Group #34302157 — subgroups

Subgroups — #34302157

Order 20224.

810 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 203 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	#23773828	C₂	1	1	yes	maximal, characteristic
2	#23772117	C₂	1	2	yes	maximal, complemented
3	#23764231	C₂	1	2	yes	maximal, complemented
4	#23763728	C₂	1	8	yes	maximal, complemented
5	#23763151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#1837	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14579183	C₂²	1	4	yes	—
8	C₂×#14579169	C₂²	1	4	yes	—
9	#19099113	C₂²	1	2	yes	—
10	#19098947	C₄	1	4	yes	complemented
11	#19098943	C₄	1	1	yes	characteristic, complemented
12	#19098940	C₄	1	1	yes	characteristic, complemented
13	#19098936	C₄	1	2	yes	complemented
14	#19098633	—	2	8	no	—
15	C₂×#14579087	C₂²	1	8	yes	—
16	#19098531	C₂²	1	4	yes	—
17	C₂×#14579072	C₂²	1	1	yes	characteristic
18	#19098409	C₂²	1	1	yes	characteristic
19	#19098317	C₂²	1	4	yes	—
20	#423×C₇₉	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	#341×C₇₉	C₂²	1	4	yes	—
23	C₂×#11929624	C₂³	1	4	yes	—
24	#14579183	—	4	8	no	—
25	C₂×Dic₃₁₆	C₂×C₄	1	4	yes	—
26	C₂×#11929613	C₂×C₄	1	8	yes	—
27	C₂×D₆₃₂	C₂×C₄	1	4	yes	—
28	#14579169	—	4	8	no	—
29	C₂×#11929607	—	2	4	no	—
30	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
31	C₂×C₈×D₇₉	—	2	4	no	—
32	#14579161	C₂×C₄	1	2	yes	—
33	#14579158	C₂×C₄	1	2	yes	—
34	#14579149	C₂×C₄	1	4	yes	—
35	#14579135	—	2	4	no	—
36	C₄×D₃₁₆	—	2	4	no	—
37	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
38	#14579087	—	4	8	no	—
39	(C₂×D₇₉)⋊C₈	—	2	8	no	—
40	#14579072	D₄	1	4	yes	—
41	C₇₉⋊#95	—	2	2	no	—
42	C₂×M₁₆×C₇₉	C₂³	1	4	yes	—
43	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
44	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
45	C₄⋊C₈×C₇₉	—	2	4	no	—
46	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
49	#11929624	—	2	8	no	—
50	#11929624	—	2	8	no	—
51	C₂×Dic₁₅₈	C₂²×C₄	1	4	yes	—
52	C₂×D₃₁₆	—	2	4	no	—
53	C₂×D₃₁₆	C₂²×C₄	1	4	yes	—
54	C₂×C₂²⋊D₇₉	—	2	4	no	—
55	C₂²×Dic₇₉	—	2	2	no	—
56	C₂×C₄×D₇₉	—	2	4	no	—
57	Dic₃₁₆	—	4	4	no	—
58	#11929613	—	4	8	no	—
59	D₆₃₂	—	4	4	no	—
60	#11929607	—	4	8	no	—
61	C₂×C₇₉⋊C₈	—	2	4	no	—
62	C₂×C₇₉⋊C₈	C₂×D₄	1	4	yes	—
63	C₈×D₇₉	—	4	8	no	—
64	C₄⋊Dic₇₉	—	2	4	no	—
65	(C₂×D₇₉)⋊C₄	—	2	8	no	—
66	C₄×Dic₇₉	—	2	4	no	—
67	C₂²×C₄×C₇₉	#41	1	2	yes	—
68	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
69	M₁₆×C₇₉	—	2	8	no	—
70	C₂×C₈×C₇₉	—	2	4	no	—
71	C₂×C₈×C₇₉	—	2	4	no	—
72	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
73	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
74	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	2	yes	—
77	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
78	C₂²×D₇₉	—	2	4	no	—
79	C₂×C₄×C₇₉	—	4	2	no	—
80	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
81	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
82	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
85	C₂²⋊D₇₉	—	4	8	no	—
86	C₂×Dic₇₉	—	2	4	no	—
87	C₂×Dic₇₉	—	4	4	no	—
88	C₂×Dic₇₉	—	4	2	no	—
89	D₃₁₆	—	2	8	no	—
90	D₃₁₆	—	8	4	no	—
91	C₄×D₇₉	—	4	4	no	—
92	C₄×D₇₉	—	4	4	no	—
93	Dic₁₅₈	—	2	8	no	—
94	C₈×C₇₉	—	2	2	no	—
95	C₈×C₇₉	—	2	2	no	—
96	C₈×C₇₉	—	4	4	no	—
97	C₇₉⋊C₈	—	2	4	no	—
98	C₂²×C₇₉	—	2	2	no	—
99	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
100	C₂²×C₇₉	#540	1	2	yes	—
101	C₂×D₇₉	—	4	4	no	—
102	C₂×D₇₉	—	4	8	no	—
103	C₄×C₇₉	—	2	2	no	—
104	C₄×C₇₉	—	2	2	no	—
105	C₄×C₇₉	#518	1	2	yes	—
106	C₄×C₇₉	#535	1	2	yes	—
107	Dic₇₉	—	4	4	no	—
108	Dic₇₉	—	8	2	no	—
109	#22282	—	79	1	no	maximal, Sylow
110	C₂×C₇₉	—	2	2	no	—
111	C₂×C₇₉	#2328	1	1	yes	characteristic
112	C₂×C₇₉	#2957	1	2	yes	—
113	D₇₉	—	8	4	no	—
114	#3147	—	79	1	no	—
115	#2932	—	79	2	no	—
116	#1963	—	79	2	no	—
117	#1876	—	79	8	no	—
118	#1837	D₇₉	1	1	yes	characteristic, complemented
119	#1746	—	79	1	no	—
120	C₇₉	#22282	1	1	yes	characteristic, complemented, Sylow
121	C₂×#135	—	79	4	no	—
122	C₂×#131	—	79	4	no	—
123	#532	—	79	2	no	—
124	#495	—	79	4	no	—
125	#494	—	79	1	no	—
126	#493	—	79	1	no	—
127	#492	—	79	2	no	—
128	#435	—	158	8	no	—
129	#423	C₂×D₇₉	1	2	yes	—
130	C₂×#104	—	79	8	no	—
131	#408	—	79	4	no	—
132	C₂×#97	—	79	1	no	—
133	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
134	#376	—	79	1	no	—
135	#341	C₂×D₇₉	1	4	yes	—
136	#336	—	79	4	no	—
137	C₂×#41	—	79	4	no	—
138	#135	—	316	8	no	—
139	C₂×Q₁₆	—	79	4	no	—
140	C₂×SD₁₆	—	79	8	no	—
141	C₂×D₈	—	79	4	no	—
142	#131	—	316	8	no	—
143	C₂×M₁₆	—	158	4	no	—
144	C₂×M₁₆	C₂²×D₇₉	1	4	yes	—
145	C₂²×C₈	—	79	2	no	—
146	C₂²×C₈	—	158	4	no	—
147	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
148	C₄⋊Q₈	—	79	2	no	—
149	#127	—	79	2	no	—
150	#124	—	79	4	no	—
151	#121	—	158	4	no	—
152	C₄×D₄	—	158	4	no	—
153	C₂×C₄²	—	79	2	no	—
154	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
155	C₄⋊C₈	—	2	4	no	—
156	#104	—	316	8	no	—
157	C₂²⋊C₈	—	158	8	no	—
158	#97	—	79	4	no	—
159	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
160	C₄×C₈	C₄×D₇₉	1	1	yes	characteristic
161	C₄×C₈	C₄×D₇₉	1	2	yes	—
162	#95	—	158	2	no	—
163	#41	—	158	8	no	—
164	#41	—	158	8	no	—
165	C₂×Q₈	—	79	4	no	—
166	C₂×D₄	—	79	4	no	—
167	C₂×D₄	—	158	4	no	—
168	C₂×D₄	—	158	4	no	—
169	C₂²×C₄	—	158	2	no	—
170	C₂²×C₄	—	158	4	no	—
171	C₂²×C₄	#11929625	1	2	yes	—
172	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
173	Q₁₆	—	316	4	no	—
174	SD₁₆	—	316	8	no	—
175	D₈	—	316	4	no	—
176	M₁₆	—	2	8	no	—
177	M₁₆	—	316	8	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	316	8	no	—
181	C₂×C₈	—	79	4	no	—
182	C₂×C₈	—	158	4	no	—
183	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
184	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
185	C₄⋊C₄	—	158	4	no	—
186	C₂²⋊C₄	—	158	8	no	—
187	C₄²	—	158	4	no	—
188	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
190	C₄²	D₄×D₇₉	1	2	yes	—
191	C₂³	—	158	4	no	—
192	C₂³	C₂×#11929625	1	1	yes	characteristic
193	Q₈	—	158	8	no	—
194	D₄	—	316	8	no	—
195	D₄	—	632	4	no	—
196	D₄	—	158	8	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	316	4	no	—
199	C₂×C₄	—	316	4	no	—
200	C₂×C₄	—	316	4	no	—
201	C₂×C₄	—	316	2	no	—
202	C₂×C₄	—	158	4	no	—
203	C₂×C₄	#14579123	1	2	yes	—
204	C₂×C₄	#14579123	1	2	yes	—
205	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
206	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
207	C₂×C₄	#14579207	1	4	yes	—
208	C₈	—	2	2	no	—
209	C₈	—	2	2	no	—
210	C₈	—	4	4	no	—
211	C₈	—	158	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	316	4	no	—
214	C₂²	—	316	8	no	—
215	C₂²	C₂×#14579123	1	1	yes	characteristic
216	C₂²	#19099169	1	2	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	316	4	no	—
220	C₄	—	632	2	no	—
221	C₄	#19099037	1	2	yes	—
222	C₄	#19099131	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	—	632	4	no	—
225	C₂	#23766123	1	1	yes	characteristic
226	C₂	#23772316	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23773828

C₂

yes

maximal, characteristic

#23772117

C₂

yes

maximal, complemented

#23764231

C₂

yes

maximal, complemented

#23763728

C₂

yes

maximal, complemented

#23763151

C₂

yes

maximal, characteristic, complemented

C₇₉×#1837

C₂

yes

maximal, characteristic, complemented

C₂×#14579183

C₂²

yes

—

C₂×#14579169

C₂²

yes

—

#19099113

C₂²

yes

—

#19098947

C₄

yes

complemented

#19098943

C₄

yes

characteristic, complemented

#19098940

C₄

yes

characteristic, complemented

#19098936

C₄

yes

complemented

#19098633

—

C₂×#14579087

C₂²

yes

—

#19098531

C₂²

yes

—

C₂×#14579072

C₂²

yes

characteristic

#19098409

C₂²

yes

characteristic

#19098317

C₂²

yes

—

#423×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#341×C₇₉

C₂²

yes

—

C₂×#11929624

C₂³

yes

—

#14579183

—

C₂×Dic₃₁₆

C₂×C₄

yes

—

C₂×#11929613

C₂×C₄

yes

—

C₂×D₆₃₂

C₂×C₄

yes

—

#14579169

—

C₂×#11929607

—

C₂²×C₇₉⋊C₈

C₂³

yes

—

C₂×C₈×D₇₉

—

#14579161

C₂×C₄

yes

—

#14579158

C₂×C₄

yes

—

#14579149

C₂×C₄

yes

—

#14579135

—

C₄×D₃₁₆

—

C₂×C₄×Dic₇₉

C₂³

yes

—

#14579087

—

(C₂×D₇₉)⋊C₈

—

#14579072

D₄

yes

—

C₇₉⋊#95

—

C₂×M₁₆×C₇₉

C₂³

yes

—

C₂²×C₈×C₇₉

C₂³

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

characteristic

C₄×C₈×C₇₉

C₂×C₄

yes

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

C₂²×C₄

yes

—

C₂×D₃₁₆

—

C₂×D₃₁₆

C₂²×C₄

yes

—

C₂×C₂²⋊D₇₉

—

C₂²×Dic₇₉

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

#11929613

—

D₆₃₂

—

#11929607

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×D₄

yes

—

C₈×D₇₉

—

C₄⋊Dic₇₉

—

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

#41

yes

—

C₂²×C₄×C₇₉

C₂⁴

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²×C₄

yes

—

C₂×C₈×C₇₉

C₂²×C₄

yes

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

C₂×#41

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

C₂³×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²×D₄

yes

characteristic

C₂×C₄×C₇₉

H(5,𝔽₂)

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₄×D₄

yes

characteristic

100

C₂²×C₇₉

#540

yes

—

101

C₂×D₇₉

—

102

C₂×D₇₉

—

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

#518

yes

—

106

C₄×C₇₉

#535

yes

—

107

Dic₇₉

—

108

Dic₇₉

—

109

#22282

—

maximal, Sylow

110

C₂×C₇₉

—

111

C₂×C₇₉

#2328

yes

characteristic

112

C₂×C₇₉

#2957

yes

—

113

D₇₉

—

114

#3147

—

115

#2932

—

116

#1963

—

117

#1876

—

118

#1837

D₇₉

yes

characteristic, complemented

119

#1746

—

120

C₇₉

#22282

yes

characteristic, complemented, Sylow

121

C₂×#135

—

122

C₂×#131

—

123

#532

—

124

#495

—

125

#494

—

126

#493

—

127

#492

—

128

#435

—

158

—

129

#423

C₂×D₇₉

yes

—

130

C₂×#104

—

131

#408

—

132

C₂×#97

—

133

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

134

#376

—

135

#341

C₂×D₇₉

yes

—

136

#336

—

137

C₂×#41

—

138

#135

—

316

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×D₈

—

142

#131

—

316

—

143

C₂×M₁₆

—

158

—

144

C₂×M₁₆

C₂²×D₇₉

yes

—

145

C₂²×C₈

—

146

C₂²×C₈

—

158

—

147

C₂²×C₈

C₂²×D₇₉

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

151

#121

—

158

—

152

C₄×D₄

—

158

—

153

C₂×C₄²

—

154

C₂×C₄²

C₂²×D₇₉

yes

characteristic

155

C₄⋊C₈

—

156

#104

—

316

—

157

C₂²⋊C₈

—

158

—

158

#97

—

159

C₄×C₈

C₄×D₇₉

yes

characteristic

160

C₄×C₈

C₄×D₇₉

yes

characteristic

161

C₄×C₈

C₄×D₇₉

yes

—

162

#95

—

158

—

163

#41

—

158

—

164

#41

—

158

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

158

—

168

C₂×D₄

—

158

—

169

C₂²×C₄

—

158

—

170

C₂²×C₄

—

158

—

171

C₂²×C₄

#11929625

yes

—

172

C₂²×C₄

C₂³×D₇₉

yes

characteristic

173

Q₁₆

—

316

—

174

SD₁₆

—

316

—

175

D₈

—

316

—

176

M₁₆

—

177

M₁₆

—

316

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

316

—

181

C₂×C₈

—

182

C₂×C₈

—

158

—

183

C₂×C₈

C₂×C₄×D₇₉

yes

—

184

C₂×C₈

C₂×C₄×D₇₉

yes

—

185

C₄⋊C₄

—

158

—

186

C₂²⋊C₄

—

158

—

187

C₄²

—

158

—

188

C₄²

C₂×C₄×D₇₉

yes

characteristic

189

C₄²

C₂×C₄×D₇₉

yes

characteristic

190

C₄²

D₄×D₇₉

yes

—

191

C₂³

—

158

—

192

C₂³

C₂×#11929625

yes

characteristic

193

Q₈

—

158

—

194

D₄

—

316

—

195

D₄

—

632

—

196

D₄

—

158

—

197

C₂×C₄

—

198

C₂×C₄

—

316

—

199

C₂×C₄

—

316

—

200

C₂×C₄

—

316

—

201

C₂×C₄

—

316

—

202

C₂×C₄

—

158

—

203

C₂×C₄

#14579123

yes

—

204

C₂×C₄

#14579123

yes

—

205

C₂×C₄

C₂²×C₄×D₇₉

yes

characteristic

206

C₂×C₄

C₂×D₄×D₇₉

yes

characteristic

207

C₂×C₄

#14579207

yes

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₈

—

158

—

212

C₂²

—

213

C₂²

—

316

—

214

C₂²

—

316

—

215

C₂²

C₂×#14579123

yes

characteristic

216

C₂²

#19099169

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

316

—

220

C₄

—

632

—

221

C₄

#19099037

yes

—

222

C₄

#19099131

yes

—

223

C₂

—

224

C₂

—

632

—

225

C₂

#23766123

yes

characteristic

226

C₂

#23772316

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1837	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773828	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1837	D₇₉
hypocenter	C₇₉	#22282
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

subgroup

G/H

center

C₂×C₄

C₂×D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₇₉

Fitting

C₇₉×#1837

C₂

socle

C₂²×C₇₉

C₂×C₄×D₄

prime radical

#23773828

C₂

cosocle

C₂²×C₄×C₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

N	H ≅ G/N	type
2. #23772117	C₂	semidirect
3. #23764231	C₂	semidirect
4. #23763728	C₂	semidirect
5. #23763151	C₂	semidirect
6. C₇₉×#1837	C₂	semidirect
10. #19098947	C₄	semidirect
11. #19098943	C₄	semidirect
12. #19098940	C₄	semidirect
13. #19098936	C₄	semidirect
118. #1837	D₇₉	semidirect
120. C₇₉	#22282	semidirect

H ≅ G/N

type

2. #23772117

C₂

semidirect

3. #23764231

C₂

semidirect

4. #23763728

C₂

semidirect

5. #23763151

C₂

semidirect

6. C₇₉×#1837

C₂

semidirect

10. #19098947

C₄

semidirect

11. #19098943

C₄

semidirect

12. #19098940

C₄

semidirect

13. #19098936

C₄

semidirect

118. #1837

D₇₉

semidirect

120. C₇₉

#22282

semidirect

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

subgroup	index
#23773828	2
#23772117	2
#23764231	2
#23763728	2
#23763151	2
C₇₉×#1837	2
#22282	79

subgroup

index

C₇₉×#1837

Subgroups — #34302157

Conjugacy classes of subgroups

Complements

Maximal subgroups