Group #13091265 — subgroups

Subgroups — #10624823⋊C₂ #13091265

Order 1458.

221 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 221 conjugacy classes of subgroups — too many to draw. Only its 25 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	#10624823	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊AGL(1,ℤ/9)	—	3	1	no	maximal
3	#4169⋊C₃	—	3	1	no	maximal
4	#4169⋊C₃	—	3	1	no	maximal
5	C₃×#4169	—	3	1	no	maximal
6	(3₋¹⁺²⋊C₉)⋊C₂	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×3₋¹⁺²	D₃	1	1	yes	characteristic
8	#6891	D₃	1	1	yes	characteristic
9	#6891	D₃	1	1	yes	characteristic
10	C₃×C₃²⋊C₉	D₃	1	1	yes	characteristic
11	3₋¹⁺²⋊C₉	—	2	1	no	—
12	3₋¹⁺²⋊C₉	—	2	1	no	—
13	3₋¹⁺²⋊C₉	—	2	1	no	—
14	3₋¹⁺²⋊C₉	—	2	1	no	—
15	3₋¹⁺²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
16	C₃²×C₃⋊D₃	—	9	1	no	—
17	C₃⋊AGL(1,ℤ/9)	—	3	2	no	—
18	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
19	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
20	C₃⋊AGL(1,ℤ/9)	—	3	1	no	—
21	C₃×C₃⋊D₉	—	3	1	no	—
22	C₃×C₃⋊D₉	—	3	1	no	—
23	C₃×AGL(1,ℤ/9)	—	9	3	no	—
24	#4169	—	3	2	no	—
25	#4169	—	3	2	no	—
26	#4169	—	3	2	no	—
27	#4169	—	3	1	no	—
28	#4169	—	3	1	no	—
29	#4169	—	3	1	no	—
30	C₃⁴	C₃⋊D₃	1	1	yes	characteristic
31	C₃×3₋¹⁺²	—	2	1	no	—
32	C₃×3₋¹⁺²	—	3	3	no	—
33	C₃×3₋¹⁺²	—	3	2	no	—
34	C₃×3₋¹⁺²	—	3	1	no	—
35	C₃×3₋¹⁺²	—	3	1	no	—
36	C₃×3₋¹⁺²	—	6	3	no	—
37	C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
38	C₃²×C₉	—	2	1	no	—
39	C₃²×C₉	—	3	1	no	—
40	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
41	C₃²⋊C₉	—	2	1	no	—
42	C₃²⋊C₉	—	2	1	no	—
43	C₃²⋊C₉	—	3	2	no	—
44	C₃²⋊C₉	—	3	1	no	—
45	C₃²⋊C₉	—	3	2	no	—
46	C₃²⋊C₉	—	3	2	no	—
47	C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
48	C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
49	C₃×C₃⋊D₃	—	9	2	no	—
50	C₃×C₃⋊D₃	—	9	1	no	—
51	C₃×C₃⋊D₃	—	9	1	no	—
52	C₃²×D₃	—	27	1	no	—
53	C₃²×D₃	—	27	1	no	—
54	C₃²×D₃	—	27	1	no	—
55	C₃²×D₃	—	27	1	no	—
56	C₃⋊D₉	—	3	1	no	—
57	C₃⋊D₉	—	3	1	no	—
58	C₃⋊D₉	—	3	1	no	—
59	C₃⋊D₉	—	3	1	no	—
60	AGL(1,ℤ/9)	—	9	6	no	—
61	AGL(1,ℤ/9)	—	9	3	no	—
62	AGL(1,ℤ/9)	—	27	1	no	—
63	AGL(1,ℤ/9)	—	27	1	no	—
64	C₃×D₉	—	9	3	no	—
65	C₃×D₉	—	27	1	no	—
66	C₃³	—	3	1	no	—
67	C₃³	—	3	1	no	—
68	C₃³	—	6	1	no	—
69	C₃³	—	6	1	no	—
70	C₃³	—	9	1	no	—
71	C₃³	—	9	1	no	—
72	C₃³	#272	1	1	yes	characteristic
73	C₃³	#272	1	2	yes	—
74	C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
75	3₋¹⁺²	—	3	6	no	—
76	3₋¹⁺²	—	3	3	no	—
77	3₋¹⁺²	—	3	1	no	—
78	3₋¹⁺²	—	6	3	no	—
79	3₋¹⁺²	—	6	6	no	—
80	3₋¹⁺²	—	6	1	no	—
81	3₋¹⁺²	—	6	2	no	—
82	3₋¹⁺²	—	6	1	no	—
83	3₋¹⁺²	—	9	1	no	—
84	3₋¹⁺²	—	18	1	no	—
85	C₃×C₉	—	3	1	no	—
86	C₃×C₉	—	3	3	no	—
87	C₃×C₉	—	3	1	no	—
88	C₃×C₉	—	3	1	no	—
89	C₃×C₉	—	3	1	no	—
90	C₃×C₉	—	6	1	no	—
91	C₃×C₉	—	6	3	no	—
92	C₃×C₉	—	6	1	no	—
93	C₃×C₉	—	6	1	no	—
94	C₃×C₉	—	6	1	no	—
95	C₃×C₉	—	9	1	no	—
96	C₃×C₉	—	18	1	no	—
97	C₂×C₃²	—	81	1	no	—
98	C₃⋊D₃	—	9	1	no	—
99	C₃×D₃	—	27	1	no	—
100	C₃×D₃	—	27	1	no	—
101	C₃×D₃	—	27	2	no	—
102	C₃×D₃	—	27	1	no	—
103	C₃×D₃	—	27	2	no	—
104	C₃×D₃	—	27	1	no	—
105	C₃×D₃	—	27	2	no	—
106	C₃×D₃	—	27	1	no	—
107	C₃×D₃	—	27	1	no	—
108	C₃×D₃	—	27	2	no	—
109	C₃×D₃	—	27	1	no	—
110	C₃×D₃	—	27	1	no	—
111	D₉	—	9	3	no	—
112	D₉	—	27	1	no	—
113	D₉	—	27	1	no	—
114	D₉	—	27	1	no	—
115	C₃²	—	2	1	no	—
116	C₃²	—	2	1	no	—
117	C₃²	—	3	1	no	—
118	C₃²	—	3	1	no	—
119	C₃²	—	3	1	no	—
120	C₃²	—	3	1	no	—
121	C₃²	—	3	1	no	—
122	C₃²	—	3	1	no	—
123	C₃²	—	3	2	no	—
124	C₃²	—	3	2	no	—
125	C₃²	—	3	2	no	—
126	C₃²	—	3	2	no	—
127	C₃²	—	9	1	no	—
128	C₃²	—	18	1	no	—
129	C₃²	—	18	1	no	—
130	C₃²	—	18	2	no	—
131	C₃²	#4183	1	1	yes	characteristic
132	C₃²	C₃×#272	1	1	yes	characteristic
133	C₃²	#4207	1	1	yes	characteristic
134	C₉	—	3	3	no	—
135	C₉	—	6	3	no	—
136	C₉	—	9	1	no	—
137	C₉	—	9	1	no	—
138	C₉	—	9	1	no	—
139	C₉	—	18	1	no	—
140	C₉	—	18	1	no	—
141	C₉	—	18	1	no	—
142	C₂×C₃	—	81	1	no	—
143	C₂×C₃	—	81	1	no	—
144	C₂×C₃	—	81	2	no	—
145	D₃	—	27	1	no	—
146	D₃	—	27	1	no	—
147	D₃	—	27	1	no	—
148	D₃	—	27	1	no	—
149	C₃	—	3	1	no	—
150	C₃	—	3	1	no	—
151	C₃	—	6	1	no	—
152	C₃	—	6	1	no	—
153	C₃	—	9	2	no	—
154	C₃	#92304	1	1	yes	characteristic
155	C₃	C₃×#4183	1	1	yes	characteristic
156	C₃	#4184⋊C₃	1	1	yes	characteristic
157	C₃	#6912⋊C₂	1	1	yes	characteristic
158	C₂	—	81	1	no	Sylow

subgroup

G/H

class size

multiplicity

normal?

properties

#10624823

C₂

yes

maximal, characteristic, complemented, Sylow

—

—

—

—

(3₋¹⁺²⋊C₉)⋊C₂

C₃

yes

maximal, characteristic, complemented

C₃²×3₋¹⁺²

D₃

yes

characteristic

#6891

D₃

yes

characteristic

#6891

D₃

yes

characteristic

C₃×C₃²⋊C₉

D₃

yes

characteristic

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

—

3₋¹⁺²⋊C₉

C₂×C₃

yes

characteristic, complemented

C₃²×C₃⋊D₃

—

—

—

—

—

C₃×C₃⋊D₉

—

C₃×C₃⋊D₉

—

—

—

—

—

—

—

—

C₃⁴

C₃⋊D₃

yes

characteristic

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

—

C₃×3₋¹⁺²

C₃×D₃

yes

characteristic

C₃²×C₉

—

C₃²×C₉

—

C₃²×C₉

C₃×D₃

yes

characteristic

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

—

C₃²⋊C₉

C₃×D₃

yes

characteristic

C₃²⋊C₉

C₃×D₃

yes

characteristic

C₃×C₃⋊D₃

—

C₃×C₃⋊D₃

—

C₃×C₃⋊D₃

—

C₃²×D₃

—

C₃²×D₃

—

C₃²×D₃

—

C₃²×D₃

—

C₃⋊D₉

—

C₃⋊D₉

—

C₃⋊D₉

—

C₃⋊D₉

—

—

—

—

—

C₃×D₉

—

C₃×D₉

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

—

C₃³

#272

yes

characteristic

C₃³

#272

yes

—

C₃³

C₃×C₃⋊D₃

yes

characteristic

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

3₋¹⁺²

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₃×C₉

—

C₂×C₃²

—

C₃⋊D₃

—

C₃×D₃

—

100

C₃×D₃

—

101

C₃×D₃

—

102

C₃×D₃

—

103

C₃×D₃

—

104

C₃×D₃

—

105

C₃×D₃

—

106

C₃×D₃

—

107

C₃×D₃

—

108

C₃×D₃

—

109

C₃×D₃

—

110

C₃×D₃

—

111

D₉

—

112

D₉

—

113

D₉

—

114

D₉

—

115

C₃²

—

116

C₃²

—

117

C₃²

—

118

C₃²

—

119

C₃²

—

120

C₃²

—

121

C₃²

—

122

C₃²

—

123

C₃²

—

124

C₃²

—

125

C₃²

—

126

C₃²

—

127

C₃²

—

128

C₃²

—

129

C₃²

—

130

C₃²

—

131

C₃²

#4183

yes

characteristic

132

C₃²

C₃×#272

yes

characteristic

133

C₃²

#4207

yes

characteristic

134

C₉

—

135

C₉

—

136

C₉

—

137

C₉

—

138

C₉

—

139

C₉

—

140

C₉

—

141

C₉

—

142

C₂×C₃

—

143

C₂×C₃

—

144

C₂×C₃

—

145

D₃

—

146

D₃

—

147

D₃

—

148

D₃

—

149

C₃

—

150

C₃

—

151

C₃

—

152

C₃

—

153

C₃

—

154

C₃

#92304

yes

characteristic

155

C₃

C₃×#4183

yes

characteristic

156

C₃

#4184⋊C₃

yes

characteristic

157

C₃

#6912⋊C₂

yes

characteristic

158

C₂

—

Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	3₋¹⁺²⋊C₉	C₂×C₃
Frattini	C₃³	C₃×C₃⋊D₃
Fitting	#10624823	C₂
socle	C₃²	C₃×#272
LCS	G ▷ 3₋¹⁺²⋊C₉
UCS	C₁

subgroup

G/H

center, hypercenter

C₁

commutator, cosocle, hypocenter

3₋¹⁺²⋊C₉

C₂×C₃

Frattini

C₃³

C₃×C₃⋊D₃

C₂

C₃²

G ▷ 3₋¹⁺²⋊C₉

C₁

N	H ≅ G/N	type
1. #10624823	C₂	semidirect
6. (3₋¹⁺²⋊C₉)⋊C₂	C₃	semidirect
15. 3₋¹⁺²⋊C₉	C₂×C₃	semidirect

H ≅ G/N

type

1. #10624823

C₂

semidirect

6. (3₋¹⁺²⋊C₉)⋊C₂

C₃

semidirect

15. 3₋¹⁺²⋊C₉

C₂×C₃

semidirect

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

subgroup	index
#10624823	2
C₃×C₃⋊AGL(1,ℤ/9)	3
#4169⋊C₃	3
C₃×#4169	3
(3₋¹⁺²⋊C₉)⋊C₂	3

subgroup

index

(3₋¹⁺²⋊C₉)⋊C₂

Subgroups — #10624823⋊C₂ #13091265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624823⋊C2 #13091265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624823⋊C₂ #13091265