Group #34207033 — subgroups

Subgroups — #34207033

Order 20224.

516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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×Dic₆₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098838	C₂	1	2	yes	maximal
3	C₂×#19098380	C₂	1	2	yes	maximal, complemented
4	#23761494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#2113	C₂	1	1	yes	maximal, characteristic
6	C₂×#14579191	—	2	2	no	—
7	C₂²×Dic₃₁₆	C₂²	1	2	yes	—
8	C₂×Dic₆₃₂	—	2	4	no	—
9	C₂×Dic₆₃₂	—	2	2	no	—
10	#19098838	—	2	4	no	—
11	#19098838	—	2	4	no	—
12	C₂×#14579097	C₂²	1	2	yes	—
13	C₂×#14579079	—	2	2	no	—
14	#19098380	—	2	4	no	—
15	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₁₆×C₇₉	—	2	2	no	—
19	C₂²×Dic₁₅₈	—	2	2	no	—
20	#14579191	—	2	8	no	—
21	#14579191	—	4	4	no	—
22	C₂×Dic₃₁₆	—	2	2	no	—
23	C₂×Dic₃₁₆	—	2	2	no	—
24	C₂×Dic₃₁₆	—	2	2	no	—
25	C₂×Dic₃₁₆	—	2	2	no	—
26	C₂×Dic₃₁₆	—	2	2	no	—
27	C₂×Dic₃₁₆	D₄	1	4	yes	—
28	C₂×#11929614	—	4	2	no	—
29	C₂×#11929612	—	4	2	no	—
30	C₂×#11929608	—	2	2	no	—
31	Dic₆₃₂	—	2	8	no	—
32	#14579097	—	2	2	no	—
33	#14579097	D₄	1	4	yes	—
34	#14579079	—	2	8	no	—
35	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
36	#131×C₇₉	—	2	2	no	—
37	#131×C₇₉	—	2	2	no	—
38	C₂×M₁₆×C₇₉	—	2	1	no	—
39	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₇₉	—	2	1	no	—
41	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
42	M₃₂×C₇₉	—	2	2	no	—
43	C₂×C₁₆×C₇₉	—	2	2	no	—
44	C₂×C₁₆×C₇₉	—	2	1	no	—
45	C₂×C₁₆×C₇₉	D₄	1	2	yes	—
46	C₂×Dic₁₅₈	—	2	4	no	—
47	C₂×Dic₁₅₈	—	4	2	no	—
48	C₂×Dic₁₅₈	—	4	2	no	—
49	C₂×Dic₁₅₈	—	4	2	no	—
50	C₂×Dic₁₅₈	—	4	2	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂²×Dic₇₉	—	4	2	no	—
53	Dic₃₁₆	—	2	4	no	—
54	Dic₃₁₆	—	2	4	no	—
55	Dic₃₁₆	—	4	2	no	—
56	Dic₃₁₆	—	4	2	no	—
57	#11929614	—	4	8	no	—
58	#11929612	—	4	8	no	—
59	#11929608	—	2	4	no	—
60	#11929608	—	4	2	no	—
61	C₂×C₇₉⋊C₈	—	4	2	no	—
62	#41×C₇₉	—	2	2	no	—
63	#41×C₇₉	—	2	2	no	—
64	C₂×Q₈×C₇₉	D₈	1	1	yes	characteristic
65	C₂×D₄×C₇₉	—	2	1	no	—
66	C₂×D₄×C₇₉	D₈	1	1	yes	characteristic
67	C₂²×C₄×C₇₉	—	2	1	no	—
68	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
69	M₁₆×C₇₉	—	2	2	no	—
70	M₁₆×C₇₉	—	4	2	no	—
71	C₂×C₈×C₇₉	—	2	1	no	—
72	C₂×C₈×C₇₉	—	4	1	no	—
73	C₂×C₈×C₇₉	—	4	1	no	—
74	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
76	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
78	C₁₆×C₇₉	—	2	2	no	—
79	C₁₆×C₇₉	—	4	1	no	—
80	C₂³×C₇₉	—	2	1	no	—
81	C₂³×C₇₉	#135	1	1	yes	characteristic
82	Q₈×C₇₉	—	2	2	no	—
83	D₄×C₇₉	—	2	2	no	—
84	D₄×C₇₉	—	4	2	no	—
85	C₂×C₄×C₇₉	—	2	1	no	—
86	C₂×C₄×C₇₉	—	4	1	no	—
87	C₂×C₄×C₇₉	—	4	1	no	—
88	C₂×C₄×C₇₉	#120	1	2	yes	—
89	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×Dic₇₉	—	4	4	no	—
93	C₂×Dic₇₉	—	8	2	no	—
94	C₂×Dic₇₉	—	8	2	no	—
95	Dic₁₅₈	—	4	4	no	—
96	Dic₁₅₈	—	4	4	no	—
97	Dic₁₅₈	—	8	2	no	—
98	Dic₁₅₈	—	8	2	no	—
99	C₈×C₇₉	—	4	1	no	—
100	C₈×C₇₉	#120	1	1	yes	characteristic
101	C₈×C₇₉	#121	1	2	yes	—
102	C₈×C₇₉	#127	1	1	yes	characteristic
103	C₇₉⋊C₈	—	4	4	no	—
104	C₂²×C₇₉	—	2	2	no	—
105	C₂²×C₇₉	—	4	2	no	—
106	C₂²×C₇₉	—	4	1	no	—
107	C₂²×C₇₉	#449	1	2	yes	—
108	C₂²×C₇₉	#466	1	1	yes	characteristic
109	C₄×C₇₉	—	4	1	no	—
110	C₄×C₇₉	#392	1	1	yes	characteristic
111	C₄×C₇₉	#447	1	2	yes	—
112	C₄×C₇₉	#469	1	1	yes	characteristic
113	Dic₇₉	—	8	4	no	—
114	#13315	—	79	1	no	maximal, Sylow
115	C₂×C₇₉	—	2	2	no	—
116	C₂×C₇₉	—	8	1	no	—
117	C₂×C₇₉	#1999	1	1	yes	characteristic
118	C₂×C₇₉	#2222	1	2	yes	—
119	C₂²×Q₃₂	—	79	1	no	—
120	C₂×#473	—	79	2	no	—
121	C₂×#362	—	79	2	no	—
122	#2113	D₇₉	1	1	yes	characteristic
123	#1381	—	79	1	no	—
124	C₇₉	#13315	1	1	yes	characteristic, complemented, Sylow
125	C₂×#137	—	158	2	no	—
126	C₂²×Q₁₆	—	79	2	no	—
127	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
128	C₂×Q₃₂	—	158	4	no	—
129	C₂×Q₃₂	—	158	2	no	—
130	C₂×M₃₂	C₂×D₇₉	1	1	yes	characteristic
131	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
132	#473	—	158	4	no	—
133	#473	—	158	4	no	—
134	C₂×#108	—	79	2	no	—
135	C₂×#101	—	158	2	no	—
136	#362	—	158	4	no	—
137	C₂²⋊C₁₆	—	2	2	no	—
138	C₂×#41	D₃₁₆	1	1	yes	characteristic
139	C₂²×Q₈	—	158	2	no	—
140	#137	—	316	4	no	—
141	#137	—	158	8	no	—
142	C₂×Q₁₆	—	316	2	no	—
143	C₂×Q₁₆	—	79	4	no	—
144	C₂×Q₁₆	—	158	2	no	—
145	C₂×Q₁₆	—	158	2	no	—
146	C₂×Q₁₆	—	158	2	no	—
147	C₂×Q₁₆	—	158	2	no	—
148	C₂×Q₁₆	—	158	2	no	—
149	C₂×SD₁₆	—	316	2	no	—
150	#131	—	2	2	no	—
151	#131	—	2	2	no	—
152	C₂×M₁₆	—	2	1	no	—
153	C₂×M₁₆	—	158	2	no	—
154	C₂×M₁₆	D₃₁₆	1	1	yes	characteristic
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
157	Q₃₂	—	158	8	no	—
158	M₃₂	—	2	2	no	—
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	—	2	1	no	—
161	C₂×C₁₆	C₂²⋊D₇₉	1	2	yes	—
162	#108	—	79	4	no	—
163	#108	—	158	2	no	—
164	#101	—	158	8	no	—
165	#41	—	2	2	no	—
166	#41	—	2	2	no	—
167	C₂×Q₈	—	316	2	no	—
168	C₂×Q₈	—	316	2	no	—
169	C₂×Q₈	—	316	2	no	—
170	C₂×Q₈	—	316	2	no	—
171	C₂×Q₈	—	316	2	no	—
172	C₂×Q₈	—	158	4	no	—
173	C₂×Q₈	D₆₃₂	1	1	yes	characteristic
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	D₆₃₂	1	1	yes	characteristic
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	316	2	no	—
178	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
179	Q₁₆	—	316	8	no	—
180	Q₁₆	—	316	2	no	—
181	Q₁₆	—	316	2	no	—
182	Q₁₆	—	158	4	no	—
183	Q₁₆	—	158	4	no	—
184	SD₁₆	—	316	8	no	—
185	M₁₆	—	2	2	no	—
186	M₁₆	—	4	2	no	—
187	M₁₆	—	316	2	no	—
188	M₁₆	—	158	4	no	—
189	C₂×C₈	—	2	1	no	—
190	C₂×C₈	—	4	1	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	316	2	no	—
193	C₂×C₈	D₄×D₇₉	1	2	yes	—
194	C₂×C₈	D₄×D₇₉	1	2	yes	—
195	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
196	C₂×C₈	#11929624	1	1	yes	characteristic
197	C₁₆	—	2	2	no	—
198	C₁₆	—	4	1	no	—
199	C₂³	—	2	1	no	—
200	C₂³	#14579183	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	316	4	no	—
203	Q₈	—	316	4	no	—
204	Q₈	—	632	2	no	—
205	Q₈	—	632	2	no	—
206	D₄	—	2	2	no	—
207	D₄	—	4	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	316	4	no	—
212	C₂×C₄	—	632	2	no	—
213	C₂×C₄	—	632	2	no	—
214	C₂×C₄	#14579131	1	2	yes	—
215	C₂×C₄	#14579135	1	1	yes	characteristic
216	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
217	C₂×C₄	#14579189	1	2	yes	—
218	C₈	—	4	1	no	—
219	C₈	—	316	4	no	—
220	C₈	#14579129	1	1	yes	characteristic
221	C₈	#14579134	1	2	yes	—
222	C₈	#14579157	1	1	yes	characteristic
223	C₂²	—	2	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	—	4	1	no	—
226	C₂²	#19098710	1	2	yes	—
227	C₂²	#19098799	1	1	yes	characteristic
228	C₄	—	4	1	no	—
229	C₄	—	632	4	no	—
230	C₄	#19098472	1	1	yes	characteristic
231	C₄	#19098699	1	2	yes	—
232	C₄	#19098816	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	—	8	1	no	—
235	C₂	#23764398	1	1	yes	characteristic
236	C₂	#23765525	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₆₃₂

C₂

yes

maximal, characteristic, complemented

C₂×#19098838

C₂

yes

maximal

C₂×#19098380

C₂

yes

maximal, complemented

#23761494

C₂

yes

maximal, characteristic, complemented

C₇₉×#2113

C₂

yes

maximal, characteristic

C₂×#14579191

—

C₂²×Dic₃₁₆

C₂²

yes

—

C₂×Dic₆₃₂

—

C₂×Dic₆₃₂

—

#19098838

—

#19098838

—

C₂×#14579097

C₂²

yes

—

C₂×#14579079

—

#19098380

—

C₂×#131×C₇₉

C₂²

yes

characteristic

C₂×M₃₂×C₇₉

C₂²

yes

characteristic

C₂²×C₁₆×C₇₉

C₂²

yes

characteristic

C₂²⋊C₁₆×C₇₉

—

C₂²×Dic₁₅₈

—

#14579191

—

#14579191

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

D₄

yes

—

C₂×#11929614

—

C₂×#11929612

—

C₂×#11929608

—

Dic₆₃₂

—

#14579097

—

#14579097

D₄

yes

—

#14579079

—

C₂×#41×C₇₉

D₄

yes

characteristic

#131×C₇₉

—

#131×C₇₉

—

C₂×M₁₆×C₇₉

—

C₂×M₁₆×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

—

C₂²×C₈×C₇₉

C₂³

yes

characteristic

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

—

C₂×C₁₆×C₇₉

D₄

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

—

—

—

—

C₂×C₇₉⋊C₈

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

D₈

yes

characteristic

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

D₈

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

M₁₆×C₇₉

—

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

#41

yes

characteristic

C₁₆×C₇₉

—

C₁₆×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

#135

yes

characteristic

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#121

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

100

C₈×C₇₉

#120

yes

characteristic

101

C₈×C₇₉

#121

yes

—

102

C₈×C₇₉

#127

yes

characteristic

103

C₇₉⋊C₈

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

#449

yes

—

108

C₂²×C₇₉

#466

yes

characteristic

109

C₄×C₇₉

—

110

C₄×C₇₉

#392

yes

characteristic

111

C₄×C₇₉

#447

yes

—

112

C₄×C₇₉

#469

yes

characteristic

113

Dic₇₉

—

114

#13315

—

maximal, Sylow

115

C₂×C₇₉

—

116

C₂×C₇₉

—

117

C₂×C₇₉

#1999

yes

characteristic

118

C₂×C₇₉

#2222

yes

—

119

C₂²×Q₃₂

—

120

C₂×#473

—

121

C₂×#362

—

122

#2113

D₇₉

yes

characteristic

123

#1381

—

124

C₇₉

#13315

yes

characteristic, complemented, Sylow

125

C₂×#137

—

158

—

126

C₂²×Q₁₆

—

127

C₂×#131

C₂×D₇₉

yes

characteristic

128

C₂×Q₃₂

—

158

—

129

C₂×Q₃₂

—

158

—

130

C₂×M₃₂

C₂×D₇₉

yes

characteristic

131

C₂²×C₁₆

C₂×D₇₉

yes

characteristic

132

#473

—

158

—

133

#473

—

158

—

134

C₂×#108

—

135

C₂×#101

—

158

—

136

#362

—

158

—

137

C₂²⋊C₁₆

—

138

C₂×#41

D₃₁₆

yes

characteristic

139

C₂²×Q₈

—

158

—

140

#137

—

316

—

141

#137

—

158

—

142

C₂×Q₁₆

—

316

—

143

C₂×Q₁₆

—

144

C₂×Q₁₆

—

158

—

145

C₂×Q₁₆

—

158

—

146

C₂×Q₁₆

—

158

—

147

C₂×Q₁₆

—

158

—

148

C₂×Q₁₆

—

158

—

149

C₂×SD₁₆

—

316

—

150

#131

—

151

#131

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

158

—

154

C₂×M₁₆

D₃₁₆

yes

characteristic

155

C₂²×C₈

—

156

C₂²×C₈

C₂²×D₇₉

yes

characteristic

157

Q₃₂

—

158

—

158

M₃₂

—

159

C₂×C₁₆

—

160

C₂×C₁₆

—

161

C₂×C₁₆

C₂²⋊D₇₉

yes

—

162

#108

—

163

#108

—

158

—

164

#101

—

158

—

165

#41

—

166

#41

—

167

C₂×Q₈

—

316

—

168

C₂×Q₈

—

316

—

169

C₂×Q₈

—

316

—

170

C₂×Q₈

—

316

—

171

C₂×Q₈

—

316

—

172

C₂×Q₈

—

158

—

173

C₂×Q₈

D₆₃₂

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

D₆₃₂

yes

characteristic

176

C₂²×C₄

—

177

C₂²×C₄

—

316

—

178

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

179

Q₁₆

—

316

—

180

Q₁₆

—

316

—

181

Q₁₆

—

316

—

182

Q₁₆

—

158

—

183

Q₁₆

—

158

—

184

SD₁₆

—

316

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

316

—

188

M₁₆

—

158

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

316

—

193

C₂×C₈

D₄×D₇₉

yes

—

194

C₂×C₈

D₄×D₇₉

yes

—

195

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

196

C₂×C₈

#11929624

yes

characteristic

197

C₁₆

—

198

C₁₆

—

199

C₂³

—

200

C₂³

#14579183

yes

characteristic

201

Q₈

—

202

Q₈

—

316

—

203

Q₈

—

316

—

204

Q₈

—

632

—

205

Q₈

—

632

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

316

—

212

C₂×C₄

—

632

—

213

C₂×C₄

—

632

—

214

C₂×C₄

#14579131

yes

—

215

C₂×C₄

#14579135

yes

characteristic

216

C₂×C₄

C₂×D₆₃₂

yes

characteristic

217

C₂×C₄

#14579189

yes

—

218

C₈

—

219

C₈

—

316

—

220

C₈

#14579129

yes

characteristic

221

C₈

#14579134

yes

—

222

C₈

#14579157

yes

characteristic

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

#19098710

yes

—

227

C₂²

#19098799

yes

characteristic

228

C₄

—

229

C₄

—

632

—

230

C₄

#19098472

yes

characteristic

231

C₄

#19098699

yes

—

232

C₄

#19098816

yes

characteristic

233

C₂

—

234

C₂

—

235

C₂

#23764398

yes

characteristic

236

C₂

#23765525

yes

—

	subgroup	G/H
center	C₂²	#19098799
commutator, cosocle	C₂²×C₈×C₇₉	C₂³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#2113	C₂
socle	C₂²×C₇₉	#466
prime radical	C₂×#41×C₇₉	D₄
hypercenter	#2113	D₇₉
hypocenter	C₇₉	#13315
LCS	G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ #2113

subgroup

G/H

center

C₂²

#19098799

commutator, cosocle

C₂²×C₈×C₇₉

C₂³

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#2113

C₂

socle

C₂²×C₇₉

#466

prime radical

C₂×#41×C₇₉

D₄

D₇₉

C₇₉

G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ #2113

N	H ≅ G/N	type
1. C₂²×Dic₆₃₂	C₂	semidirect
3. C₂×#19098380	C₂	semidirect
4. #23761494	C₂	semidirect
124. C₇₉	#13315	semidirect

H ≅ G/N

type

1. C₂²×Dic₆₃₂

C₂

semidirect

3. C₂×#19098380

C₂

semidirect

4. #23761494

C₂

semidirect

124. C₇₉

#13315

semidirect

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

subgroup	index
C₂²×Dic₆₃₂	2
C₂×#19098838	2
C₂×#19098380	2
#23761494	2
C₇₉×#2113	2
#13315	79

subgroup

index

C₂²×Dic₆₃₂

C₇₉×#2113

Subgroups — #34207033

Conjugacy classes of subgroups

Complements

Maximal subgroups