Group #34207378 — subgroups

Subgroups — #34207378

Order 20224.

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

normal subgroups only

This group has 402 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	C₂×#19098961	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098374	C₂	1	2	yes	maximal
3	#23764288	C₂	1	1	yes	maximal, characteristic
4	#23761499	C₂	1	2	yes	maximal, complemented
5	C₇₉×#1376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14579183	C₂²	1	1	yes	characteristic
7	C₂×#14579161	—	2	1	no	—
8	#19098961	—	2	4	no	—
9	C₂×#14579097	C₂²	1	1	yes	characteristic
10	C₂×#14579093	—	2	1	no	—
11	C₂×#14579093	C₂²	1	2	yes	—
12	C₂×#14579089	—	2	1	no	—
13	#19098529	—	2	1	no	—
14	#19098374	—	2	4	no	—
15	C₂×M₃₂×C₇₉	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#11929624	—	2	1	no	—
18	C₂²×Dic₁₅₈	—	4	1	no	—
19	#14579183	—	2	2	no	—
20	#14579183	—	2	2	no	—
21	C₂×Dic₃₁₆	Q₈	1	1	yes	characteristic, complemented
22	C₂×#11929613	—	2	1	no	—
23	C₂×D₆₃₂	Q₈	1	1	yes	characteristic, complemented
24	C₂×#11929608	—	2	1	no	—
25	#14579161	—	2	4	no	—
26	#14579161	—	4	2	no	—
27	C₂×C₄⋊Dic₇₉	—	2	2	no	—
28	C₂×C₄⋊Dic₇₉	—	4	1	no	—
29	#14579097	—	2	2	no	—
30	#14579093	—	2	4	no	—
31	#14579093	—	2	2	no	—
32	#14579093	D₄	1	4	yes	—
33	#14579089	—	4	2	no	—
34	(C₂×D₇₉)⋊C₈	—	4	2	no	—
35	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
37	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
38	M₃₂×C₇₉	—	2	2	no	—
39	M₃₂×C₇₉	—	2	2	no	—
40	C₂×C₁₆×C₇₉	—	2	2	no	—
41	C₄×C₈×C₇₉	—	2	2	no	—
42	#11929624	—	4	1	no	—
43	#11929624	—	4	1	no	—
44	#11929624	—	4	1	no	—
45	#11929624	—	4	1	no	—
46	C₂×Dic₁₅₈	—	2	1	no	—
47	C₂×Dic₁₅₈	—	4	4	no	—
48	C₂×Dic₁₅₈	—	8	4	no	—
49	C₂×D₃₁₆	—	2	1	no	—
50	C₂×C₂²⋊D₇₉	—	4	1	no	—
51	C₂²×Dic₇₉	—	4	2	no	—
52	C₂×C₄×D₇₉	—	4	1	no	—
53	Dic₃₁₆	—	2	2	no	—
54	#11929613	—	4	2	no	—
55	D₆₃₂	—	2	2	no	—
56	#11929608	—	4	1	no	—
57	#11929608	—	4	1	no	—
58	C₂×C₇₉⋊C₈	—	4	1	no	—
59	C₄⋊Dic₇₉	—	2	4	no	—
60	C₄⋊Dic₇₉	—	4	4	no	—
61	C₄⋊Dic₇₉	—	4	2	no	—
62	C₂²×C₄×C₇₉	—	2	1	no	—
63	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₇₉	—	2	1	no	—
65	C₂×C₈×C₇₉	—	2	1	no	—
66	C₂×C₈×C₇₉	SD₁₆	1	2	yes	—
67	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₇₉	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
70	C₂×C₈×C₇₉	#41	1	2	yes	—
71	C₄²×C₇₉	—	2	1	no	—
72	C₄²×C₇₉	D₈	1	2	yes	—
73	C₁₆×C₇₉	—	4	2	no	—
74	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
75	C₂²×D₇₉	—	4	1	no	—
76	C₂×C₄×C₇₉	—	2	4	no	—
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
79	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₇₉	#124	1	1	yes	characteristic
81	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
83	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
84	C₂²⋊D₇₉	—	8	1	no	—
85	C₂²⋊D₇₉	—	8	1	no	—
86	C₂×Dic₇₉	—	4	4	no	—
87	C₂×Dic₇₉	—	4	1	no	—
88	C₂×Dic₇₉	—	8	4	no	—
89	D₃₁₆	—	4	1	no	—
90	D₃₁₆	—	4	1	no	—
91	C₄×D₇₉	—	8	1	no	—
92	C₄×D₇₉	—	8	1	no	—
93	Dic₁₅₈	—	4	1	no	—
94	Dic₁₅₈	—	4	1	no	—
95	Dic₁₅₈	—	8	8	no	—
96	C₈×C₇₉	—	2	2	no	—
97	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
98	C₈×C₇₉	#124	1	2	yes	—
99	C₇₉⋊C₈	—	8	1	no	—
100	C₂²×C₇₉	—	2	2	no	—
101	C₂²×C₇₉	#447	1	1	yes	characteristic
102	C₂²×C₇₉	#476	1	1	yes	characteristic
103	C₂²×C₇₉	#489	1	1	yes	characteristic
104	C₂×D₇₉	—	8	2	no	—
105	C₂×D₇₉	—	8	1	no	—
106	C₄×C₇₉	—	2	4	no	—
107	C₄×C₇₉	#393	1	1	yes	characteristic
108	C₄×C₇₉	#448	1	1	yes	characteristic
109	C₄×C₇₉	#474	1	1	yes	characteristic
110	C₄×C₇₉	#486	1	1	yes	characteristic
111	Dic₇₉	—	8	4	no	—
112	Dic₇₉	—	8	1	no	—
113	#13371	—	79	1	no	maximal, Sylow
114	C₂×C₇₉	—	2	1	no	—
115	C₂×C₇₉	—	2	1	no	—
116	C₂×C₇₉	#2023	1	1	yes	characteristic
117	C₂×C₇₉	#2230	1	2	yes	—
118	D₇₉	—	16	1	no	—
119	C₂×#498	—	79	1	no	—
120	C₂×#360	—	79	2	no	—
121	#1974	—	79	1	no	—
122	#1383	—	79	2	no	—
123	#1376	D₇₉	1	1	yes	characteristic, complemented
124	C₇₉	#13371	1	1	yes	characteristic, complemented, Sylow
125	C₂×#135	—	79	1	no	—
126	C₂×C₄⋊Q₈	—	158	1	no	—
127	C₂×M₃₂	C₂×D₇₉	1	2	yes	—
128	#498	—	158	4	no	—
129	C₂×#108	—	79	1	no	—
130	C₂×#106	—	79	2	no	—
131	C₂×#106	—	158	1	no	—
132	C₂×#104	—	158	1	no	—
133	#408	—	158	1	no	—
134	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
135	#360	—	158	4	no	—
136	C₂×#41	—	158	1	no	—
137	C₂²×Q₈	—	316	1	no	—
138	#135	—	158	2	no	—
139	#135	—	158	2	no	—
140	C₂×Q₁₆	—	79	1	no	—
141	C₂×SD₁₆	—	158	1	no	—
142	C₂×D₈	—	79	1	no	—
143	C₂×M₁₆	—	158	1	no	—
144	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
145	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
146	C₄⋊Q₈	—	316	2	no	—
147	C₄⋊Q₈	—	158	4	no	—
148	C₂×C₄⋊C₄	—	316	1	no	—
149	C₂×C₄⋊C₄	—	158	2	no	—
150	C₂×C₄²	D₃₁₆	1	1	yes	characteristic
151	M₃₂	—	2	2	no	—
152	M₃₂	—	2	2	no	—
153	C₂×C₁₆	—	2	2	no	—
154	#108	—	158	2	no	—
155	#106	—	79	4	no	—
156	#106	—	158	4	no	—
157	#106	—	158	2	no	—
158	#104	—	316	2	no	—
159	C₂²⋊C₈	—	316	2	no	—
160	C₄×C₈	—	2	2	no	—
161	#41	—	316	1	no	—
162	#41	—	316	1	no	—
163	#41	—	316	1	no	—
164	#41	—	316	1	no	—
165	C₂×Q₈	—	316	4	no	—
166	C₂×Q₈	—	632	4	no	—
167	C₂×Q₈	—	158	1	no	—
168	C₂×D₄	—	316	1	no	—
169	C₂×D₄	—	158	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	316	2	no	—
172	C₂²×C₄	—	316	1	no	—
173	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
174	Q₁₆	—	158	2	no	—
175	SD₁₆	—	316	2	no	—
176	D₈	—	158	2	no	—
177	M₁₆	—	316	1	no	—
178	M₁₆	—	316	1	no	—
179	C₂×C₈	—	2	1	no	—
180	C₂×C₈	—	2	1	no	—
181	C₂×C₈	—	316	1	no	—
182	C₂×C₈	#11929613	1	2	yes	—
183	C₂×C₈	D₄×D₇₉	1	2	yes	—
184	C₂×C₈	Q₈×D₇₉	1	1	yes	characteristic
185	C₂×C₈	#11929623	1	1	yes	characteristic
186	C₂×C₈	#11929624	1	2	yes	—
187	C₄⋊C₄	—	316	4	no	—
188	C₄⋊C₄	—	316	2	no	—
189	C₄⋊C₄	—	158	4	no	—
190	C₄²	—	2	1	no	—
191	C₄²	D₆₃₂	1	2	yes	—
192	C₁₆	—	4	2	no	—
193	C₂³	—	316	1	no	—
194	C₂³	#14579189	1	1	yes	characteristic
195	Q₈	—	316	1	no	—
196	Q₈	—	316	1	no	—
197	Q₈	—	632	8	no	—
198	D₄	—	316	1	no	—
199	D₄	—	316	1	no	—
200	D₄	—	632	1	no	—
201	D₄	—	632	1	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	316	4	no	—
205	C₂×C₄	—	316	1	no	—
206	C₂×C₄	—	632	4	no	—
207	C₂×C₄	—	632	1	no	—
208	C₂×C₄	—	632	1	no	—
209	C₂×C₄	#14579131	1	1	yes	characteristic
210	C₂×C₄	#14579141	1	1	yes	characteristic
211	C₂×C₄	#14579149	1	1	yes	characteristic
212	C₂×C₄	C₂×D₆₃₂	1	1	yes	characteristic
213	C₂×C₄	C₂×#11929613	1	1	yes	characteristic
214	C₂×C₄	#14579194	1	1	yes	characteristic
215	C₈	—	2	2	no	—
216	C₈	—	632	1	no	—
217	C₈	#14579139	1	2	yes	—
218	C₈	#14579147	1	2	yes	—
219	C₂²	—	2	2	no	—
220	C₂²	—	632	1	no	—
221	C₂²	—	632	2	no	—
222	C₂²	#19098699	1	1	yes	characteristic
223	C₂²	#19098854	1	1	yes	characteristic
224	C₂²	#19098923	1	1	yes	characteristic
225	C₄	—	2	4	no	—
226	C₄	—	632	4	no	—
227	C₄	—	632	1	no	—
228	C₄	#19098476	1	1	yes	characteristic
229	C₄	#19098704	1	1	yes	characteristic
230	C₄	#19098844	1	1	yes	characteristic
231	C₄	#19098910	1	1	yes	characteristic
232	C₂	—	2	1	no	—
233	C₂	—	2	1	no	—
234	C₂	—	1264	1	no	—
235	C₂	#23764537	1	1	yes	characteristic
236	C₂	#23765572	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098961

C₂

yes

maximal, characteristic, complemented

C₂×#19098374

C₂

yes

maximal

#23764288

C₂

yes

maximal, characteristic

#23761499

C₂

yes

maximal, complemented

C₇₉×#1376

C₂

yes

maximal, characteristic, complemented

C₂×#14579183

C₂²

yes

—

—

C₂²

yes

characteristic

C₂×#14579093

—

C₂×#14579093

C₂²

yes

—

C₂×#14579089

—

#19098529

—

#19098374

—

C₂×M₃₂×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×#11929624

—

C₂²×Dic₁₅₈

—

#14579183

—

#14579183

—

C₂×Dic₃₁₆

Q₈

yes

characteristic, complemented

C₂×#11929613

—

C₂×D₆₃₂

Q₈

yes

characteristic, complemented

C₂×#11929608

—

#14579161

—

#14579161

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

—

—

—

D₄

yes

—

#14579089

—

(C₂×D₇₉)⋊C₈

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

D₄

yes

characteristic

M₃₂×C₇₉

—

M₃₂×C₇₉

—

C₂×C₁₆×C₇₉

—

C₄×C₈×C₇₉

—

—

—

—

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

#11929613

—

D₆₃₂

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

SD₁₆

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×Q₈

yes

C₂×C₈×C₇₉

yes

C₂×C₈×C₇₉

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

D₈

yes

—

C₁₆×C₇₉

—

C₂³×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

#124

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₇₉

#137

yes

characteristic

C₂²⋊D₇₉

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

C₂²⋊Q₈

yes

—

C₈×C₇₉

#124

yes

—

C₇₉⋊C₈

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

#447

yes

characteristic

102

C₂²×C₇₉

#476

yes

characteristic

103

C₂²×C₇₉

#489

yes

characteristic

104

C₂×D₇₉

—

105

C₂×D₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

#393

yes

characteristic

108

C₄×C₇₉

#448

yes

characteristic

109

C₄×C₇₉

#474

yes

characteristic

110

C₄×C₇₉

#486

yes

characteristic

111

Dic₇₉

—

112

Dic₇₉

—

113

#13371

—

maximal, Sylow

114

C₂×C₇₉

—

115

C₂×C₇₉

—

116

C₂×C₇₉

#2023

yes

characteristic

117

C₂×C₇₉

#2230

yes

—

118

D₇₉

—

119

C₂×#498

—

120

C₂×#360

—

121

#1974

—

122

#1383

—

123

#1376

D₇₉

yes

characteristic, complemented

124

C₇₉

#13371

yes

characteristic, complemented, Sylow

125

C₂×#135

—

126

C₂×C₄⋊Q₈

—

158

—

127

C₂×M₃₂

C₂×D₇₉

yes

—

128

#498

—

158

—

129

C₂×#108

—

130

C₂×#106

—

131

C₂×#106

—

158

—

132

C₂×#104

—

158

—

133

#408

—

158

—

134

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

135

#360

—

158

—

136

C₂×#41

—

158

—

137

C₂²×Q₈

—

316

—

138

#135

—

158

—

139

#135

—

158

—

140

C₂×Q₁₆

—

141

C₂×SD₁₆

—

158

—

142

C₂×D₈

—

143

C₂×M₁₆

—

158

—

144

C₂²×C₈

D₃₁₆

yes

characteristic

145

C₂²×C₈

C₂²×D₇₉

yes

characteristic

146

C₄⋊Q₈

—

316

—

147

C₄⋊Q₈

—

158

—

148

C₂×C₄⋊C₄

—

316

—

149

C₂×C₄⋊C₄

—

158

—

150

C₂×C₄²

D₃₁₆

yes

characteristic

151

M₃₂

—

152

M₃₂

—

153

C₂×C₁₆

—

154

#108

—

158

—

155

#106

—

156

#106

—

158

—

157

#106

—

158

—

158

#104

—

316

—

159

C₂²⋊C₈

—

316

—

160

C₄×C₈

—

161

#41

—

316

—

162

#41

—

316

—

163

#41

—

316

—

164

#41

—

316

—

165

C₂×Q₈

—

316

—

166

C₂×Q₈

—

632

—

167

C₂×Q₈

—

158

—

168

C₂×D₄

—

316

—

169

C₂×D₄

—

158

—

170

C₂²×C₄

—

171

C₂²×C₄

—

316

—

172

C₂²×C₄

—

316

—

173

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

174

Q₁₆

—

158

—

175

SD₁₆

—

316

—

176

D₈

—

158

—

177

M₁₆

—

316

—

178

M₁₆

—

316

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

316

—

182

C₂×C₈

#11929613

yes

—

183

C₂×C₈

D₄×D₇₉

yes

—

184

C₂×C₈

Q₈×D₇₉

yes

characteristic

185

C₂×C₈

#11929623

yes

characteristic

186

C₂×C₈

#11929624

yes

—

187

C₄⋊C₄

—

316

—

188

C₄⋊C₄

—

316

—

189

C₄⋊C₄

—

158

—

190

C₄²

—

191

C₄²

D₆₃₂

yes

—

192

C₁₆

—

193

C₂³

—

316

—

194

C₂³

#14579189

yes

characteristic

195

Q₈

—

316

—

196

Q₈

—

316

—

197

Q₈

—

632

—

198

D₄

—

316

—

199

D₄

—

316

—

200

D₄

—

632

—

201

D₄

—

632

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

316

—

205

C₂×C₄

—

316

—

206

C₂×C₄

—

632

—

207

C₂×C₄

—

632

—

208

C₂×C₄

—

632

—

209

C₂×C₄

#14579131

yes

characteristic

210

C₂×C₄

#14579141

yes

characteristic

211

C₂×C₄

#14579149

yes

characteristic

212

C₂×C₄

C₂×D₆₃₂

yes

characteristic

213

C₂×C₄

C₂×#11929613

yes

characteristic

214

C₂×C₄

#14579194

yes

characteristic

215

C₈

—

216

C₈

—

632

—

217

C₈

#14579139

yes

—

218

C₈

#14579147

yes

—

219

C₂²

—

220

C₂²

—

632

—

221

C₂²

—

632

—

222

C₂²

#19098699

yes

characteristic

223

C₂²

#19098854

yes

characteristic

224

C₂²

#19098923

yes

characteristic

225

C₄

—

226

C₄

—

632

—

227

C₄

—

632

—

228

C₄

#19098476

yes

characteristic

229

C₄

#19098704

yes

characteristic

230

C₄

#19098844

yes

characteristic

231

C₄

#19098910

yes

characteristic

232

C₂

—

233

C₂

—

234

C₂

—

1264

—

235

C₂

#23764537

yes

characteristic

236

C₂

#23765572

yes

—

	subgroup	G/H
center	C₂²	#19098854
commutator, cosocle	C₂²×C₈×C₇₉	C₂³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1376	C₂
socle	C₂²×C₇₉	#476
prime radical	C₂×#14579183	C₂²
hypercenter	#1376	D₇₉
hypocenter	C₇₉	#13371
LCS	G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1376

subgroup

G/H

center

C₂²

#19098854

commutator, cosocle

C₂²×C₈×C₇₉

C₂³

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1376

C₂

C₂²×C₇₉

C₂²

D₇₉

C₇₉

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ #1376

N	H ≅ G/N	type
1. C₂×#19098961	C₂	semidirect
4. #23761499	C₂	semidirect
5. C₇₉×#1376	C₂	semidirect
21. C₂×Dic₃₁₆	Q₈	semidirect
23. C₂×D₆₃₂	Q₈	semidirect
123. #1376	D₇₉	semidirect
124. C₇₉	#13371	semidirect

H ≅ G/N

type

1. C₂×#19098961

C₂

semidirect

4. #23761499

C₂

semidirect

5. C₇₉×#1376

C₂

semidirect

21. C₂×Dic₃₁₆

Q₈

semidirect

23. C₂×D₆₃₂

Q₈

semidirect

123. #1376

D₇₉

semidirect

124. C₇₉

#13371

semidirect

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

subgroup	index
C₂×#19098961	2
C₂×#19098374	2
#23764288	2
#23761499	2
C₇₉×#1376	2
#13371	79

subgroup

index

C₇₉×#1376

Subgroups — #34207378

Conjugacy classes of subgroups

Complements

Maximal subgroups