Subgroups — C₃×#17987431 #28355956

Order 13851.

1232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587025	C₃	1	2	yes	maximal, complemented
2	C₃²×C₃²⋊(C₁₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#17987431	C₃	1	27	yes	maximal, direct product factor
4	C₃×#13095303	C₃	1	9	yes	maximal, complemented
5	C₃³×C₉×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₁₉⋊C₃	C₃²	1	3	yes	—
7	C₃×#10587025	—	3	18	no	—
8	C₃×#10587025	C₃²	1	18	yes	complemented
9	C₃×C₃²⋊(C₁₉⋊C₃)	—	3	9	no	—
10	C₃×C₃²⋊(C₁₉⋊C₃)	C₃²	1	9	yes	—
11	C₃²×#4294	C₃²	1	6	yes	—
12	#13095303	C₃²	1	81	yes	complemented
13	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
14	C₃²×C₉×C₁₉	—	3	9	no	—
15	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
16	C₃²×C₉×C₁₉	C₃²	1	9	yes	complemented
17	C₃×#6893	—	19	1	no	maximal, Sylow
18	C₃³×C₁₉	—	3	9	no	—
19	C₃³×C₁₉	H(3,𝔽₃)	1	9	yes	—
20	C₃³×C₁₉	C₃³	1	3	yes	—
21	C₃³×C₁₉	C₃³	1	1	yes	characteristic
22	C₃²×C₁₉⋊C₃	—	3	9	no	—
23	C₃²×C₁₉⋊C₃	—	3	27	no	—
24	C₃²×C₁₉⋊C₃	C₃³	1	9	yes	—
25	C₃×C₉×C₁₉	—	3	9	no	—
26	C₃×C₉×C₁₉	—	3	27	no	—
27	C₃×C₉×C₁₉	C₃³	1	9	yes	—
28	C₃²⋊(C₁₉⋊C₃)	—	3	27	no	—
29	#10587025	—	3	54	no	—
30	C₃×#4294	—	3	18	no	—
31	C₃×#4294	C₃³	1	18	yes	—
32	C₃²×3₋¹⁺²	—	19	2	no	—
33	C₃²×H(3,𝔽₃)	—	19	1	no	—
34	C₃³×C₉	C₁₉⋊C₃	1	1	yes	characteristic, complemented
35	#6893	—	19	27	no	—
36	C₃×C₃²⋊C₉	—	19	9	no	—
37	C₃²×C₁₉	—	3	9	no	—
38	C₃²×C₁₉	—	3	27	no	—
39	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₁₉	C₃×H(3,𝔽₃)	1	3	yes	—
41	C₃²×C₁₉	#737	1	9	yes	—
42	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
43	C₃×C₁₉⋊C₃	—	3	9	no	—
44	C₃×C₁₉⋊C₃	—	3	27	no	—
45	C₃×C₁₉⋊C₃	—	9	27	no	—
46	C₉×C₁₉	—	3	9	no	—
47	#4294	—	3	18	no	—
48	C₃⁴	—	19	3	no	—
49	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	19	18	no	—
51	C₃×3₋¹⁺²	—	57	18	no	—
52	C₃×H(3,𝔽₃)	—	19	9	no	—
53	C₃×H(3,𝔽₃)	—	57	9	no	—
54	C₃²×C₉	—	3	9	no	—
55	C₃²×C₉	—	19	6	no	—
56	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
57	C₃²×C₉	C₃×C₁₉⋊C₃	1	9	yes	complemented
58	C₃²⋊C₉	—	19	81	no	—
59	C₃×C₁₉	—	3	9	no	—
60	C₃×C₁₉	#6893	1	9	yes	complemented
61	C₃×C₁₉	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
62	C₃×C₁₉	C₃×#737	1	3	yes	—
63	C₁₉⋊C₃	—	9	9	no	—
64	C₃³	—	3	9	no	—
65	C₃³	—	19	9	no	—
66	C₃³	—	57	9	no	—
67	C₃³	—	57	27	no	—
68	C₃³	C₃²⋊(C₁₉⋊C₃)	1	9	yes	—
69	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
70	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
71	3₋¹⁺²	—	57	54	no	—
72	H(3,𝔽₃)	—	57	27	no	—
73	C₃×C₉	—	3	9	no	—
74	C₃×C₉	—	3	27	no	—
75	C₃×C₉	—	19	18	no	—
76	C₃×C₉	—	57	18	no	—
77	C₃×C₉	C₃²×C₁₉⋊C₃	1	9	yes	—
78	C₁₉	C₃×#6893	1	1	yes	characteristic, complemented, Sylow
79	C₃²	—	3	27	no	—
80	C₃²	—	3	9	no	—
81	C₃²	—	57	9	no	—
82	C₃²	—	57	27	no	—
83	C₃²	—	171	27	no	—
84	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	9	yes	—
85	C₃²	C₃×C₃²⋊(C₁₉⋊C₃)	1	3	yes	—
86	C₃²	#13095332	1	9	yes	—
87	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
88	C₉	—	3	9	no	—
89	C₉	—	57	18	no	—
90	C₃	—	3	9	no	—
91	C₃	—	171	9	no	—
92	C₃	#17987431	1	9	yes	direct product factor
93	C₃	C₃²×C₃²⋊(C₁₉⋊C₃)	1	1	yes	characteristic
94	C₃	C₃×#13095332	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₃³×C₉×C₁₉	C₃
socle	C₃³×C₁₉	C₃³
prime radical	C₃²×C₃²⋊(C₁₉⋊C₃)	C₃
hypercenter	C₃³×C₉	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6893
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. C₃²×#10587025	C₃	semidirect
3. #17987431	C₃	direct (N × H)
4. C₃×#13095303	C₃	semidirect
5. C₃³×C₉×C₁₉	C₃	semidirect
8. C₃×#10587025	C₃²	semidirect
12. #13095303	C₃²	semidirect
16. C₃²×C₉×C₁₉	C₃²	semidirect
34. C₃³×C₉	C₁₉⋊C₃	semidirect
57. C₃²×C₉	C₃×C₁₉⋊C₃	semidirect
60. C₃×C₁₉	#6893	semidirect
78. C₁₉	C₃×#6893	semidirect
92. C₃	#17987431	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
C₃²×C₃²⋊(C₁₉⋊C₃)	3
#17987431	3
C₃×#13095303	3
C₃³×C₉×C₁₉	3
C₃×#6893	19

Subgroups — C3×#17987431 #28355956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987431 #28355956