Subgroups — #13091525

Order 1458.

331 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624900	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	D₃×#737	—	3	1	no	maximal
3	#6894⋊C₂	C₃	1	8	yes	maximal, complemented
4	D₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃×D₉⋊C₉	C₃	1	4	yes	maximal, complemented
6	C₃×#737	D₃	1	1	yes	characteristic
7	#6895	—	2	4	no	—
8	#6894	—	2	8	no	—
9	#6894	C₂×C₃	1	8	yes	complemented
10	C₉×H(3,𝔽₃)	—	2	1	no	—
11	C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
12	C₃×C₉⋊C₉	C₂×C₃	1	4	yes	complemented
13	C₂×#737	—	9	1	no	—
14	D₃×3₋¹⁺²	—	3	8	no	—
15	D₃×H(3,𝔽₃)	—	3	1	no	—
16	C₃×D₃×C₉	—	3	4	no	—
17	C₃²×D₉	C₃²	1	4	yes	—
18	D₉⋊C₉	C₃²	1	1	yes	characteristic
19	D₉⋊C₉	C₃²	1	8	yes	—
20	#737	—	3	1	no	—
21	#737	—	6	4	no	—
22	C₃×3₋¹⁺²	C₃×D₃	1	8	yes	—
23	C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
24	C₃²×C₉	—	2	4	no	—
25	C₃²×C₉	C₃×D₃	1	4	yes	—
26	C₃²×C₉	C₂×C₃²	1	4	yes	—
27	C₉⋊C₉	—	2	8	no	—
28	C₉⋊C₉	—	2	4	no	—
29	C₉⋊C₉	—	2	24	no	—
30	C₉⋊C₉	C₂×C₃²	1	1	yes	characteristic
31	C₉⋊C₉	C₂×C₃²	1	8	yes	—
32	C₃²⋊C₉	—	2	8	no	—
33	C₃²⋊C₉	—	2	4	no	—
34	C₃²×D₃	—	3	4	no	—
35	C₂×3₋¹⁺²	—	9	8	no	—
36	C₂×H(3,𝔽₃)	—	9	1	no	—
37	C₂×C₃×C₉	—	9	4	no	—
38	D₃×C₉	—	3	1	no	—
39	D₃×C₉	—	3	8	no	—
40	C₃×D₉	—	3	4	no	—
41	C₃×D₉	C₃³	1	1	yes	characteristic
42	C₃³	C₃²×D₃	1	4	yes	—
43	3₋¹⁺²	—	3	8	no	—
44	3₋¹⁺²	—	6	8	no	—
45	H(3,𝔽₃)	—	2	4	no	—
46	H(3,𝔽₃)	AGL(1,ℤ/9)	1	1	yes	characteristic
47	C₃×C₉	—	2	4	no	—
48	C₃×C₉	—	2	8	no	—
49	C₃×C₉	—	2	1	no	—
50	C₃×C₉	—	3	4	no	—
51	C₃×C₉	—	3	4	no	—
52	C₃×C₉	—	6	4	no	—
53	C₃×C₉	—	6	4	no	—
54	C₃×C₉	—	18	4	no	—
55	C₃×C₉	C₃²×D₃	1	1	yes	characteristic
56	C₃×C₉	C₃²×D₃	1	8	yes	—
57	C₃×C₉	C₂×C₃³	1	1	yes	characteristic
58	C₂×C₃²	—	9	4	no	—
59	C₃×D₃	—	3	1	no	—
60	C₃×D₃	—	9	4	no	—
61	C₂×C₉	—	9	1	no	—
62	C₂×C₉	—	9	8	no	—
63	D₉	#737	1	1	yes	characteristic, complemented
64	C₃²	—	2	4	no	—
65	C₃²	—	3	4	no	—
66	C₃²	—	6	4	no	—
67	C₃²	C₃×AGL(1,ℤ/9)	1	4	yes	—
68	C₃²	C₃³×D₃	1	1	yes	characteristic
69	C₉	—	2	1	no	—
70	C₉	—	3	1	no	—
71	C₉	—	3	8	no	—
72	C₉	—	6	8	no	—
73	C₉	—	6	1	no	—
74	C₉	—	6	4	no	—
75	C₉	C₂×#737	1	1	yes	characteristic, complemented
76	C₂×C₃	—	9	1	no	—
77	C₂×C₃	—	27	4	no	—
78	D₃	—	3	1	no	—
79	C₃	—	2	1	no	—
80	C₃	—	3	4	no	—
81	C₃	—	6	4	no	—
82	C₃	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
83	C₃	D₃×#737	1	1	yes	characteristic
84	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃×C₉	C₂×C₃³
Frattini, socle	C₃²	C₃³×D₃
Fitting	#10624900	C₂
prime radical	D₉×H(3,𝔽₃)	C₃
hypercenter	H(3,𝔽₃)	AGL(1,ℤ/9)
hypocenter	C₉	C₂×#737
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₃ ◁ H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #10624900	C₂	semidirect
3. #6894⋊C₂	C₃	semidirect
5. C₃×D₉⋊C₉	C₃	semidirect
9. #6894	C₂×C₃	semidirect
12. C₃×C₉⋊C₉	C₂×C₃	semidirect
63. D₉	#737	semidirect
75. C₉	C₂×#737	semidirect

Maximal subgroups

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

subgroup	index
#10624900	2
D₃×#737	3
#6894⋊C₂	3
D₉×H(3,𝔽₃)	3
C₃×D₉⋊C₉	3