Group #34197621 — subgroups

Subgroups — #34197621

Order 20224.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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	#23765203	C₂	1	1	yes	maximal, characteristic
3	#23761341	C₂	1	4	yes	maximal
4	C₇₉×#2162	C₂	1	1	yes	maximal, characteristic
5	#19099120	C₄	1	1	yes	characteristic
6	#19098693	—	2	1	no	—
7	#19098693	—	2	1	no	—
8	C₈×Dic₁₅₈	—	2	1	no	—
9	C₈×Dic₁₅₈	—	2	1	no	—
10	#19098589	C₂²	1	2	yes	—
11	#19098587	C₄	1	1	yes	characteristic
12	#19098518	C₄	1	2	yes	—
13	C₄⋊(C₇₉⋊C₁₆)	—	2	1	no	—
14	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	—
15	#19098339	—	2	1	no	—
16	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₁₆×C₇₉	—	2	1	no	—
18	C₂²⋊C₁₆×C₇₉	C₂²	1	2	yes	—
19	C₄×C₁₆×C₇₉	—	2	1	no	—
20	C₂×#11929608	C₂×C₄	1	2	yes	—
21	#14579161	C₈	1	1	yes	characteristic
22	#14579161	C₈	1	1	yes	characteristic
23	#14579153	C₈	1	2	yes	—
24	#14579140	—	2	1	no	—
25	#14579140	—	2	1	no	—
26	C₄×Dic₁₅₈	—	2	1	no	—
27	C₄×Dic₁₅₈	—	2	1	no	—
28	#14579120	C₂×C₄	1	2	yes	—
29	C₂×C₇₉⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
31	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
32	Dic₇₉⋊C₈	—	2	2	no	—
33	Dic₇₉⋊C₈	—	2	2	no	—
34	#14579071	—	2	2	no	—
35	C₈×Dic₇₉	—	2	2	no	—
36	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
38	C₂×C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₆×C₇₉	—	2	2	no	—
40	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
41	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
42	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
43	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
44	C₂×Dic₁₅₈	—	2	1	no	—
45	C₂×Dic₁₅₈	—	2	1	no	—
46	#11929608	—	4	2	no	—
47	C₂×C₇₉⋊C₈	—	2	2	no	—
48	C₄⋊Dic₇₉	—	2	1	no	—
49	C₄⋊Dic₇₉	—	2	1	no	—
50	C₄⋊Dic₇₉	C₂×C₈	1	2	yes	—
51	C₄⋊Dic₇₉	C₂×C₈	1	2	yes	—
52	Dic₇₉⋊C₄	—	2	2	no	—
53	Dic₇₉⋊C₄	—	2	2	no	—
54	C₂²⋊Dic₇₉	—	2	2	no	—
55	C₄×Dic₇₉	—	2	2	no	—
56	C₇₉⋊C₁₆	—	4	2	no	—
57	C₂²×C₄×C₇₉	M₁₆	1	1	yes	characteristic
58	C₂²×C₄×C₇₉	M₁₆	1	1	yes	characteristic
59	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₈×C₇₉	—	2	2	no	—
61	C₂×C₈×C₇₉	—	4	1	no	—
62	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
65	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
68	C₄²×C₇₉	C₂×C₈	1	1	yes	characteristic
69	C₄²×C₇₉	C₂×C₈	1	1	yes	characteristic
70	C₁₆×C₇₉	—	4	2	no	—
71	C₂³×C₇₉	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₇₉	—	2	2	no	—
73	C₂×C₄×C₇₉	—	2	1	no	—
74	C₂×C₄×C₇₉	—	2	1	no	—
75	C₂×C₄×C₇₉	—	4	1	no	—
76	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
77	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
78	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
82	C₂×Dic₇₉	—	2	2	no	—
83	C₂×Dic₇₉	—	2	2	no	—
84	Dic₁₅₈	—	4	2	no	—
85	Dic₁₅₈	—	4	2	no	—
86	C₈×C₇₉	—	2	1	no	—
87	C₈×C₇₉	—	2	1	no	—
88	C₈×C₇₉	—	2	1	no	—
89	C₈×C₇₉	#101	1	2	yes	—
90	C₇₉⋊C₈	—	4	2	no	—
91	C₂²×C₇₉	—	2	1	no	—
92	C₂²×C₇₉	—	2	1	no	—
93	C₂²×C₇₉	—	2	1	no	—
94	C₂²×C₇₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
95	C₄×C₇₉	—	2	1	no	—
96	C₄×C₇₉	—	2	1	no	—
97	C₄×C₇₉	—	2	1	no	—
98	C₄×C₇₉	—	2	1	no	—
99	C₄×C₇₉	#350	1	2	yes	—
100	C₄×C₇₉	#410	1	1	yes	characteristic
101	C₄×C₇₉	C₂×#101	1	1	yes	characteristic
102	Dic₇₉	—	4	2	no	—
103	Dic₇₉	—	4	2	no	—
104	#11498	—	79	1	no	maximal, Sylow
105	C₂×C₇₉	—	4	1	no	—
106	C₂×C₇₉	#1461	1	1	yes	characteristic
107	C₂×C₇₉	C₂×#350	1	1	yes	characteristic
108	C₂×C₇₉	#2117	1	1	yes	characteristic
109	#2960	—	79	1	no	—
110	#2163	—	79	1	no	—
111	#2162	D₇₉	1	1	yes	characteristic
112	#1323	—	79	4	no	—
113	C₇₉	#11498	1	1	yes	characteristic, complemented, Sylow
114	#533	—	79	1	no	—
115	#446	—	158	1	no	—
116	#446	—	158	1	no	—
117	C₈×Q₈	—	158	1	no	—
118	C₈×Q₈	—	158	1	no	—
119	#424	—	79	2	no	—
120	#423	—	79	1	no	—
121	#405	—	79	2	no	—
122	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
123	C₄⋊C₁₆	—	2	1	no	—
124	C₄⋊C₁₆	—	158	1	no	—
125	C₂²⋊C₁₆	—	79	2	no	—
126	C₂²⋊C₁₆	C₂×D₇₉	1	2	yes	—
127	#346	—	158	1	no	—
128	C₄×C₁₆	—	2	1	no	—
129	C₂×M₁₆	—	79	2	no	—
130	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
131	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
132	C₄⋊Q₈	—	79	1	no	—
133	C₄⋊Q₈	—	79	1	no	—
134	#125	—	79	2	no	—
135	C₂²⋊Q₈	—	158	1	no	—
136	C₂²⋊Q₈	—	158	1	no	—
137	C₄×Q₈	—	158	1	no	—
138	C₄×Q₈	—	158	1	no	—
139	#117	—	79	2	no	—
140	C₂×C₄²	C₄×D₇₉	1	1	yes	characteristic
141	C₂×C₁₆	—	2	2	no	—
142	C₂×C₁₆	—	158	2	no	—
143	C₄⋊C₈	—	158	2	no	—
144	C₄⋊C₈	—	158	2	no	—
145	C₄⋊C₈	—	158	1	no	—
146	C₄⋊C₈	—	158	1	no	—
147	#97	—	158	2	no	—
148	C₄×C₈	—	158	2	no	—
149	C₄×C₈	D₃₁₆	1	1	yes	characteristic
150	C₄×C₈	D₃₁₆	1	1	yes	characteristic
151	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
152	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
153	C₂×Q₈	—	158	1	no	—
154	C₂×Q₈	—	158	1	no	—
155	C₂²×C₄	#11929607	1	1	yes	characteristic
156	C₂²×C₄	#11929607	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
158	M₁₆	—	316	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	4	1	no	—
161	C₂×C₈	—	158	2	no	—
162	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
163	C₂×C₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
164	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
165	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
166	C₄⋊C₄	—	79	2	no	—
167	C₄⋊C₄	—	79	2	no	—
168	C₄⋊C₄	—	158	2	no	—
169	C₄⋊C₄	—	158	2	no	—
170	C₄⋊C₄	—	158	1	no	—
171	C₄⋊C₄	—	158	1	no	—
172	C₂²⋊C₄	—	158	2	no	—
173	C₄²	—	158	2	no	—
174	C₄²	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
175	C₄²	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
176	C₄²	C₈×D₇₉	1	1	yes	characteristic
177	C₄²	C₈×D₇₉	1	1	yes	characteristic
178	C₁₆	—	4	2	no	—
179	C₁₆	—	316	2	no	—
180	C₂³	C₂×#11929607	1	1	yes	characteristic
181	Q₈	—	316	2	no	—
182	Q₈	—	316	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	158	2	no	—
188	C₂×C₄	—	158	2	no	—
189	C₂×C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
190	C₂×C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
191	C₂×C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
192	C₂×C₄	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
193	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
194	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
195	C₈	—	2	1	no	—
196	C₈	—	2	1	no	—
197	C₈	—	2	1	no	—
198	C₈	—	316	2	no	—
199	C₈	#14579079	1	2	yes	—
200	C₂²	—	2	1	no	—
201	C₂²	—	2	1	no	—
202	C₂²	—	2	1	no	—
203	C₂²	C₂×(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	316	2	no	—
209	C₄	—	316	2	no	—
210	C₄	#19098346	1	2	yes	—
211	C₄	#19098536	1	1	yes	characteristic
212	C₄	C₂×#14579079	1	1	yes	characteristic
213	C₂	—	4	1	no	—
214	C₂	#23761723	1	1	yes	characteristic
215	C₂	C₂×#19098346	1	1	yes	characteristic
216	C₂	#23765029	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772334

C₂

yes

maximal, characteristic

#23765203

C₂

yes

maximal, characteristic

#23761341

C₂

yes

maximal

C₇₉×#2162

C₂

yes

maximal, characteristic

#19099120

C₄

yes

characteristic

#19098693

—

#19098693

—

C₈×Dic₁₅₈

—

C₈×Dic₁₅₈

—

#19098589

C₂²

yes

—

#19098587

C₄

yes

characteristic

#19098518

C₄

yes

—

C₄⋊(C₇₉⋊C₁₆)

—

C₂²⋊(C₇₉⋊C₁₆)

C₂²

yes

—

#19098339

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₇₉

—

C₂²⋊C₁₆×C₇₉

C₂²

yes

—

C₄×C₁₆×C₇₉

—

C₂×#11929608

C₂×C₄

yes

—

#14579161

C₈

yes

characteristic

#14579161

C₈

yes

characteristic

#14579153

C₈

yes

—

#14579140

—

#14579140

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

—

#14579120

C₂×C₄

yes

—

C₂×C₇₉⋊C₁₆

—

C₄⋊(C₇₉⋊C₈)

—

C₄⋊(C₇₉⋊C₈)

—

Dic₇₉⋊C₈

—

Dic₇₉⋊C₈

—

#14579071

—

C₈×Dic₇₉

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

C₂×C₄²×C₇₉

C₂×C₄

yes

characteristic

C₂×C₁₆×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

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂×C₈

yes

—

C₄⋊Dic₇₉

C₂×C₈

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

M₁₆

yes

characteristic

C₂²×C₄×C₇₉

M₁₆

yes

characteristic

C₂²×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂²⋊C₄

yes

characteristic

C₄²×C₇₉

C₂²⋊C₄

yes

characteristic

C₄²×C₇₉

C₂×C₈

yes

characteristic

C₄²×C₇₉

C₂×C₈

yes

characteristic

C₁₆×C₇₉

—

C₂³×C₇₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

#101

yes

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#350

yes

—

100

C₄×C₇₉

#410

yes

characteristic

101

C₄×C₇₉

C₂×#101

yes

characteristic

102

Dic₇₉

—

103

Dic₇₉

—

104

#11498

—

maximal, Sylow

105

C₂×C₇₉

—

106

C₂×C₇₉

#1461

yes

characteristic

107

C₂×C₇₉

C₂×#350

yes

characteristic

108

C₂×C₇₉

#2117

yes

characteristic

109

#2960

—

110

#2163

—

111

#2162

D₇₉

yes

characteristic

112

#1323

—

113

C₇₉

#11498

yes

characteristic, complemented, Sylow

114

#533

—

115

#446

—

158

—

116

#446

—

158

—

117

C₈×Q₈

—

158

—

118

C₈×Q₈

—

158

—

119

#424

—

120

#423

—

121

#405

—

122

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

123

C₄⋊C₁₆

—

124

C₄⋊C₁₆

—

158

—

125

C₂²⋊C₁₆

—

126

C₂²⋊C₁₆

C₂×D₇₉

yes

—

127

#346

—

158

—

128

C₄×C₁₆

—

129

C₂×M₁₆

—

130

C₂²×C₈

C₄×D₇₉

yes

characteristic

131

C₂²×C₈

C₂²×D₇₉

yes

characteristic

132

C₄⋊Q₈

—

133

C₄⋊Q₈

—

134

#125

—

135

C₂²⋊Q₈

—

158

—

136

C₂²⋊Q₈

—

158

—

137

C₄×Q₈

—

158

—

138

C₄×Q₈

—

158

—

139

#117

—

140

C₂×C₄²

C₄×D₇₉

yes

characteristic

141

C₂×C₁₆

—

142

C₂×C₁₆

—

158

—

143

C₄⋊C₈

—

158

—

144

C₄⋊C₈

—

158

—

145

C₄⋊C₈

—

158

—

146

C₄⋊C₈

—

158

—

147

#97

—

158

—

148

C₄×C₈

—

158

—

149

C₄×C₈

D₃₁₆

yes

characteristic

150

C₄×C₈

D₃₁₆

yes

characteristic

151

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

152

C₄×C₈

C₂²⋊D₇₉

yes

characteristic

153

C₂×Q₈

—

158

—

154

C₂×Q₈

—

158

—

155

C₂²×C₄

#11929607

yes

characteristic

156

C₂²×C₄

#11929607

yes

characteristic

157

C₂²×C₄

C₂×C₄×D₇₉

yes

characteristic

158

M₁₆

—

316

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

158

—

162

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

163

C₂×C₈

(C₂×D₇₉)⋊C₄

yes

characteristic

164

C₂×C₈

C₂×C₂²⋊D₇₉

yes

characteristic

165

C₂×C₈

C₂×D₃₁₆

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

158

—

169

C₄⋊C₄

—

158

—

170

C₄⋊C₄

—

158

—

171

C₄⋊C₄

—

158

—

172

C₂²⋊C₄

—

158

—

173

C₄²

—

158

—

174

C₄²

(C₂×D₇₉)⋊C₄

yes

characteristic

175

C₄²

(C₂×D₇₉)⋊C₄

yes

characteristic

176

C₄²

C₈×D₇₉

yes

characteristic

177

C₄²

C₈×D₇₉

yes

characteristic

178

C₁₆

—

179

C₁₆

—

316

—

180

C₂³

C₂×#11929607

yes

characteristic

181

Q₈

—

316

—

182

Q₈

—

316

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

158

—

188

C₂×C₄

—

158

—

189

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

characteristic

190

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

characteristic

191

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

characteristic

192

C₂×C₄

(C₂×D₇₉)⋊C₈

yes

characteristic

193

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

yes

characteristic

194

C₂×C₄

C₂×C₈×D₇₉

yes

characteristic

195

C₈

—

196

C₈

—

197

C₈

—

198

C₈

—

316

—

199

C₈

#14579079

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

C₂×(C₂×D₇₉)⋊C₈

yes

characteristic

204

C₄

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

316

—

209

C₄

—

316

—

210

C₄

#19098346

yes

—

211

C₄

#19098536

yes

characteristic

212

C₄

C₂×#14579079

yes

characteristic

213

C₂

—

214

C₂

#23761723

yes

characteristic

215

C₂

C₂×#19098346

yes

characteristic

216

C₂

#23765029

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#2162	C₂
socle	C₂²×C₇₉	C₂×C₂²⋊C₈
prime radical	C₂³×C₇₉	C₂×M₁₆
cosocle	C₂²×C₈×C₇₉	C₂³
hypercenter	#2162	D₇₉
hypocenter	C₇₉	#11498
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2162

subgroup

G/H

center

C₂×C₄

C₂×(C₂×D₇₉)⋊C₄

commutator

C₂×C₄×C₇₉

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#2162

C₂

socle

C₂²×C₇₉

C₂×C₂²⋊C₈

prime radical

C₂³×C₇₉

C₂×M₁₆

cosocle

C₂²×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2162

N	H ≅ G/N	type
113. C₇₉	#11498	semidirect

H ≅ G/N

type

113. C₇₉

#11498

semidirect

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

subgroup	index
#23772334	2
#23765203	2
#23761341	2
C₇₉×#2162	2
#11498	79

subgroup

index

C₇₉×#2162

Subgroups — #34197621

Conjugacy classes of subgroups

Complements

Maximal subgroups