Group #22626591 — subgroups

Subgroups — D₇₃⋊#430 #22626591

Order 9344.

460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 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	C₂×D₇₃⋊M₁₆	C₂	1	2	yes	maximal
2	#17989602	C₂	1	8	yes	maximal, complemented
3	D₇₃⋊#108	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924038	C₂²	1	4	yes	—
6	D₇₃⋊M₁₆	—	2	2	no	—
7	D₇₃⋊M₁₆	—	2	2	no	—
8	D₇₃⋊M₁₆	C₂²	1	4	yes	—
9	D₇₃⋊M₁₆	C₂²	1	4	yes	—
10	C₂×#11924037	—	2	2	no	—
11	C₂×#11924036	—	2	2	no	—
12	#14556662	C₂²	1	8	yes	complemented
13	#14556661	C₂²	1	8	yes	complemented
14	C₂²×C₄×D₇₃	C₂²	1	1	yes	characteristic
15	C₂×#11924012	C₄	1	1	yes	characteristic
16	C₂×#11924011	C₄	1	2	yes	—
17	M₁₆×D₇₃	C₄	1	4	yes	—
18	M₁₆×D₇₃	C₂²	1	4	yes	—
19	C₂×C₈×D₇₃	C₂²	1	2	yes	—
20	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
21	#11924038	—	2	4	no	—
22	#11924038	C₂³	1	8	yes	—
23	#11924037	—	2	4	no	—
24	#11924037	—	2	4	no	—
25	#11924036	—	2	4	no	—
26	#11924036	—	2	4	no	—
27	C₂×#10596833	—	2	4	no	—
28	C₂³×D₇₃	Q₈	1	1	yes	characteristic
29	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
30	C₂×C₄×D₇₃	C₂×C₄	1	2	yes	—
31	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₇₃	D₄	1	2	yes	—
33	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
34	C₂×C₄×D₇₃	Q₈	1	1	yes	characteristic
35	C₂×C₄×D₇₃	Q₈	1	2	yes	—
36	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
37	C₂×C₄×D₇₃	C₂³	1	2	yes	—
38	#11924012	C₂×C₄	1	4	yes	—
39	#11924011	C₂×C₄	1	8	yes	—
40	C₂×#10596831	C₂×C₄	1	2	yes	—
41	C₈×D₇₃	C₂×C₄	1	4	yes	—
42	C₈×D₇₃	C₂³	1	4	yes	—
43	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
44	M₁₆×C₇₃	C₂×C₄	1	4	yes	—
45	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
46	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
47	C₂²×D₇₃	—	4	2	no	—
48	C₂²×D₇₃	C₄⋊C₄	1	2	yes	—
49	C₂²×D₇₃	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×D₇₃	C₂×Q₈	1	1	yes	characteristic
51	C₂²×D₇₃	C₂×Q₈	1	2	yes	—
52	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
54	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
56	C₂×Dic₇₃	C₄⋊C₄	1	2	yes	—
57	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
58	C₂×Dic₇₃	C₂×D₄	1	2	yes	—
59	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
60	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
61	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
62	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
63	C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
64	C₄×D₇₃	C₂²×C₄	1	2	yes	—
65	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
66	C₄×D₇₃	C₂×D₄	1	2	yes	—
67	C₄×D₇₃	C₂×Q₈	1	2	yes	—
68	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
69	C₄×D₇₃	C₂⁴	1	1	yes	characteristic
70	#10596833	—	2	8	no	—
71	C₈×C₇₃	C₂²×C₄	1	4	yes	—
72	#10596831	C₂²×C₄	1	4	yes	—
73	C₂²×C₇₃	—	4	1	no	—
74	C₂²×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
75	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂×D₇₃	—	2	4	no	—
77	C₂×D₇₃	—	2	2	no	—
78	C₂×D₇₃	—	4	1	no	—
79	C₂×D₇₃	—	4	2	no	—
80	C₂×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
81	C₂×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×D₇₃	C₂²×Q₈	1	1	yes	characteristic
83	C₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
84	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
86	Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	Dic₇₃	C₂×C₄⋊C₄	1	2	yes	—
88	Dic₇₃	C₂²×D₄	1	1	yes	characteristic
89	C₂×C₇₃	—	2	2	no	—
90	C₂×C₇₃	—	2	1	no	—
91	C₂×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
92	D₇₃	—	2	2	no	—
93	D₇₃	—	2	1	no	—
94	D₇₃	#430	1	2	yes	complemented
95	C₂×#430	—	73	1	no	maximal, Sylow
96	C₇₃	C₂×#430	1	1	yes	characteristic, complemented, Sylow
97	C₂²×M₁₆	—	73	1	no	—
98	C₂²×M₁₆	—	73	2	no	—
99	#430	—	73	8	no	—
100	C₂×#108	—	73	4	no	—
101	C₂³×C₄	—	73	1	no	—
102	C₂×M₁₆	—	73	1	no	—
103	C₂×M₁₆	—	73	4	no	—
104	C₂×M₁₆	—	73	4	no	—
105	C₂×M₁₆	—	73	2	no	—
106	C₂×M₁₆	—	73	4	no	—
107	C₂×M₁₆	—	73	4	no	—
108	C₂×M₁₆	—	73	4	no	—
109	C₂×M₁₆	—	146	2	no	—
110	C₂×M₁₆	—	146	2	no	—
111	C₂×M₁₆	—	146	2	no	—
112	C₂×M₁₆	#64408	1	1	yes	characteristic
113	C₂²×C₈	—	73	2	no	—
114	C₂²×C₈	—	146	2	no	—
115	#108	—	73	8	no	—
116	#108	—	73	8	no	—
117	C₂⁴	—	73	1	no	—
118	C₂²×C₄	—	73	1	no	—
119	C₂²×C₄	—	73	2	no	—
120	C₂²×C₄	—	73	1	no	—
121	C₂²×C₄	—	73	1	no	—
122	C₂²×C₄	—	73	2	no	—
123	C₂²×C₄	—	73	2	no	—
124	C₂²×C₄	—	73	1	no	—
125	C₂²×C₄	—	73	1	no	—
126	C₂²×C₄	—	73	2	no	—
127	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
128	M₁₆	—	73	4	no	—
129	M₁₆	—	73	8	no	—
130	M₁₆	—	73	8	no	—
131	M₁₆	—	146	4	no	—
132	M₁₆	—	146	4	no	—
133	M₁₆	—	146	4	no	—
134	M₁₆	C₂×#64408	1	4	yes	—
135	C₂×C₈	—	73	2	no	—
136	C₂×C₈	—	73	4	no	—
137	C₂×C₈	—	73	4	no	—
138	C₂×C₈	—	146	4	no	—
139	C₂×C₈	—	146	4	no	—
140	C₂×C₈	—	146	4	no	—
141	C₂×C₈	C₂×#64408	1	2	yes	—
142	C₂³	—	292	2	no	—
143	C₂³	—	73	1	no	—
144	C₂³	—	73	2	no	—
145	C₂³	—	73	2	no	—
146	C₂³	—	73	1	no	—
147	C₂³	C₄⋊#64408	1	1	yes	characteristic
148	C₂×C₄	—	73	2	no	—
149	C₂×C₄	—	73	1	no	—
150	C₂×C₄	—	73	1	no	—
151	C₂×C₄	—	73	2	no	—
152	C₂×C₄	—	73	1	no	—
153	C₂×C₄	—	73	1	no	—
154	C₂×C₄	—	73	2	no	—
155	C₂×C₄	—	73	2	no	—
156	C₂×C₄	—	73	2	no	—
157	C₂×C₄	—	73	2	no	—
158	C₂×C₄	—	73	2	no	—
159	C₂×C₄	—	73	1	no	—
160	C₂×C₄	—	73	2	no	—
161	C₂×C₄	—	73	1	no	—
162	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
163	C₂×C₄	C₄⋊#64408	1	2	yes	—
164	C₂×C₄	C₂²×#64408	1	2	yes	—
165	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
166	C₈	—	73	4	no	—
167	C₈	—	146	8	no	—
168	C₈	C₂²×#64408	1	4	yes	—
169	C₂²	—	4	1	no	—
170	C₂²	—	292	1	no	—
171	C₂²	—	292	2	no	—
172	C₂²	—	73	1	no	—
173	C₂²	—	73	2	no	—
174	C₂²	—	73	1	no	—
175	C₂²	—	146	4	no	—
176	C₂²	—	146	2	no	—
177	C₂²	C₂×C₄⋊#64408	1	2	yes	—
178	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
179	C₄	—	73	1	no	—
180	C₄	—	73	2	no	—
181	C₄	—	73	1	no	—
182	C₄	C₂×C₄⋊#64408	1	2	yes	—
183	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
184	C₄	C₂³×#64408	1	1	yes	characteristic
185	C₂	—	2	1	no	—
186	C₂	—	2	2	no	—
187	C₂	—	73	2	no	—
188	C₂	—	146	2	no	—
189	C₂	—	146	1	no	—
190	C₂	C₂²×C₄⋊#64408	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₇₃⋊M₁₆

C₂

yes

maximal

#17989602

C₂

yes

maximal, complemented

D₇₃⋊#108

C₂

yes

maximal, complemented

C₂×M₁₆×D₇₃

C₂

yes

maximal, characteristic

C₂×#11924038

C₂²

yes

—

D₇₃⋊M₁₆

—

D₇₃⋊M₁₆

—

D₇₃⋊M₁₆

C₂²

yes

—

D₇₃⋊M₁₆

C₂²

yes

—

C₂×#11924037

—

C₂×#11924036

—

#14556662

C₂²

yes

complemented

#14556661

C₂²

yes

complemented

C₂²×C₄×D₇₃

C₂²

yes

characteristic

C₂×#11924012

C₄

yes

characteristic

C₂×#11924011

C₄

yes

—

M₁₆×D₇₃

C₄

yes

—

M₁₆×D₇₃

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

—

C₂×M₁₆×C₇₃

C₄

yes

characteristic

#11924038

—

#11924038

C₂³

yes

—

—

—

—

—

—

C₂³×D₇₃

Q₈

yes

characteristic

C₂²×Dic₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

D₄

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

characteristic

C₂×C₄×D₇₃

Q₈

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₂×C₄×D₇₃

C₂³

yes

—

#11924012

C₂×C₄

yes

—

#11924011

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₈×D₇₃

C₂×C₄

yes

—

C₈×D₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

M₁₆×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

C₄⋊C₄

yes

—

C₂²×D₇₃

C₄⋊C₄

yes

characteristic

C₂²×D₇₃

C₂×Q₈

yes

characteristic

C₂²×D₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

—

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

C₂²×C₄

yes

characteristic

C₄×D₇₃

C₂²×C₄

yes

—

C₄×D₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

C₂×D₄

yes

—

C₄×D₇₃

C₂×Q₈

yes

—

C₄×D₇₃

C₂×Q₈

yes

characteristic

C₄×D₇₃

C₂⁴

yes

characteristic

#10596833

—

C₈×C₇₃

C₂²×C₄

yes

—

#10596831

C₂²×C₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

C₂×C₄⋊C₄

yes

—

C₂×D₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₇₃

C₂²×Q₈

yes

characteristic

C₄×C₇₃

C₂×C₄⋊C₄

yes

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂³×C₄

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

characteristic

Dic₇₃

C₂×C₄⋊C₄

yes

—

Dic₇₃

C₂²×D₄

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂²×C₄⋊C₄

yes

characteristic

D₇₃

—

D₇₃

—

D₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂²×M₁₆

—

C₂²×M₁₆

—

#430

—

100

C₂×#108

—

101

C₂³×C₄

—

102

C₂×M₁₆

—

103

C₂×M₁₆

—

104

C₂×M₁₆

—

105

C₂×M₁₆

—

106

C₂×M₁₆

—

107

C₂×M₁₆

—

108

C₂×M₁₆

—

109

C₂×M₁₆

—

146

—

110

C₂×M₁₆

—

146

—

111

C₂×M₁₆

—

146

—

112

C₂×M₁₆

#64408

yes

characteristic

113

C₂²×C₈

—

114

C₂²×C₈

—

146

—

115

#108

—

116

#108

—

117

C₂⁴

—

118

C₂²×C₄

—

119

C₂²×C₄

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

—

124

C₂²×C₄

—

125

C₂²×C₄

—

126

C₂²×C₄

—

127

C₂²×C₄

C₂×#64408

yes

characteristic

128

M₁₆

—

129

M₁₆

—

130

M₁₆

—

131

M₁₆

—

146

—

132

M₁₆

—

146

—

133

M₁₆

—

146

—

134

M₁₆

C₂×#64408

yes

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

146

—

139

C₂×C₈

—

146

—

140

C₂×C₈

—

146

—

141

C₂×C₈

C₂×#64408

yes

—

142

C₂³

—

292

—

143

C₂³

—

144

C₂³

—

145

C₂³

—

146

C₂³

—

147

C₂³

C₄⋊#64408

yes

characteristic

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

C₄⋊#64408

yes

characteristic

163

C₂×C₄

C₄⋊#64408

yes

—

164

C₂×C₄

C₂²×#64408

yes

—

165

C₂×C₄

C₂²×#64408

yes

characteristic

166

C₈

—

167

C₈

—

146

—

168

C₈

C₂²×#64408

yes

—

169

C₂²

—

170

C₂²

—

292

—

171

C₂²

—

292

—

172

C₂²

—

173

C₂²

—

174

C₂²

—

175

C₂²

—

146

—

176

C₂²

—

146

—

177

C₂²

C₂×C₄⋊#64408

yes

—

178

C₂²

C₂×C₄⋊#64408

yes

characteristic

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

C₂×C₄⋊#64408

yes

—

183

C₄

C₂×C₄⋊#64408

yes

characteristic

184

C₄

C₂³×#64408

yes

characteristic

185

C₂

—

186

C₂

—

187

C₂

—

188

C₂

—

146

—

189

C₂

—

146

—

190

C₂

C₂²×C₄⋊#64408

yes

characteristic

	subgroup	G/H
center	C₄	C₂×C₄⋊#64408
commutator	C₄×C₇₃	C₂³×C₄
Frattini	C₄	C₂³×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂×C₇₃	C₂²×C₄⋊C₄
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	C₂×#430
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

subgroup

G/H

center

C₄

C₂×C₄⋊#64408

commutator

C₄×C₇₃

C₂³×C₄

Frattini

C₄

C₂³×#64408

Fitting

C₂×M₁₆×C₇₃

C₄

socle

C₂×C₇₃

C₂²×C₄⋊C₄

C₂×M₁₆

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

N	H ≅ G/N	type
2. #17989602	C₂	semidirect
3. D₇₃⋊#108	C₂	semidirect
12. #14556662	C₂²	semidirect
13. #14556661	C₂²	semidirect
94. D₇₃	#430	semidirect
96. C₇₃	C₂×#430	semidirect

H ≅ G/N

type

2. #17989602

C₂

semidirect

3. D₇₃⋊#108

C₂

semidirect

12. #14556662

C₂²

semidirect

13. #14556661

C₂²

semidirect

94. D₇₃

#430

semidirect

96. C₇₃

C₂×#430

semidirect

Subgroups — D₇₃⋊#430 #22626591

Conjugacy classes of subgroups

Complements

Subgroups — D73⋊#430 #22626591

Conjugacy classes of subgroups

Complements

Subgroups — D₇₃⋊#430 #22626591