Group #32990963 — subgroups

Subgroups — #32990963

Order 18688.

372 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 97 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	#22610729	C₂	1	1	yes	maximal, characteristic
2	#22608707	C₂	1	2	yes	maximal, complemented
3	#22608355	C₂	1	2	yes	maximal
4	#22607762	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1849	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
7	#17988640	C₂²	1	2	yes	—
8	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
9	C₂×#14556503	—	2	2	no	—
10	#17988339	—	2	4	no	—
11	#17988314	—	2	4	no	—
12	C₂×#108×C₇₃	—	2	2	no	—
13	#423×C₇₃	C₂²	1	2	yes	—
14	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×D₂₉₂	Q₈	1	1	yes	characteristic
16	C₂²×C₄×D₇₃	—	2	1	no	—
17	C₂²×#10596831	—	2	1	no	—
18	C₄×D₂₉₂	—	2	2	no	—
19	C₄×D₂₉₂	—	2	2	no	—
20	C₂×C₄⋊Dic₇₃	Q₈	1	1	yes	characteristic
21	C₂×#11924005	—	2	1	no	—
22	C₄⋊#10596831	—	2	2	no	—
23	C₄⋊#10596831	—	2	2	no	—
24	C₂²⋊#10596831	—	2	2	no	—
25	#14556503	—	4	4	no	—
26	C₄×#10596831	D₄	1	4	yes	—
27	C₂×M₁₆×C₇₃	—	2	2	no	—
28	C₂²×C₈×C₇₃	D₄	1	2	yes	—
29	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
30	#108×C₇₃	—	4	4	no	—
31	C₄⋊C₈×C₇₃	—	2	2	no	—
32	C₄⋊C₈×C₇₃	—	2	2	no	—
33	#97×C₇₃	—	2	2	no	—
34	C₂³×D₇₃	—	2	1	no	—
35	C₂×D₂₉₂	—	2	2	no	—
36	C₂×D₂₉₂	—	4	2	no	—
37	C₂²×Dic₇₃	—	2	1	no	—
38	C₂×C₄×D₇₃	—	4	1	no	—
39	C₂×C₄×D₇₃	—	4	1	no	—
40	C₂×C₄×D₇₃	—	4	2	no	—
41	C₂×C₄×D₇₃	—	4	2	no	—
42	C₂×#10596831	—	2	4	no	—
43	C₂×#10596831	—	4	1	no	—
44	C₂×#10596831	—	4	2	no	—
45	C₄⋊Dic₇₃	—	2	2	no	—
46	#11924005	—	4	2	no	—
47	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
49	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
50	M₁₆×C₇₃	—	4	4	no	—
51	C₂×C₈×C₇₃	—	2	2	no	—
52	C₂×C₈×C₇₃	—	2	2	no	—
53	C₂×C₈×C₇₃	—	4	2	no	—
54	C₂×C₈×C₇₃	D₈	1	4	yes	—
55	C₄²×C₇₃	C₂×D₄	1	2	yes	—
56	C₄²×C₇₃	#41	1	2	yes	—
57	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
58	C₂²×D₇₃	—	2	2	no	—
59	C₂²×D₇₃	—	4	1	no	—
60	C₂²×D₇₃	—	4	2	no	—
61	C₂²×D₇₃	—	4	1	no	—
62	C₂²×D₇₃	—	4	2	no	—
63	C₂×C₄×C₇₃	—	4	1	no	—
64	C₂×C₄×C₇₃	—	4	1	no	—
65	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
66	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
67	C₂×C₄×C₇₃	#123	1	2	yes	—
68	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
69	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
70	C₂×C₄×C₇₃	#137	1	2	yes	—
71	C₂×Dic₇₃	—	4	1	no	—
72	C₂×Dic₇₃	—	4	2	no	—
73	D₂₉₂	—	2	4	no	—
74	D₂₉₂	—	4	2	no	—
75	C₄×D₇₃	—	8	2	no	—
76	C₄×D₇₃	—	8	1	no	—
77	C₄×D₇₃	—	8	1	no	—
78	C₈×C₇₃	—	2	4	no	—
79	C₈×C₇₃	—	8	2	no	—
80	#10596831	—	4	4	no	—
81	#10596831	—	8	1	no	—
82	C₂²×C₇₃	—	2	1	no	—
83	C₂²×C₇₃	—	2	1	no	—
84	C₂²×C₇₃	#399	1	1	yes	characteristic
85	C₂²×C₇₃	#474	1	2	yes	—
86	C₂×D₇₃	—	4	4	no	—
87	C₂×D₇₃	—	4	2	no	—
88	C₂×D₇₃	—	8	2	no	—
89	C₂×D₇₃	—	8	1	no	—
90	C₂×D₇₃	—	8	1	no	—
91	C₄×C₇₃	—	2	2	no	—
92	C₄×C₇₃	—	2	2	no	—
93	C₄×C₇₃	#480	1	2	yes	—
94	C₄×C₇₃	#493	1	1	yes	characteristic
95	C₄×C₇₃	#497	1	1	yes	characteristic
96	Dic₇₃	—	8	1	no	—
97	#10660	—	73	1	no	maximal, Sylow
98	C₂×C₇₃	—	2	2	no	—
99	C₂×C₇₃	#2091	1	1	yes	characteristic
100	C₂×C₇₃	#2093	1	1	yes	characteristic
101	C₂×C₇₃	#2098	1	1	yes	characteristic
102	D₇₃	—	8	2	no	—
103	#1955	—	73	1	no	—
104	#1849	D₇₃	1	1	yes	characteristic, complemented
105	#1571	—	73	2	no	—
106	#1486	—	73	2	no	—
107	#1275	—	73	1	no	—
108	C₇₃	#10660	1	1	yes	characteristic, complemented, Sylow
109	C₂×C₄×D₄	—	73	1	no	—
110	#431	—	73	2	no	—
111	C₂×#108	—	2	2	no	—
112	#423	C₂×D₇₃	1	2	yes	—
113	C₂×C₄⋊C₈	—	73	1	no	—
114	C₂×C₂²⋊C₈	—	146	2	no	—
115	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
116	#335	—	146	4	no	—
117	D₄⋊C₈	—	146	4	no	—
118	C₂²×D₄	—	73	1	no	—
119	C₂³×C₄	—	146	1	no	—
120	C₂×M₁₆	—	2	2	no	—
121	C₂²×C₈	—	146	1	no	—
122	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
123	C₄×D₄	—	146	2	no	—
124	C₄×D₄	—	146	2	no	—
125	C₂×C₄⋊C₄	—	73	1	no	—
126	C₂×C₂²⋊C₄	—	146	1	no	—
127	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
128	#108	—	4	4	no	—
129	C₄⋊C₈	—	2	2	no	—
130	C₄⋊C₈	—	2	2	no	—
131	C₄⋊C₈	—	146	2	no	—
132	C₄⋊C₈	—	146	2	no	—
133	C₂²⋊C₈	—	292	4	no	—
134	C₂²⋊C₈	—	146	2	no	—
135	#97	—	2	2	no	—
136	C₄×C₈	—	73	4	no	—
137	C₂⁴	—	146	1	no	—
138	C₂×D₄	—	292	2	no	—
139	C₂×D₄	—	146	2	no	—
140	C₂²×C₄	—	292	1	no	—
141	C₂²×C₄	—	292	1	no	—
142	C₂²×C₄	—	292	2	no	—
143	C₂²×C₄	—	292	2	no	—
144	C₂²×C₄	—	146	1	no	—
145	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
146	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
147	C₂²×C₄	#11924029	1	1	yes	characteristic
148	M₁₆	—	4	4	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	2	2	no	—
151	C₂×C₈	—	4	2	no	—
152	C₂×C₈	—	292	1	no	—
153	C₂×C₈	—	292	2	no	—
154	C₂×C₈	—	146	4	no	—
155	C₂×C₈	#11924013	1	4	yes	—
156	C₄⋊C₄	—	146	2	no	—
157	C₂²⋊C₄	—	292	2	no	—
158	C₄²	D₄×D₇₃	1	2	yes	—
159	C₄²	#11924028	1	2	yes	—
160	C₂³	—	292	1	no	—
161	C₂³	—	292	2	no	—
162	C₂³	—	292	2	no	—
163	C₂³	—	292	1	no	—
164	C₂³	—	146	2	no	—
165	C₂³	#14556567	1	1	yes	characteristic
166	D₄	—	292	2	no	—
167	D₄	—	146	4	no	—
168	C₂×C₄	—	4	1	no	—
169	C₂×C₄	—	4	1	no	—
170	C₂×C₄	—	292	2	no	—
171	C₂×C₄	—	292	1	no	—
172	C₂×C₄	—	584	2	no	—
173	C₂×C₄	—	584	1	no	—
174	C₂×C₄	—	584	1	no	—
175	C₂×C₄	#14556569	1	2	yes	—
176	C₂×C₄	#14556574	1	1	yes	characteristic
177	C₂×C₄	#14556576	1	2	yes	—
178	C₂×C₄	#14556587	1	1	yes	characteristic
179	C₂×C₄	C₂×#11924013	1	2	yes	—
180	C₂×C₄	#14556622	1	2	yes	—
181	C₈	—	2	4	no	—
182	C₈	—	8	2	no	—
183	C₈	—	292	4	no	—
184	C₈	—	584	1	no	—
185	C₂²	—	2	1	no	—
186	C₂²	—	2	1	no	—
187	C₂²	—	292	4	no	—
188	C₂²	—	292	2	no	—
189	C₂²	—	584	2	no	—
190	C₂²	—	584	1	no	—
191	C₂²	—	584	1	no	—
192	C₂²	#17988522	1	1	yes	characteristic
193	C₂²	#17988864	1	2	yes	—
194	C₄	—	2	2	no	—
195	C₄	—	2	2	no	—
196	C₄	—	584	1	no	—
197	C₄	#17988900	1	2	yes	—
198	C₄	#17988963	1	1	yes	characteristic
199	C₄	#17988979	1	1	yes	characteristic
200	C₂	—	2	2	no	—
201	C₂	—	584	2	no	—
202	C₂	#22611446	1	1	yes	characteristic
203	C₂	#22611460	1	1	yes	characteristic
204	C₂	#22611483	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22610729

C₂

yes

maximal, characteristic

#22608707

C₂

yes

maximal, complemented

#22608355

C₂

yes

maximal

#22607762

C₂

yes

maximal, characteristic, complemented

C₇₃×#1849

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₂₉₂

C₂²

yes

characteristic

#17988640

C₂²

yes

—

C₂×C₄⋊#10596831

C₂²

yes

—

—

—

C₂×#108×C₇₃

—

#423×C₇₃

C₂²

yes

—

C₂×#97×C₇₃

C₂²

yes

characteristic

C₂²×D₂₉₂

Q₈

yes

characteristic

C₂²×C₄×D₇₃

—

C₂²×#10596831

—

C₄×D₂₉₂

—

C₄×D₂₉₂

—

C₂×C₄⋊Dic₇₃

Q₈

yes

—

—

—

—

—

D₄

yes

—

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

D₄

yes

—

C₂×C₄²×C₇₃

C₂³

yes

characteristic

#108×C₇₃

—

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

—

#97×C₇₃

—

C₂³×D₇₃

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×#10596831

—

C₂×#10596831

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

#11924005

—

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂²×C₄×C₇₃

#41

yes

characteristic

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

D₈

yes

—

C₄²×C₇₃

C₂×D₄

yes

—

C₄²×C₇₃

#41

yes

—

C₂³×C₇₃

C₂²⋊Q₈

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₃

#123

yes

characteristic

C₂×C₄×C₇₃

#123

yes

—

C₂×C₄×C₇₃

#127

yes

characteristic

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

#137

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

#10596831

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#399

yes

characteristic

C₂²×C₇₃

#474

yes

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#480

yes

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

#10660

—

maximal, Sylow

C₂×C₇₃

—

C₂×C₇₃

#2091

yes

characteristic

100

C₂×C₇₃

#2093

yes

characteristic

101

C₂×C₇₃

#2098

yes

characteristic

102

D₇₃

—

103

#1955

—

104

#1849

D₇₃

yes

characteristic, complemented

105

#1571

—

106

#1486

—

107

#1275

—

108

C₇₃

#10660

yes

characteristic, complemented, Sylow

109

C₂×C₄×D₄

—

110

#431

—

111

C₂×#108

—

112

#423

C₂×D₇₃

yes

—

113

C₂×C₄⋊C₈

—

114

C₂×C₂²⋊C₈

—

146

—

115

C₂×#97

C₂×D₇₃

yes

characteristic

116

#335

—

146

—

117

D₄⋊C₈

—

146

—

118

C₂²×D₄

—

119

C₂³×C₄

—

146

—

120

C₂×M₁₆

—

121

C₂²×C₈

—

146

—

122

C₂²×C₈

C₂²⋊D₇₃

yes

—

123

C₄×D₄

—

146

—

124

C₄×D₄

—

146

—

125

C₂×C₄⋊C₄

—

126

C₂×C₂²⋊C₄

—

146

—

127

C₂×C₄²

C₂²×D₇₃

yes

characteristic

128

#108

—

129

C₄⋊C₈

—

130

C₄⋊C₈

—

131

C₄⋊C₈

—

146

—

132

C₄⋊C₈

—

146

—

133

C₂²⋊C₈

—

292

—

134

C₂²⋊C₈

—

146

—

135

#97

—

136

C₄×C₈

—

137

C₂⁴

—

146

—

138

C₂×D₄

—

292

—

139

C₂×D₄

—

146

—

140

C₂²×C₄

—

292

—

141

C₂²×C₄

—

292

—

142

C₂²×C₄

—

292

—

143

C₂²×C₄

—

292

—

144

C₂²×C₄

—

146

—

145

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

146

C₂²×C₄

Q₈×D₇₃

yes

characteristic

147

C₂²×C₄

#11924029

yes

characteristic

148

M₁₆

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

292

—

153

C₂×C₈

—

292

—

154

C₂×C₈

—

146

—

155

C₂×C₈

#11924013

yes

—

156

C₄⋊C₄

—

146

—

157

C₂²⋊C₄

—

292

—

158

C₄²

D₄×D₇₃

yes

—

159

C₄²

#11924028

yes

—

160

C₂³

—

292

—

161

C₂³

—

292

—

162

C₂³

—

292

—

163

C₂³

—

292

—

164

C₂³

—

146

—

165

C₂³

#14556567

yes

characteristic

166

D₄

—

292

—

167

D₄

—

146

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

292

—

171

C₂×C₄

—

292

—

172

C₂×C₄

—

584

—

173

C₂×C₄

—

584

—

174

C₂×C₄

—

584

—

175

C₂×C₄

#14556569

yes

—

176

C₂×C₄

#14556574

yes

characteristic

177

C₂×C₄

#14556576

yes

—

178

C₂×C₄

#14556587

yes

characteristic

179

C₂×C₄

C₂×#11924013

yes

—

180

C₂×C₄

#14556622

yes

—

181

C₈

—

182

C₈

—

183

C₈

—

292

—

184

C₈

—

584

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

292

—

188

C₂²

—

292

—

189

C₂²

—

584

—

190

C₂²

—

584

—

191

C₂²

—

584

—

192

C₂²

#17988522

yes

characteristic

193

C₂²

#17988864

yes

—

194

C₄

—

195

C₄

—

196

C₄

—

584

—

197

C₄

#17988900

yes

—

198

C₄

#17988963

yes

characteristic

199

C₄

#17988979

yes

characteristic

200

C₂

—

201

C₂

—

584

—

202

C₂

#22611446

yes

characteristic

203

C₂

#22611460

yes

characteristic

204

C₂

#22611483

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14556587
commutator, cosocle	C₂×C₄²×C₇₃	C₂³
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1849	C₂
socle	C₂²×C₇₃	#399
prime radical	C₂²×D₂₉₂	Q₈
hypercenter	#1849	D₇₃
hypocenter	C₇₃	#10660
LCS	G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

subgroup

G/H

center

C₂×C₄

#14556587

commutator, cosocle

C₂×C₄²×C₇₃

C₂³

Frattini

C₂×C₄²

C₂²×D₇₃

Fitting

C₇₃×#1849

C₂

socle

C₂²×C₇₃

#399

prime radical

C₂²×D₂₉₂

Q₈

D₇₃

C₇₃

G ▷ C₂×C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

N	H ≅ G/N	type
2. #22608707	C₂	semidirect
4. #22607762	C₂	semidirect
5. C₇₃×#1849	C₂	semidirect
104. #1849	D₇₃	semidirect
108. C₇₃	#10660	semidirect

H ≅ G/N

type

2. #22608707

C₂

semidirect

4. #22607762

C₂

semidirect

5. C₇₃×#1849

C₂

semidirect

104. #1849

D₇₃

semidirect

108. C₇₃

#10660

semidirect

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

subgroup	index
#22610729	2
#22608707	2
#22608355	2
#22607762	2
C₇₃×#1849	2
#10660	73

subgroup

index

C₇₃×#1849

Subgroups — #32990963

Conjugacy classes of subgroups

Complements

Maximal subgroups