Subgroups — C₃×#17987421 #28355944

Order 13851.

2636 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587025	C₃	1	3	yes	maximal, complemented
2	#17987421	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₃²⋊#4294	C₃	1	9	yes	maximal, complemented
4	C₃⁵×C₁₉	C₃	1	1	yes	maximal, characteristic
5	C₃×#10587025	—	3	27	no	—
6	C₃×#10587025	C₃²	1	27	yes	complemented
7	C₃²×#4294	C₃²	1	9	yes	complemented
8	C₃²⋊#4294	C₃²	1	81	yes	complemented
9	C₃⁴×C₁₉	—	3	9	no	—
10	C₃⁴×C₁₉	—	3	27	no	—
11	C₃⁴×C₁₉	C₃²	1	9	yes	—
12	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
13	C₃⁴×C₁₉	C₃²	1	3	yes	—
14	C₃×#6891	—	19	1	no	maximal, Sylow
15	C₃³×C₁₉	—	3	243	no	—
16	C₃³×C₁₉	—	3	27	no	—
17	C₃³×C₁₉	—	3	9	no	—
18	C₃³×C₁₉	—	3	9	no	—
19	C₃³×C₁₉	—	3	18	no	—
20	C₃³×C₁₉	—	3	81	no	—
21	C₃³×C₁₉	H(3,𝔽₃)	1	9	yes	—
22	C₃³×C₁₉	3₋¹⁺²	1	27	yes	complemented
23	C₃³×C₁₉	C₃³	1	3	yes	—
24	C₃³×C₁₉	C₃³	1	9	yes	—
25	C₃³×C₁₉	C₃³	1	1	yes	characteristic
26	#10587025	—	3	81	no	—
27	C₃×#4294	—	3	27	no	—
28	C₃×#4294	C₃³	1	27	yes	complemented
29	C₃⁵	C₁₉⋊C₃	1	1	yes	characteristic
30	C₃²×3₋¹⁺²	—	19	3	no	—
31	#6891	—	19	27	no	—
32	C₃×C₃²⋊C₉	—	19	9	no	—
33	C₃²×C₁₉	—	3	243	no	—
34	C₃²×C₁₉	—	3	9	no	—
35	C₃²×C₁₉	—	3	9	no	—
36	C₃²×C₁₉	—	3	18	no	—
37	C₃²×C₁₉	—	3	27	no	—
38	C₃²×C₁₉	—	3	81	no	—
39	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	3	yes	—
41	C₃²×C₁₉	C₃×3₋¹⁺²	1	9	yes	—
42	C₃²×C₁₉	C₃×3₋¹⁺²	1	27	yes	complemented
43	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
44	#4294	—	3	27	no	—
45	C₃⁴	—	3	27	no	—
46	C₃⁴	—	3	9	no	—
47	C₃⁴	C₃×C₁₉⋊C₃	1	9	yes	—
48	C₃⁴	C₃×C₁₉⋊C₃	1	3	yes	—
49	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	19	27	no	—
51	C₃×3₋¹⁺²	—	57	27	no	—
52	C₃²×C₉	—	19	9	no	—
53	C₃²⋊C₉	—	19	81	no	—
54	C₃×C₁₉	—	3	9	no	—
55	C₃×C₁₉	—	3	27	no	—
56	C₃×C₁₉	#6891	1	9	yes	complemented
57	C₃×C₁₉	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
58	C₃×C₁₉	C₃²×3₋¹⁺²	1	3	yes	—
59	C₃³	—	3	243	no	—
60	C₃³	—	3	27	no	—
61	C₃³	—	3	9	no	—
62	C₃³	—	3	18	no	—
63	C₃³	—	3	9	no	—
64	C₃³	—	3	81	no	—
65	C₃³	#10587025	1	27	yes	complemented
66	C₃³	C₃²⋊(C₁₉⋊C₃)	1	9	yes	—
67	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
68	C₃³	C₃²×C₁₉⋊C₃	1	9	yes	—
69	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
70	3₋¹⁺²	—	57	81	no	—
71	C₃×C₉	—	19	27	no	—
72	C₃×C₉	—	57	27	no	—
73	C₁₉	C₃×#6891	1	1	yes	characteristic, complemented, Sylow
74	C₃²	—	3	243	no	—
75	C₃²	—	3	81	no	—
76	C₃²	—	3	27	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	18	no	—
80	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	9	yes	—
81	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
82	C₃²	C₃×#10587025	1	9	yes	—
83	C₃²	C₃×#10587025	1	27	yes	complemented
84	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
85	C₉	—	57	27	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	27	no	—
88	C₃	#17987421	1	9	yes	direct product factor
89	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
90	C₃	C₃²×#10587025	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting, prime radical	C₃⁵×C₁₉	C₃
socle	C₃³×C₁₉	C₃³
hypercenter	C₃⁵	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6891
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃²×#10587025	C₃	semidirect
2. #17987421	C₃	direct (N × H)
3. C₃×C₃²⋊#4294	C₃	semidirect
6. C₃×#10587025	C₃²	semidirect
7. C₃²×#4294	C₃²	semidirect
8. C₃²⋊#4294	C₃²	semidirect
22. C₃³×C₁₉	3₋¹⁺²	semidirect
28. C₃×#4294	C₃³	semidirect
42. C₃²×C₁₉	C₃×3₋¹⁺²	semidirect
56. C₃×C₁₉	#6891	semidirect
65. C₃³	#10587025	semidirect
73. C₁₉	C₃×#6891	semidirect
83. C₃²	C₃×#10587025	semidirect
88. C₃	#17987421	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#10587025	3
#17987421	3
C₃×C₃²⋊#4294	3
C₃⁵×C₁₉	3
C₃×#6891	19

Subgroups — C3×#17987421 #28355944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987421 #28355944