Group #34206501 — subgroups

Subgroups — #34206501

Order 20224.

590 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 163 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×#19098940	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098365	C₂	1	4	yes	maximal, complemented
3	#23763564	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#346×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₃₂	—	2	1	no	—
6	C₂²×D₆₃₂	C₂²	1	2	yes	—
7	C₂×#14579158	—	2	1	no	—
8	#19098940	—	2	2	no	—
9	#19098940	C₄	1	4	yes	complemented
10	C₂×#14579095	C₂²	1	2	yes	—
11	C₂×#14579093	—	2	1	no	—
12	#19098429	—	2	1	no	—
13	#19098365	—	2	8	no	—
14	C₂²×C₁₆×C₇₉	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
16	#346×C₇₉	—	2	2	no	—
17	C₂²×D₃₁₆	—	2	2	no	—
18	C₂²×D₃₁₆	—	4	2	no	—
19	C₂×D₆₃₂	—	2	4	no	—
20	C₂×D₆₃₂	—	2	4	no	—
21	C₂×D₆₃₂	—	2	4	no	—
22	C₂×D₆₃₂	—	2	2	no	—
23	C₂×D₆₃₂	—	4	2	no	—
24	C₂×D₆₃₂	—	4	2	no	—
25	C₂×D₆₃₂	C₂×C₄	1	4	yes	—
26	#14579158	—	2	4	no	—
27	#14579158	—	4	2	no	—
28	C₂×C₄⋊Dic₇₉	—	2	2	no	—
29	#14579095	—	2	4	no	—
30	#14579093	—	4	2	no	—
31	C₇₉⋊#95	—	4	2	no	—
32	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₇₉	—	2	2	no	—
36	C₂×C₁₆×C₇₉	—	2	2	no	—
37	C₂×C₁₆×C₇₉	D₄	1	4	yes	complemented
38	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₇₉	D₄	1	2	yes	—
40	C₂³×D₇₉	—	4	2	no	—
41	C₂×D₃₁₆	—	2	4	no	—
42	C₂×D₃₁₆	—	4	8	no	—
43	C₂×D₃₁₆	—	4	2	no	—
44	C₂×D₃₁₆	—	4	2	no	—
45	C₂×D₃₁₆	—	4	2	no	—
46	C₂×D₃₁₆	—	4	2	no	—
47	C₂×D₃₁₆	—	4	2	no	—
48	C₂×D₃₁₆	—	8	8	no	—
49	C₂²×Dic₇₉	—	4	2	no	—
50	D₆₃₂	—	2	8	no	—
51	D₆₃₂	—	4	8	no	—
52	D₆₃₂	—	4	4	no	—
53	C₄⋊Dic₇₉	—	4	2	no	—
54	C₄⋊Dic₇₉	—	4	2	no	—
55	C₂²×C₄×C₇₉	D₈	1	2	yes	—
56	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₇₉	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₇₉	D₈	1	2	yes	—
59	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
60	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₇₉	#41	1	2	yes	—
64	C₄²×C₇₉	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₇₉	SD₁₆	1	2	yes	—
66	C₁₆×C₇₉	—	2	4	no	—
67	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
68	C₂²×D₇₉	—	4	4	no	—
69	C₂²×D₇₉	—	8	2	no	—
70	C₂²×D₇₉	—	8	2	no	—
71	C₂²×D₇₉	—	8	8	no	—
72	C₂×C₄×C₇₉	—	2	4	no	—
73	C₂×C₄×C₇₉	#102	1	4	yes	—
74	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
76	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
77	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
78	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
80	C₂×Dic₇₉	—	8	2	no	—
81	C₂×Dic₇₉	—	8	4	no	—
82	D₃₁₆	—	4	4	no	—
83	D₃₁₆	—	4	4	no	—
84	D₃₁₆	—	8	16	no	—
85	D₃₁₆	—	8	2	no	—
86	D₃₁₆	—	8	2	no	—
87	C₈×C₇₉	#102	1	4	yes	—
88	C₈×C₇₉	C₄×D₄	1	2	yes	—
89	C₈×C₇₉	#121	1	2	yes	—
90	C₂²×C₇₉	C₂×#102	1	1	yes	characteristic
91	C₂²×C₇₉	#486	1	1	yes	characteristic
92	C₂²×C₇₉	#493	1	1	yes	characteristic
93	C₂²×C₇₉	#509	1	4	yes	—
94	C₂×D₇₉	—	8	8	no	—
95	C₂×D₇₉	—	8	4	no	—
96	C₂×D₇₉	—	16	4	no	—
97	C₂×D₇₉	—	16	4	no	—
98	C₄×C₇₉	—	2	4	no	—
99	C₄×C₇₉	#390	1	1	yes	characteristic
100	C₄×C₇₉	C₂×#102	1	1	yes	characteristic
101	C₄×C₇₉	#486	1	1	yes	characteristic
102	C₄×C₇₉	#492	1	1	yes	characteristic
103	Dic₇₉	—	16	2	no	—
104	#13206	—	79	1	no	maximal, Sylow
105	C₂×C₇₉	#1957	1	1	yes	characteristic
106	C₂×C₇₉	#2140	1	2	yes	—
107	C₂×C₇₉	#2244	1	2	yes	—
108	C₂×C₇₉	#2250	1	2	yes	—
109	D₇₉	—	16	4	no	—
110	C₂×#493	—	79	1	no	—
111	C₂×#357	—	79	4	no	—
112	C₂×#346	D₇₉	1	1	yes	characteristic, complemented
113	#1846	—	79	1	no	—
114	C₇₉	#13206	1	1	yes	characteristic, complemented, Sylow
115	C₂²×D₈	—	79	2	no	—
116	C₂²×D₈	—	158	1	no	—
117	C₂×#127	—	158	1	no	—
118	C₂²×C₁₆	C₂×D₇₉	1	2	yes	—
119	#493	—	79	4	no	—
120	#493	—	158	2	no	—
121	C₂×#107	—	79	2	no	—
122	C₂×#106	—	158	1	no	—
123	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
124	#382	—	158	1	no	—
125	#357	—	158	8	no	—
126	#346	—	2	2	no	—
127	C₂²×D₄	—	316	2	no	—
128	C₂²×D₄	—	158	2	no	—
129	C₂×D₈	—	316	2	no	—
130	C₂×D₈	—	316	2	no	—
131	C₂×D₈	—	79	4	no	—
132	C₂×D₈	—	158	4	no	—
133	C₂×D₈	—	158	2	no	—
134	C₂×D₈	—	158	4	no	—
135	C₂×D₈	—	158	4	no	—
136	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
137	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
138	#127	—	316	2	no	—
139	#127	—	158	4	no	—
140	C₂×C₄⋊C₄	—	158	2	no	—
141	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
142	C₂×C₁₆	—	2	2	no	—
143	C₂×C₁₆	—	2	2	no	—
144	C₂×C₁₆	D₃₁₆	1	4	yes	complemented
145	#107	—	158	4	no	—
146	#106	—	316	2	no	—
147	C₄×C₈	C₄×D₇₉	1	2	yes	—
148	C₄×C₈	C₂²⋊D₇₉	1	2	yes	—
149	#95	—	316	2	no	—
150	C₂⁴	—	316	2	no	—
151	C₂×D₄	—	316	8	no	—
152	C₂×D₄	—	316	2	no	—
153	C₂×D₄	—	316	2	no	—
154	C₂×D₄	—	316	2	no	—
155	C₂×D₄	—	316	2	no	—
156	C₂×D₄	—	316	2	no	—
157	C₂×D₄	—	632	8	no	—
158	C₂×D₄	—	158	4	no	—
159	C₂²×C₄	—	316	2	no	—
160	C₂²×C₄	D₆₃₂	1	2	yes	—
161	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
162	D₈	—	316	8	no	—
163	D₈	—	316	4	no	—
164	D₈	—	158	8	no	—
165	C₂×C₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
166	C₂×C₈	D₆₃₂	1	2	yes	—
167	C₂×C₈	#11929613	1	2	yes	—
168	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
169	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
170	C₂×C₈	C₂×D₃₁₆	1	2	yes	—
171	C₂×C₈	#11929624	1	2	yes	—
172	C₄⋊C₄	—	316	2	no	—
173	C₄⋊C₄	—	316	2	no	—
174	C₄²	(C₂×D₇₉)⋊C₄	1	2	yes	—
175	C₄²	#11929613	1	2	yes	—
176	C₁₆	—	2	4	no	—
177	C₂³	—	316	4	no	—
178	C₂³	—	632	2	no	—
179	C₂³	—	632	2	no	—
180	C₂³	—	632	8	no	—
181	C₂³	C₂×D₆₃₂	1	1	yes	characteristic
182	D₄	—	316	4	no	—
183	D₄	—	316	4	no	—
184	D₄	—	632	16	no	—
185	D₄	—	632	2	no	—
186	D₄	—	632	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	632	2	no	—
189	C₂×C₄	—	632	4	no	—
190	C₂×C₄	#14579083	1	4	yes	—
191	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#14579149	1	1	yes	characteristic
193	C₂×C₄	#14579158	1	1	yes	characteristic
194	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
195	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
196	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
197	C₈	#14579083	1	4	yes	—
198	C₈	C₄×D₃₁₆	1	2	yes	—
199	C₈	#14579135	1	2	yes	—
200	C₂²	—	632	8	no	—
201	C₂²	—	632	4	no	—
202	C₂²	—	1264	4	no	—
203	C₂²	—	1264	4	no	—
204	C₂²	C₂×#14579083	1	1	yes	characteristic
205	C₂²	#19098910	1	1	yes	characteristic
206	C₂²	#19098940	1	1	yes	characteristic
207	C₂²	#19099001	1	4	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	1264	2	no	—
210	C₄	#19098465	1	1	yes	characteristic
211	C₄	C₂×#14579083	1	1	yes	characteristic
212	C₄	#19098910	1	1	yes	characteristic
213	C₄	#19098936	1	1	yes	characteristic
214	C₂	—	1264	4	no	—
215	C₂	#23764206	1	1	yes	characteristic
216	C₂	#23765117	1	2	yes	—
217	C₂	#23765642	1	2	yes	—
218	C₂	#23765666	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098940

C₂

yes

maximal, characteristic

C₂×#19098365

C₂

yes

maximal, complemented

#23763564

C₂

yes

maximal, characteristic, complemented

C₂×#346×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₆₃₂

—

C₂²×D₆₃₂

C₂²

yes

—

C₂×#14579158

—

#19098940

—

#19098940

C₄

yes

complemented

C₂×#14579095

C₂²

yes

—

C₂×#14579093

—

#19098429

—

#19098365

—

C₂²×C₁₆×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#346×C₇₉

—

C₂²×D₃₁₆

—

C₂²×D₃₁₆

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

—

C₂×D₆₃₂

C₂×C₄

yes

—

#14579158

—

#14579158

—

C₂×C₄⋊Dic₇₉

—

#14579095

—

#14579093

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

D₄

yes

complemented

C₄×C₈×C₇₉

C₂×C₄

yes

—

C₄×C₈×C₇₉

D₄

yes

—

C₂³×D₇₉

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂²×Dic₇₉

—

D₆₃₂

—

D₆₃₂

—

D₆₃₂

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

D₈

yes

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

—

C₂×C₈×C₇₉

D₈

yes

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₂×C₈×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

#41

yes

—

C₄²×C₇₉

C₂²⋊C₄

yes

—

C₄²×C₇₉

SD₁₆

yes

—

C₁₆×C₇₉

—

C₂³×C₇₉

C₂×D₈

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#102

yes

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

C₈×C₇₉

#102

yes

—

C₈×C₇₉

C₄×D₄

yes

—

C₈×C₇₉

#121

yes

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#390

yes

characteristic

100

C₄×C₇₉

C₂×#102

yes

characteristic

101

C₄×C₇₉

#486

yes

characteristic

102

C₄×C₇₉

#492

yes

characteristic

103

Dic₇₉

—

104

#13206

—

maximal, Sylow

105

C₂×C₇₉

#1957

yes

characteristic

106

C₂×C₇₉

#2140

yes

—

107

C₂×C₇₉

#2244

yes

—

108

C₂×C₇₉

#2250

yes

—

109

D₇₉

—

110

C₂×#493

—

111

C₂×#357

—

112

C₂×#346

D₇₉

yes

characteristic, complemented

113

#1846

—

114

C₇₉

#13206

yes

characteristic, complemented, Sylow

115

C₂²×D₈

—

116

C₂²×D₈

—

158

—

117

C₂×#127

—

158

—

118

C₂²×C₁₆

C₂×D₇₉

yes

—

119

#493

—

120

#493

—

158

—

121

C₂×#107

—

122

C₂×#106

—

158

—

123

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

124

#382

—

158

—

125

#357

—

158

—

126

#346

—

127

C₂²×D₄

—

316

—

128

C₂²×D₄

—

158

—

129

C₂×D₈

—

316

—

130

C₂×D₈

—

316

—

131

C₂×D₈

—

132

C₂×D₈

—

158

—

133

C₂×D₈

—

158

—

134

C₂×D₈

—

158

—

135

C₂×D₈

—

158

—

136

C₂²×C₈

D₃₁₆

yes

characteristic

137

C₂²×C₈

C₂²×D₇₉

yes

characteristic

138

#127

—

316

—

139

#127

—

158

—

140

C₂×C₄⋊C₄

—

158

—

141

C₂×C₄²

D₃₁₆

yes

characteristic

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

D₃₁₆

yes

complemented

145

#107

—

158

—

146

#106

—

316

—

147

C₄×C₈

C₄×D₇₉

yes

—

148

C₄×C₈

C₂²⋊D₇₉

yes

—

149

#95

—

316

—

150

C₂⁴

—

316

—

151

C₂×D₄

—

316

—

152

C₂×D₄

—

316

—

153

C₂×D₄

—

316

—

154

C₂×D₄

—

316

—

155

C₂×D₄

—

316

—

156

C₂×D₄

—

316

—

157

C₂×D₄

—

632

—

158

C₂×D₄

—

158

—

159

C₂²×C₄

—

316

—

160

C₂²×C₄

D₆₃₂

yes

—

161

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

162

D₈

—

316

—

163

D₈

—

316

—

164

D₈

—

158

—

165

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

—

166

C₂×C₈

D₆₃₂

yes

—

167

C₂×C₈

#11929613

yes

—

168

C₂×C₈

C₂×C₄×D₇₉

yes

characteristic

169

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

170

C₂×C₈

C₂×D₃₁₆

yes

—

171

C₂×C₈

#11929624

yes

—

172

C₄⋊C₄

—

316

—

173

C₄⋊C₄

—

316

—

174

C₄²

(C₂×D₇₉)⋊C₄

yes

—

175

C₄²

#11929613

yes

—

176

C₁₆

—

177

C₂³

—

316

—

178

C₂³

—

632

—

179

C₂³

—

632

—

180

C₂³

—

632

—

181

C₂³

C₂×D₆₃₂

yes

characteristic

182

D₄

—

316

—

183

D₄

—

316

—

184

D₄

—

632

—

185

D₄

—

632

—

186

D₄

—

632

—

187

C₂×C₄

—

188

C₂×C₄

—

632

—

189

C₂×C₄

—

632

—

190

C₂×C₄

#14579083

yes

—

191

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

192

C₂×C₄

#14579149

yes

characteristic

193

C₂×C₄

#14579158

yes

characteristic

194

C₂×C₄

C₂×D₆₃₂

yes

characteristic

195

C₂×C₄

C₂×#11929613

yes

characteristic

196

C₂×C₄

C₂×#11929613

yes

characteristic

197

C₈

#14579083

yes

—

198

C₈

C₄×D₃₁₆

yes

—

199

C₈

#14579135

yes

—

200

C₂²

—

632

—

201

C₂²

—

632

—

202

C₂²

—

1264

—

203

C₂²

—

1264

—

204

C₂²

C₂×#14579083

yes

characteristic

205

C₂²

#19098910

yes

characteristic

206

C₂²

#19098940

yes

characteristic

207

C₂²

#19099001

yes

—

208

C₄

—

209

C₄

—

1264

—

210

C₄

#19098465

yes

characteristic

211

C₄

C₂×#14579083

yes

characteristic

212

C₄

#19098910

yes

characteristic

213

C₄

#19098936

yes

characteristic

214

C₂

—

1264

—

215

C₂

#23764206

yes

characteristic

216

C₂

#23765117

yes

—

217

C₂

#23765642

yes

—

218

C₂

#23765666

yes

—

	subgroup	G/H
center	C₂³	C₂×D₆₃₂
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₂×#346×C₇₉	C₂
socle	C₂³×C₇₉	C₂×D₈
prime radical	C₂×#19098940	C₂
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	C₂×#346	D₇₉
hypocenter	C₇₉	#13206
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂³

C₂×D₆₃₂

commutator

C₂×C₈×C₇₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₂×#346×C₇₉

C₂

socle

C₂³×C₇₉

C₂×D₈

prime radical

C₂×#19098940

C₂

cosocle

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
2. C₂×#19098365	C₂	semidirect
3. #23763564	C₂	semidirect
4. C₂×#346×C₇₉	C₂	semidirect
9. #19098940	C₄	semidirect
37. C₂×C₁₆×C₇₉	D₄	semidirect
112. C₂×#346	D₇₉	semidirect
114. C₇₉	#13206	semidirect
144. C₂×C₁₆	D₃₁₆	semidirect

H ≅ G/N

type

2. C₂×#19098365

C₂

semidirect

3. #23763564

C₂

semidirect

4. C₂×#346×C₇₉

C₂

semidirect

9. #19098940

C₄

semidirect

37. C₂×C₁₆×C₇₉

D₄

semidirect

112. C₂×#346

D₇₉

semidirect

114. C₇₉

#13206

semidirect

144. C₂×C₁₆

D₃₁₆

semidirect

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

subgroup	index
C₂×#19098940	2
C₂×#19098365	2
#23763564	2
C₂×#346×C₇₉	2
#13206	79

subgroup

index

C₂×#346×C₇₉

Subgroups — #34206501

Conjugacy classes of subgroups

Complements

Maximal subgroups