Group #34192705 — subgroups

Subgroups — #34192705

Order 20224.

494 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 137 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	#23768429	C₂	1	1	yes	maximal, characteristic
2	#23764159	C₂	1	2	yes	maximal
3	#23763559	C₂	1	1	yes	maximal, characteristic
4	#23761239	C₂	1	2	yes	maximal
5	C₇₉×#1296	C₂	1	1	yes	maximal, characteristic
6	C₂×#14579160	—	2	2	no	—
7	C₂×#14579095	—	2	2	no	—
8	C₂×#14579094	—	2	2	no	—
9	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
10	#19098483	—	2	2	no	—
11	#19098459	—	2	2	no	—
12	#19098433	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₇₉	C₂²	1	2	yes	—
14	#19098326	—	2	2	no	—
15	C₂×C₄⋊C₈×C₇₉	C₂²	1	2	yes	—
16	#384×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₅₈	—	2	2	no	—
18	C₂²×C₇₉⋊C₈	—	2	1	no	—
19	#14579160	—	4	4	no	—
20	#14579160	—	4	4	no	—
21	C₂×C₄⋊Dic₇₉	—	2	2	no	—
22	C₂×C₄⋊Dic₇₉	—	2	1	no	—
23	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
24	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
25	C₂×Dic₇₉⋊C₄	—	2	4	no	—
26	C₂×C₄×Dic₇₉	—	2	2	no	—
27	#14579095	—	4	4	no	—
28	#14579094	—	4	4	no	—
29	C₄×C₇₉⋊C₈	—	2	1	no	—
30	C₄×C₇₉⋊C₈	Q₈	1	2	yes	complemented
31	C₇₉⋊#95	—	2	2	no	—
32	C₇₉⋊#95	—	2	2	no	—
33	C₂²×C₈×C₇₉	—	2	2	no	—
34	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
36	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₇₉	—	2	2	no	—
38	C₄⋊C₈×C₇₉	Q₈	1	4	yes	complemented
39	C₂×Dic₁₅₈	—	4	8	no	—
40	C₂×Dic₁₅₈	—	8	2	no	—
41	C₂²×Dic₇₉	—	2	2	no	—
42	C₂²×Dic₇₉	—	2	2	no	—
43	C₂²×Dic₇₉	—	4	1	no	—
44	C₂×C₇₉⋊C₈	—	2	2	no	—
45	C₂×C₇₉⋊C₈	—	2	2	no	—
46	C₂×C₇₉⋊C₈	—	2	2	no	—
47	C₄⋊Dic₇₉	—	2	2	no	—
48	C₄⋊Dic₇₉	—	2	2	no	—
49	C₄⋊Dic₇₉	—	4	2	no	—
50	C₄⋊Dic₇₉	—	4	2	no	—
51	C₄⋊Dic₇₉	—	4	2	no	—
52	C₄⋊Dic₇₉	D₈	1	4	yes	—
53	C₄⋊Dic₇₉	Q₁₆	1	4	yes	—
54	Dic₇₉⋊C₄	—	4	8	no	—
55	C₄×Dic₇₉	—	4	2	no	—
56	C₄×Dic₇₉	—	4	2	no	—
57	C₂²×C₄×C₇₉	—	2	2	no	—
58	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₇₉	—	2	4	no	—
61	C₂×C₈×C₇₉	—	4	2	no	—
62	C₂×C₈×C₇₉	—	4	2	no	—
63	C₄⋊C₄×C₇₉	—	4	2	no	—
64	C₄⋊C₄×C₇₉	—	4	2	no	—
65	C₄⋊C₄×C₇₉	—	4	2	no	—
66	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
67	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
68	C₄²×C₇₉	#41	1	1	yes	characteristic
69	C₂³×C₇₉	#120	1	1	yes	characteristic
70	C₂×C₄×C₇₉	—	2	1	no	—
71	C₂×C₄×C₇₉	—	2	1	no	—
72	C₂×C₄×C₇₉	—	4	4	no	—
73	C₂×C₄×C₇₉	—	4	2	no	—
74	C₂×C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
75	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
76	C₂×C₄×C₇₉	C₄⋊Q₈	1	2	yes	—
77	C₂×C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
79	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
80	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
81	C₂×C₄×C₇₉	#137	1	2	yes	—
82	C₂×Dic₇₉	—	2	4	no	—
83	C₂×Dic₇₉	—	2	4	no	—
84	C₂×Dic₇₉	—	4	2	no	—
85	C₂×Dic₇₉	—	4	2	no	—
86	C₂×Dic₇₉	—	4	2	no	—
87	C₂×Dic₇₉	—	4	2	no	—
88	C₂×Dic₇₉	—	8	2	no	—
89	C₂×Dic₇₉	—	8	1	no	—
90	Dic₁₅₈	—	8	8	no	—
91	C₈×C₇₉	—	4	4	no	—
92	C₇₉⋊C₈	—	2	4	no	—
93	C₂²×C₇₉	#395	1	1	yes	characteristic
94	C₂²×C₇₉	#447	1	2	yes	—
95	C₂²×C₇₉	#451	1	2	yes	—
96	C₂²×C₇₉	#453	1	1	yes	characteristic
97	C₂²×C₇₉	#456	1	1	yes	characteristic
98	C₄×C₇₉	—	2	1	no	—
99	C₄×C₇₉	—	2	1	no	—
100	C₄×C₇₉	—	8	2	no	—
101	C₄×C₇₉	#474	1	2	yes	—
102	C₄×C₇₉	#477	1	2	yes	—
103	C₄×C₇₉	#500	1	2	yes	—
104	C₄×C₇₉	#501	1	2	yes	—
105	Dic₇₉	—	4	4	no	—
106	Dic₇₉	—	4	4	no	—
107	Dic₇₉	—	16	1	no	—
108	#10573	—	79	1	no	maximal, Sylow
109	C₂×C₇₉	#1619	1	1	yes	characteristic
110	C₂×C₇₉	#1633	1	1	yes	characteristic
111	C₂×C₇₉	#1649	1	2	yes	—
112	C₂×C₇₉	#2057	1	2	yes	—
113	C₂×C₇₉	#2060	1	1	yes	characteristic
114	#2551	—	79	1	no	—
115	#1947	—	79	2	no	—
116	#1845	—	79	1	no	—
117	#1296	D₇₉	1	1	yes	characteristic
118	#1279	—	79	2	no	—
119	C₇₉	#10573	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₄⋊Q₈	—	158	2	no	—
121	C₂×#107	—	158	2	no	—
122	C₂×#107	—	158	2	no	—
123	C₂×C₄⋊C₈	C₂×D₇₉	1	2	yes	—
124	C₂×C₄×C₈	—	79	1	no	—
125	#395	—	158	2	no	—
126	#389	—	158	2	no	—
127	#384	—	79	1	no	—
128	#384	C₂×D₇₉	1	1	yes	characteristic
129	C₄×C₄⋊C₄	—	79	2	no	—
130	#340	—	158	2	no	—
131	C₂²×Q₈	—	158	2	no	—
132	C₂²×C₈	—	2	2	no	—
133	C₂²×C₈	—	158	1	no	—
134	C₄⋊Q₈	—	316	4	no	—
135	C₄⋊Q₈	—	316	4	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	79	2	no	—
138	C₂×C₄⋊C₄	—	79	2	no	—
139	C₂×C₄⋊C₄	—	158	4	no	—
140	C₂×C₄⋊C₄	—	158	2	no	—
141	C₂×C₄⋊C₄	—	158	1	no	—
142	C₂×C₄⋊C₄	D₃₁₆	1	2	yes	—
143	C₂×C₄²	—	158	2	no	—
144	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
145	#107	—	316	4	no	—
146	#107	—	316	4	no	—
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	Dic₁₅₈	1	4	yes	complemented
149	C₄×C₈	—	79	2	no	—
150	C₄×C₈	—	158	1	no	—
151	#95	—	158	2	no	—
152	#95	—	158	2	no	—
153	C₂×Q₈	—	316	8	no	—
154	C₂×Q₈	—	632	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	316	1	no	—
157	C₂²×C₄	—	158	2	no	—
158	C₂²×C₄	—	158	2	no	—
159	C₂²×C₄	D₄×D₇₉	1	2	yes	—
160	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	4	2	no	—
163	C₂×C₈	—	4	2	no	—
164	C₂×C₈	—	158	2	no	—
165	C₂×C₈	—	158	2	no	—
166	C₂×C₈	—	158	2	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	316	2	no	—
171	C₄⋊C₄	—	316	8	no	—
172	C₄⋊C₄	—	316	2	no	—
173	C₄⋊C₄	—	316	2	no	—
174	C₄⋊C₄	—	79	4	no	—
175	C₄⋊C₄	—	79	4	no	—
176	C₄⋊C₄	—	158	2	no	—
177	C₄⋊C₄	—	158	2	no	—
178	C₄²	—	316	2	no	—
179	C₄²	—	316	2	no	—
180	C₄²	Q₈×D₇₉	1	1	yes	characteristic
181	C₄²	C₂×Dic₁₅₈	1	2	yes	—
182	C₄²	#11929623	1	1	yes	characteristic
183	C₂³	#14579131	1	1	yes	characteristic
184	Q₈	—	632	8	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	316	2	no	—
190	C₂×C₄	—	316	2	no	—
191	C₂×C₄	—	316	2	no	—
192	C₂×C₄	—	316	2	no	—
193	C₂×C₄	—	632	2	no	—
194	C₂×C₄	—	632	1	no	—
195	C₂×C₄	—	158	4	no	—
196	C₂×C₄	—	158	4	no	—
197	C₂×C₄	#14579138	1	2	yes	—
198	C₂×C₄	#14579141	1	1	yes	characteristic
199	C₂×C₄	#14579160	1	2	yes	—
200	C₂×C₄	#14579161	1	1	yes	characteristic
201	C₂×C₄	D₈×D₇₉	1	2	yes	—
202	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
203	C₂×C₄	#14579188	1	2	yes	—
204	C₂×C₄	#14579190	1	2	yes	—
205	C₈	—	4	4	no	—
206	C₈	—	158	4	no	—
207	C₂²	#19098484	1	1	yes	characteristic
208	C₂²	#19098698	1	2	yes	—
209	C₂²	#19098720	1	2	yes	—
210	C₂²	#19098733	1	1	yes	characteristic
211	C₂²	#19098748	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	8	2	no	—
215	C₄	—	316	4	no	—
216	C₄	—	316	4	no	—
217	C₄	—	1264	1	no	—
218	C₄	#19098841	1	2	yes	—
219	C₄	#19098856	1	2	yes	—
220	C₄	#19098967	1	2	yes	—
221	C₄	#19098970	1	2	yes	—
222	C₂	#23762455	1	1	yes	characteristic
223	C₂	#23762541	1	1	yes	characteristic
224	C₂	#23762650	1	2	yes	—
225	C₂	#23764727	1	2	yes	—
226	C₂	#23764746	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23768429

C₂

yes

maximal, characteristic

#23764159

C₂

yes

maximal

#23763559

C₂

yes

maximal, characteristic

#23761239

C₂

yes

maximal

C₇₉×#1296

C₂

yes

maximal, characteristic

C₂×#14579160

—

C₂×#14579095

—

C₂×#14579094

—

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

—

C₂²

yes

characteristic

C₄×C₄⋊Dic₇₉

C₂²

yes

—

#19098326

—

C₂×C₄⋊C₈×C₇₉

C₂²

yes

—

#384×C₇₉

C₂²

yes

characteristic

C₂²×Dic₁₅₈

—

C₂²×C₇₉⋊C₈

—

#14579160

—

#14579160

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

D₄

yes

—

C₂×C₄⋊Dic₇₉

D₄

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579095

—

#14579094

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

Q₈

yes

complemented

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₄⋊C₈×C₇₉

Q₈

yes

complemented

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₈

yes

—

C₄⋊Dic₇₉

Q₁₆

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂×Q₈

yes

characteristic

C₄²×C₇₉

C₂×Q₈

yes

—

C₄²×C₇₉

yes

C₂³×C₇₉

yes

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₄⋊Q₈

yes

—

C₂×C₄×C₇₉

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₈

yes

—

C₂×C₄×C₇₉

C₂×Q₁₆

yes

—

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₇₉

#137

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#395

yes

characteristic

C₂²×C₇₉

#447

yes

—

C₂²×C₇₉

#451

yes

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₄×C₇₉

—

C₄×C₇₉

—

100

C₄×C₇₉

—

101

C₄×C₇₉

#474

yes

—

102

C₄×C₇₉

#477

yes

—

103

C₄×C₇₉

#500

yes

—

104

C₄×C₇₉

#501

yes

—

105

Dic₇₉

—

106

Dic₇₉

—

107

Dic₇₉

—

108

#10573

—

maximal, Sylow

109

C₂×C₇₉

#1619

yes

characteristic

110

C₂×C₇₉

#1633

yes

characteristic

111

C₂×C₇₉

#1649

yes

—

112

C₂×C₇₉

#2057

yes

—

113

C₂×C₇₉

#2060

yes

characteristic

114

#2551

—

115

#1947

—

116

#1845

—

117

#1296

D₇₉

yes

characteristic

118

#1279

—

119

C₇₉

#10573

yes

characteristic, complemented, Sylow

120

C₂×C₄⋊Q₈

—

158

—

121

C₂×#107

—

158

—

122

C₂×#107

—

158

—

123

C₂×C₄⋊C₈

C₂×D₇₉

yes

—

124

C₂×C₄×C₈

—

125

#395

—

158

—

126

#389

—

158

—

127

#384

—

128

#384

C₂×D₇₉

yes

characteristic

129

C₄×C₄⋊C₄

—

130

#340

—

158

—

131

C₂²×Q₈

—

158

—

132

C₂²×C₈

—

133

C₂²×C₈

—

158

—

134

C₄⋊Q₈

—

316

—

135

C₄⋊Q₈

—

316

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

158

—

140

C₂×C₄⋊C₄

—

158

—

141

C₂×C₄⋊C₄

—

158

—

142

C₂×C₄⋊C₄

D₃₁₆

yes

—

143

C₂×C₄²

—

158

—

144

C₂×C₄²

C₂²×D₇₉

yes

characteristic

145

#107

—

316

—

146

#107

—

316

—

147

C₄⋊C₈

—

148

C₄⋊C₈

Dic₁₅₈

yes

complemented

149

C₄×C₈

—

150

C₄×C₈

—

158

—

151

#95

—

158

—

152

#95

—

158

—

153

C₂×Q₈

—

316

—

154

C₂×Q₈

—

632

—

155

C₂²×C₄

—

156

C₂²×C₄

—

316

—

157

C₂²×C₄

—

158

—

158

C₂²×C₄

—

158

—

159

C₂²×C₄

D₄×D₇₉

yes

—

160

C₂²×C₄

C₂×D₃₁₆

yes

characteristic

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

158

—

165

C₂×C₈

—

158

—

166

C₂×C₈

—

158

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

316

—

171

C₄⋊C₄

—

316

—

172

C₄⋊C₄

—

316

—

173

C₄⋊C₄

—

316

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

158

—

177

C₄⋊C₄

—

158

—

178

C₄²

—

316

—

179

C₄²

—

316

—

180

C₄²

Q₈×D₇₉

yes

characteristic

181

C₄²

C₂×Dic₁₅₈

yes

—

182

C₄²

#11929623

yes

characteristic

183

C₂³

#14579131

yes

characteristic

184

Q₈

—

632

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

316

—

190

C₂×C₄

—

316

—

191

C₂×C₄

—

316

—

192

C₂×C₄

—

316

—

193

C₂×C₄

—

632

—

194

C₂×C₄

—

632

—

195

C₂×C₄

—

158

—

196

C₂×C₄

—

158

—

197

C₂×C₄

#14579138

yes

—

198

C₂×C₄

#14579141

yes

characteristic

199

C₂×C₄

#14579160

yes

—

200

C₂×C₄

#14579161

yes

characteristic

201

C₂×C₄

D₈×D₇₉

yes

—

202

C₂×C₄

Q₁₆×D₇₉

yes

—

203

C₂×C₄

#14579188

yes

—

204

C₂×C₄

#14579190

yes

—

205

C₈

—

206

C₈

—

158

—

207

C₂²

#19098484

yes

characteristic

208

C₂²

#19098698

yes

—

209

C₂²

#19098720

yes

—

210

C₂²

#19098733

yes

characteristic

211

C₂²

#19098748

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

316

—

216

C₄

—

316

—

217

C₄

—

1264

—

218

C₄

#19098841

yes

—

219

C₄

#19098856

yes

—

220

C₄

#19098967

yes

—

221

C₄

#19098970

yes

—

222

C₂

#23762455

yes

characteristic

223

C₂

#23762541

yes

characteristic

224

C₂

#23762650

yes

—

225

C₂

#23764727

yes

—

226

C₂

#23764746

yes

characteristic

	subgroup	G/H
center	C₂³	#14579131
commutator, cosocle	C₂×C₄²×C₇₉	C₂³
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1296	C₂
socle, prime radical	C₂³×C₇₉	#120
hypercenter	#1296	D₇₉
hypocenter	C₇₉	#10573
LCS	G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

subgroup

G/H

center

C₂³

#14579131

commutator, cosocle

C₂×C₄²×C₇₉

C₂³

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1296

C₂

C₂³×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

N	H ≅ G/N	type
30. C₄×C₇₉⋊C₈	Q₈	semidirect
38. C₄⋊C₈×C₇₉	Q₈	semidirect
119. C₇₉	#10573	semidirect
148. C₄⋊C₈	Dic₁₅₈	semidirect

H ≅ G/N

type

30. C₄×C₇₉⋊C₈

Q₈

semidirect

38. C₄⋊C₈×C₇₉

Q₈

semidirect

119. C₇₉

#10573

semidirect

148. C₄⋊C₈

Dic₁₅₈

semidirect

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

subgroup	index
#23768429	2
#23764159	2
#23763559	2
#23761239	2
C₇₉×#1296	2
#10573	79

subgroup

index

C₇₉×#1296

Subgroups — #34192705

Conjugacy classes of subgroups

Complements

Maximal subgroups