Subgroups — C₃×#17987445 #28355979

Order 13851.

836 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987445	C₃	1	27	yes	maximal, direct product factor
2	C₃×#13095305	C₃	1	9	yes	maximal, complemented
3	C₃×C₃²⋊#4294	C₃	1	3	yes	maximal
4	C₃³×C₉×C₁₉	C₃	1	1	yes	maximal, characteristic
5	C₃²×#4294	C₃²	1	9	yes	—
6	#13095305	C₃²	1	81	yes	complemented
7	C₃²⋊#4294	C₃²	1	27	yes	—
8	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₁₉	—	3	9	no	—
10	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
11	C₃²×C₉×C₁₉	C₃²	1	9	yes	—
12	C₃×#6895	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	—	3	9	no	—
14	C₃³×C₁₉	3₋¹⁺²	1	9	yes	—
15	C₃³×C₁₉	C₃³	1	3	yes	—
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₃×C₉×C₁₉	—	3	27	no	—
18	C₃×C₉×C₁₉	—	3	9	no	—
19	C₃×C₉×C₁₉	C₃³	1	9	yes	—
20	C₃×#4294	—	3	27	no	—
21	C₃×#4294	C₃³	1	27	yes	—
22	C₃³×C₉	C₁₉⋊C₃	1	1	yes	characteristic
23	#6895	—	19	27	no	—
24	C₃×C₉⋊C₉	—	19	9	no	—
25	C₃×C₃²⋊C₉	—	19	3	no	—
26	C₃²×C₁₉	—	3	9	no	—
27	C₃²×C₁₉	—	3	27	no	—
28	C₃²×C₁₉	C₃×3₋¹⁺²	1	9	yes	—
29	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
30	C₃²×C₁₉	#737	1	9	yes	—
31	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
32	C₉×C₁₉	—	3	9	no	—
33	#4294	—	3	27	no	—
34	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
35	C₃²×C₉	—	3	9	no	—
36	C₃²×C₉	—	19	9	no	—
37	C₃²×C₉	C₃×C₁₉⋊C₃	1	9	yes	—
38	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
39	C₉⋊C₉	—	19	81	no	—
40	C₃²⋊C₉	—	19	27	no	—
41	C₃×C₁₉	—	3	9	no	—
42	C₃×C₁₉	#6895	1	9	yes	complemented
43	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
44	C₃×C₁₉	C₃×#737	1	3	yes	—
45	C₃³	—	3	9	no	—
46	C₃³	#10587025	1	9	yes	—
47	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
48	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
49	C₃×C₉	—	3	27	no	—
50	C₃×C₉	—	3	9	no	—
51	C₃×C₉	—	19	27	no	—
52	C₃×C₉	—	57	27	no	—
53	C₃×C₉	C₃²×C₁₉⋊C₃	1	9	yes	—
54	C₁₉	C₃×#6895	1	1	yes	characteristic, complemented, Sylow
55	C₃²	—	3	27	no	—
56	C₃²	—	3	9	no	—
57	C₃²	C₃×#10587025	1	9	yes	—
58	C₃²	C₃×#10587025	1	3	yes	—
59	C₃²	#13095332	1	9	yes	—
60	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
61	C₉	—	3	9	no	—
62	C₉	—	57	27	no	—
63	C₃	—	3	9	no	—
64	C₃	#17987445	1	9	yes	direct product factor
65	C₃	C₃²×#10587025	1	1	yes	characteristic
66	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	C₃⁴×C₁₉	C₃²
hypercenter	C₃³×C₉	C₁₉⋊C₃
hypocenter	C₁₉	C₃×#6895
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. #17987445	C₃	direct (N × H)
2. C₃×#13095305	C₃	semidirect
6. #13095305	C₃²	semidirect
42. C₃×C₁₉	#6895	semidirect
54. C₁₉	C₃×#6895	semidirect
64. C₃	#17987445	direct (N × H)

Maximal subgroups

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

subgroup	index
#17987445	3
C₃×#13095305	3
C₃×C₃²⋊#4294	3
C₃³×C₉×C₁₉	3
C₃×#6895	19

Subgroups — C3×#17987445 #28355979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17987445 #28355979