Group #28356083 — subgroups

Subgroups — #28356083

Order 13851.

728 conjugacy classes of subgroups; only the 292 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 292 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#10587025	C₃	1	1	yes	maximal, characteristic
2	#17987442	C₃	1	9	yes	maximal, complemented
3	#17987440	C₃	1	18	yes	maximal, complemented
4	#17987439	C₃	1	9	yes	maximal, complemented
5	C₃×C₃²⋊#4294	C₃	1	2	yes	maximal
6	C₃×C₁₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
7	C₃×#10587025	—	3	9	no	—
8	C₃×#10587025	C₃²	1	3	yes	—
9	C₃×#10587025	C₃²	1	6	yes	—
10	C₃²×#4294	C₃²	1	3	yes	—
11	C₃²×#4294	C₃²	1	6	yes	—
12	#13095307	C₃²	1	27	yes	complemented
13	#13095305	C₃²	1	54	yes	complemented
14	C₃²⋊#4294	C₃²	1	6	yes	—
15	C₃²⋊#4294	C₃²	1	6	yes	—
16	C₃²⋊#4294	C₃²	1	6	yes	—
17	C₃⁴×C₁₉	C₃²	1	1	yes	characteristic
18	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
19	C₁₉×C₃²⋊C₉	C₃²	1	6	yes	—
20	C₁₉×C₃²⋊C₉	C₃²	1	3	yes	—
21	#10624886	—	19	1	no	maximal, Sylow
22	C₃³×C₁₉	—	9	2	no	—
23	C₃³×C₁₉	—	9	1	no	—
24	C₃³×C₁₉	3₋¹⁺²	1	9	yes	—
25	C₃³×C₁₉	C₃³	1	1	yes	characteristic
26	C₃³×C₁₉	C₃³	1	2	yes	—
27	C₃³×C₁₉	C₃³	1	1	yes	characteristic
28	C₃×C₉×C₁₉	—	9	3	no	—
29	C₃×C₉×C₁₉	C₃³	1	9	yes	—
30	#10587025	—	3	9	no	—
31	#10587025	—	3	18	no	—
32	C₃×#4294	—	3	9	no	—
33	C₃×#4294	—	9	6	no	—
34	C₃×#4294	C₃³	1	18	yes	—
35	C₃×#4294	C₃³	1	9	yes	—
36	C₃²×3₋¹⁺²	—	19	1	no	—
37	#6895	—	19	9	no	—
38	#6894	—	19	9	no	—
39	#6894	—	19	18	no	—
40	C₃×C₃²⋊C₉	—	19	2	no	—
41	C₃×C₃²⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic
42	C₃²×C₁₉	—	3	2	no	—
43	C₃²×C₁₉	—	3	1	no	—
44	C₃²×C₁₉	—	3	2	no	—
45	C₃²×C₁₉	—	3	2	no	—
46	C₃²×C₁₉	—	3	2	no	—
47	C₃²×C₁₉	—	3	1	no	—
48	C₃²×C₁₉	—	3	2	no	—
49	C₃²×C₁₉	—	9	9	no	—
50	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
51	C₃²×C₁₉	C₃×3₋¹⁺²	1	6	yes	—
52	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
53	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
54	C₉×C₁₉	—	3	9	no	—
55	#4294	—	3	9	no	—
56	#4294	—	3	18	no	—
57	C₃⁴	C₃×C₁₉⋊C₃	1	1	yes	characteristic
58	C₃×3₋¹⁺²	—	19	3	no	—
59	C₃×3₋¹⁺²	—	19	6	no	—
60	C₃×3₋¹⁺²	—	57	9	no	—
61	C₃²×C₉	—	19	3	no	—
62	C₃²×C₉	—	19	6	no	—
63	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
64	C₉⋊C₉	—	19	54	no	—
65	C₉⋊C₉	—	19	27	no	—
66	C₃²⋊C₉	—	19	6	no	—
67	C₃²⋊C₉	—	19	6	no	—
68	C₃²⋊C₉	—	19	6	no	—
69	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	6	yes	—
70	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	3	yes	—
71	C₃×C₁₉	—	3	6	no	—
72	C₃×C₁₉	—	3	3	no	—
73	C₃×C₁₉	—	3	3	no	—
74	C₃×C₁₉	C₃²×3₋¹⁺²	1	1	yes	characteristic
75	C₃×C₁₉	3₋¹⁺⁴	1	2	yes	—
76	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
77	C₃³	—	9	2	no	—
78	C₃³	—	9	1	no	—
79	C₃³	#10587023	1	9	yes	—
80	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
81	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
82	C₃³	C₃²×C₁₉⋊C₃	1	2	yes	—
83	3₋¹⁺²	—	57	9	no	—
84	3₋¹⁺²	—	57	18	no	—
85	C₃×C₉	—	9	3	no	—
86	C₃×C₉	—	19	18	no	—
87	C₃×C₉	—	19	9	no	—
88	C₃×C₉	—	57	9	no	—
89	C₃×C₉	—	171	6	no	—
90	C₃×C₉	C₃²×C₁₉⋊C₃	1	9	yes	—
91	C₁₉	#10624886	1	1	yes	characteristic, complemented, Sylow
92	C₃²	—	3	2	no	—
93	C₃²	—	3	2	no	—
94	C₃²	—	3	2	no	—
95	C₃²	—	3	2	no	—
96	C₃²	—	3	1	no	—
97	C₃²	—	3	1	no	—
98	C₃²	—	3	2	no	—
99	C₃²	—	9	9	no	—
100	C₃²	C₃×#10587023	1	3	yes	—
101	C₃²	C₃×#10587023	1	3	yes	—
102	C₃²	C₃×#10587023	1	6	yes	—
103	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
104	C₉	—	3	9	no	—
105	C₉	—	57	9	no	—
106	C₉	—	57	18	no	—
107	C₃	—	3	6	no	—
108	C₃	—	3	3	no	—
109	C₃	—	3	3	no	—
110	C₃	C₃²×#10587023	1	1	yes	characteristic
111	C₃	#17987546	1	2	yes	—
112	C₃	#17987547	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃²×#10587025

C₃

yes

maximal, characteristic

#17987442

C₃

yes

maximal, complemented

#17987440

C₃

yes

maximal, complemented

#17987439

C₃

yes

maximal, complemented

C₃×C₃²⋊#4294

C₃

yes

maximal

C₃×C₁₉×C₃²⋊C₉

C₃

yes

maximal, characteristic

C₃×#10587025

—

C₃×#10587025

C₃²

yes

—

C₃×#10587025

C₃²

yes

—

C₃²×#4294

C₃²

yes

—

C₃²×#4294

C₃²

yes

—

#13095307

C₃²

yes

complemented

#13095305

C₃²

yes

complemented

C₃²⋊#4294

C₃²

yes

—

C₃²⋊#4294

C₃²

yes

—

C₃²⋊#4294

C₃²

yes

—

C₃⁴×C₁₉

C₃²

yes

characteristic

C₃²×C₉×C₁₉

C₃²

yes

—

C₁₉×C₃²⋊C₉

C₃²

yes

—

C₁₉×C₃²⋊C₉

C₃²

yes

—

#10624886

—

maximal, Sylow

C₃³×C₁₉

—

C₃³×C₁₉

—

C₃³×C₁₉

3₋¹⁺²

yes

—

C₃³×C₁₉

C₃³

yes

characteristic

C₃³×C₁₉

C₃³

yes

—

C₃³×C₁₉

C₃³

yes

characteristic

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

C₃³

yes

—

—

—

—

—

C₃³

yes

—

C₃×#4294

C₃³

yes

—

C₃²×3₋¹⁺²

—

#6895

—

#6894

—

#6894

—

C₃×C₃²⋊C₉

—

C₃×C₃²⋊C₉

C₁₉⋊C₃

yes

characteristic

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃⁴

yes

characteristic

C₉×C₁₉

—

#4294

—

#4294

—

C₃⁴

C₃×C₁₉⋊C₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×C₁₉⋊C₃

yes

—

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃×C₁₉⋊C₃

yes

—

C₃²⋊C₉

C₃×C₁₉⋊C₃

yes

—

C₃×C₁₉

—

C₃×C₁₉

—

C₃×C₁₉

—

C₃×C₁₉

C₃²×3₋¹⁺²

yes

characteristic

C₃×C₁₉

3₋¹⁺⁴

yes

—

C₃×C₁₉

3₋¹⁺⁴

yes

characteristic

C₃³

—

C₃³

—

C₃³

#10587023

yes

—

C₃³

C₃²×C₁₉⋊C₃

yes

characteristic

C₃³

C₃²×C₁₉⋊C₃

yes

characteristic

C₃³

C₃²×C₁₉⋊C₃

yes

—

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

171

—

C₃×C₉

C₃²×C₁₉⋊C₃

yes

—

C₁₉

#10624886

yes

characteristic, complemented, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

C₃²

—

100

C₃²

C₃×#10587023

yes

—

101

C₃²

C₃×#10587023

yes

—

102

C₃²

C₃×#10587023

yes

—

103

C₃²

C₃³×C₁₉⋊C₃

yes

characteristic

104

C₉

—

105

C₉

—

106

C₉

—

107

C₃

—

108

C₃

—

109

C₃

—

110

C₃

C₃²×#10587023

yes

characteristic

111

C₃

#17987546

yes

—

112

C₃

#17987547

yes

characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃⁴
Fitting	C₃×C₁₉×C₃²⋊C₉	C₃
prime radical	C₃⁴×C₁₉	C₃²
hypercenter	C₃×C₃²⋊C₉	C₁₉⋊C₃
hypocenter	C₁₉	#10624886
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃×C₃²⋊C₉

subgroup

G/H

center, Frattini

C₃²

C₃³×C₁₉⋊C₃

commutator, socle, cosocle

C₃²×C₁₉

C₃⁴

Fitting

C₃×C₁₉×C₃²⋊C₉

C₃

prime radical

C₃⁴×C₁₉

C₃²

hypercenter

C₃×C₃²⋊C₉

C₁₉⋊C₃

C₁₉

G ▷ C₃²×C₁₉ ▷ C₁₉

C₁ ◁ C₃² ◁ C₃×C₃²⋊C₉

N	H ≅ G/N	type
2. #17987442	C₃	semidirect
3. #17987440	C₃	semidirect
4. #17987439	C₃	semidirect
12. #13095307	C₃²	semidirect
13. #13095305	C₃²	semidirect
91. C₁₉	#10624886	semidirect

H ≅ G/N

type

2. #17987442

C₃

semidirect

3. #17987440

C₃

semidirect

4. #17987439

C₃

semidirect

12. #13095307

C₃²

semidirect

13. #13095305

C₃²

semidirect

91. C₁₉

#10624886

semidirect

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

subgroup	index
C₃²×#10587025	3
#17987442	3
#17987440	3
#17987439	3
C₃×C₃²⋊#4294	3
C₃×C₁₉×C₃²⋊C₉	3
#10624886	19

subgroup

index

C₃×C₃²⋊#4294

C₃×C₁₉×C₃²⋊C₉

#10624886

Subgroups — #28356083

Conjugacy classes of subgroups

Complements

Maximal subgroups