Group #34181262 — subgroups

Subgroups — #34181262

Order 20224.

320 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 103 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	#23772334	C₂	1	1	yes	maximal, characteristic
2	#23762163	C₂	1	1	yes	maximal, characteristic
3	#23762037	C₂	1	2	yes	maximal
4	#23761310	C₂	1	2	yes	maximal
5	C₇₉×#1568	C₂	1	1	yes	maximal, characteristic
6	#19099120	C₂²	1	1	yes	characteristic
7	#19098693	—	2	1	no	—
8	#19098693	—	2	1	no	—
9	C₈×Dic₁₅₈	—	2	1	no	—
10	C₈×Dic₁₅₈	—	2	1	no	—
11	#19098620	C₂²	1	2	yes	—
12	#19098589	C₄	1	2	yes	—
13	#19098587	C₂²	1	1	yes	characteristic
14	#19098518	C₄	1	2	yes	—
15	#19098316	—	2	1	no	—
16	#19098314	—	2	1	no	—
17	#19098304	—	2	4	no	—
18	#432×C₇₉	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	#335×C₇₉	—	2	1	no	—
21	#334×C₇₉	—	2	1	no	—
22	C₂×#11929608	C₂×C₄	1	2	yes	—
23	#14579161	Q₈	1	1	yes	characteristic
24	#14579161	Q₈	1	1	yes	characteristic
25	#14579153	D₄	1	2	yes	—
26	#14579140	—	2	1	no	—
27	#14579140	—	2	1	no	—
28	C₄×Dic₁₅₈	—	2	1	no	—
29	C₄×Dic₁₅₈	—	2	1	no	—
30	#14579120	C₂×C₄	1	2	yes	—
31	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
32	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
33	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
34	Dic₇₉⋊C₈	—	2	2	no	—
35	Dic₇₉⋊C₈	—	2	2	no	—
36	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
37	#14579072	—	2	2	no	—
38	#14579071	—	2	2	no	—
39	C₈×Dic₇₉	—	2	2	no	—
40	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₇₉	—	2	2	no	—
44	C₂²⋊C₈×C₇₉	—	2	2	no	—
45	#97×C₇₉	—	2	2	no	—
46	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
47	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
48	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
49	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
50	C₂×Dic₁₅₈	—	2	1	no	—
51	C₂×Dic₁₅₈	—	2	1	no	—
52	#11929608	—	4	2	no	—
53	C₂×C₇₉⋊C₈	—	2	2	no	—
54	C₂×C₇₉⋊C₈	—	4	2	no	—
55	C₄⋊Dic₇₉	—	2	1	no	—
56	C₄⋊Dic₇₉	—	2	1	no	—
57	C₄⋊Dic₇₉	C₄⋊C₄	1	2	yes	—
58	C₄⋊Dic₇₉	C₄⋊C₄	1	2	yes	—
59	Dic₇₉⋊C₄	—	2	2	no	—
60	Dic₇₉⋊C₄	—	2	2	no	—
61	C₂²⋊Dic₇₉	—	2	2	no	—
62	C₄×Dic₇₉	—	2	2	no	—
63	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
65	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
66	C₂×C₈×C₇₉	—	2	2	no	—
67	C₂×C₈×C₇₉	—	4	1	no	—
68	C₂×C₈×C₇₉	—	4	2	no	—
69	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
77	C₂³×C₇₉	#117	1	1	yes	characteristic
78	C₂×C₄×C₇₉	—	2	1	no	—
79	C₂×C₄×C₇₉	—	2	1	no	—
80	C₂×C₄×C₇₉	—	4	1	no	—
81	C₂×C₄×C₇₉	—	4	1	no	—
82	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
85	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
86	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×Dic₇₉	—	2	2	no	—
89	C₂×Dic₇₉	—	2	2	no	—
90	Dic₁₅₈	—	4	2	no	—
91	Dic₁₅₈	—	4	2	no	—
92	C₈×C₇₉	—	2	1	no	—
93	C₈×C₇₉	—	2	1	no	—
94	C₈×C₇₉	—	2	1	no	—
95	C₈×C₇₉	—	8	2	no	—
96	C₈×C₇₉	#101	1	2	yes	—
97	C₇₉⋊C₈	—	4	2	no	—
98	C₇₉⋊C₈	—	8	2	no	—
99	C₂²×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	—	2	1	no	—
102	C₂²×C₇₉	#380	1	1	yes	characteristic
103	C₄×C₇₉	—	2	1	no	—
104	C₄×C₇₉	—	2	1	no	—
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	2	1	no	—
108	C₄×C₇₉	C₂×#101	1	1	yes	characteristic
109	C₄×C₇₉	#413	1	1	yes	characteristic
110	Dic₇₉	—	4	2	no	—
111	Dic₇₉	—	4	2	no	—
112	#8631	—	79	1	no	maximal, Sylow
113	C₂×C₇₉	—	4	1	no	—
114	C₂×C₇₉	#1801	1	1	yes	characteristic
115	C₂×C₇₉	#1814	1	1	yes	characteristic
116	C₂×C₇₉	#1814	1	1	yes	characteristic
117	#2960	—	79	1	no	—
118	#1568	—	79	1	no	—
119	#1568	D₇₉	1	1	yes	characteristic
120	#1537	—	79	2	no	—
121	#1307	—	79	2	no	—
122	C₇₉	#8631	1	1	yes	characteristic, complemented, Sylow
123	#533	—	79	1	no	—
124	#446	—	158	1	no	—
125	#446	—	158	1	no	—
126	C₈×Q₈	—	158	1	no	—
127	C₈×Q₈	—	158	1	no	—
128	#432	—	79	2	no	—
129	#432	C₂×D₇₉	1	2	yes	—
130	#424	—	79	2	no	—
131	#423	—	79	1	no	—
132	#405	—	79	2	no	—
133	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
134	#335	—	2	1	no	—
135	#335	—	158	1	no	—
136	#334	—	2	1	no	—
137	#334	—	158	1	no	—
138	#330	—	158	4	no	—
139	C₂×M₁₆	—	79	2	no	—
140	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
141	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
142	C₄⋊Q₈	—	79	1	no	—
143	C₄⋊Q₈	—	79	1	no	—
144	#125	—	79	2	no	—
145	C₂²⋊Q₈	—	158	1	no	—
146	C₂²⋊Q₈	—	158	1	no	—
147	C₄×Q₈	—	158	1	no	—
148	C₄×Q₈	—	158	1	no	—
149	#117	—	79	2	no	—
150	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	158	2	no	—
153	C₄⋊C₈	—	158	2	no	—
154	C₄⋊C₈	—	158	1	no	—
155	C₄⋊C₈	—	158	2	no	—
156	C₄⋊C₈	—	158	1	no	—
157	C₂²⋊C₈	—	2	2	no	—
158	C₂²⋊C₈	—	158	2	no	—
159	#97	—	2	2	no	—
160	#97	—	158	2	no	—
161	#97	—	158	2	no	—
162	C₄×C₈	—	158	2	no	—
163	C₄×C₈	D₃₁₆	1	1	yes	characteristic
164	C₄×C₈	D₃₁₆	1	1	yes	characteristic
165	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
167	C₂×Q₈	—	158	1	no	—
168	C₂×Q₈	—	158	1	no	—
169	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
170	C₂²×C₄	#11929623	1	1	yes	characteristic
171	C₂²×C₄	#11929625	1	1	yes	characteristic
172	M₁₆	—	316	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	316	2	no	—
177	C₂×C₈	—	158	2	no	—
178	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
179	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
180	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
181	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄	—	79	2	no	—
183	C₄⋊C₄	—	79	2	no	—
184	C₄⋊C₄	—	158	2	no	—
185	C₄⋊C₄	—	158	2	no	—
186	C₄⋊C₄	—	158	1	no	—
187	C₄⋊C₄	—	158	1	no	—
188	C₂²⋊C₄	—	158	2	no	—
189	C₄²	—	158	2	no	—
190	C₄²	D₄×D₇₉	1	1	yes	characteristic
191	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
192	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
193	C₄²	Q₈×D₇₉	1	1	yes	characteristic
194	C₂³	#14579119	1	1	yes	characteristic
195	Q₈	—	316	2	no	—
196	Q₈	—	316	2	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	158	2	no	—
202	C₂×C₄	—	158	2	no	—
203	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
205	C₂×C₄	#14579132	1	1	yes	characteristic
206	C₂×C₄	#14579136	1	1	yes	characteristic
207	C₂×C₄	#14579137	1	1	yes	characteristic
208	C₂×C₄	#14579141	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	8	2	no	—
213	C₈	—	316	2	no	—
214	C₈	—	632	2	no	—
215	C₈	#14579079	1	2	yes	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	#19098420	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	2	1	no	—
225	C₄	—	316	2	no	—
226	C₄	—	316	2	no	—
227	C₄	C₂×#14579079	1	1	yes	characteristic
228	C₄	#19098545	1	1	yes	characteristic
229	C₂	—	4	1	no	—
230	C₂	#23763393	1	1	yes	characteristic
231	C₂	#23763451	1	1	yes	characteristic
232	C₂	#23763455	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772334

C₂

yes

maximal, characteristic

#23762163

C₂

yes

maximal, characteristic

#23762037

C₂

yes

maximal

#23761310

C₂

yes

maximal

C₇₉×#1568

C₂

yes

maximal, characteristic

#19099120

C₂²

yes

characteristic

#19098693

—

#19098693

—

C₈×Dic₁₅₈

—

C₈×Dic₁₅₈

—

#19098620

C₂²

yes

—

#19098589

C₄

yes

—

#19098587

C₂²

yes

characteristic

#19098518

C₄

yes

—

#19098316

—

#19098314

—

#19098304

—

#432×C₇₉

C₂²

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#335×C₇₉

—

#334×C₇₉

—

C₂×#11929608

C₂×C₄

yes

—

#14579161

Q₈

yes

characteristic

#14579161

Q₈

yes

characteristic

#14579153

D₄

yes

—

#14579140

—

#14579140

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

#14579120

C₂×C₄

yes

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

Dic₇₉⋊C₈

—

Dic₇₉⋊C₈

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

#14579071

—

C₈×Dic₇₉

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²⋊C₈×C₇₉

—

#97×C₇₉

—

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

D₄

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₄⋊C₄

yes

—

C₄⋊Dic₇₉

C₄⋊C₄

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

C₂²×C₄×C₇₉

yes

C₂²×C₄×C₇₉

yes

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×Q₈

yes

characteristic

C₂³×C₇₉

#117

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊Q₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#101

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

—

102

C₂²×C₇₉

#380

yes

characteristic

103

C₄×C₇₉

—

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

C₂×#101

yes

characteristic

109

C₄×C₇₉

#413

yes

characteristic

110

Dic₇₉

—

111

Dic₇₉

—

112

#8631

—

maximal, Sylow

113

C₂×C₇₉

—

114

C₂×C₇₉

#1801

yes

characteristic

115

C₂×C₇₉

#1814

yes

characteristic

116

C₂×C₇₉

#1814

yes

characteristic

117

#2960

—

118

#1568

—

119

#1568

D₇₉

yes

characteristic

120

#1537

—

121

#1307

—

122

C₇₉

#8631

yes

characteristic, complemented, Sylow

123

#533

—

124

#446

—

158

—

125

#446

—

158

—

126

C₈×Q₈

—

158

—

127

C₈×Q₈

—

158

—

128

#432

—

129

#432

C₂×D₇₉

yes

—

130

#424

—

131

#423

—

132

#405

—

133

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

134

#335

—

135

#335

—

158

—

136

#334

—

137

#334

—

158

—

138

#330

—

158

—

139

C₂×M₁₆

—

140

C₂²×C₈

C₄×D₇₉

yes

characteristic

141

C₂²×C₈

C₄×D₇₉

yes

characteristic

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

#125

—

145

C₂²⋊Q₈

—

158

—

146

C₂²⋊Q₈

—

158

—

147

C₄×Q₈

—

158

—

148

C₄×Q₈

—

158

—

149

#117

—

150

C₂×C₄²

C₂²×D₇₉

yes

characteristic

151

C₄⋊C₈

—

152

C₄⋊C₈

—

158

—

153

C₄⋊C₈

—

158

—

154

C₄⋊C₈

—

158

—

155

C₄⋊C₈

—

158

—

156

C₄⋊C₈

—

158

—

157

C₂²⋊C₈

—

158

C₂²⋊C₈

—

158

—

159

#97

—

160

#97

—

158

—

161

#97

—

158

—

162

C₄×C₈

—

158

—

163

C₄×C₈

D₃₁₆

yes

characteristic

164

C₄×C₈

D₃₁₆

yes

characteristic

165

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

166

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

167

C₂×Q₈

—

158

—

168

C₂×Q₈

—

158

—

169

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

170

C₂²×C₄

#11929623

yes

characteristic

171

C₂²×C₄

#11929625

yes

characteristic

172

M₁₆

—

316

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

316

—

177

C₂×C₈

—

158

—

178

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

179

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

180

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

181

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

158

—

185

C₄⋊C₄

—

158

—

186

C₄⋊C₄

—

158

—

187

C₄⋊C₄

—

158

—

188

C₂²⋊C₄

—

158

—

189

C₄²

—

158

—

190

C₄²

D₄×D₇₉

yes

characteristic

191

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

192

C₄²

C₂×D₃₁₆

yes

characteristic

193

C₄²

Q₈×D₇₉

yes

characteristic

194

C₂³

#14579119

yes

characteristic

195

Q₈

—

316

—

196

Q₈

—

316

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

158

—

202

C₂×C₄

—

158

—

203

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

204

C₂×C₄

C₄⋊C₄×D₇₉

yes

characteristic

205

C₂×C₄

#14579132

yes

characteristic

206

C₂×C₄

#14579136

yes

characteristic

207

C₂×C₄

#14579137

yes

characteristic

208

C₂×C₄

#14579141

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

213

C₈

—

316

—

214

C₈

—

632

—

215

C₈

#14579079

yes

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

219

C₂²

#19098420

yes

characteristic

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

316

—

226

C₄

—

316

—

227

C₄

C₂×#14579079

yes

characteristic

228

C₄

#19098545

yes

characteristic

229

C₂

—

230

C₂

#23763393

yes

characteristic

231

C₂

#23763451

yes

characteristic

232

C₂

#23763455

yes

characteristic

	subgroup	G/H
center	C₂²	#19098420
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1568	C₂
socle	C₂²×C₇₉	#380
prime radical	C₂³×C₇₉	#117
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1568	D₇₉
hypocenter	C₇₉	#8631
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

subgroup

G/H

center

C₂²

#19098420

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#1568

C₂

C₂²×C₇₉

C₂³×C₇₉

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

N	H ≅ G/N	type
122. C₇₉	#8631	semidirect

H ≅ G/N

type

122. C₇₉

#8631

semidirect

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

subgroup	index
#23772334	2
#23762163	2
#23762037	2
#23761310	2
C₇₉×#1568	2
#8631	79

subgroup

index

C₇₉×#1568

Subgroups — #34181262

Conjugacy classes of subgroups

Complements

Maximal subgroups