Group #34189262 — subgroups

Subgroups — #34189262

Order 20224.

476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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	#23773435	C₂	1	2	yes	maximal
2	#23764340	C₂	1	1	yes	maximal, characteristic
3	#23761803	C₂	1	2	yes	maximal
4	#23761231	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#3162	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	#19098896	—	2	2	no	—
8	#19098855	—	2	2	no	—
9	#19098770	—	2	2	no	—
10	#19098718	—	2	2	no	—
11	C₄×#11929614	—	2	4	no	—
12	#19098616	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	#19098317	—	2	2	no	—
15	Q₈⋊(C₇₉⋊C₈)	—	2	4	no	—
16	#533×C₇₉	C₂²	1	2	yes	—
17	#501×C₇₉	—	2	2	no	—
18	#501×C₇₉	—	2	2	no	—
19	#427×C₇₉	—	2	2	no	—
20	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
21	C₂²×Dic₁₅₈	D₄	1	1	yes	characteristic
22	C₂×#11929614	—	2	4	no	—
23	C₂²×C₇₉⋊C₈	—	2	1	no	—
24	C₄×Dic₁₅₈	—	2	2	no	—
25	C₄×Dic₁₅₈	—	2	2	no	—
26	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
27	C₂×Dic₇₉⋊C₄	—	2	1	no	—
28	C₂×C₄×Dic₇₉	—	2	1	no	—
29	#14579094	—	2	4	no	—
30	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
32	#14579085	—	2	4	no	—
33	#14579084	—	2	4	no	—
34	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
35	C₄×C₇₉⋊C₈	D₄	1	4	yes	—
36	C₂²×C₈×C₇₉	D₄	1	2	yes	—
37	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
38	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
39	#125×C₇₉	—	2	2	no	—
40	C₂²⋊Q₈×C₇₉	—	2	2	no	—
41	C₂²⋊Q₈×C₇₉	—	2	2	no	—
42	C₄×Q₈×C₇₉	—	2	2	no	—
43	C₄×Q₈×C₇₉	—	2	2	no	—
44	#117×C₇₉	—	2	2	no	—
45	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
46	#107×C₇₉	—	2	2	no	—
47	#107×C₇₉	—	2	2	no	—
48	#106×C₇₉	—	2	4	no	—
49	#97×C₇₉	—	2	2	no	—
50	C₂×Dic₁₅₈	—	2	2	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂²×Dic₇₉	—	2	1	no	—
53	C₂²×Dic₇₉	—	2	1	no	—
54	#11929614	—	4	8	no	—
55	C₂×C₇₉⋊C₈	—	2	4	no	—
56	C₂×C₇₉⋊C₈	—	4	1	no	—
57	C₂×C₇₉⋊C₈	—	4	2	no	—
58	C₄⋊Dic₇₉	—	2	2	no	—
59	Dic₇₉⋊C₄	—	4	2	no	—
60	C₄×Dic₇₉	—	4	1	no	—
61	C₄×Dic₇₉	—	4	1	no	—
62	C₂×Q₈×C₇₉	—	2	2	no	—
63	C₂×Q₈×C₇₉	—	2	2	no	—
64	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
67	C₂×C₈×C₇₉	—	2	2	no	—
68	C₂×C₈×C₇₉	—	2	2	no	—
69	C₂×C₈×C₇₉	Q₁₆	1	4	yes	complemented
70	C₄⋊C₄×C₇₉	—	2	2	no	—
71	C₄⋊C₄×C₇₉	—	2	2	no	—
72	C₄⋊C₄×C₇₉	—	2	2	no	—
73	C₄⋊C₄×C₇₉	—	2	2	no	—
74	C₄⋊C₄×C₇₉	—	4	2	no	—
75	C₄⋊C₄×C₇₉	—	4	2	no	—
76	C₂²⋊C₄×C₇₉	—	4	2	no	—
77	C₄²×C₇₉	—	4	2	no	—
78	C₄²×C₇₉	C₂×D₄	1	2	yes	—
79	C₄²×C₇₉	C₂×D₄	1	2	yes	—
80	C₂³×C₇₉	#121	1	1	yes	characteristic
81	Q₈×C₇₉	—	4	4	no	—
82	Q₈×C₇₉	—	4	4	no	—
83	C₂×C₄×C₇₉	—	4	1	no	—
84	C₂×C₄×C₇₉	—	4	1	no	—
85	C₂×C₄×C₇₉	—	4	2	no	—
86	C₂×C₄×C₇₉	—	4	2	no	—
87	C₂×C₄×C₇₉	#120	1	2	yes	—
88	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
89	C₂×C₄×C₇₉	#121	1	2	yes	—
90	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
91	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
92	C₂×C₄×C₇₉	#137	1	2	yes	—
93	C₂×Dic₇₉	—	2	2	no	—
94	C₂×Dic₇₉	—	4	1	no	—
95	C₂×Dic₇₉	—	4	1	no	—
96	C₂×Dic₇₉	—	4	2	no	—
97	C₂×Dic₇₉	—	4	1	no	—
98	Dic₁₅₈	—	2	4	no	—
99	Dic₁₅₈	—	4	2	no	—
100	C₈×C₇₉	—	2	4	no	—
101	C₇₉⋊C₈	—	4	4	no	—
102	C₇₉⋊C₈	—	8	1	no	—
103	C₂²×C₇₉	—	2	1	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	#392	1	1	yes	characteristic
106	C₂²×C₇₉	#462	1	2	yes	—
107	C₄×C₇₉	—	2	2	no	—
108	C₄×C₇₉	—	2	2	no	—
109	C₄×C₇₉	—	8	2	no	—
110	C₄×C₇₉	—	8	2	no	—
111	C₄×C₇₉	#451	1	2	yes	—
112	C₄×C₇₉	#494	1	1	yes	characteristic
113	C₄×C₇₉	#497	1	1	yes	characteristic
114	Dic₇₉	—	4	2	no	—
115	Dic₇₉	—	8	1	no	—
116	#10037	—	79	1	no	maximal, Sylow
117	C₂×C₇₉	—	2	2	no	—
118	C₂×C₇₉	#2010	1	1	yes	characteristic
119	C₂×C₇₉	#2016	1	1	yes	characteristic
120	C₂×C₇₉	#2017	1	1	yes	characteristic
121	#3162	D₇₉	1	1	yes	characteristic
122	#3104	—	79	2	no	—
123	#1985	—	79	1	no	—
124	#1481	—	79	2	no	—
125	#1275	—	79	1	no	—
126	C₇₉	#10037	1	1	yes	characteristic, complemented, Sylow
127	#533	C₂×D₇₉	1	2	yes	—
128	C₂×C₄×Q₈	—	79	1	no	—
129	#501	—	2	2	no	—
130	#501	—	2	2	no	—
131	#484	—	158	2	no	—
132	#477	—	158	2	no	—
133	#462	—	158	2	no	—
134	#451	—	158	2	no	—
135	C₄×Q₁₆	—	158	4	no	—
136	#431	—	79	2	no	—
137	#427	—	2	2	no	—
138	C₂×C₄⋊C₈	—	79	1	no	—
139	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
140	#336	—	158	2	no	—
141	Q₈⋊C₈	—	158	4	no	—
142	C₂²×Q₈	—	79	1	no	—
143	C₂×Q₁₆	—	158	4	no	—
144	C₂²×C₈	—	158	1	no	—
145	C₂²×C₈	C₂²⋊D₇₉	1	2	yes	—
146	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
147	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
148	#125	—	2	2	no	—
149	C₂²⋊Q₈	—	2	2	no	—
150	C₂²⋊Q₈	—	2	2	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₄×Q₈	—	2	2	no	—
153	C₄×Q₈	—	158	2	no	—
154	C₄×Q₈	—	158	2	no	—
155	#117	—	2	2	no	—
156	C₂×C₄⋊C₄	—	79	1	no	—
157	C₂×C₄⋊C₄	—	158	1	no	—
158	C₂×C₄²	—	158	1	no	—
159	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
160	#107	—	2	2	no	—
161	#107	—	2	2	no	—
162	#107	—	158	4	no	—
163	#106	—	2	4	no	—
164	C₄⋊C₈	—	158	2	no	—
165	C₄⋊C₈	—	158	2	no	—
166	#103	—	158	4	no	—
167	#103	—	158	4	no	—
168	C₂²⋊C₈	—	158	2	no	—
169	#97	—	2	2	no	—
170	C₄×C₈	—	79	4	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	316	2	no	—
174	C₂×Q₈	—	158	2	no	—
175	C₂²×C₄	—	158	1	no	—
176	C₂²×C₄	—	158	1	no	—
177	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
179	C₂²×C₄	#11929623	1	1	yes	characteristic
180	Q₁₆	—	316	8	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	316	1	no	—
184	C₂×C₈	—	316	2	no	—
185	C₂×C₈	—	158	4	no	—
186	C₂×C₈	#11929614	1	4	yes	complemented
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	4	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₄⋊C₄	—	316	2	no	—
194	C₄⋊C₄	—	158	2	no	—
195	C₂²⋊C₄	—	4	2	no	—
196	C₄²	—	4	2	no	—
197	C₄²	—	316	1	no	—
198	C₄²	—	316	1	no	—
199	C₄²	D₄×D₇₉	1	2	yes	—
200	C₄²	C₂×C₂²⋊D₇₉	1	2	yes	—
201	C₂³	#14579132	1	1	yes	characteristic
202	Q₈	—	4	4	no	—
203	Q₈	—	4	4	no	—
204	Q₈	—	316	2	no	—
205	Q₈	—	158	4	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	1	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	—	316	1	no	—
211	C₂×C₄	—	316	1	no	—
212	C₂×C₄	—	316	2	no	—
213	C₂×C₄	—	316	1	no	—
214	C₂×C₄	—	158	2	no	—
215	C₂×C₄	#14579129	1	2	yes	—
216	C₂×C₄	#14579130	1	1	yes	characteristic
217	C₂×C₄	#14579133	1	2	yes	—
218	C₂×C₄	#14579157	1	1	yes	characteristic
219	C₂×C₄	C₂×#11929614	1	2	yes	—
220	C₂×C₄	#14579192	1	2	yes	—
221	C₈	—	2	4	no	—
222	C₈	—	316	4	no	—
223	C₈	—	632	1	no	—
224	C₂²	—	2	1	no	—
225	C₂²	—	2	1	no	—
226	C₂²	#19098471	1	1	yes	characteristic
227	C₂²	#19098770	1	2	yes	—
228	C₄	—	2	2	no	—
229	C₄	—	2	2	no	—
230	C₄	—	8	2	no	—
231	C₄	—	8	2	no	—
232	C₄	—	316	2	no	—
233	C₄	—	632	1	no	—
234	C₄	#19098719	1	2	yes	—
235	C₄	#19098942	1	1	yes	characteristic
236	C₄	#19098955	1	1	yes	characteristic
237	C₂	—	2	2	no	—
238	C₂	#23764464	1	1	yes	characteristic
239	C₂	#23764500	1	1	yes	characteristic
240	C₂	#23764503	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23773435

C₂

yes

maximal

#23764340

C₂

yes

maximal, characteristic

#23761803

C₂

yes

maximal

#23761231

C₂

yes

maximal, characteristic

C₇₉×#3162

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×C₄⋊(C₇₉⋊C₈)

C₂²

yes

characteristic

#19098317

—

Q₈⋊(C₇₉⋊C₈)

—

#533×C₇₉

C₂²

yes

—

#501×C₇₉

—

#501×C₇₉

—

#427×C₇₉

—

C₂×#97×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

D₄

yes

characteristic

C₂×#11929614

—

C₂²×C₇₉⋊C₈

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

C₂×C₄⋊Dic₇₉

D₄

yes

characteristic

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579094

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579085

—

#14579084

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

D₄

yes

—

C₂²×C₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

C₄⋊Q₈×C₇₉

D₄

yes

—

#125×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₂²⋊Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

#117×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#107×C₇₉

—

#107×C₇₉

—

#106×C₇₉

—

#97×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

#11929614

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

Q₁₆

yes

complemented

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂×D₄

yes

—

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

#121

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

#120

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₂×C₄×C₇₉

#127

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

100

C₈×C₇₉

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

#392

yes

characteristic

106

C₂²×C₇₉

#462

yes

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

#451

yes

—

112

C₄×C₇₉

#494

yes

characteristic

113

C₄×C₇₉

#497

yes

characteristic

114

Dic₇₉

—

115

Dic₇₉

—

116

#10037

—

maximal, Sylow

117

C₂×C₇₉

—

118

C₂×C₇₉

#2010

yes

characteristic

119

C₂×C₇₉

#2016

yes

characteristic

120

C₂×C₇₉

#2017

yes

characteristic

121

#3162

D₇₉

yes

characteristic

122

#3104

—

123

#1985

—

124

#1481

—

125

#1275

—

126

C₇₉

#10037

yes

characteristic, complemented, Sylow

127

#533

C₂×D₇₉

yes

—

128

C₂×C₄×Q₈

—

129

#501

—

130

#501

—

131

#484

—

158

—

132

#477

—

158

—

133

#462

—

158

—

134

#451

—

158

—

135

C₄×Q₁₆

—

158

—

136

#431

—

137

#427

—

138

C₂×C₄⋊C₈

—

139

C₂×#97

C₂×D₇₉

yes

characteristic

140

#336

—

158

—

141

Q₈⋊C₈

—

158

—

142

C₂²×Q₈

—

143

C₂×Q₁₆

—

158

—

144

C₂²×C₈

—

158

—

145

C₂²×C₈

C₂²⋊D₇₉

yes

—

146

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

147

C₄⋊Q₈

C₂²⋊D₇₉

yes

—

148

#125

—

149

C₂²⋊Q₈

—

150

C₂²⋊Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₄×Q₈

—

158

—

154

C₄×Q₈

—

158

—

155

#117

—

156

C₂×C₄⋊C₄

—

157

C₂×C₄⋊C₄

—

158

—

158

C₂×C₄²

—

158

—

159

C₂×C₄²

C₂²×D₇₉

yes

characteristic

160

#107

—

161

#107

—

162

#107

—

158

—

163

#106

—

164

C₄⋊C₈

—

158

—

165

C₄⋊C₈

—

158

—

166

#103

—

158

—

167

#103

—

158

—

168

C₂²⋊C₈

—

158

—

169

#97

—

170

C₄×C₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

316

—

174

C₂×Q₈

—

158

—

175

C₂²×C₄

—

158

—

176

C₂²×C₄

—

158

—

177

C₂²×C₄

D₄×D₇₉

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

179

C₂²×C₄

#11929623

yes

characteristic

180

Q₁₆

—

316

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

316

—

184

C₂×C₈

—

316

—

185

C₂×C₈

—

158

—

186

C₂×C₈

#11929614

yes

complemented

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

316

—

194

C₄⋊C₄

—

158

—

195

C₂²⋊C₄

—

196

C₄²

—

197

C₄²

—

316

—

198

C₄²

—

316

—

199

C₄²

D₄×D₇₉

yes

—

200

C₄²

C₂×C₂²⋊D₇₉

yes

—

201

C₂³

#14579132

yes

characteristic

202

Q₈

—

203

Q₈

—

204

Q₈

—

316

—

205

Q₈

—

158

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

316

—

211

C₂×C₄

—

316

—

212

C₂×C₄

—

316

—

213

C₂×C₄

—

316

—

214

C₂×C₄

—

158

—

215

C₂×C₄

#14579129

yes

—

216

C₂×C₄

#14579130

yes

characteristic

217

C₂×C₄

#14579133

yes

—

218

C₂×C₄

#14579157

yes

characteristic

219

C₂×C₄

C₂×#11929614

yes

—

220

C₂×C₄

#14579192

yes

—

221

C₈

—

222

C₈

—

316

—

223

C₈

—

632

—

224

C₂²

—

225

C₂²

—

226

C₂²

#19098471

yes

characteristic

227

C₂²

#19098770

yes

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

316

—

233

C₄

—

632

—

234

C₄

#19098719

yes

—

235

C₄

#19098942

yes

characteristic

236

C₄

#19098955

yes

characteristic

237

C₂

—

238

C₂

#23764464

yes

characteristic

239

C₂

#23764500

yes

characteristic

240

C₂

#23764503

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579157
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3162	C₂
socle	C₂²×C₇₉	#392
prime radical	C₂³×C₇₉	#121
hypercenter	#3162	D₇₉
hypocenter	C₇₉	#10037
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3162

subgroup

G/H

center

C₂×C₄

#14579157

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3162

C₂

C₂²×C₇₉

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3162

N	H ≅ G/N	type
69. C₂×C₈×C₇₉	Q₁₆	semidirect
126. C₇₉	#10037	semidirect
186. C₂×C₈	#11929614	semidirect

H ≅ G/N

type

69. C₂×C₈×C₇₉

Q₁₆

semidirect

126. C₇₉

#10037

semidirect

186. C₂×C₈

#11929614

semidirect

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

subgroup	index
#23773435	2
#23764340	2
#23761803	2
#23761231	2
C₇₉×#3162	2
#10037	79

subgroup

index

C₇₉×#3162

Subgroups — #34189262

Conjugacy classes of subgroups

Complements

Maximal subgroups