Subgroups — #28356081

Order 13851.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987447	C₃	1	27	yes	maximal, complemented
2	#17987445	C₃	1	6	yes	maximal, complemented
3	#17987421	C₃	1	3	yes	maximal
4	#17987405	C₃	1	3	yes	maximal, complemented
5	C₃²×C₁₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
6	C₃×#10587025	C₃²	1	9	yes	—
7	#13095307	C₃²	1	9	yes	complemented
8	#13095306	C₃²	1	9	yes	complemented
9	#13095305	C₃²	1	54	yes	complemented
10	C₃²⋊#4294	C₃²	1	9	yes	—
11	C₃²⋊#4294	C₃²	1	18	yes	—
12	C₉×#4294	C₃²	1	9	yes	complemented
13	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
14	C₃×C₁₉×3₋¹⁺²	—	3	9	no	—
15	C₃×C₁₉×3₋¹⁺²	C₃²	1	9	yes	—
16	C₃²×C₉×C₁₉	C₃²	1	2	yes	—
17	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
18	#10624885	—	19	1	no	maximal, Sylow
19	C₃³×C₁₉	—	3	3	no	—
20	C₃³×C₁₉	—	9	3	no	—
21	C₃³×C₁₉	C₃³	1	3	yes	—
22	C₃³×C₁₉	C₃³	1	1	yes	characteristic
23	C₁₉×3₋¹⁺²	—	3	27	no	—
24	C₃×C₉×C₁₉	—	3	6	no	—
25	C₃×C₉×C₁₉	3₋¹⁺²	1	9	yes	complemented
26	C₃×C₉×C₁₉	C₃³	1	6	yes	—
27	C₃×C₉×C₁₉	C₃³	1	3	yes	—
28	#10587025	—	9	9	no	—
29	C₃×#4294	C₃³	1	27	yes	—
30	C₃²×3₋¹⁺²	C₁₉⋊C₃	1	1	yes	characteristic
31	#6896	—	19	27	no	—
32	#6895	—	19	6	no	—
33	#6891	—	19	3	no	—
34	#6887	—	19	3	no	—
35	C₃²×C₁₉	—	3	3	no	—
36	C₃²×C₁₉	—	3	3	no	—
37	C₃²×C₁₉	—	3	3	no	—
38	C₃²×C₁₉	—	3	6	no	—
39	C₃²×C₁₉	—	9	9	no	—
40	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
41	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
42	C₉×C₁₉	—	3	6	no	—
43	C₉×C₁₉	C₃×3₋¹⁺²	1	9	yes	—
44	#4294	—	3	27	no	—
45	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
46	C₃×3₋¹⁺²	—	3	9	no	—
47	C₃×3₋¹⁺²	—	19	9	no	—
48	C₃×3₋¹⁺²	C₃×C₁₉⋊C₃	1	9	yes	—
49	C₃²×C₉	C₃×C₁₉⋊C₃	1	2	yes	—
50	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
51	C₉⋊C₉	—	19	54	no	—
52	C₉⋊C₉	—	19	9	no	—
53	C₉⋊C₉	—	19	9	no	—
54	C₃²⋊C₉	—	19	9	no	—
55	C₃²⋊C₉	—	19	18	no	—
56	C₉²	—	19	9	no	—
57	C₃×C₁₉	—	3	3	no	—
58	C₃×C₁₉	—	9	3	no	—
59	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
60	C₃×C₁₉	3₋¹⁺⁴	1	3	yes	—
61	C₃³	—	3	3	no	—
62	C₃³	—	9	3	no	—
63	C₃³	C₃²×C₁₉⋊C₃	1	3	yes	—
64	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
65	3₋¹⁺²	—	3	27	no	—
66	3₋¹⁺²	—	171	9	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	—	19	27	no	—
69	C₃×C₉	#10587025	1	9	yes	complemented
70	C₃×C₉	C₃²×C₁₉⋊C₃	1	6	yes	—
71	C₃×C₉	C₃²×C₁₉⋊C₃	1	3	yes	—
72	C₁₉	#10624885	1	1	yes	characteristic, complemented, Sylow
73	C₃²	—	3	3	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	6	no	—
77	C₃²	—	9	9	no	—
78	C₃²	C₃×#10587025	1	3	yes	—
79	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
80	C₉	—	3	6	no	—
81	C₉	—	57	27	no	—
82	C₉	C₃×#10587025	1	9	yes	—
83	C₃	—	3	3	no	—
84	C₃	—	9	3	no	—
85	C₃	C₃²×#10587025	1	1	yes	characteristic
86	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	#10624885
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. #17987447	C₃	semidirect
2. #17987445	C₃	semidirect
4. #17987405	C₃	semidirect
7. #13095307	C₃²	semidirect
8. #13095306	C₃²	semidirect
9. #13095305	C₃²	semidirect
12. C₉×#4294	C₃²	semidirect
25. C₃×C₉×C₁₉	3₋¹⁺²	semidirect
69. C₃×C₉	#10587025	semidirect
72. C₁₉	#10624885	semidirect

Maximal subgroups

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

subgroup	index
#17987447	3
#17987445	3
#17987421	3
#17987405	3
C₃²×C₁₉×3₋¹⁺²	3
#10624885	19