Group #34183581 — subgroups

Subgroups — #34183581

Order 20224.

444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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	#23772467	C₂	1	1	yes	maximal, characteristic
2	#23761992	C₂	1	1	yes	maximal, characteristic
3	#23761821	C₂	1	2	yes	maximal, complemented
4	#23761237	C₂	1	2	yes	maximal, complemented
5	C₇₉×#3131	C₂	1	1	yes	maximal, characteristic
6	#19098641	—	2	2	no	—
7	D₄×C₇₉⋊C₈	—	2	2	no	—
8	#19098616	C₂²	1	2	yes	—
9	#19098530	—	2	2	no	—
10	C₄×#11929608	C₂²	1	2	yes	—
11	#19098303	—	2	2	no	—
12	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
13	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
14	#533×C₇₉	C₂²	1	1	yes	characteristic
15	#532×C₇₉	C₂²	1	1	yes	characteristic
16	#488×C₇₉	—	2	2	no	—
17	#487×C₇₉	C₄	1	2	yes	—
18	#486×C₇₉	C₄	1	2	yes	—
19	#416×C₇₉	—	2	2	no	—
20	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#11929608	—	2	2	no	—
22	C₂×#11929608	—	2	2	no	—
23	C₂²×C₇₉⋊C₈	—	2	2	no	—
24	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
25	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
26	C₂²⋊(C₇₉⋊C₈)	—	2	4	no	—
27	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
28	#14579072	—	2	2	no	—
29	C₄×C₇₉⋊C₈	—	2	2	no	—
30	C₄×C₇₉⋊C₈	—	2	2	no	—
31	C₂×#41×C₇₉	D₄	1	2	yes	—
32	C₂²×C₈×C₇₉	—	2	1	no	—
33	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
34	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
35	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
36	#125×C₇₉	—	2	1	no	—
37	#124×C₇₉	D₄	1	2	yes	—
38	C₂²⋊Q₈×C₇₉	—	2	2	no	—
39	#121×C₇₉	—	2	2	no	—
40	C₄×Q₈×C₇₉	—	2	2	no	—
41	C₄×D₄×C₇₉	—	2	2	no	—
42	#117×C₇₉	—	2	1	no	—
43	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
44	#103×C₇₉	—	2	4	no	—
45	#102×C₇₉	—	2	4	no	—
46	C₄×C₈×C₇₉	—	2	1	no	—
47	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
48	#11929608	—	2	4	no	—
49	#11929608	—	4	2	no	—
50	#11929608	—	8	2	no	—
51	C₂×C₇₉⋊C₈	—	2	2	no	—
52	C₂×C₇₉⋊C₈	—	2	2	no	—
53	C₂×C₇₉⋊C₈	—	4	2	no	—
54	C₂×C₇₉⋊C₈	—	8	2	no	—
55	#41×C₇₉	—	4	2	no	—
56	#41×C₇₉	—	4	2	no	—
57	C₂×Q₈×C₇₉	—	2	2	no	—
58	C₂×Q₈×C₇₉	C₂²⋊C₄	1	2	yes	—
59	C₂×D₄×C₇₉	—	2	2	no	—
60	C₂×D₄×C₇₉	—	2	2	no	—
61	C₂×D₄×C₇₉	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₇₉	—	2	2	no	—
63	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₇₉	#41	1	2	yes	—
65	C₂×C₈×C₇₉	—	2	2	no	—
66	C₂×C₈×C₇₉	—	4	1	no	—
67	C₂×C₈×C₇₉	—	4	1	no	—
68	C₄⋊C₄×C₇₉	—	2	2	no	—
69	C₄⋊C₄×C₇₉	—	2	2	no	—
70	C₄⋊C₄×C₇₉	—	2	2	no	—
71	C₄⋊C₄×C₇₉	—	4	2	no	—
72	C₂²⋊C₄×C₇₉	—	2	4	no	—
73	C₂²⋊C₄×C₇₉	—	4	1	no	—
74	C₄²×C₇₉	—	4	1	no	—
75	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₇₉	C₂×D₄	1	2	yes	—
78	C₂³×C₇₉	—	2	2	no	—
79	C₂³×C₇₉	#123	1	1	yes	characteristic
80	Q₈×C₇₉	—	4	2	no	—
81	Q₈×C₇₉	—	4	2	no	—
82	Q₈×C₇₉	—	4	2	no	—
83	D₄×C₇₉	—	4	2	no	—
84	D₄×C₇₉	—	4	2	no	—
85	D₄×C₇₉	—	4	2	no	—
86	D₄×C₇₉	—	8	2	no	—
87	C₂×C₄×C₇₉	—	2	2	no	—
88	C₂×C₄×C₇₉	—	2	2	no	—
89	C₂×C₄×C₇₉	—	2	1	no	—
90	C₂×C₄×C₇₉	—	2	1	no	—
91	C₂×C₄×C₇₉	—	2	2	no	—
92	C₂×C₄×C₇₉	—	4	2	no	—
93	C₂×C₄×C₇₉	—	4	2	no	—
94	C₂×C₄×C₇₉	—	4	2	no	—
95	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
98	C₂×C₄×C₇₉	#121	1	2	yes	—
99	C₈×C₇₉	—	4	2	no	—
100	C₇₉⋊C₈	—	4	4	no	—
101	C₇₉⋊C₈	—	4	2	no	—
102	C₇₉⋊C₈	—	4	2	no	—
103	C₂²×C₇₉	—	2	2	no	—
104	C₂²×C₇₉	—	2	1	no	—
105	C₂²×C₇₉	—	4	4	no	—
106	C₂²×C₇₉	—	4	2	no	—
107	C₂²×C₇₉	#386	1	1	yes	characteristic
108	C₄×C₇₉	—	2	2	no	—
109	C₄×C₇₉	—	2	1	no	—
110	C₄×C₇₉	—	4	2	no	—
111	C₄×C₇₉	—	8	2	no	—
112	C₄×C₇₉	#443	1	2	yes	—
113	C₄×C₇₉	#444	1	2	yes	—
114	C₄×C₇₉	#455	1	1	yes	characteristic
115	C₄×C₇₉	#455	1	1	yes	characteristic
116	#9067	—	79	1	no	maximal, Sylow
117	C₂×C₇₉	—	4	1	no	—
118	C₂×C₇₉	—	8	2	no	—
119	C₂×C₇₉	#1876	1	2	yes	—
120	C₂×C₇₉	#1885	1	1	yes	characteristic
121	#3131	D₇₉	1	1	yes	characteristic
122	#2979	—	79	1	no	—
123	#1525	—	79	1	no	—
124	#1485	—	79	2	no	—
125	#1278	—	79	2	no	—
126	C₇₉	#9067	1	1	yes	characteristic, complemented, Sylow
127	#533	C₂×D₇₉	1	1	yes	characteristic
128	#532	C₂×D₇₉	1	1	yes	characteristic
129	#488	—	2	2	no	—
130	#487	Dic₇₉	1	2	yes	—
131	#486	Dic₇₉	1	2	yes	—
132	#436	—	158	2	no	—
133	C₈×D₄	—	158	2	no	—
134	#431	—	79	2	no	—
135	#416	—	2	2	no	—
136	#408	—	158	2	no	—
137	C₄×M₁₆	—	79	2	no	—
138	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
139	#329	—	158	2	no	—
140	Q₈⋊C₈	—	158	2	no	—
141	Q₈⋊C₈	—	158	2	no	—
142	C₂×#41	C₂²⋊D₇₉	1	2	yes	—
143	C₂×M₁₆	—	158	2	no	—
144	C₂×M₁₆	—	158	2	no	—
145	C₂²×C₈	—	2	1	no	—
146	C₂²×C₈	—	158	2	no	—
147	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
148	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
149	#127	C₂×Dic₇₉	1	1	yes	characteristic
150	#125	—	2	1	no	—
151	#124	C₂²⋊D₇₉	1	2	yes	—
152	C₂²⋊Q₈	—	2	2	no	—
153	#121	—	2	2	no	—
154	C₄×Q₈	—	2	2	no	—
155	C₄×D₄	—	2	2	no	—
156	#117	—	2	1	no	—
157	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
158	C₄⋊C₈	—	79	2	no	—
159	C₄⋊C₈	—	79	2	no	—
160	#103	—	2	4	no	—
161	#102	—	2	4	no	—
162	C₂²⋊C₈	—	158	4	no	—
163	C₂²⋊C₈	—	158	2	no	—
164	#97	—	158	2	no	—
165	C₄×C₈	—	2	1	no	—
166	C₄×C₈	—	158	2	no	—
167	C₄×C₈	—	158	2	no	—
168	C₄×C₈	C₂×Dic₇₉	1	2	yes	—
169	#41	—	4	2	no	—
170	#41	—	4	2	no	—
171	C₂×Q₈	—	2	2	no	—
172	C₂×Q₈	C₂²⋊Dic₇₉	1	2	yes	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	C₂²⋊Dic₇₉	1	2	yes	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
178	C₂²×C₄	#11929623	1	2	yes	—
179	M₁₆	—	316	2	no	—
180	M₁₆	—	632	2	no	—
181	M₁₆	—	158	4	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	4	1	no	—
185	C₂×C₈	—	316	2	no	—
186	C₂×C₈	—	632	2	no	—
187	C₂×C₈	—	158	2	no	—
188	C₂×C₈	—	158	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	4	2	no	—
193	C₂²⋊C₄	—	2	4	no	—
194	C₂²⋊C₄	—	4	1	no	—
195	C₄²	—	4	1	no	—
196	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
197	C₄²	D₄×D₇₉	1	2	yes	—
198	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
199	C₂³	—	2	2	no	—
200	C₂³	#14579142	1	1	yes	characteristic
201	Q₈	—	4	2	no	—
202	Q₈	—	4	2	no	—
203	Q₈	—	4	2	no	—
204	D₄	—	4	2	no	—
205	D₄	—	4	2	no	—
206	D₄	—	4	2	no	—
207	D₄	—	8	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
217	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
218	C₂×C₄	#14579129	1	1	yes	characteristic
219	C₂×C₄	#14579133	1	2	yes	—
220	C₈	—	4	2	no	—
221	C₈	—	316	4	no	—
222	C₈	—	316	2	no	—
223	C₈	—	316	2	no	—
224	C₂²	—	2	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	4	4	no	—
227	C₂²	—	4	2	no	—
228	C₂²	#19098443	1	1	yes	characteristic
229	C₄	—	2	2	no	—
230	C₄	—	2	1	no	—
231	C₄	—	4	2	no	—
232	C₄	—	8	2	no	—
233	C₄	#19098680	1	2	yes	—
234	C₄	#19098685	1	2	yes	—
235	C₄	#19098740	1	1	yes	characteristic
236	C₄	#19098740	1	1	yes	characteristic
237	C₂	—	4	1	no	—
238	C₂	—	8	2	no	—
239	C₂	#23763729	1	2	yes	—
240	C₂	#23763789	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#23772467

C₂

yes

maximal, characteristic

#23761992

C₂

yes

maximal, characteristic

#23761821

C₂

yes

maximal, complemented

#23761237

C₂

yes

maximal, complemented

C₇₉×#3131

C₂

yes

maximal, characteristic

#19098641

—

D₄×C₇₉⋊C₈

—

#19098616

C₂²

yes

—

#19098530

—

C₄×#11929608

C₂²

yes

—

#19098303

—

Q₈⋊(C₇₉⋊C₈)

—

Q₈⋊(C₇₉⋊C₈)

—

#533×C₇₉

C₂²

yes

characteristic

#532×C₇₉

C₂²

yes

characteristic

#488×C₇₉

—

#487×C₇₉

C₄

yes

—

#486×C₇₉

C₄

yes

—

#416×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×#11929608

—

C₂×#11929608

—

C₂²×C₇₉⋊C₈

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₄⋊(C₇₉⋊C₈)

D₄

yes

—

C₂²⋊(C₇₉⋊C₈)

—

C₂²⋊(C₇₉⋊C₈)

—

#14579072

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂×#41×C₇₉

D₄

yes

—

C₂²×C₈×C₇₉

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

—

C₄⋊Q₈×C₇₉

C₂×C₄

yes

characteristic

#127×C₇₉

C₂×C₄

yes

characteristic

#125×C₇₉

—

#124×C₇₉

D₄

yes

—

C₂²⋊Q₈×C₇₉

—

#121×C₇₉

—

C₄×Q₈×C₇₉

—

C₄×D₄×C₇₉

—

#117×C₇₉

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

#103×C₇₉

—

#102×C₇₉

—

C₄×C₈×C₇₉

—

C₄×C₈×C₇₉

C₂×C₄

yes

—

#11929608

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

#41×C₇₉

—

#41×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

C₂²⋊C₄

yes

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₇₉

#41

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

C₂²×C₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

characteristic

C₄²×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

#123

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×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×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₉

C₄×D₄

yes

—

C₂×C₄×C₇₉

#120

yes

characteristic

C₂×C₄×C₇₉

#121

yes

—

C₈×C₇₉

—

100

C₇₉⋊C₈

—

101

C₇₉⋊C₈

—

102

C₇₉⋊C₈

—

103

C₂²×C₇₉

—

104

C₂²×C₇₉

—

105

C₂²×C₇₉

—

106

C₂²×C₇₉

—

107

C₂²×C₇₉

#386

yes

characteristic

108

C₄×C₇₉

—

109

C₄×C₇₉

—

110

C₄×C₇₉

—

111

C₄×C₇₉

—

112

C₄×C₇₉

#443

yes

—

113

C₄×C₇₉

#444

yes

—

114

C₄×C₇₉

#455

yes

characteristic

115

C₄×C₇₉

yes

116

—

117

C₂×C₇₉

—

118

C₂×C₇₉

—

119

C₂×C₇₉

#1876

yes

—

120

C₂×C₇₉

#1885

yes

characteristic

121

#3131

D₇₉

yes

characteristic

122

#2979

—

123

#1525

—

124

#1485

—

125

#1278

—

126

C₇₉

#9067

yes

characteristic, complemented, Sylow

127

#533

C₂×D₇₉

yes

characteristic

128

#532

C₂×D₇₉

yes

characteristic

129

#488

—

130

#487

Dic₇₉

yes

—

131

#486

Dic₇₉

yes

—

132

#436

—

158

—

133

C₈×D₄

—

158

—

134

#431

—

135

#416

—

136

#408

—

158

—

137

C₄×M₁₆

—

138

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

139

#329

—

158

—

140

Q₈⋊C₈

—

158

—

141

Q₈⋊C₈

—

158

—

142

C₂×#41

C₂²⋊D₇₉

yes

—

143

C₂×M₁₆

—

158

—

144

C₂×M₁₆

—

158

—

145

C₂²×C₈

—

146

C₂²×C₈

—

158

—

147

C₄⋊Q₈

C₂×Dic₇₉

yes

—

148

C₄⋊Q₈

C₂×Dic₇₉

yes

characteristic

149

#127

C₂×Dic₇₉

yes

characteristic

150

#125

—

151

#124

C₂²⋊D₇₉

yes

—

152

C₂²⋊Q₈

—

153

#121

—

154

C₄×Q₈

—

155

C₄×D₄

—

156

#117

—

157

C₂×C₄²

C₂²×D₇₉

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

161

#102

—

162

C₂²⋊C₈

—

158

—

163

C₂²⋊C₈

—

158

—

164

#97

—

158

—

165

C₄×C₈

—

166

C₄×C₈

—

158

—

167

C₄×C₈

—

158

—

168

C₄×C₈

C₂×Dic₇₉

yes

—

169

#41

—

170

#41

—

171

C₂×Q₈

—

172

C₂×Q₈

C₂²⋊Dic₇₉

yes

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

C₂²⋊Dic₇₉

yes

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

178

C₂²×C₄

#11929623

yes

—

179

M₁₆

—

316

—

180

M₁₆

—

632

—

181

M₁₆

—

158

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

316

—

186

C₂×C₈

—

632

—

187

C₂×C₈

—

158

—

188

C₂×C₈

—

158

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

195

C₄²

—

196

C₄²

C₂²×Dic₇₉

yes

characteristic

197

C₄²

D₄×D₇₉

yes

—

198

C₄²

C₂×C₂²⋊D₇₉

yes

characteristic

199

C₂³

—

200

C₂³

#14579142

yes

characteristic

201

Q₈

—

202

Q₈

—

203

Q₈

—

204

D₄

—

205

D₄

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

C₂×C₂²⋊Dic₇₉

yes

characteristic

217

C₂×C₄

D₄×Dic₇₉

yes

—

218

C₂×C₄

#14579129

yes

characteristic

219

C₂×C₄

#14579133

yes

—

220

C₈

—

221

C₈

—

316

—

222

C₈

—

316

—

223

C₈

—

316

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

#19098443

yes

characteristic

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

#19098680

yes

—

234

C₄

#19098685

yes

—

235

C₄

#19098740

yes

characteristic

236

C₄

#19098740

yes

characteristic

237

C₂

—

238

C₂

—

239

C₂

#23763729

yes

—

240

C₂

#23763789

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#3131	C₂
socle	C₂²×C₇₉	#386
prime radical	#532×C₇₉	C₂²
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3131	D₇₉
hypocenter	C₇₉	#9067
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3131

subgroup

G/H

center

C₂×C₄

#14579129

commutator

C₄²×C₇₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₇₉

Fitting

C₇₉×#3131

C₂

socle

C₂²×C₇₉

#386

prime radical

#532×C₇₉

C₂²

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3131

N	H ≅ G/N	type
3. #23761821	C₂	semidirect
4. #23761237	C₂	semidirect
126. C₇₉	#9067	semidirect

H ≅ G/N

type

3. #23761821

C₂

semidirect

4. #23761237

C₂

semidirect

126. C₇₉

#9067

semidirect

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

subgroup	index
#23772467	2
#23761992	2
#23761821	2
#23761237	2
C₇₉×#3131	2
#9067	79

subgroup

index

C₇₉×#3131

Subgroups — #34183581

Conjugacy classes of subgroups

Complements

Maximal subgroups