Subgroups — #28356087

Order 13851.

728 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987445	C₃	1	9	yes	maximal, complemented
2	#17987435	C₃	1	27	yes	maximal, complemented
3	C₃×C₃²⋊#4294	C₃	1	3	yes	maximal
4	C₃²×C₁₉×3₋¹⁺²	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	18	yes	—
8	C₃²⋊#4294	C₃²	1	9	yes	—
9	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
10	C₃×C₁₉×3₋¹⁺²	—	3	9	no	—
11	C₃×C₁₉×3₋¹⁺²	C₃²	1	9	yes	—
12	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
13	#10624886	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	—	9	3	no	—
15	C₃³×C₁₉	3₋¹⁺²	1	9	yes	—
16	C₃³×C₁₉	C₃³	1	1	yes	characteristic
17	C₃³×C₁₉	C₃³	1	3	yes	—
18	C₁₉×3₋¹⁺²	—	3	27	no	—
19	C₃×C₉×C₁₉	—	3	9	no	—
20	C₃×C₉×C₁₉	C₃³	1	9	yes	—
21	C₃×#4294	—	9	9	no	—
22	C₃×#4294	C₃³	1	27	yes	—
23	C₃²×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
24	#6895	—	19	9	no	—
25	#6894	—	19	27	no	—
26	C₃×C₃²⋊C₉	—	19	3	no	—
27	C₃²×C₁₉	—	3	3	no	—
28	C₃²×C₁₉	—	3	3	no	—
29	C₃²×C₁₉	—	3	6	no	—
30	C₃²×C₁₉	—	9	9	no	—
31	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
32	C₃²×C₁₉	C₃×3₋¹⁺²	1	9	yes	—
33	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
34	C₉×C₁₉	—	3	9	no	—
35	#4294	—	3	27	no	—
36	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	9	no	—
38	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	9	yes	—
39	C₃²×C₉	—	19	9	no	—
40	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
41	C₉⋊C₉	—	19	81	no	—
42	C₃²⋊C₉	—	19	18	no	—
43	C₃²⋊C₉	—	19	9	no	—
44	C₃×C₁₉	—	3	9	no	—
45	C₃×C₁₉	—	3	3	no	—
46	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
47	C₃×C₁₉	3₋¹⁺⁴	1	3	yes	—
48	C₃³	—	9	3	no	—
49	C₃³	#10587025	1	9	yes	—
50	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
51	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
52	3₋¹⁺²	—	3	27	no	—
53	C₃×C₉	—	3	9	no	—
54	C₃×C₉	—	19	27	no	—
55	C₃×C₉	—	171	9	no	—
56	C₃×C₉	C₃²×C₁₉⋊C₃	1	9	yes	—
57	C₁₉	#10624886	1	1	yes	characteristic, complemented, Sylow
58	C₃²	—	3	3	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	3	6	no	—
61	C₃²	—	9	9	no	—
62	C₃²	C₃×#10587025	1	3	yes	—
63	C₃²	C₃×#10587025	1	9	yes	—
64	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
65	C₉	—	3	9	no	—
66	C₉	—	57	27	no	—
67	C₃	—	3	9	no	—
68	C₃	—	3	3	no	—
69	C₃	C₃²×#10587025	1	1	yes	characteristic
70	C₃	#17987546	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃⁴
Fitting	C₃²×C₁₉×3₋¹⁺²	C₃
prime radical	C₃⁴×C₁₉	C₃²
hypercenter	C₃²×3₋¹⁺²	C₁₉⋊C₃
hypocenter	C₁₉	#10624886
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #17987445	C₃	semidirect
2. #17987435	C₃	semidirect
6. #13095305	C₃²	semidirect
57. C₁₉	#10624886	semidirect

Maximal subgroups

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

subgroup	index
#17987445	3
#17987435	3
C₃×C₃²⋊#4294	3
C₃²×C₁₉×3₋¹⁺²	3
#10624886	19