Group #22609039 — subgroups

Subgroups — #22609039

Order 9344.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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	#17989307	C₂	1	1	yes	maximal, characteristic, complemented
2	#17988933	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988784	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988334	C₂	1	1	yes	maximal, characteristic, complemented
5	#17988317	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄⋊#10596831	C₂	1	1	yes	maximal, characteristic, complemented
7	#459×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924016	—	2	1	no	—
9	#14556591	C₂²	1	1	yes	characteristic
10	#14556584	—	2	2	no	—
11	#14556578	—	2	1	no	—
12	#14556570	—	2	1	no	—
13	C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
14	#14556556	—	2	1	no	—
15	#14556550	—	2	1	no	—
16	C₄⋊#10596831	C₂²	1	1	yes	characteristic
17	#14556512	—	2	2	no	—
18	#14556512	—	2	1	no	—
19	C₄×#10596831	C₂²	1	1	yes	characteristic
20	C₂×D₈×C₇₃	—	2	1	no	—
21	#127×C₇₃	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
24	#102×C₇₃	—	2	1	no	—
25	C₂×Dic₁₄₆	—	2	1	no	—
26	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
27	#11924016	—	4	2	no	—
28	C₂×#10596831	—	2	1	no	—
29	C₂×#10596831	—	2	1	no	—
30	C₄⋊Dic₇₃	—	2	1	no	—
31	C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
32	C₄⋊Dic₇₃	D₄	1	2	yes	—
33	#11924007	—	2	2	no	—
34	#11924007	—	2	1	no	—
35	C₂²⋊Dic₇₃	—	2	2	no	—
36	C₂²⋊Dic₇₃	—	2	2	no	—
37	C₄×Dic₇₃	—	2	2	no	—
38	C₄×Dic₇₃	—	2	1	no	—
39	C₂×D₄×C₇₃	—	2	1	no	—
40	C₂×D₄×C₇₃	—	2	1	no	—
41	C₂×D₄×C₇₃	—	2	1	no	—
42	C₂×D₄×C₇₃	D₄	1	1	yes	characteristic
43	C₂²×C₄×C₇₃	—	2	1	no	—
44	D₈×C₇₃	—	4	2	no	—
45	C₂×C₈×C₇₃	—	2	1	no	—
46	C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
47	C₂²⋊C₄×C₇₃	—	2	1	no	—
48	C₄²×C₇₃	C₂³	1	1	yes	characteristic
49	C₂³×C₇₃	—	2	1	no	—
50	C₂³×C₇₃	—	4	1	no	—
51	D₄×C₇₃	—	2	1	no	—
52	D₄×C₇₃	—	2	1	no	—
53	D₄×C₇₃	—	4	2	no	—
54	D₄×C₇₃	—	4	1	no	—
55	D₄×C₇₃	—	4	1	no	—
56	D₄×C₇₃	—	4	1	no	—
57	D₄×C₇₃	—	4	1	no	—
58	C₂×C₄×C₇₃	—	2	1	no	—
59	C₂×C₄×C₇₃	—	4	1	no	—
60	C₂×C₄×C₇₃	—	4	1	no	—
61	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
63	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
64	C₂×Dic₇₃	—	2	1	no	—
65	C₂×Dic₇₃	—	2	1	no	—
66	C₂×Dic₇₃	—	2	2	no	—
67	Dic₁₄₆	—	2	1	no	—
68	Dic₁₄₆	—	2	1	no	—
69	Dic₁₄₆	—	4	1	no	—
70	Dic₁₄₆	—	4	1	no	—
71	C₈×C₇₃	—	4	1	no	—
72	#10596831	—	4	1	no	—
73	#10596831	—	4	1	no	—
74	C₂²×C₇₃	—	4	1	no	—
75	C₂²×C₇₃	—	4	1	no	—
76	C₂²×C₇₃	—	4	1	no	—
77	C₂²×C₇₃	—	8	1	no	—
78	C₂²×C₇₃	—	8	1	no	—
79	C₂²×C₇₃	—	8	1	no	—
80	C₂²×C₇₃	#120	1	1	yes	characteristic
81	C₄×C₇₃	—	2	1	no	—
82	C₄×C₇₃	—	4	1	no	—
83	C₄×C₇₃	#135	1	1	yes	characteristic
84	C₄×C₇₃	#135	1	1	yes	characteristic
85	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
87	Dic₇₃	—	4	1	no	—
88	Dic₇₃	—	4	2	no	—
89	Dic₇₃	—	4	1	no	—
90	C₂×C₇₃	—	8	1	no	—
91	C₂×C₇₃	—	16	1	no	—
92	C₂×C₇₃	#449	1	1	yes	characteristic
93	C₂×C₇₃	#449	1	1	yes	characteristic
94	C₂×C₇₃	#454	1	1	yes	characteristic
95	#1628	—	73	1	no	maximal, Sylow
96	C₇₃	#1628	1	1	yes	characteristic, complemented, Sylow
97	#556	—	73	1	no	—
98	#486	—	73	1	no	—
99	#460	—	73	1	no	—
100	#459	D₇₃	1	1	yes	characteristic
101	#332	—	73	1	no	—
102	Q₈⋊C₈	—	73	1	no	—
103	D₄⋊C₈	—	73	1	no	—
104	C₂×SD₁₆	—	146	1	no	—
105	C₂×D₈	—	2	1	no	—
106	C₄⋊Q₈	—	73	1	no	—
107	#127	C₂×D₇₃	1	1	yes	characteristic
108	#126	—	146	2	no	—
109	#124	—	146	1	no	—
110	C₂²⋊Q₈	—	146	1	no	—
111	C₄×Q₈	—	73	1	no	—
112	C₄×Q₈	—	146	1	no	—
113	C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
114	#117	—	146	1	no	—
115	C₄⋊C₈	—	73	1	no	—
116	C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
117	#102	—	2	1	no	—
118	#102	—	146	1	no	—
119	#102	—	146	2	no	—
120	C₄×C₈	—	73	1	no	—
121	C₂×Q₈	—	73	1	no	—
122	C₂×Q₈	—	146	1	no	—
123	C₂×D₄	—	2	1	no	—
124	C₂×D₄	—	2	1	no	—
125	C₂×D₄	—	2	1	no	—
126	C₂×D₄	C₂²⋊D₇₃	1	1	yes	characteristic
127	C₂²×C₄	—	2	1	no	—
128	SD₁₆	—	292	2	no	—
129	D₈	—	4	2	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	146	1	no	—
132	C₂×C₈	—	146	1	no	—
133	C₄⋊C₄	—	73	1	no	—
134	C₄⋊C₄	—	73	2	no	—
135	C₄⋊C₄	—	146	2	no	—
136	C₄⋊C₄	—	146	1	no	—
137	C₄⋊C₄	—	146	1	no	—
138	C₄⋊C₄	C₂²⋊D₇₃	1	1	yes	characteristic
139	C₂²⋊C₄	—	2	1	no	—
140	C₂²⋊C₄	—	146	2	no	—
141	C₂²⋊C₄	—	146	2	no	—
142	C₄²	—	146	2	no	—
143	C₄²	—	146	1	no	—
144	C₄²	C₂²×D₇₃	1	1	yes	characteristic
145	C₂³	—	2	1	no	—
146	C₂³	—	4	1	no	—
147	Q₈	—	292	1	no	—
148	Q₈	—	292	1	no	—
149	Q₈	—	146	1	no	—
150	Q₈	—	146	1	no	—
151	D₄	—	2	1	no	—
152	D₄	—	2	1	no	—
153	D₄	—	4	2	no	—
154	D₄	—	4	1	no	—
155	D₄	—	4	1	no	—
156	D₄	—	4	1	no	—
157	D₄	—	4	1	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	4	1	no	—
160	C₂×C₄	—	4	1	no	—
161	C₂×C₄	—	146	1	no	—
162	C₂×C₄	—	146	2	no	—
163	C₂×C₄	—	146	1	no	—
164	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
165	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
166	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
167	C₈	—	4	1	no	—
168	C₈	—	292	1	no	—
169	C₈	—	292	1	no	—
170	C₂²	—	4	1	no	—
171	C₂²	—	4	1	no	—
172	C₂²	—	4	1	no	—
173	C₂²	—	8	1	no	—
174	C₂²	—	8	1	no	—
175	C₂²	—	8	1	no	—
176	C₂²	#14556559	1	1	yes	characteristic
177	C₄	—	2	1	no	—
178	C₄	—	4	1	no	—
179	C₄	—	292	1	no	—
180	C₄	—	292	2	no	—
181	C₄	—	292	1	no	—
182	C₄	#14556610	1	1	yes	characteristic
183	C₄	#14556611	1	1	yes	characteristic
184	C₄	#14556615	1	1	yes	characteristic
185	C₄	#14556617	1	1	yes	characteristic
186	C₂	—	8	1	no	—
187	C₂	—	16	1	no	—
188	C₂	#17988729	1	1	yes	characteristic
189	C₂	#17988730	1	1	yes	characteristic
190	C₂	#17988758	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989307

C₂

yes

maximal, characteristic, complemented

#17988933

C₂

yes

maximal, characteristic, complemented

#17988784

C₂

yes

maximal, characteristic, complemented

#17988334

C₂

yes

maximal, characteristic, complemented

#17988317

C₂

yes

maximal, characteristic, complemented

D₄⋊#10596831

C₂

yes

maximal, characteristic, complemented

#459×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924016

—

#14556591

C₂²

yes

—

—

—

C₄×Dic₁₄₆

C₂²

yes

—

—

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×D₈×C₇₃

—

#127×C₇₃

C₂²

yes

characteristic

C₄×D₄×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

characteristic

#102×C₇₃

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

—

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

D₄

yes

characteristic

C₄⋊Dic₇₃

D₄

yes

—

#11924007

—

#11924007

—

C₂²⋊Dic₇₃

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

—

C₂×D₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

—

D₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

D₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#120

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#556

—

#486

—

#460

—

100

#459

D₇₃

yes

characteristic

101

#332

—

102

Q₈⋊C₈

—

103

D₄⋊C₈

—

104

C₂×SD₁₆

—

146

—

105

C₂×D₈

—

106

C₄⋊Q₈

—

107

#127

C₂×D₇₃

yes

characteristic

108

#126

—

146

—

109

#124

—

146

—

110

C₂²⋊Q₈

—

146

—

111

C₄×Q₈

—

112

C₄×Q₈

—

146

—

113

C₄×D₄

C₂×D₇₃

yes

characteristic

114

#117

—

146

—

115

C₄⋊C₈

—

116

C₄⋊C₈

C₂×D₇₃

yes

characteristic

117

#102

—

118

#102

—

146

—

119

#102

—

146

—

120

C₄×C₈

—

121

C₂×Q₈

—

122

C₂×Q₈

—

146

—

123

C₂×D₄

—

124

C₂×D₄

—

125

C₂×D₄

—

126

C₂×D₄

C₂²⋊D₇₃

yes

characteristic

127

C₂²×C₄

—

128

SD₁₆

—

292

—

129

D₈

—

130

C₂×C₈

—

131

C₂×C₈

—

146

—

132

C₂×C₈

—

146

—

133

C₄⋊C₄

—

134

C₄⋊C₄

—

135

C₄⋊C₄

—

146

—

136

C₄⋊C₄

—

146

—

137

C₄⋊C₄

—

146

—

138

C₄⋊C₄

C₂²⋊D₇₃

yes

characteristic

139

C₂²⋊C₄

—

140

C₂²⋊C₄

—

146

—

141

C₂²⋊C₄

—

146

—

142

C₄²

—

146

—

143

C₄²

—

146

—

144

C₄²

C₂²×D₇₃

yes

characteristic

145

C₂³

—

146

C₂³

—

147

Q₈

—

292

—

148

Q₈

—

292

—

149

Q₈

—

146

—

150

Q₈

—

146

—

151

D₄

—

152

D₄

—

153

D₄

—

154

D₄

—

155

D₄

—

156

D₄

—

157

D₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

146

—

162

C₂×C₄

—

146

—

163

C₂×C₄

—

146

—

164

C₂×C₄

D₄×D₇₃

yes

characteristic

165

C₂×C₄

D₄×D₇₃

yes

characteristic

166

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

167

C₈

—

168

C₈

—

292

—

169

C₈

—

292

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

176

C₂²

#14556559

yes

characteristic

177

C₄

—

178

C₄

—

179

C₄

—

292

—

180

C₄

—

292

—

181

C₄

—

292

—

182

C₄

#14556610

yes

characteristic

183

C₄

#14556611

yes

characteristic

184

C₄

#14556615

yes

characteristic

185

C₄

#14556617

yes

characteristic

186

C₂

—

187

C₂

—

188

C₂

#17988729

yes

characteristic

189

C₂

#17988730

yes

characteristic

190

C₂

#17988758

yes

characteristic

	subgroup	G/H
center	C₂²	#14556559
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#459×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#459	D₇₃
hypocenter	C₇₃	#1628
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

subgroup

G/H

center

C₂²

#14556559

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#459×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #459

N	H ≅ G/N	type
1. #17989307	C₂	semidirect
2. #17988933	C₂	semidirect
3. #17988784	C₂	semidirect
4. #17988334	C₂	semidirect
5. #17988317	C₂	semidirect
6. D₄⋊#10596831	C₂	semidirect
96. C₇₃	#1628	semidirect

H ≅ G/N

type

1. #17989307

C₂

semidirect

2. #17988933

C₂

semidirect

3. #17988784

C₂

semidirect

4. #17988334

C₂

semidirect

5. #17988317

C₂

semidirect

6. D₄⋊#10596831

C₂

semidirect

96. C₇₃

#1628

semidirect

Subgroups — #22609039

Conjugacy classes of subgroups

Complements