Group #28353581 — subgroups

Subgroups — #28353581

Order 13851.

374 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 175 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	C₃×#13095307	C₃	1	1	yes	maximal, characteristic
2	C₃×#13095306	C₃	1	3	yes	maximal
3	C₃×#13095306	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉×#4294	C₃	1	1	yes	maximal, characteristic
5	#17987308	C₃	1	6	yes	maximal
6	C₃×C₁₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
7	C₃²×#4294	C₃²	1	1	yes	characteristic
8	C₃²×#4294	C₃²	1	3	yes	—
9	C₃²×#4294	C₃²	1	2	yes	—
10	C₃²×#4294	C₃²	1	3	yes	—
11	#13095307	—	3	3	no	—
12	#13095306	—	3	3	no	—
13	#13095306	—	3	9	no	—
14	C₉×#4294	—	3	3	no	—
15	C₃²×C₉×C₁₉	C₃²	1	3	yes	—
16	C₃²×C₉×C₁₉	C₃²	1	1	yes	characteristic
17	C₁₉×C₉⋊C₉	C₉	1	9	yes	complemented
18	#10624561	—	19	1	no	maximal, Sylow
19	C₃³×C₁₉	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₁₉	—	3	3	no	—
21	C₃×C₉×C₁₉	—	3	6	no	—
22	C₃×C₉×C₁₉	C₃×C₉	1	9	yes	—
23	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
24	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
25	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
26	C₃×C₉×C₁₉	3₋¹⁺²	1	3	yes	—
27	C₃×#4294	—	3	3	no	—
28	C₃×#4294	—	3	6	no	—
29	C₃×#4294	—	3	3	no	—
30	C₃×#4294	—	3	3	no	—
31	C₃×#4294	—	3	2	no	—
32	C₃×#4294	—	3	1	no	—
33	C₃×#4294	—	3	3	no	—
34	C₃×#4294	—	3	6	no	—
35	C₃×#4294	—	3	6	no	—
36	C₃×#4294	3₋¹⁺²	1	9	yes	—
37	C₃×C₉⋊C₉	—	19	3	no	—
38	C₃×C₉⋊C₉	—	19	1	no	—
39	C₃×C₉⋊C₉	—	19	1	no	—
40	C₃×C₉⋊C₉	C₁₉⋊C₃	1	1	yes	characteristic
41	C₃×C₉²	—	19	1	no	—
42	#6855	—	19	6	no	—
43	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
44	C₃²×C₁₉	C₃×3₋¹⁺²	1	3	yes	—
45	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
46	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
47	C₃²×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
48	C₃²×C₁₉	#737	1	6	yes	—
49	C₉×C₁₉	—	3	9	no	—
50	C₉×C₁₉	C₉⋊C₉	1	9	yes	complemented
51	#4294	—	3	9	no	—
52	#4294	—	9	3	no	—
53	#4294	—	9	2	no	—
54	#4294	—	9	1	no	—
55	C₃²×C₉	—	19	3	no	—
56	C₃²×C₉	—	19	2	no	—
57	C₃²×C₉	—	19	3	no	—
58	C₃²×C₉	—	19	1	no	—
59	C₃²×C₉	C₃×C₁₉⋊C₃	1	3	yes	—
60	C₃²×C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
61	C₉⋊C₉	—	57	9	no	—
62	C₉⋊C₉	—	57	3	no	—
63	C₉⋊C₉	—	57	3	no	—
64	C₉⋊C₉	#4294	1	9	yes	complemented
65	C₉²	—	57	3	no	—
66	C₃×C₁₉	C₃×C₉⋊C₉	1	1	yes	characteristic
67	C₃×C₁₉	C₉×3₋¹⁺²	1	3	yes	—
68	C₃×C₁₉	#6894	1	3	yes	—
69	C₃×C₁₉	#6896	1	3	yes	—
70	C₃×C₁₉	#6899	1	2	yes	—
71	C₃×C₁₉	#6900	1	1	yes	characteristic
72	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
73	C₃×C₉	—	3	3	no	—
74	C₃×C₉	—	3	6	no	—
75	C₃×C₉	—	19	9	no	—
76	C₃×C₉	—	57	3	no	—
77	C₃×C₉	—	57	6	no	—
78	C₃×C₉	—	57	3	no	—
79	C₃×C₉	—	57	3	no	—
80	C₃×C₉	—	57	3	no	—
81	C₃×C₉	—	57	2	no	—
82	C₃×C₉	—	57	1	no	—
83	C₃×C₉	—	57	6	no	—
84	C₃×C₉	—	57	6	no	—
85	C₃×C₉	#10587022	1	3	yes	—
86	C₃×C₉	#10587022	1	3	yes	—
87	C₃×C₉	#10587022	1	3	yes	—
88	C₃×C₉	C₃×#4294	1	9	yes	—
89	C₃×C₉	C₃×#4294	1	3	yes	—
90	C₁₉	#10624561	1	1	yes	characteristic, complemented, Sylow
91	C₃²	C₃²×#4294	1	1	yes	characteristic
92	C₃²	3₋¹⁺²×C₁₉⋊C₃	1	3	yes	—
93	C₃²	C₃×#10587022	1	1	yes	characteristic
94	C₃²	C₃×#10587022	1	1	yes	characteristic
95	C₃²	C₃×#10587022	1	1	yes	characteristic
96	C₃²	#13095333	1	6	yes	—
97	C₉	—	3	9	no	—
98	C₉	—	57	9	no	—
99	C₉	—	171	3	no	—
100	C₉	—	171	2	no	—
101	C₉	—	171	1	no	—
102	C₉	#13095306	1	9	yes	complemented
103	C₃	C₃×#13095306	1	1	yes	characteristic
104	C₃	3₋¹⁺²×#4294	1	3	yes	—
105	C₃	#17987434	1	3	yes	—
106	C₃	#17987450	1	3	yes	—
107	C₃	#17987466	1	2	yes	—
108	C₃	#17987472	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#13095307

C₃

yes

maximal, characteristic

C₃×#13095306

C₃

yes

maximal

C₃×#13095306

C₃

yes

maximal, characteristic

C₃×C₉×#4294

C₃

yes

maximal, characteristic

#17987308

C₃

yes

maximal

C₃×C₁₉×C₉⋊C₉

C₃

yes

maximal, characteristic

C₃²×#4294

C₃²

yes

characteristic

C₃²×#4294

C₃²

yes

—

C₃²×#4294

C₃²

yes

—

C₃²×#4294

C₃²

yes

—

—

—

—

—

C₃²×C₉×C₁₉

C₃²

yes

—

C₃²×C₉×C₁₉

C₃²

yes

characteristic

C₁₉×C₉⋊C₉

C₉

yes

complemented

#10624561

—

maximal, Sylow

C₃³×C₁₉

C₃³

yes

characteristic

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

—

C₃×C₉×C₁₉

C₃×C₉

yes

—

C₃×C₉×C₁₉

C₃×C₉

yes

—

C₃×C₉×C₁₉

3₋¹⁺²

yes

—

C₃×C₉×C₁₉

3₋¹⁺²

yes

—

C₃×C₉×C₁₉

3₋¹⁺²

yes

—

—

—

—

—

—

—

—

—

—

3₋¹⁺²

yes

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

—

C₃×C₉⋊C₉

C₁₉⋊C₃

yes

characteristic

C₃×C₉²

—

#6855

—

C₃²×C₁₉

C₃²×C₉

yes

characteristic

C₃²×C₁₉

C₃×3₋¹⁺²

yes

—

C₃²×C₁₉

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₉

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₉

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₁₉

#737

yes

—

C₉×C₁₉

—

C₉×C₁₉

C₉⋊C₉

yes

—

—

—

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×C₁₉⋊C₃

yes

—

C₃²×C₉

C₃×C₁₉⋊C₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

—

C₉⋊C₉

#4294

yes

complemented

C₉²

—

C₃×C₁₉

C₃×C₉⋊C₉

yes

characteristic

C₃×C₁₉

C₉×3₋¹⁺²

yes

—

C₃×C₁₉

#6894

yes

—

C₃×C₁₉

#6896

yes

—

C₃×C₁₉

#6899

yes

—

C₃×C₁₉

#6900

yes

characteristic

C₃³

C₃²×C₁₉⋊C₃

yes

characteristic

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

#10587022

yes

—

C₃×C₉

#10587022

yes

—

C₃×C₉

#10587022

yes

—

C₃×C₉

C₃×#4294

yes

—

C₃×C₉

C₃×#4294

yes

—

C₁₉

#10624561

yes

characteristic, complemented, Sylow

C₃²

C₃²×#4294

yes

characteristic

C₃²

3₋¹⁺²×C₁₉⋊C₃

yes

—

C₃²

yes

C₃²

yes

C₃²

yes

C₃²

yes

—

C₉

—

C₉

—

C₉

—

171

—

100

C₉

—

171

—

101

C₉

—

171

—

102

C₉

#13095306

yes

complemented

103

C₃

C₃×#13095306

yes

characteristic

104

C₃

3₋¹⁺²×#4294

yes

—

105

C₃

#17987434

yes

—

106

C₃

#17987450

yes

—

107

C₃

#17987466

yes

—

108

C₃

#17987472

yes

characteristic

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₁₉⋊C₃
commutator	C₃²×C₁₉	C₃²×C₉
Fitting	C₃×C₁₉×C₉⋊C₉	C₃
socle, prime radical, cosocle	C₃³×C₁₉	C₃³
hypercenter	C₃×C₉⋊C₉	C₁₉⋊C₃
hypocenter	C₁₉	#10624561
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

subgroup

G/H

center, Frattini

C₃³

C₃²×C₁₉⋊C₃

commutator

C₃²×C₁₉

C₃²×C₉

Fitting

C₃×C₁₉×C₉⋊C₉

C₃

socle, prime radical, cosocle

C₃³×C₁₉

C₃³

hypercenter

C₃×C₉⋊C₉

C₁₉⋊C₃

C₁₉

G ▷ C₃²×C₁₉ ▷ C₁₉

C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

N	H ≅ G/N	type
17. C₁₉×C₉⋊C₉	C₉	semidirect
50. C₉×C₁₉	C₉⋊C₉	semidirect
64. C₉⋊C₉	#4294	semidirect
90. C₁₉	#10624561	semidirect
102. C₉	#13095306	semidirect

H ≅ G/N

type

17. C₁₉×C₉⋊C₉

C₉

semidirect

50. C₉×C₁₉

C₉⋊C₉

semidirect

64. C₉⋊C₉

#4294

semidirect

90. C₁₉

#10624561

semidirect

102. C₉

#13095306

semidirect

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

subgroup	index
C₃×#13095307	3
C₃×#13095306	3
C₃×C₉×#4294	3
#17987308	3
C₃×C₁₉×C₉⋊C₉	3
#10624561	19

subgroup

index

C₃×C₉×#4294

C₃×C₁₉×C₉⋊C₉

Subgroups — #28353581

Conjugacy classes of subgroups

Complements

Maximal subgroups