
7	C₃×C₃²⋊C₉	—	2	1	no	—
8	#6861	—	2	3	no	—
9	#6861	C₂×C₃	1	3	yes	complemented
10	C₃²×C₃⋊D₃	—	3	1	no	—
11	D₃×3₋¹⁺²	—	9	1	no	—
12	C₃×AGL(1,ℤ/9)	—	9	1	no	—
13	#4181	C₃²	1	1	yes	characteristic
14	(C₃⋊D₃)⋊C₉	—	3	3	no	—
15	C₃⁴	C₃×D₃	1	1	yes	characteristic
16	C₃×3₋¹⁺²	—	3	1	no	—
17	C₃×3₋¹⁺²	—	3	1	no	—
18	C₃²×C₉	—	6	1	no	—
19	C₃²⋊C₉	—	2	1	no	—
20	C₃²⋊C₉	—	2	3	no	—
21	C₃²⋊C₉	—	6	1	no	—
22	C₃²⋊C₉	—	6	1	no	—
23	C₃²⋊C₉	—	6	1	no	—
24	C₃²⋊C₉	—	6	1	no	—
25	C₃²⋊C₉	C₃×D₃	1	3	yes	—
26	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
27	C₃×C₃⋊D₃	—	3	1	no	—
28	C₃×C₃⋊D₃	—	9	1	no	—
29	C₃²×D₃	—	9	1	no	—
30	C₃²×D₃	—	27	1	no	—
31	C₂×3₋¹⁺²	—	27	1	no	—
32	AGL(1,ℤ/9)	—	9	3	no	—
33	D₃×C₉	—	9	3	no	—
34	C₃×D₉	—	9	1	no	—
35	C₃³	—	2	1	no	—
36	C₃³	—	6	3	no	—
37	C₃³	—	9	1	no	—
38	C₃³	—	9	1	no	—
39	C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
40	C₃³	C₃²×D₃	1	1	yes	characteristic
41	3₋¹⁺²	—	9	1	no	—
42	3₋¹⁺²	—	9	3	no	—
43	3₋¹⁺²	—	18	1	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	—	6	3	no	—
47	C₃×C₉	—	6	1	no	—
48	C₃×C₉	—	18	3	no	—
49	C₂×C₃²	—	27	1	no	—
50	C₃⋊D₃	—	3	1	no	—
51	C₃×D₃	—	9	1	no	—
52	C₃×D₃	—	27	1	no	—
53	C₃×D₃	—	27	1	no	—
54	C₃×D₃	—	27	3	no	—
55	C₂×C₉	—	27	3	no	—
56	D₉	—	9	1	no	—
57	C₃²	—	2	3	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	3	1	no	—
60	C₃²	—	3	1	no	—
61	C₃²	—	3	1	no	—
62	C₃²	—	6	1	no	—
63	C₃²	—	6	1	no	—
64	C₃²	—	6	1	no	—
65	C₃²	—	6	1	no	—
66	C₃²	—	6	1	no	—
67	C₃²	—	9	3	no	—
68	C₃²	—	18	3	no	—
69	C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
70	C₉	—	9	3	no	—
71	C₉	—	9	1	no	—
72	C₉	—	18	3	no	—
73	C₉	—	18	1	no	—
74	C₂×C₃	—	27	1	no	—
75	C₂×C₃	—	81	1	no	—
76	D₃	—	9	1	no	—
77	D₃	—	27	1	no	—
78	C₃	—	2	1	no	—
79	C₃	—	6	3	no	—
80	C₃	—	9	1	no	—
81	C₃	—	9	1	no	—
82	C₃	#4177⋊C₃	1	1	yes	characteristic
83	C₃	#92285	1	1	yes	characteristic
84	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4177⋊C₃
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃²
Frattini	C₃³	C₃²×D₃
Fitting	#10624617	C₂
socle	C₃²	C₃×(C₃⋊D₃)⋊C₃
prime radical	#92302	C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #10624617	C₂	semidirect
4. #92165	C₃	semidirect
9. #6861	C₂×C₃	semidirect

Maximal subgroups

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

subgroup	index
#10624617	2
#92302	3
#92259	3
#92165	3