Subgroups — #13091299

Order 1458.

111 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624839	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	#92296	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#4179	—	3	1	no	maximal
4	#92192	C₃	1	3	yes	maximal, complemented
5	C₃×#732	—	2	1	no	—
6	C₃×#732	D₃	1	1	yes	characteristic
7	#6887	C₂×C₃	1	1	yes	characteristic, complemented
8	#6879	—	2	3	no	—
9	#6879	C₂×C₃	1	3	yes	complemented
10	C₃×C₃⋊D₉	—	3	1	no	—
11	C₃×(C₃⋊D₃)⋊C₃	—	9	1	no	—
12	C₉⋊D₉	C₃²	1	1	yes	characteristic, complemented
13	#4179	—	3	3	no	—
14	#4169	—	9	1	no	—
15	C₃×H(3,𝔽₃)	—	3	1	no	—
16	C₃×H(3,𝔽₃)	—	6	1	no	—
17	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
18	#732	—	2	3	no	—
19	#732	—	6	1	no	—
20	#732	—	6	2	no	—
21	#732	C₃×D₃	1	3	yes	—
22	C₉⋊C₉	—	6	1	no	—
23	C₃²⋊C₉	—	3	1	no	—
24	C₉²	—	2	1	no	—
25	C₉²	C₂×C₃²	1	1	yes	characteristic, complemented
26	C₃×C₃⋊D₃	—	9	1	no	—
27	C₃²×D₃	—	27	1	no	—
28	C₃⋊D₉	—	3	1	no	—
29	C₃⋊D₉	—	9	1	no	—
30	(C₃⋊D₃)⋊C₃	—	9	3	no	—
31	C₃×D₉	—	27	1	no	—
32	C₃³	—	9	1	no	—
33	C₃³	—	18	1	no	—
34	C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
35	H(3,𝔽₃)	—	3	3	no	—
36	H(3,𝔽₃)	—	6	3	no	—
37	H(3,𝔽₃)	—	18	1	no	—
38	H(3,𝔽₃)	—	18	1	no	—
39	H(3,𝔽₃)	—	18	1	no	—
40	C₃×C₉	—	2	1	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	—	3	1	no	—
43	C₃×C₉	—	6	1	no	—
44	C₃×C₉	—	6	1	no	—
45	C₃×C₉	C₃²×D₃	1	1	yes	characteristic
46	C₂×C₃²	—	81	1	no	—
47	C₃⋊D₃	—	9	1	no	—
48	C₃×D₃	—	27	3	no	—
49	C₃×D₃	—	27	1	no	—
50	C₃×D₃	—	81	1	no	—
51	D₉	—	27	1	no	—
52	D₉	—	81	1	no	—
53	C₃²	—	2	1	no	—
54	C₃²	—	9	1	no	—
55	C₃²	—	9	3	no	—
56	C₃²	—	18	3	no	—
57	C₃²	—	27	1	no	—
58	C₃²	—	54	1	no	—
59	C₃²	—	54	3	no	—
60	C₃²	#4179	1	1	yes	characteristic
61	C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
62	C₉	—	3	1	no	—
63	C₉	—	6	1	no	—
64	C₉	—	9	1	no	—
65	C₉	—	18	1	no	—
66	C₂×C₃	—	81	1	no	—
67	C₂×C₃	—	81	3	no	—
68	D₃	—	27	1	no	—
69	D₃	—	81	1	no	—
70	C₃	—	3	1	no	—
71	C₃	—	3	1	no	—
72	C₃	—	6	1	no	—
73	C₃	—	27	3	no	—
74	C₃	—	54	3	no	—
75	C₃	C₃×#4179	1	1	yes	characteristic
76	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉²	C₂×C₃²
Frattini	C₃×C₉	C₃²×D₃
Fitting	#10624839	C₂
socle	C₃	C₃×#4179
LCS	G ▷ C₉²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. #10624839	C₂	semidirect
2. #92296	C₃	semidirect
4. #92192	C₃	semidirect
7. #6887	C₂×C₃	semidirect
9. #6879	C₂×C₃	semidirect
12. C₉⋊D₉	C₃²	semidirect
25. C₉²	C₂×C₃²	semidirect

Maximal subgroups

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

subgroup	index
#10624839	2
#92296	3
C₃×#4179	3
#92192	3