Subgroups — C₃×C₉×#272 #13091365

Order 1458.

812 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃²×#272	C₃	1	1	yes	maximal, characteristic
3	C₃²×D₃×C₉	—	3	4	no	maximal
4	C₉×#272	C₃	1	3	yes	maximal, direct product factor
5	C₃²×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	C₃³×C₉	D₃	1	4	yes	complemented
7	C₉×H(3,𝔽₃)	—	2	12	no	—
8	C₉×H(3,𝔽₃)	C₂×C₃	1	3	yes	complemented
9	C₃×C₃²⋊C₉	—	2	4	no	—
10	C₃³×D₃	—	3	4	no	—
11	C₂×C₃²×C₉	—	9	1	no	—
12	C₃×#272	C₉	1	3	yes	direct product factor
13	C₃×#272	C₃²	1	1	yes	characteristic
14	C₃×D₃×C₉	—	3	36	no	—
15	C₃×D₃×C₉	—	3	12	no	—
16	C₃⁴	C₃×D₃	1	4	yes	—
17	C₃×H(3,𝔽₃)	—	2	12	no	—
18	C₃×H(3,𝔽₃)	—	2	4	no	—
19	C₃×H(3,𝔽₃)	C₂×C₉	1	3	yes	complemented
20	C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
21	C₃²×C₉	—	2	4	no	—
22	C₃²×C₉	—	2	12	no	—
23	C₃²×C₉	—	3	36	no	—
24	C₃²×C₉	C₃×D₃	1	12	yes	complemented
25	C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
26	C₃²⋊C₉	—	2	24	no	—
27	C₃²⋊C₉	—	2	12	no	—
28	C₂×C₃³	—	9	1	no	—
29	C₃²×D₃	—	3	12	no	—
30	C₃²×D₃	—	3	24	no	—
31	C₃²×D₃	—	3	12	no	—
32	C₃²×D₃	—	3	4	no	—
33	C₂×C₃×C₉	—	9	9	no	—
34	C₂×C₃×C₉	—	9	3	no	—
35	#272	C₃×C₉	1	1	yes	characteristic, direct product factor
36	D₃×C₉	—	3	36	no	—
37	C₃³	—	2	12	no	—
38	C₃³	—	2	4	no	—
39	C₃³	—	3	12	no	—
40	C₃³	—	3	24	no	—
41	C₃³	D₃×C₉	1	12	yes	complemented
42	C₃³	C₃²×D₃	1	4	yes	—
43	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
44	H(3,𝔽₃)	—	2	24	no	—
45	H(3,𝔽₃)	—	2	12	no	—
46	H(3,𝔽₃)	—	2	4	no	—
47	H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic, complemented
48	C₃×C₉	—	2	12	no	—
49	C₃×C₉	—	3	36	no	—
50	C₃×C₉	—	6	12	no	—
51	C₃×C₉	—	6	36	no	—
52	C₃×C₉	#272	1	9	yes	direct product factor
53	C₃×C₉	C₃×C₃⋊D₃	1	3	yes	—
54	C₂×C₃²	—	9	3	no	—
55	C₂×C₃²	—	9	3	no	—
56	C₂×C₃²	—	9	6	no	—
57	C₂×C₃²	—	9	1	no	—
58	C₃×D₃	—	3	4	no	—
59	C₃×D₃	—	3	36	no	—
60	C₃×D₃	—	3	8	no	—
61	C₃×D₃	—	3	4	no	—
62	C₂×C₉	—	9	9	no	—
63	C₃²	—	2	12	no	—
64	C₃²	—	2	4	no	—
65	C₃²	—	3	36	no	—
66	C₃²	—	3	4	no	—
67	C₃²	—	3	8	no	—
68	C₃²	—	6	36	no	—
69	C₃²	—	6	4	no	—
70	C₃²	—	6	8	no	—
71	C₃²	C₃×D₃×C₉	1	4	yes	complemented
72	C₃²	C₉×C₃⋊D₃	1	3	yes	—
73	C₃²	C₃×#272	1	3	yes	—
74	C₃²	#4208	1	6	yes	—
75	C₃²	C₃²×C₃⋊D₃	1	1	yes	characteristic
76	C₉	—	6	12	no	—
77	C₉	C₃×#272	1	9	yes	direct product factor
78	C₂×C₃	—	9	9	no	—
79	C₂×C₃	—	9	1	no	—
80	C₂×C₃	—	9	1	no	—
81	C₂×C₃	—	9	2	no	—
82	D₃	—	3	4	no	—
83	C₃	—	3	4	no	—
84	C₃	—	6	12	no	—
85	C₃	—	6	4	no	—
86	C₃	C₉×#272	1	9	yes	direct product factor
87	C₃	C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
88	C₃	C₃²×#272	1	1	yes	characteristic
89	C₃	C₃×#4208	1	2	yes	—
90	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₉	C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂×C₃×C₉
Frattini	C₃²	C₃²×C₃⋊D₃
Fitting	C₃×C₉×H(3,𝔽₃)	C₂
socle	C₃³	C₃×C₃⋊D₃
prime radical	C₃²×#272	C₃
cosocle	C₃×H(3,𝔽₃)	C₂×C₃²
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×H(3,𝔽₃)	C₂	semidirect
4. C₉×#272	C₃	direct (N × H)
6. C₃³×C₉	D₃	semidirect
8. C₉×H(3,𝔽₃)	C₂×C₃	semidirect
12. C₃×#272	C₉	direct (N × H)
19. C₃×H(3,𝔽₃)	C₂×C₉	semidirect
24. C₃²×C₉	C₃×D₃	semidirect
35. #272	C₃×C₉	direct (N × H)
41. C₃³	D₃×C₉	semidirect
47. H(3,𝔽₃)	C₂×C₃×C₉	semidirect
52. C₃×C₉	#272	direct (N × H)
71. C₃²	C₃×D₃×C₉	semidirect
77. C₉	C₃×#272	direct (N × H)
86. C₃	C₉×#272	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₉×H(3,𝔽₃)	2
C₃²×#272	3
C₃²×D₃×C₉	3
C₉×#272	3

Subgroups — C3×C9×#272 #13091365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#272 #13091365