Subgroups — #13091196

Order 1458.

179 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624776	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊D₃×3₋¹⁺²	—	3	1	no	maximal
3	#92302	C₃	1	1	yes	maximal, characteristic
4	#92178	C₃	1	3	yes	maximal, complemented
5	C₃²×3₋¹⁺²	D₃	1	1	yes	characteristic
6	#6891	—	2	1	no	—
7	#6891	C₂×C₃	1	1	yes	characteristic
8	#6868	—	2	3	no	—
9	#6868	C₂×C₃	1	3	yes	complemented
10	C₃²×C₃⋊D₃	—	3	1	no	—
11	C₉×C₃⋊D₃	—	3	3	no	—
12	D₃×3₋¹⁺²	—	9	1	no	—
13	D₃×3₋¹⁺²	—	9	3	no	—
14	C₃×AGL(1,ℤ/9)	—	9	1	no	—
15	#4181	C₃²	1	1	yes	characteristic
16	C₃⁴	C₃×D₃	1	1	yes	characteristic
17	C₃×3₋¹⁺²	—	3	1	no	—
18	C₃×3₋¹⁺²	—	3	3	no	—
19	C₃×3₋¹⁺²	—	3	1	no	—
20	C₃×3₋¹⁺²	—	6	3	no	—
21	C₃×3₋¹⁺²	—	6	1	no	—
22	C₃×3₋¹⁺²	—	6	1	no	—
23	C₃²×C₉	C₃×D₃	1	3	yes	—
24	C₃²⋊C₉	—	2	1	no	—
25	C₃²⋊C₉	—	2	3	no	—
26	C₃²⋊C₉	—	6	1	no	—
27	C₃²⋊C₉	—	6	1	no	—
28	C₃²⋊C₉	—	6	1	no	—
29	C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
30	C₃×C₃⋊D₃	—	3	1	no	—
31	C₃×C₃⋊D₃	—	9	1	no	—
32	C₃²×D₃	—	9	3	no	—
33	C₃²×D₃	—	9	1	no	—
34	C₂×3₋¹⁺²	—	27	1	no	—
35	AGL(1,ℤ/9)	—	9	3	no	—
36	D₃×C₉	—	9	3	no	—
37	D₃×C₉	—	9	6	no	—
38	D₃×C₉	—	9	3	no	—
39	C₃×D₉	—	9	1	no	—
40	C₃³	—	2	1	no	—
41	C₃³	—	3	3	no	—
42	C₃³	—	9	1	no	—
43	C₃³	—	18	1	no	—
44	C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
45	C₃³	C₃²×D₃	1	1	yes	characteristic
46	3₋¹⁺²	—	3	1	no	—
47	3₋¹⁺²	—	6	3	no	—
48	3₋¹⁺²	—	6	3	no	—
49	3₋¹⁺²	—	6	3	no	—
50	3₋¹⁺²	—	6	1	no	—
51	3₋¹⁺²	—	6	3	no	—
52	3₋¹⁺²	—	9	3	no	—
53	3₋¹⁺²	—	18	3	no	—
54	C₃×C₉	—	2	3	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	3	6	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	6	3	no	—
59	C₃×C₉	—	6	1	no	—
60	C₃×C₉	AGL(1,ℤ/9)	1	3	yes	complemented
61	C₂×C₃²	—	27	1	no	—
62	C₃⋊D₃	—	3	1	no	—
63	C₃×D₃	—	9	1	no	—
64	C₃×D₃	—	9	3	no	—
65	C₃×D₃	—	27	1	no	—
66	C₃×D₃	—	27	3	no	—
67	C₂×C₉	—	27	3	no	—
68	D₉	—	9	1	no	—
69	C₃²	—	3	1	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	3	1	no	—
72	C₃²	—	6	1	no	—
73	C₃²	—	6	1	no	—
74	C₃²	—	6	2	no	—
75	C₃²	—	6	1	no	—
76	C₃²	—	6	1	no	—
77	C₃²	—	9	3	no	—
78	C₃²	—	18	3	no	—
79	C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
80	C₃²	C₃×AGL(1,ℤ/9)	1	3	yes	—
81	C₉	—	3	3	no	—
82	C₉	—	6	3	no	—
83	C₉	—	9	1	no	—
84	C₉	—	18	1	no	—
85	C₉	—	18	3	no	—
86	C₂×C₃	—	27	1	no	—
87	C₂×C₃	—	81	1	no	—
88	D₃	—	9	3	no	—
89	D₃	—	9	1	no	—
90	C₃	—	2	1	no	—
91	C₃	—	3	3	no	—
92	C₃	—	9	1	no	—
93	C₃	—	18	1	no	—
94	C₃	#4169⋊C₃	1	1	yes	characteristic
95	C₃	#92285	1	1	yes	characteristic
96	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#4169⋊C₃
commutator, cosocle, hypocenter	C₃²⋊C₉	C₂×C₃²
Frattini	C₃³	C₃²×D₃
Fitting	#10624776	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. #10624776	C₂	semidirect
4. #92178	C₃	semidirect
9. #6868	C₂×C₃	semidirect
60. 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
#10624776	2
C₃⋊D₃×3₋¹⁺²	3
#92302	3
#92178	3