Subgroups — #13091194

Order 1458.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624775	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊AGL(1,ℤ/9)	—	3	1	no	maximal
3	#4169⋊C₃	—	3	3	no	maximal
4	#92208	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×3₋¹⁺²	D₃	1	1	yes	characteristic
6	#6891	D₃	1	3	yes	—
7	#6867	—	2	1	no	—
8	#6867	—	2	3	no	—
9	#6867	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃²×C₃⋊D₃	—	9	1	no	—
11	C₃⋊AGL(1,ℤ/9)	—	3	3	no	—
12	C₃⋊AGL(1,ℤ/9)	—	3	3	no	—
13	C₃×C₃⋊D₉	—	3	1	no	—
14	C₃×AGL(1,ℤ/9)	—	9	3	no	—
15	#4169	—	3	6	no	—
16	#4169	—	3	3	no	—
17	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
18	C₃×3₋¹⁺²	—	3	3	no	—
19	C₃×3₋¹⁺²	—	3	3	no	—
20	C₃×3₋¹⁺²	—	3	3	no	—
21	C₃×3₋¹⁺²	—	6	3	no	—
22	C₃²×C₉	—	2	1	no	—
23	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
24	C₃²⋊C₉	—	2	3	no	—
25	C₃²⋊C₉	—	3	6	no	—
26	C₃²⋊C₉	C₃×D₃	1	3	yes	—
27	C₃×C₃⋊D₃	—	9	3	no	—
28	C₃×C₃⋊D₃	—	9	1	no	—
29	C₃²×D₃	—	27	1	no	—
30	C₃²×D₃	—	27	3	no	—
31	C₃⋊D₉	—	3	1	no	—
32	C₃⋊D₉	—	3	3	no	—
33	AGL(1,ℤ/9)	—	9	9	no	—
34	AGL(1,ℤ/9)	—	27	3	no	—
35	C₃×D₉	—	9	3	no	—
36	C₃³	—	3	1	no	—
37	C₃³	—	6	1	no	—
38	C₃³	—	9	3	no	—
39	C₃³	#272	1	3	yes	—
40	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
41	3₋¹⁺²	—	3	9	no	—
42	3₋¹⁺²	—	6	9	no	—
43	3₋¹⁺²	—	9	3	no	—
44	3₋¹⁺²	—	18	3	no	—
45	C₃×C₉	—	2	3	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	—	6	1	no	—
49	C₃×C₉	—	6	1	no	—
50	C₃×C₉	—	6	1	no	—
51	C₃×C₉	—	6	1	no	—
52	C₃×C₉	—	6	3	no	—
53	C₃×C₉	AGL(1,ℤ/9)	1	3	yes	complemented
54	C₂×C₃²	—	81	1	no	—
55	C₃⋊D₃	—	9	1	no	—
56	C₃×D₃	—	27	3	no	—
57	C₃×D₃	—	27	3	no	—
58	C₃×D₃	—	27	3	no	—
59	C₃×D₃	—	27	6	no	—
60	C₃×D₃	—	27	1	no	—
61	D₉	—	9	3	no	—
62	D₉	—	27	3	no	—
63	C₃²	—	2	1	no	—
64	C₃²	—	3	3	no	—
65	C₃²	—	3	3	no	—
66	C₃²	—	3	3	no	—
67	C₃²	—	3	6	no	—
68	C₃²	—	9	1	no	—
69	C₃²	—	18	1	no	—
70	C₃²	—	18	3	no	—
71	C₃²	C₃×#272	1	1	yes	characteristic
72	C₃²	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
73	C₉	—	3	3	no	—
74	C₉	—	6	3	no	—
75	C₉	—	9	3	no	—
76	C₉	—	18	3	no	—
77	C₂×C₃	—	81	1	no	—
78	C₂×C₃	—	81	3	no	—
79	D₃	—	27	1	no	—
80	D₃	—	27	3	no	—
81	C₃	—	3	1	no	—
82	C₃	—	6	1	no	—
83	C₃	—	9	3	no	—
84	C₃	#92302	1	1	yes	characteristic
85	C₃	#4184⋊C₃	1	3	yes	—
86	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	#6867	C₂×C₃
Frattini	C₃³	C₃×C₃⋊D₃
Fitting	#10624775	C₂
socle	C₃²	C₃×#272
LCS	G ▷ #6867
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #10624775	C₂	semidirect
4. #92208	C₃	semidirect
9. #6867	C₂×C₃	semidirect
53. 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
#10624775	2
C₃×C₃⋊AGL(1,ℤ/9)	3
#4169⋊C₃	3
#92208	3