Group #34181855 — subgroups

Subgroups — #34181855

Order 20224.

378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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	#23763396	C₂	1	1	yes	maximal, characteristic
2	#23761724	C₂	1	1	yes	maximal, characteristic
3	#23761303	C₂	1	2	yes	maximal
4	#23761258	C₂	1	2	yes	maximal
5	C₇₉×#2356	C₂	1	1	yes	maximal, characteristic
6	#19098616	C₂²	1	2	yes	—
7	#19098587	C₂²	1	2	yes	—
8	C₂×#14579080	—	2	1	no	—
9	#19098332	—	2	1	no	—
10	#19098289	—	2	2	no	—
11	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
12	#391×C₇₉	—	2	1	no	—
13	#387×C₇₉	—	2	2	no	—
14	#383×C₇₉	C₄	1	2	yes	—
15	#382×C₇₉	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
17	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
18	#376×C₇₉	C₄	1	2	yes	—
19	C₂×#11929608	—	2	2	no	—
20	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
21	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
22	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
23	#14579080	—	4	2	no	—
24	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
25	C₄×C₇₉⋊C₈	—	2	2	no	—
26	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
27	C₄×Q₈×C₇₉	—	2	2	no	—
28	C₄×Q₈×C₇₉	—	2	2	no	—
29	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
30	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₇₉	—	2	2	no	—
34	C₂×C₄²×C₇₉	—	2	1	no	—
35	C₂×C₄²×C₇₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
37	#95×C₇₉	—	2	2	no	—
38	#95×C₇₉	—	2	2	no	—
39	#95×C₇₉	—	2	2	no	—
40	#95×C₇₉	—	2	1	no	—
41	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
42	#95×C₇₉	C₂×C₄	1	2	yes	—
43	#95×C₇₉	C₂×C₄	1	1	yes	characteristic
44	#11929608	—	4	2	no	—
45	#11929608	—	4	2	no	—
46	C₂×C₇₉⋊C₈	—	4	2	no	—
47	C₂×C₇₉⋊C₈	—	4	2	no	—
48	C₂×Q₈×C₇₉	—	2	2	no	—
49	C₂×Q₈×C₇₉	—	2	2	no	—
50	C₂×Q₈×C₇₉	—	2	1	no	—
51	C₂×Q₈×C₇₉	—	2	1	no	—
52	C₂²×C₄×C₇₉	—	2	1	no	—
53	C₂²×C₄×C₇₉	—	2	2	no	—
54	C₂²×C₄×C₇₉	—	2	1	no	—
55	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
60	C₄⋊C₄×C₇₉	—	2	2	no	—
61	C₄⋊C₄×C₇₉	—	2	4	no	—
62	C₄⋊C₄×C₇₉	—	4	2	no	—
63	C₄⋊C₄×C₇₉	—	4	2	no	—
64	C₄²×C₇₉	—	2	2	no	—
65	C₄²×C₇₉	—	2	2	no	—
66	C₄²×C₇₉	—	4	4	no	—
67	C₄²×C₇₉	—	4	1	no	—
68	C₄²×C₇₉	—	4	1	no	—
69	C₄²×C₇₉	#41	1	2	yes	—
70	C₄²×C₇₉	#41	1	2	yes	—
71	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	Q₈×C₇₉	—	4	2	no	—
73	Q₈×C₇₉	—	4	2	no	—
74	C₂×C₄×C₇₉	—	2	2	no	—
75	C₂×C₄×C₇₉	—	2	2	no	—
76	C₂×C₄×C₇₉	—	2	2	no	—
77	C₂×C₄×C₇₉	—	2	2	no	—
78	C₂×C₄×C₇₉	—	2	2	no	—
79	C₂×C₄×C₇₉	—	4	1	no	—
80	C₂×C₄×C₇₉	—	4	1	no	—
81	C₂×C₄×C₇₉	—	4	1	no	—
82	C₂×C₄×C₇₉	—	4	1	no	—
83	C₂×C₄×C₇₉	—	4	2	no	—
84	C₂×C₄×C₇₉	—	4	2	no	—
85	C₂×C₄×C₇₉	—	4	1	no	—
86	C₂×C₄×C₇₉	—	4	1	no	—
87	C₂×C₄×C₇₉	—	4	2	no	—
88	C₂×C₄×C₇₉	—	4	2	no	—
89	C₂×C₄×C₇₉	—	4	1	no	—
90	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
91	C₂×C₄×C₇₉	#117	1	1	yes	characteristic
92	C₂×C₄×C₇₉	#123	1	2	yes	—
93	C₂×C₄×C₇₉	#123	1	2	yes	—
94	C₂×C₄×C₇₉	#135	1	2	yes	—
95	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
97	C₇₉⋊C₈	—	8	2	no	—
98	C₇₉⋊C₈	—	8	2	no	—
99	C₂²×C₇₉	—	2	1	no	—
100	C₂²×C₇₉	—	2	1	no	—
101	C₂²×C₇₉	#381	1	1	yes	characteristic
102	C₂²×C₇₉	#416	1	1	yes	characteristic
103	C₂²×C₇₉	#417	1	1	yes	characteristic
104	C₄×C₇₉	—	2	2	no	—
105	C₄×C₇₉	—	2	1	no	—
106	C₄×C₇₉	—	2	1	no	—
107	C₄×C₇₉	—	4	2	no	—
108	C₄×C₇₉	—	4	2	no	—
109	C₄×C₇₉	—	4	2	no	—
110	C₄×C₇₉	—	8	1	no	—
111	C₄×C₇₉	—	8	2	no	—
112	C₄×C₇₉	#482	1	2	yes	—
113	C₄×C₇₉	#485	1	2	yes	—
114	#8768	—	79	1	no	maximal, Sylow
115	C₂×C₇₉	—	2	1	no	—
116	C₂×C₇₉	—	2	1	no	—
117	C₂×C₇₉	#1825	1	1	yes	characteristic
118	C₂×C₇₉	#1827	1	1	yes	characteristic
119	C₂×C₇₉	#1830	1	1	yes	characteristic
120	#2356	D₇₉	1	1	yes	characteristic
121	#1801	—	79	1	no	—
122	#1461	—	79	1	no	—
123	#1303	—	79	2	no	—
124	#1286	—	79	2	no	—
125	C₇₉	#8768	1	1	yes	characteristic, complemented, Sylow
126	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
127	#431	—	79	2	no	—
128	#423	—	79	2	no	—
129	C₂×#101	—	158	1	no	—
130	#391	—	2	1	no	—
131	#387	—	2	2	no	—
132	#383	Dic₇₉	1	2	yes	—
133	#382	C₂×D₇₉	1	1	yes	characteristic
134	C₄×C₄⋊C₄	—	2	1	no	—
135	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
136	#376	Dic₇₉	1	2	yes	—
137	#343	—	158	1	no	—
138	#324	—	158	2	no	—
139	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
140	C₂×M₁₆	—	158	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	—	2	1	no	—
145	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
146	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
147	C₂×C₄²	—	2	2	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	C₂×Dic₇₉	1	2	yes	—
150	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
151	C₄⋊C₈	—	158	2	no	—
152	C₄⋊C₈	—	158	2	no	—
153	C₄⋊C₈	—	158	2	no	—
154	#101	—	316	2	no	—
155	C₂²⋊C₈	—	158	2	no	—
156	C₄×C₈	—	158	2	no	—
157	#95	—	2	2	no	—
158	#95	—	2	2	no	—
159	#95	—	2	2	no	—
160	#95	—	2	1	no	—
161	#95	C₂×Dic₇₉	1	1	yes	characteristic
162	#95	C₂×Dic₇₉	1	2	yes	—
163	#95	C₂×Dic₇₉	1	1	yes	characteristic
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	—	2	1	no	—
168	C₂²×C₄	—	2	1	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
172	C₂²×C₄	C₂²⋊Dic₇₉	1	2	yes	—
173	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
176	M₁₆	—	316	2	no	—
177	M₁₆	—	316	2	no	—
178	C₂×C₈	—	316	2	no	—
179	C₂×C₈	—	316	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	4	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	4	4	no	—
187	C₄²	—	4	1	no	—
188	C₄²	—	4	1	no	—
189	C₄²	#11929624	1	2	yes	—
190	C₄²	#11929624	1	2	yes	—
191	C₂³	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
192	Q₈	—	4	2	no	—
193	Q₈	—	4	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	#14579120	1	1	yes	characteristic
211	C₂×C₄	#14579120	1	1	yes	characteristic
212	C₂×C₄	#14579144	1	2	yes	—
213	C₂×C₄	#14579144	1	2	yes	—
214	C₂×C₄	#14579181	1	2	yes	—
215	C₂×C₄	#14579186	1	1	yes	characteristic
216	C₂×C₄	#14579191	1	1	yes	characteristic
217	C₈	—	632	2	no	—
218	C₈	—	632	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#19098426	1	1	yes	characteristic
222	C₂²	#19098559	1	1	yes	characteristic
223	C₂²	#19098564	1	1	yes	characteristic
224	C₄	—	2	2	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	4	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	8	1	no	—
231	C₄	—	8	2	no	—
232	C₄	#19098887	1	2	yes	—
233	C₄	#19098904	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#23763495	1	1	yes	characteristic
237	C₂	#23763504	1	1	yes	characteristic
238	C₂	#23763514	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23763396

C₂

yes

maximal, characteristic

#23761724

C₂

yes

maximal, characteristic

#23761303

C₂

yes

maximal

#23761258

C₂

yes

maximal

C₇₉×#2356

C₂

yes

maximal, characteristic

#19098616

C₂²

yes

—

#19098587

C₂²

yes

—

C₂×#14579080

—

#19098332

—

#19098289

—

C₂×C₄×Q₈×C₇₉

C₂²

yes

characteristic

#391×C₇₉

—

#387×C₇₉

—

#383×C₇₉

C₄

yes

—

#382×C₇₉

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₇₉

—

C₄×C₄⋊C₄×C₇₉

C₂²

yes

characteristic

#376×C₇₉

C₄

yes

—

C₂×#11929608

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

#14579080

—

C₂²⋊(C₇₉⋊C₈)

—

C₄×C₇₉⋊C₈

—

C₂²×Q₈×C₇₉

D₄

yes

characteristic

C₄×Q₈×C₇₉

—

C₄×Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

—

C₂×C₄⋊C₄×C₇₉

D₄

yes

characteristic

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

—

C₂×C₄²×C₇₉

C₂×C₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

—

#95×C₇₉

C₂×C₄

yes

characteristic

#95×C₇₉

C₂×C₄

yes

—

#95×C₇₉

C₂×C₄

yes

characteristic

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

#41

yes

—

C₄²×C₇₉

#41

yes

—

C₂³×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×C₄×C₇₉

#123

yes

—

C₂×C₄×C₇₉

#135

yes

—

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

100

C₂²×C₇₉

—

101

C₂²×C₇₉

#381

yes

characteristic

102

C₂²×C₇₉

#416

yes

characteristic

103

C₂²×C₇₉

#417

yes

characteristic

104

C₄×C₇₉

—

105

C₄×C₇₉

—

106

C₄×C₇₉

—

107

C₄×C₇₉

—

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#482

yes

—

113

C₄×C₇₉

#485

yes

—

114

#8768

—

maximal, Sylow

115

C₂×C₇₉

—

116

C₂×C₇₉

—

117

C₂×C₇₉

#1825

yes

characteristic

118

C₂×C₇₉

#1827

yes

characteristic

119

C₂×C₇₉

#1830

yes

characteristic

120

#2356

D₇₉

yes

characteristic

121

#1801

—

122

#1461

—

123

#1303

—

124

#1286

—

125

C₇₉

#8768

yes

characteristic, complemented, Sylow

126

C₂×C₄×Q₈

C₂×D₇₉

yes

characteristic

127

#431

—

128

#423

—

129

C₂×#101

—

158

—

130

#391

—

131

#387

—

132

#383

Dic₇₉

yes

—

133

#382

C₂×D₇₉

yes

characteristic

134

C₄×C₄⋊C₄

—

135

C₄×C₄⋊C₄

C₂×D₇₉

yes

characteristic

136

#376

Dic₇₉

yes

—

137

#343

—

158

—

138

#324

—

158

—

139

C₂²×Q₈

C₂²⋊D₇₉

yes

characteristic

140

C₂×M₁₆

—

158

—

141

C₄×Q₈

—

142

C₄×Q₈

—

143

C₂×C₄⋊C₄

—

144

C₂×C₄⋊C₄

—

145

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

—

146

C₂×C₄⋊C₄

C₂²⋊D₇₉

yes

characteristic

147

C₂×C₄²

—

148

C₂×C₄²

—

149

C₂×C₄²

C₂×Dic₇₉

yes

—

150

C₂×C₄²

C₂²×D₇₉

yes

characteristic

151

C₄⋊C₈

—

158

—

152

C₄⋊C₈

—

158

—

153

C₄⋊C₈

—

158

—

154

#101

—

316

—

155

C₂²⋊C₈

—

158

—

156

C₄×C₈

—

158

—

157

#95

—

158

#95

—

159

#95

—

160

#95

—

161

#95

C₂×Dic₇₉

yes

characteristic

162

#95

C₂×Dic₇₉

yes

—

163

#95

C₂×Dic₇₉

yes

characteristic

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

172

C₂²×C₄

C₂²⋊Dic₇₉

yes

—

173

C₂²×C₄

C₂²×Dic₇₉

yes

characteristic

174

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

175

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

176

M₁₆

—

316

—

177

M₁₆

—

316

—

178

C₂×C₈

—

316

—

179

C₂×C₈

—

316

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

189

C₄²

#11929624

yes

—

190

C₄²

#11929624

yes

—

191

C₂³

C₂×C₂²⋊Dic₇₉

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#14579120

yes

characteristic

211

C₂×C₄

#14579120

yes

characteristic

212

C₂×C₄

#14579144

yes

—

213

C₂×C₄

#14579144

yes

—

214

C₂×C₄

#14579181

yes

—

215

C₂×C₄

#14579186

yes

characteristic

216

C₂×C₄

#14579191

yes

characteristic

217

C₈

—

632

—

218

C₈

—

632

—

219

C₂²

—

220

C₂²

—

221

C₂²

#19098426

yes

characteristic

222

C₂²

#19098559

yes

characteristic

223

C₂²

#19098564

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

#19098887

yes

—

233

C₄

#19098904

yes

—

234

C₂

—

235

C₂

—

236

C₂

#23763495

yes

characteristic

237

C₂

#23763504

yes

characteristic

238

C₂

#23763514

yes

characteristic

	subgroup	G/H
center	C₂²	#19098426
commutator	C₂²×C₄×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#2356	C₂
socle	C₂²×C₇₉	#381
prime radical	C₂³×C₇₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#2356	D₇₉
hypocenter	C₇₉	#8768
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2356

subgroup

G/H

center

C₂²

#19098426

commutator

C₂²×C₄×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#2356

C₂

socle

C₂²×C₇₉

#381

prime radical

C₂³×C₇₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2356

N	H ≅ G/N	type
125. C₇₉	#8768	semidirect

H ≅ G/N

type

125. C₇₉

#8768

semidirect

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

subgroup	index
#23763396	2
#23761724	2
#23761303	2
#23761258	2
C₇₉×#2356	2
#8768	79

subgroup

index

C₇₉×#2356

Subgroups — #34181855

Conjugacy classes of subgroups

Complements

Maximal subgroups