Group #28354872 — subgroups

Subgroups — #28354872

Order 13851.

192 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13095311	C₃	1	1	yes	maximal, characteristic
2	C₉×#10587022	C₃	1	1	yes	maximal, characteristic
3	#17987357	C₃	1	1	yes	maximal, characteristic, complemented
4	#17987355	C₃	1	2	yes	maximal, complemented
5	#17987355	C₃	1	2	yes	maximal, complemented
6	#17987332	C₃	1	2	yes	maximal
7	#17987330	C₃	1	2	yes	maximal, complemented
8	C₉×#10587018	C₃	1	1	yes	maximal, characteristic, complemented
9	C₁₉×C₉⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃×#10587022	C₉	1	1	yes	characteristic
11	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
12	#13095311	—	3	3	no	—
13	C₃×#10587018	C₃²	1	2	yes	—
14	C₃×#10587018	C₃²	1	2	yes	—
15	C₃×#10587018	C₃²	1	1	yes	characteristic
16	C₃×#10587018	C₃²	1	1	yes	characteristic
17	#13095306	C₉	1	2	yes	—
18	#13095305	C₉	1	4	yes	—
19	#13095303	C₉	1	2	yes	—
20	C₉×#4294	C₃²	1	2	yes	—
21	C₃×C₁₉×C₂₇	C₃²	1	2	yes	—
22	C₃×C₁₉×C₂₇	C₃²	1	1	yes	characteristic
23	C₉²×C₁₉	C₃²	1	1	yes	characteristic
24	#10624728	—	19	1	no	maximal, Sylow
25	C₃²×C₁₉⋊C₃	C₃×C₉	1	1	yes	characteristic
26	C₃×C₉×C₁₉	C₃×C₉	1	2	yes	—
27	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
28	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
29	C₃×#4294	C₃×C₉	1	4	yes	—
30	C₃×#4294	C₃×C₉	1	2	yes	—
31	C₃×#4294	C₃×C₉	1	2	yes	—
32	#10587022	—	3	3	no	—
33	C₉×C₁₉⋊C₃	—	3	1	no	—
34	C₉×C₁₉⋊C₃	—	3	2	no	—
35	C₁₉×C₂₇	—	3	1	no	—
36	C₁₉×C₂₇	—	3	2	no	—
37	#10587018	—	3	1	no	—
38	#10587018	—	3	2	no	—
39	#10587018	—	3	2	no	—
40	#10587018	3₋¹⁺²	1	3	yes	complemented
41	C₃×C₂₇⋊C₃	—	19	1	no	—
42	C₉×3₋¹⁺²	—	19	1	no	—
43	C₉⋊C₂₇	—	19	2	no	—
44	C₉⋊C₂₇	—	19	2	no	—
45	C₉⋊C₂₇	—	19	1	no	—
46	C₉⋊C₂₇	C₁₉⋊C₃	1	1	yes	characteristic, complemented
47	C₃²⋊C₂₇	—	19	2	no	—
48	#6864	—	19	2	no	—
49	C₉×C₂₇	—	19	1	no	—
50	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
51	C₃×C₁₉⋊C₃	—	3	1	no	—
52	C₃×C₁₉⋊C₃	—	3	1	no	—
53	C₃×C₁₉⋊C₃	—	3	2	no	—
54	C₉×C₁₉	—	3	2	no	—
55	C₉×C₁₉	C₂₇⋊C₃	1	3	yes	complemented
56	C₉×C₁₉	C₃×3₋¹⁺²	1	1	yes	characteristic
57	C₉×C₁₉	#737	1	2	yes	—
58	#4294	—	3	2	no	—
59	#4294	—	3	2	no	—
60	#4294	—	3	4	no	—
61	C₃×3₋¹⁺²	—	19	1	no	—
62	C₃²×C₉	—	19	1	no	—
63	C₂₇⋊C₃	—	57	3	no	—
64	C₃×C₂₇	—	19	1	no	—
65	C₃×C₂₇	—	19	2	no	—
66	C₃×C₂₇	—	19	2	no	—
67	C₃×C₂₇	—	19	1	no	—
68	C₃×C₂₇	C₃×C₁₉⋊C₃	1	2	yes	—
69	C₃×C₂₇	C₃×C₁₉⋊C₃	1	1	yes	characteristic
70	C₉⋊C₉	—	19	4	no	—
71	C₉⋊C₉	—	19	2	no	—
72	C₃²⋊C₉	—	19	2	no	—
73	C₉²	—	19	2	no	—
74	C₉²	C₃×C₁₉⋊C₃	1	1	yes	characteristic
75	C₃×C₁₉	C₉×3₋¹⁺²	1	1	yes	characteristic
76	C₃×C₁₉	C₃×C₂₇⋊C₃	1	1	yes	characteristic
77	C₃×C₁₉	#6903	1	2	yes	—
78	C₁₉⋊C₃	—	9	1	no	—
79	C₃³	—	19	1	no	—
80	3₋¹⁺²	—	57	3	no	—
81	C₃×C₉	—	19	4	no	—
82	C₃×C₉	—	19	2	no	—
83	C₃×C₉	—	19	2	no	—
84	C₃×C₉	—	57	1	no	—
85	C₃×C₉	—	57	2	no	—
86	C₃×C₉	C₉×C₁₉⋊C₃	1	2	yes	—
87	C₃×C₉	C₉×C₁₉⋊C₃	1	1	yes	characteristic
88	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
89	C₂₇	—	3	1	no	—
90	C₂₇	—	3	2	no	—
91	C₂₇	—	19	3	no	—
92	C₂₇	—	57	1	no	—
93	C₂₇	—	57	2	no	—
94	C₂₇	—	57	2	no	—
95	C₁₉	#10624728	1	1	yes	characteristic, complemented, Sylow
96	C₃²	—	57	1	no	—
97	C₃²	—	57	1	no	—
98	C₃²	—	57	2	no	—
99	C₃²	C₃×C₉×C₁₉⋊C₃	1	1	yes	characteristic
100	C₉	—	3	2	no	—
101	C₉	—	57	2	no	—
102	C₉	—	57	2	no	—
103	C₉	—	57	4	no	—
104	C₉	#13095311	1	3	yes	complemented
105	C₉	3₋¹⁺²×C₁₉⋊C₃	1	1	yes	characteristic
106	C₉	#13095333	1	2	yes	—
107	C₃	—	171	1	no	—
108	C₃	#17987410	1	1	yes	characteristic
109	C₃	C₃×#13095311	1	1	yes	characteristic
110	C₃	#17987481	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#13095311

C₃

yes

maximal, characteristic

C₉×#10587022

C₃

yes

maximal, characteristic

#17987357

C₃

yes

maximal, characteristic, complemented

#17987355

C₃

yes

maximal, complemented

#17987355

C₃

yes

maximal, complemented

#17987332

C₃

yes

maximal

#17987330

C₃

yes

maximal, complemented

C₉×#10587018

C₃

yes

maximal, characteristic, complemented

C₁₉×C₉⋊C₂₇

C₃

yes

maximal, characteristic, complemented

C₃×#10587022

C₉

yes

characteristic

C₃×C₉×C₁₉⋊C₃

C₃²

yes

characteristic

#13095311

—

C₃×#10587018

C₃²

yes

—

C₃×#10587018

C₃²

yes

—

C₃×#10587018

C₃²

yes

characteristic

C₃×#10587018

C₃²

yes

characteristic

#13095306

C₉

yes

—

#13095305

C₉

yes

—

#13095303

C₉

yes

—

C₉×#4294

C₃²

yes

—

C₃×C₁₉×C₂₇

C₃²

yes

—

C₃×C₁₉×C₂₇

C₃²

yes

characteristic

C₉²×C₁₉

C₃²

yes

characteristic

#10624728

—

maximal, Sylow

C₃²×C₁₉⋊C₃

C₃×C₉

yes

characteristic

C₃×C₉×C₁₉

C₃×C₉

yes

—

C₃×C₉×C₁₉

C₃×C₉

yes

characteristic

C₃×C₉×C₁₉

C₃³

yes

characteristic

C₃×#4294

C₃×C₉

yes

—

C₃×#4294

C₃×C₉

yes

—

C₃×#4294

C₃×C₉

yes

—

#10587022

—

C₉×C₁₉⋊C₃

—

C₉×C₁₉⋊C₃

—

C₁₉×C₂₇

—

C₁₉×C₂₇

—

—

—

—

3₋¹⁺²

yes

complemented

C₃×C₂₇⋊C₃

—

C₉×3₋¹⁺²

—

C₉⋊C₂₇

—

C₉⋊C₂₇

—

C₉⋊C₂₇

—

C₉⋊C₂₇

C₁₉⋊C₃

yes

characteristic, complemented

C₃²⋊C₂₇

—

#6864

—

C₉×C₂₇

—

C₃²×C₁₉

C₃²×C₉

yes

characteristic

C₃×C₁₉⋊C₃

—

C₃×C₁₉⋊C₃

—

C₃×C₁₉⋊C₃

—

C₉×C₁₉

—

C₉×C₁₉

C₂₇⋊C₃

yes

complemented

C₉×C₁₉

C₃×3₋¹⁺²

yes

characteristic

C₉×C₁₉

#737

yes

—

#4294

—

#4294

—

#4294

—

C₃×3₋¹⁺²

—

C₃²×C₉

—

C₂₇⋊C₃

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

—

C₃×C₂₇

C₃×C₁₉⋊C₃

yes

—

C₃×C₂₇

C₃×C₁₉⋊C₃

yes

characteristic

C₉⋊C₉

—

C₉⋊C₉

—

C₃²⋊C₉

—

C₉²

—

C₉²

C₃×C₁₉⋊C₃

yes

characteristic

C₃×C₁₉

C₉×3₋¹⁺²

yes

characteristic

C₃×C₁₉

C₃×C₂₇⋊C₃

yes

characteristic

C₃×C₁₉

#6903

yes

—

C₁₉⋊C₃

—

C₃³

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

C₉×C₁₉⋊C₃

yes

—

C₃×C₉

C₉×C₁₉⋊C₃

yes

characteristic

C₃×C₉

C₃²×C₁₉⋊C₃

yes

characteristic

C₂₇

—

C₂₇

—

C₂₇

—

C₂₇

—

C₂₇

—

C₂₇

—

C₁₉

#10624728

yes

characteristic, complemented, Sylow

C₃²

—

C₃²

—

C₃²

—

C₃²

C₃×C₉×C₁₉⋊C₃

yes

characteristic

100

C₉

—

101

C₉

—

102

C₉

—

103

C₉

—

104

C₉

#13095311

yes

complemented

105

C₉

3₋¹⁺²×C₁₉⋊C₃

yes

characteristic

106

C₉

#13095333

yes

—

107

C₃

—

171

—

108

C₃

#17987410

yes

characteristic

109

C₃

C₃×#13095311

yes

characteristic

110

C₃

#17987481

yes

—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₁₉⋊C₃
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting	C₁₉×C₉⋊C₂₇	C₃
prime radical	C₃²×C₁₉⋊C₃	C₃×C₉
cosocle	C₃×C₉×C₁₉	C₃³
hypercenter	C₉⋊C₂₇	C₁₉⋊C₃
hypocenter	C₁₉	#10624728
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃×C₉ ◁ C₉⋊C₂₇

subgroup

G/H

center, Frattini

C₃×C₉

C₃²×C₁₉⋊C₃

commutator, socle

C₃²×C₁₉

C₃²×C₉

Fitting

C₁₉×C₉⋊C₂₇

C₃

prime radical

C₃²×C₁₉⋊C₃

C₃×C₉

cosocle

C₃×C₉×C₁₉

C₃³

hypercenter

C₉⋊C₂₇

C₁₉⋊C₃

C₁₉

G ▷ C₃²×C₁₉ ▷ C₁₉

C₁ ◁ C₃×C₉ ◁ C₉⋊C₂₇

N	H ≅ G/N	type
3. #17987357	C₃	semidirect
4. #17987355	C₃	semidirect
5. #17987355	C₃	semidirect
7. #17987330	C₃	semidirect
8. C₉×#10587018	C₃	semidirect
9. C₁₉×C₉⋊C₂₇	C₃	semidirect
40. #10587018	3₋¹⁺²	semidirect
46. C₉⋊C₂₇	C₁₉⋊C₃	semidirect
55. C₉×C₁₉	C₂₇⋊C₃	semidirect
95. C₁₉	#10624728	semidirect
104. C₉	#13095311	semidirect

H ≅ G/N

type

3. #17987357

C₃

semidirect

4. #17987355

C₃

semidirect

5. #17987355

C₃

semidirect

7. #17987330

C₃

semidirect

8. C₉×#10587018

C₃

semidirect

9. C₁₉×C₉⋊C₂₇

C₃

semidirect

40. #10587018

3₋¹⁺²

semidirect

46. C₉⋊C₂₇

C₁₉⋊C₃

semidirect

55. C₉×C₁₉

C₂₇⋊C₃

semidirect

95. C₁₉

#10624728

semidirect

104. C₉

#13095311

semidirect

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

subgroup	index
C₃×#13095311	3
C₉×#10587022	3
#17987357	3
#17987355	3
#17987332	3
#17987330	3
C₉×#10587018	3
C₁₉×C₉⋊C₂₇	3
#10624728	19

subgroup

index

C₁₉×C₉⋊C₂₇

Subgroups — #28354872

Conjugacy classes of subgroups

Complements

Maximal subgroups