Group #22607186 — subgroups

Subgroups — C₂×#462×C₇₃ #22607186

Order 9344.

480 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 232 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	C₂²×Q₁₆×C₇₃	C₂	1	2	yes	maximal
2	C₂×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
4	#462×C₇₃	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#103×C₇₃	C₂	1	2	yes	maximal
7	C₂²×Q₈×C₇₃	C₂²	1	2	yes	—
8	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
9	C₂×Q₁₆×C₇₃	—	2	8	no	—
10	C₂×Q₁₆×C₇₃	C₂²	1	8	yes	—
11	C₂²×C₈×C₇₃	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₇₃	—	2	2	no	—
13	C₄⋊Q₈×C₇₃	C₂²	1	4	yes	—
14	C₄×Q₈×C₇₃	—	2	2	no	—
15	C₄×Q₈×C₇₃	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
17	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
18	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
19	C₂×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₇₃	—	2	1	no	—
21	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
22	C₄⋊C₈×C₇₃	C₂²	1	4	yes	—
23	#103×C₇₃	C₂²	1	8	yes	—
24	C₂×Q₈×C₇₃	—	2	1	no	—
25	C₂×Q₈×C₇₃	—	2	2	no	—
26	C₂×Q₈×C₇₃	—	2	2	no	—
27	C₂×Q₈×C₇₃	—	2	4	no	—
28	C₂×Q₈×C₇₃	—	2	4	no	—
29	C₂×Q₈×C₇₃	D₄	1	4	yes	—
30	C₂×Q₈×C₇₃	C₂³	1	4	yes	—
31	C₂×Q₈×C₇₃	C₂³	1	2	yes	—
32	C₂²×C₄×C₇₃	—	2	1	no	—
33	C₂²×C₄×C₇₃	—	2	1	no	—
34	C₂²×C₄×C₇₃	—	2	2	no	—
35	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
38	Q₁₆×C₇₃	—	2	16	no	—
39	C₂×C₈×C₇₃	—	2	4	no	—
40	C₂×C₈×C₇₃	C₂³	1	4	yes	—
41	C₄⋊C₄×C₇₃	—	2	4	no	—
42	C₄⋊C₄×C₇₃	—	2	4	no	—
43	C₄⋊C₄×C₇₃	—	2	4	no	—
44	C₄⋊C₄×C₇₃	—	2	1	no	—
45	C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
46	C₄²×C₇₃	—	2	4	no	—
47	C₄²×C₇₃	D₄	1	2	yes	—
48	C₄²×C₇₃	C₂³	1	2	yes	—
49	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
50	Q₈×C₇₃	—	2	4	no	—
51	Q₈×C₇₃	—	2	2	no	—
52	Q₈×C₇₃	—	2	4	no	—
53	Q₈×C₇₃	—	2	4	no	—
54	Q₈×C₇₃	—	4	4	no	—
55	Q₈×C₇₃	C₂×D₄	1	4	yes	—
56	C₂×C₄×C₇₃	—	2	4	no	—
57	C₂×C₄×C₇₃	—	2	2	no	—
58	C₂×C₄×C₇₃	—	2	2	no	—
59	C₂×C₄×C₇₃	—	2	2	no	—
60	C₂×C₄×C₇₃	—	2	4	no	—
61	C₂×C₄×C₇₃	—	4	4	no	—
62	C₂×C₄×C₇₃	—	4	2	no	—
63	C₂×C₄×C₇₃	Q₁₆	1	4	yes	complemented
64	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
65	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
68	C₂×C₄×C₇₃	#41	1	2	yes	—
69	C₂×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
70	C₈×C₇₃	—	2	4	no	—
71	C₂²×C₇₃	#121	1	2	yes	—
72	C₂²×C₇₃	C₂×Q₁₆	1	2	yes	—
73	C₂²×C₇₃	#137	1	2	yes	—
74	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
75	C₄×C₇₃	—	2	4	no	—
76	C₄×C₇₃	—	2	2	no	—
77	C₄×C₇₃	—	4	4	no	—
78	C₄×C₇₃	—	4	2	no	—
79	C₄×C₇₃	#121	1	2	yes	—
80	C₄×C₇₃	C₂×Q₁₆	1	4	yes	complemented
81	C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
82	C₄×C₇₃	C₂×#41	1	1	yes	characteristic
83	C₂×C₇₃	#462	1	4	yes	direct product factor
84	C₂×C₇₃	C₂×#121	1	1	yes	characteristic
85	C₂×C₇₃	C₂²×Q₁₆	1	1	yes	characteristic
86	C₂×C₇₃	C₂×#137	1	1	yes	characteristic
87	C₂×#462	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₇₃	C₂×#462	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²×Q₁₆	C₂×C₇₃	1	2	yes	—
90	C₂×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
91	C₂×C₄×Q₈	C₂×C₇₃	1	1	yes	characteristic
92	#462	C₂×C₇₃	1	8	yes	direct product factor
93	C₂×C₄⋊C₈	C₂×C₇₃	1	1	yes	characteristic
94	C₂×#103	C₂×C₇₃	1	2	yes	—
95	C₂²×Q₈	C₂²×C₇₃	1	2	yes	—
96	C₂²×Q₈	C₂²×C₇₃	1	1	yes	characteristic
97	C₂×Q₁₆	—	2	8	no	—
98	C₂×Q₁₆	C₂²×C₇₃	1	8	yes	—
99	C₂²×C₈	C₂²×C₇₃	1	2	yes	—
100	C₄⋊Q₈	—	2	2	no	—
101	C₄⋊Q₈	C₂²×C₇₃	1	4	yes	—
102	C₄×Q₈	—	2	2	no	—
103	C₄×Q₈	C₂²×C₇₃	1	4	yes	—
104	C₂×C₄⋊C₄	—	2	1	no	—
105	C₂×C₄⋊C₄	—	2	1	no	—
106	C₂×C₄⋊C₄	—	2	1	no	—
107	C₂×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
108	C₂×C₄²	—	2	1	no	—
109	C₂×C₄²	C₂²×C₇₃	1	1	yes	characteristic
110	C₄⋊C₈	C₂²×C₇₃	1	4	yes	—
111	#103	C₂²×C₇₃	1	8	yes	—
112	C₂×Q₈	—	2	1	no	—
113	C₂×Q₈	—	2	2	no	—
114	C₂×Q₈	—	2	2	no	—
115	C₂×Q₈	—	2	4	no	—
116	C₂×Q₈	—	2	4	no	—
117	C₂×Q₈	D₄×C₇₃	1	4	yes	—
118	C₂×Q₈	C₂³×C₇₃	1	4	yes	—
119	C₂×Q₈	C₂³×C₇₃	1	2	yes	—
120	C₂²×C₄	—	2	1	no	—
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	—	2	2	no	—
123	C₂²×C₄	D₄×C₇₃	1	1	yes	characteristic
124	C₂²×C₄	D₄×C₇₃	1	1	yes	characteristic
125	C₂²×C₄	C₂³×C₇₃	1	1	yes	characteristic
126	Q₁₆	—	2	16	no	—
127	C₂×C₈	—	2	4	no	—
128	C₂×C₈	C₂³×C₇₃	1	4	yes	—
129	C₄⋊C₄	—	2	4	no	—
130	C₄⋊C₄	—	2	4	no	—
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	2	1	no	—
133	C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
134	C₄²	—	2	4	no	—
135	C₄²	D₄×C₇₃	1	2	yes	—
136	C₄²	C₂³×C₇₃	1	2	yes	—
137	C₂³	C₂×D₄×C₇₃	1	1	yes	characteristic
138	Q₈	—	2	4	no	—
139	Q₈	—	2	2	no	—
140	Q₈	—	2	4	no	—
141	Q₈	—	2	4	no	—
142	Q₈	—	4	4	no	—
143	Q₈	C₂×D₄×C₇₃	1	4	yes	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	4	4	no	—
150	C₂×C₄	—	4	2	no	—
151	C₂×C₄	Q₁₆×C₇₃	1	4	yes	complemented
152	C₂×C₄	C₂×D₄×C₇₃	1	2	yes	—
153	C₂×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
154	C₂×C₄	C₂×D₄×C₇₃	1	2	yes	—
155	C₂×C₄	C₂×D₄×C₇₃	1	2	yes	—
156	C₂×C₄	#41×C₇₃	1	2	yes	—
157	C₂×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
158	C₈	—	2	4	no	—
159	C₂²	#121×C₇₃	1	2	yes	—
160	C₂²	C₂×Q₁₆×C₇₃	1	2	yes	—
161	C₂²	#137×C₇₃	1	2	yes	—
162	C₂²	C₂²×D₄×C₇₃	1	1	yes	characteristic
163	C₄	—	2	4	no	—
164	C₄	—	2	2	no	—
165	C₄	—	4	4	no	—
166	C₄	—	4	2	no	—
167	C₄	#121×C₇₃	1	2	yes	—
168	C₄	C₂×Q₁₆×C₇₃	1	4	yes	complemented
169	C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
170	C₄	C₂×#41×C₇₃	1	1	yes	characteristic
171	C₂	#462×C₇₃	1	4	yes	direct product factor
172	C₂	C₂×#121×C₇₃	1	1	yes	characteristic
173	C₂	C₂²×Q₁₆×C₇₃	1	1	yes	characteristic
174	C₂	C₂×#137×C₇₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₁₆×C₇₃

C₂

yes

maximal

C₂×C₄⋊Q₈×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄×Q₈×C₇₃

C₂

yes

maximal, characteristic

#462×C₇₃

C₂

yes

maximal, direct product factor

C₂×C₄⋊C₈×C₇₃

C₂

yes

maximal, characteristic

C₂×#103×C₇₃

C₂

yes

maximal

C₂²×Q₈×C₇₃

C₂²

yes

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

—

C₄⋊Q₈×C₇₃

—

C₄⋊Q₈×C₇₃

C₂²

yes

—

C₄×Q₈×C₇₃

—

C₄×Q₈×C₇₃

C₂²

yes

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

#103×C₇₃

C₂²

yes

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×Q₈×C₇₃

C₂³

yes

—

C₂×Q₈×C₇₃

C₂³

yes

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂²×C₄×C₇₃

C₂³

yes

characteristic

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂³

yes

—

C₄²×C₇₃

—

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

Q₁₆

yes

complemented

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×C₄×C₇₃

C₂⁴

yes

characteristic

C₈×C₇₃

—

C₂²×C₇₃

#121

yes

—

C₂²×C₇₃

C₂×Q₁₆

yes

—

C₂²×C₇₃

#137

yes

—

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#121

yes

—

C₄×C₇₃

C₂×Q₁₆

yes

complemented

C₄×C₇₃

C₂²×D₄

yes

characteristic

C₄×C₇₃

C₂×#41

yes

characteristic

C₂×C₇₃

#462

yes

direct product factor

C₂×C₇₃

C₂×#121

yes

characteristic

C₂×C₇₃

C₂²×Q₁₆

yes

C₂×C₇₃

yes

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

C₇₃

C₂×#462

yes

characteristic, direct product factor, Sylow

C₂²×Q₁₆

C₂×C₇₃

yes

—

C₂×C₄⋊Q₈

C₂×C₇₃

yes

characteristic

C₂×C₄×Q₈

C₂×C₇₃

yes

characteristic

#462

C₂×C₇₃

yes

direct product factor

C₂×C₄⋊C₈

C₂×C₇₃

yes

characteristic

C₂×#103

C₂×C₇₃

yes

—

C₂²×Q₈

C₂²×C₇₃

yes

—

C₂²×Q₈

C₂²×C₇₃

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

C₂²×C₇₃

yes

—

C₂²×C₈

C₂²×C₇₃

yes

—

100

C₄⋊Q₈

—

101

C₄⋊Q₈

C₂²×C₇₃

yes

—

102

C₄×Q₈

—

103

C₄×Q₈

C₂²×C₇₃

yes

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

C₂²×C₇₃

yes

characteristic

108

C₂×C₄²

—

109

C₂×C₄²

C₂²×C₇₃

yes

characteristic

110

C₄⋊C₈

C₂²×C₇₃

yes

—

111

#103

C₂²×C₇₃

yes

—

112

C₂×Q₈

—

113

C₂×Q₈

—

114

C₂×Q₈

—

115

C₂×Q₈

—

116

C₂×Q₈

—

117

C₂×Q₈

D₄×C₇₃

yes

—

118

C₂×Q₈

C₂³×C₇₃

yes

—

119

C₂×Q₈

C₂³×C₇₃

yes

—

120

C₂²×C₄

—

121

C₂²×C₄

—

122

C₂²×C₄

—

123

C₂²×C₄

D₄×C₇₃

yes

characteristic

124

C₂²×C₄

D₄×C₇₃

yes

characteristic

125

C₂²×C₄

C₂³×C₇₃

yes

characteristic

126

Q₁₆

—

127

C₂×C₈

—

128

C₂×C₈

C₂³×C₇₃

yes

—

129

C₄⋊C₄

—

130

C₄⋊C₄

—

131

C₄⋊C₄

—

132

C₄⋊C₄

—

133

C₄⋊C₄

C₂³×C₇₃

yes

—

134

C₄²

—

135

C₄²

D₄×C₇₃

yes

—

136

C₄²

C₂³×C₇₃

yes

—

137

C₂³

C₂×D₄×C₇₃

yes

characteristic

138

Q₈

—

139

Q₈

—

140

Q₈

—

141

Q₈

—

142

Q₈

—

143

Q₈

C₂×D₄×C₇₃

yes

—

144

C₂×C₄

—

145

C₂×C₄

—

146

C₂×C₄

—

147

C₂×C₄

—

148

C₂×C₄

—

149

C₂×C₄

—

150

C₂×C₄

—

151

C₂×C₄

Q₁₆×C₇₃

yes

complemented

152

C₂×C₄

C₂×D₄×C₇₃

yes

—

153

C₂×C₄

C₂×D₄×C₇₃

yes

characteristic

154

C₂×C₄

C₂×D₄×C₇₃

yes

—

155

C₂×C₄

C₂×D₄×C₇₃

yes

—

156

C₂×C₄

#41×C₇₃

yes

—

157

C₂×C₄

C₂⁴×C₇₃

yes

characteristic

158

C₈

—

159

C₂²

#121×C₇₃

yes

—

160

C₂²

C₂×Q₁₆×C₇₃

yes

—

161

C₂²

#137×C₇₃

yes

—

162

C₂²

C₂²×D₄×C₇₃

yes

characteristic

163

C₄

—

164

C₄

—

165

C₄

—

166

C₄

—

167

C₄

#121×C₇₃

yes

—

168

C₄

C₂×Q₁₆×C₇₃

yes

complemented

169

C₄

C₂²×D₄×C₇₃

yes

characteristic

170

C₄

C₂×#41×C₇₃

yes

characteristic

171

C₂

#462×C₇₃

yes

direct product factor

172

C₂

C₂×#121×C₇₃

yes

characteristic

173

C₂

C₂²×Q₁₆×C₇₃

yes

characteristic

174

C₂

C₂×#137×C₇₃

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₇₃

C₂×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₇₃

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

N	H ≅ G/N	type
4. #462×C₇₃	C₂	direct (N × H)
63. C₂×C₄×C₇₃	Q₁₆	semidirect
80. C₄×C₇₃	C₂×Q₁₆	semidirect
83. C₂×C₇₃	#462	direct (N × H)
87. C₂×#462	C₇₃	direct (N × H)
88. C₇₃	C₂×#462	direct (N × H)
92. #462	C₂×C₇₃	direct (N × H)
151. C₂×C₄	Q₁₆×C₇₃	semidirect
168. C₄	C₂×Q₁₆×C₇₃	semidirect
171. C₂	#462×C₇₃	direct (N × H)

H ≅ G/N

type

4. #462×C₇₃

C₂

direct (N × H)

63. C₂×C₄×C₇₃

Q₁₆

semidirect

80. C₄×C₇₃

C₂×Q₁₆

semidirect

83. C₂×C₇₃

#462

direct (N × H)

87. C₂×#462

C₇₃

direct (N × H)

88. C₇₃

C₂×#462

direct (N × H)

92. #462

C₂×C₇₃

direct (N × H)

151. C₂×C₄

Q₁₆×C₇₃

semidirect

168. C₄

C₂×Q₁₆×C₇₃

semidirect

171. C₂

#462×C₇₃

direct (N × H)

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

subgroup	index
C₂²×Q₁₆×C₇₃	2
C₂×C₄⋊Q₈×C₇₃	2
C₂×C₄×Q₈×C₇₃	2
#462×C₇₃	2
C₂×C₄⋊C₈×C₇₃	2
C₂×#103×C₇₃	2
C₂×#462	73

subgroup

index

C₂²×Q₁₆×C₇₃

C₂×C₄⋊Q₈×C₇₃

C₂×C₄×Q₈×C₇₃

#462×C₇₃

C₂×C₄⋊C₈×C₇₃

C₂×#103×C₇₃

C₂×#462

Subgroups — C₂×#462×C₇₃ #22607186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#462×C73 #22607186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#462×C₇₃ #22607186