Subgroups — C₃×#17987470 #28356031

Order 13851.

1076 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587023	C₃	1	4	yes	maximal
2	#17987470	C₃	1	27	yes	maximal, direct product factor
3	C₃×#13095307	C₃	1	8	yes	maximal, complemented
4	C₃×C₉²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
6	C₃×#10587023	—	3	36	no	—
7	C₃×#10587023	C₃²	1	36	yes	—
8	C₃²×#4294	C₃²	1	8	yes	—
9	#13095307	C₃²	1	72	yes	complemented
10	C₃²×C₉×C₁₉	C₃²	1	4	yes	—
11	C₉²×C₁₉	C₃²	1	9	yes	complemented
12	C₃×#6900	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	C₃³	1	1	yes	characteristic
14	C₃²×C₁₉⋊C₃	—	3	12	no	—
15	C₃²×C₁₉⋊C₃	C₃³	1	3	yes	—
16	C₃×C₉×C₁₉	3₋¹⁺²	1	36	yes	complemented
17	C₃×C₉×C₁₉	C₃³	1	12	yes	—
18	C₃×#4294	—	3	24	no	—
19	C₃×#4294	C₃³	1	24	yes	—
20	#10587023	—	3	108	no	—
21	C₃²×3₋¹⁺²	—	19	4	no	—
22	#6900	—	19	27	no	—
23	C₃×C₉⋊C₉	—	19	8	no	—
24	C₃×C₉²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
25	C₃²×C₁₉	C₃×3₋¹⁺²	1	12	yes	—
26	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
27	C₃×C₁₉⋊C₃	—	3	12	no	—
28	C₃×C₁₉⋊C₃	—	9	9	no	—
29	C₉×C₁₉	C₃×3₋¹⁺²	1	36	yes	complemented
30	#4294	—	3	24	no	—
31	C₃⁴	—	19	1	no	—
32	C₃×3₋¹⁺²	—	19	36	no	—
33	C₃×3₋¹⁺²	—	57	36	no	—
34	C₃²×C₉	—	19	8	no	—
35	C₃²×C₉	C₃×C₁₉⋊C₃	1	4	yes	—
36	C₉⋊C₉	—	19	72	no	—
37	C₉²	C₃×C₁₉⋊C₃	1	9	yes	complemented
38	C₃×C₁₉	#6900	1	9	yes	complemented
39	C₃×C₁₉	C₃²×3₋¹⁺²	1	4	yes	—
40	C₁₉⋊C₃	—	9	3	no	—
41	C₃³	—	19	3	no	—
42	C₃³	—	57	12	no	—
43	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
44	3₋¹⁺²	—	57	108	no	—
45	C₃×C₉	—	19	24	no	—
46	C₃×C₉	—	57	24	no	—
47	C₃×C₉	#10587023	1	36	yes	complemented
48	C₃×C₉	C₃²×C₁₉⋊C₃	1	12	yes	—
49	C₁₉	C₃×#6900	1	1	yes	characteristic, complemented, Sylow
50	C₃²	—	57	12	no	—
51	C₃²	—	171	9	no	—
52	C₃²	C₃×#10587023	1	12	yes	—
53	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
54	C₉	—	57	24	no	—
55	C₉	C₃×#10587023	1	36	yes	complemented
56	C₃	—	171	3	no	—
57	C₃	#17987470	1	9	yes	direct product factor
58	C₃	C₃²×#10587023	1	4	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₁₉⋊C₃
commutator, cosocle	C₃²×C₁₉	C₃⁴
Frattini	C₃²	C₃³×C₁₉⋊C₃
Fitting	C₃×C₉²×C₁₉	C₃
socle	C₃³×C₁₉	C₃³
prime radical	C₃³×C₁₉⋊C₃	C₃²
hypercenter	C₃×C₉²	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6900
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #17987470	C₃	direct (N × H)
3. C₃×#13095307	C₃	semidirect
4. C₃×C₉²×C₁₉	C₃	semidirect
9. #13095307	C₃²	semidirect
11. C₉²×C₁₉	C₃²	semidirect
16. C₃×C₉×C₁₉	3₋¹⁺²	semidirect
24. C₃×C₉²	C₁₉⋊C₃	semidirect
29. C₉×C₁₉	C₃×3₋¹⁺²	semidirect
37. C₉²	C₃×C₁₉⋊C₃	semidirect
38. C₃×C₁₉	#6900	semidirect
47. C₃×C₉	#10587023	semidirect
49. C₁₉	C₃×#6900	semidirect
55. C₉	C₃×#10587023	semidirect
57. C₃	#17987470	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×#10587023	3
#17987470	3
C₃×#13095307	3
C₃×C₉²×C₁₉	3
C₃×#6900	19

Subgroups — C3×#17987470 #28356031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987470 #28356031