Group #28492814 — subgroups

Subgroups — #28492814

Order 15104.

402 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 99 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	#21425074	C₂	1	2	yes	maximal
2	#21424247	C₂	1	1	yes	maximal, characteristic
3	#21422786	C₂	1	2	yes	maximal
4	#21421971	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#3249	C₂	1	1	yes	maximal, characteristic
6	#16837426	C₂²	1	2	yes	—
7	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
8	C₂×Dic₅₉⋊C₈	—	2	2	no	—
9	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
10	#16837161	—	2	2	no	—
11	#16837161	—	2	2	no	—
12	#16837151	—	2	2	no	—
13	#16837148	—	2	2	no	—
14	C₅₉×#533	C₂²	1	2	yes	—
15	C₅₉×#477	—	2	2	no	—
16	C₅₉×#467	—	2	2	no	—
17	C₅₉×#462	—	2	2	no	—
18	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#11745664	—	2	2	no	—
20	C₂²×C₅₉⋊C₈	—	2	1	no	—
21	C₂×C₄×Dic₅₉	—	2	1	no	—
22	C₂×C₄×Dic₅₉	—	2	1	no	—
23	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
24	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
25	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
26	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
27	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
28	Dic₅₉⋊C₈	—	4	4	no	—
29	C₂×Q₁₆×C₅₉	—	2	2	no	—
30	C₂²×C₈×C₅₉	D₄	1	2	yes	—
31	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
32	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
33	#125×C₅₉	—	2	2	no	—
34	C₂²⋊Q₈×C₅₉	—	2	2	no	—
35	C₂²⋊Q₈×C₅₉	—	2	2	no	—
36	C₄×Q₈×C₅₉	—	2	2	no	—
37	C₄×Q₈×C₅₉	—	2	2	no	—
38	#117×C₅₉	—	2	2	no	—
39	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
40	#107×C₅₉	—	2	2	no	—
41	C₄⋊C₈×C₅₉	—	2	2	no	—
42	#103×C₅₉	—	2	4	no	—
43	C₂×Q₈×C₅₉	—	2	2	no	—
44	C₂×Q₈×C₅₉	—	2	2	no	—
45	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
48	C₂²×Dic₅₉	—	2	1	no	—
49	C₂²×Dic₅₉	—	2	1	no	—
50	Q₁₆×C₅₉	—	8	2	no	—
51	C₂×C₈×C₅₉	—	2	2	no	—
52	C₂×C₈×C₅₉	—	4	2	no	—
53	C₄⋊C₄×C₅₉	—	2	2	no	—
54	C₄⋊C₄×C₅₉	—	2	2	no	—
55	C₄⋊C₄×C₅₉	—	2	2	no	—
56	C₄⋊C₄×C₅₉	—	2	2	no	—
57	C₄⋊C₄×C₅₉	—	4	2	no	—
58	C₄⋊C₄×C₅₉	—	4	2	no	—
59	C₂²⋊C₄×C₅₉	—	4	2	no	—
60	C₄²×C₅₉	—	4	2	no	—
61	C₄²×C₅₉	C₂×D₄	1	2	yes	—
62	C₄²×C₅₉	#41	1	2	yes	—
63	C₄×Dic₅₉	—	2	2	no	—
64	C₄×Dic₅₉	—	2	2	no	—
65	C₄×Dic₅₉	—	2	1	no	—
66	C₄×Dic₅₉	—	2	2	no	—
67	C₄×Dic₅₉	—	4	2	no	—
68	C₄×Dic₅₉	Q₁₆	1	2	yes	complemented
69	#11745664	—	4	2	no	—
70	#11745664	—	4	2	no	—
71	C₂×C₅₉⋊C₈	—	4	2	no	—
72	C₂×C₅₉⋊C₈	—	4	1	no	—
73	C₂×C₅₉⋊C₈	—	4	2	no	—
74	C₂³×C₅₉	#121	1	1	yes	characteristic
75	Q₈×C₅₉	—	4	2	no	—
76	Q₈×C₅₉	—	4	2	no	—
77	Q₈×C₅₉	—	8	2	no	—
78	C₂×C₄×C₅₉	—	2	1	no	—
79	C₂×C₄×C₅₉	—	2	1	no	—
80	C₂×C₄×C₅₉	—	4	1	no	—
81	C₂×C₄×C₅₉	—	4	2	no	—
82	C₂×C₄×C₅₉	—	4	2	no	—
83	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#121	1	2	yes	—
85	C₂×C₄×C₅₉	#123	1	2	yes	—
86	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
89	C₂×C₄×C₅₉	#137	1	2	yes	—
90	C₂×Dic₅₉	—	2	2	no	—
91	C₂×Dic₅₉	—	2	2	no	—
92	C₂×Dic₅₉	—	2	2	no	—
93	C₂×Dic₅₉	—	2	2	no	—
94	C₂×Dic₅₉	—	4	1	no	—
95	C₂×Dic₅₉	—	4	1	no	—
96	C₈×C₅₉	—	4	2	no	—
97	C₅₉⋊C₈	—	8	1	no	—
98	C₅₉⋊C₈	—	8	2	no	—
99	#10522	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	—	2	1	no	—
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	#394	1	1	yes	characteristic
103	C₂²×C₅₉	#467	1	1	yes	characteristic
104	C₂²×C₅₉	#470	1	1	yes	characteristic
105	C₄×C₅₉	—	2	2	no	—
106	C₄×C₅₉	—	2	1	no	—
107	C₄×C₅₉	—	8	2	no	—
108	C₄×C₅₉	—	8	2	no	—
109	C₄×C₅₉	#453	1	1	yes	characteristic
110	C₄×C₅₉	#456	1	1	yes	characteristic
111	C₄×C₅₉	#462	1	2	yes	—
112	C₄×C₅₉	#464	1	2	yes	—
113	Dic₅₉	—	2	4	no	—
114	Dic₅₉	—	4	2	no	—
115	#3249	D₅₉	1	1	yes	characteristic
116	#1994	—	59	2	no	—
117	#1842	—	59	1	no	—
118	#1550	—	59	2	no	—
119	#1292	—	59	1	no	—
120	C₂×C₅₉	—	2	1	no	—
121	C₂×C₅₉	—	2	1	no	—
122	C₂×C₅₉	#2039	1	1	yes	characteristic
123	C₂×C₅₉	#2050	1	1	yes	characteristic
124	C₂×C₅₉	#2056	1	1	yes	characteristic
125	#533	C₂×D₅₉	1	2	yes	—
126	#477	—	2	2	no	—
127	#467	—	2	2	no	—
128	#462	—	2	2	no	—
129	#423	—	59	2	no	—
130	C₂×C₄⋊C₈	—	59	1	no	—
131	C₂×C₄⋊C₈	—	118	2	no	—
132	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
133	C₄³	—	59	1	no	—
134	#339	—	118	2	no	—
135	#339	—	118	2	no	—
136	#333	—	118	2	no	—
137	#332	—	118	2	no	—
138	C₅₉	#10522	1	1	yes	characteristic, complemented, Sylow
139	C₂×Q₁₆	—	2	2	no	—
140	C₂×M₁₆	—	118	2	no	—
141	C₂²×C₈	—	118	1	no	—
142	C₂²×C₈	C₂²⋊D₅₉	1	2	yes	—
143	C₄⋊Q₈	C₂²⋊D₅₉	1	2	yes	—
144	C₄⋊Q₈	C₂²⋊D₅₉	1	2	yes	—
145	#125	—	2	2	no	—
146	C₂²⋊Q₈	—	2	2	no	—
147	C₂²⋊Q₈	—	2	2	no	—
148	C₄×Q₈	—	2	2	no	—
149	C₄×Q₈	—	2	2	no	—
150	#117	—	2	2	no	—
151	C₂×C₄²	—	59	1	no	—
152	C₂×C₄²	—	59	1	no	—
153	C₂×C₄²	—	118	1	no	—
154	C₂×C₄²	—	118	1	no	—
155	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
156	#107	—	2	2	no	—
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	118	2	no	—
159	C₄⋊C₈	—	118	2	no	—
160	C₄⋊C₈	—	118	2	no	—
161	C₄⋊C₈	—	236	4	no	—
162	#103	—	2	4	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂²×C₄	—	118	1	no	—
166	C₂²×C₄	—	118	1	no	—
167	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
168	C₂²×C₄	#11745687	1	1	yes	characteristic
169	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
170	Q₁₆	—	8	2	no	—
171	M₁₆	—	236	2	no	—
172	M₁₆	—	236	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	4	2	no	—
175	C₂×C₈	—	236	2	no	—
176	C₂×C₈	—	236	1	no	—
177	C₂×C₈	—	236	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₄⋊C₄	—	4	2	no	—
184	C₂²⋊C₄	—	4	2	no	—
185	C₄²	—	4	2	no	—
186	C₄²	—	59	2	no	—
187	C₄²	—	118	2	no	—
188	C₄²	—	118	2	no	—
189	C₄²	—	118	1	no	—
190	C₄²	—	118	2	no	—
191	C₄²	—	236	2	no	—
192	C₄²	#11745687	1	2	yes	—
193	C₄²	C₂×C₂²⋊D₅₉	1	2	yes	—
194	C₂³	#14273698	1	1	yes	characteristic
195	Q₈	—	4	2	no	—
196	Q₈	—	4	2	no	—
197	Q₈	—	8	2	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	1	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	118	2	no	—
204	C₂×C₄	—	118	2	no	—
205	C₂×C₄	—	118	2	no	—
206	C₂×C₄	—	118	2	no	—
207	C₂×C₄	—	236	1	no	—
208	C₂×C₄	—	236	1	no	—
209	C₂×C₄	#14273696	1	1	yes	characteristic
210	C₂×C₄	#14273699	1	2	yes	—
211	C₂×C₄	#14273708	1	2	yes	—
212	C₂×C₄	#14273714	1	1	yes	characteristic
213	C₂×C₄	Q₁₆×D₅₉	1	1	yes	characteristic
214	C₂×C₄	#14273750	1	1	yes	characteristic
215	C₂×C₄	#14273759	1	2	yes	—
216	C₈	—	4	2	no	—
217	C₈	—	472	1	no	—
218	C₈	—	472	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	#16837316	1	1	yes	characteristic
222	C₂²	#16837640	1	1	yes	characteristic
223	C₂²	#16837657	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	2	no	—
226	C₄	—	8	2	no	—
227	C₄	—	8	2	no	—
228	C₄	—	118	4	no	—
229	C₄	—	236	2	no	—
230	C₄	#16837570	1	1	yes	characteristic
231	C₄	#16837585	1	1	yes	characteristic
232	C₄	#16837610	1	2	yes	—
233	C₄	#16837626	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#21425317	1	1	yes	characteristic
237	C₂	#21425380	1	1	yes	characteristic
238	C₂	#21425416	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425074

C₂

yes

maximal

#21424247

C₂

yes

maximal, characteristic

#21422786

C₂

yes

maximal

#21421971

C₂

yes

maximal, characteristic

C₅₉×#3249

C₂

yes

maximal, characteristic

#16837426

C₂²

yes

—

C₂×C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₂×Dic₅₉⋊C₈

—

C₄²×Dic₅₉

C₂²

yes

—

—

—

—

C₅₉×#533

C₂²

yes

—

C₅₉×#477

—

C₅₉×#467

—

C₅₉×#462

—

C₂×C₄⋊C₈×C₅₉

C₂²

yes

characteristic

C₂×#11745664

—

C₂²×C₅₉⋊C₈

—

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

—

C₂×C₄×Dic₅₉

D₄

yes

characteristic

C₂×C₄×Dic₅₉

D₄

yes

characteristic

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

Dic₅₉⋊C₈

—

C₂×Q₁₆×C₅₉

—

C₂²×C₈×C₅₉

D₄

yes

—

C₄⋊Q₈×C₅₉

D₄

yes

—

C₄⋊Q₈×C₅₉

D₄

yes

—

#125×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₂²⋊Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

C₄×Q₈×C₅₉

—

#117×C₅₉

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

#107×C₅₉

—

C₄⋊C₈×C₅₉

—

#103×C₅₉

—

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂²×Dic₅₉

—

C₂²×Dic₅₉

—

Q₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₂²⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

—

C₄²×C₅₉

#41

yes

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₄×Dic₅₉

Q₁₆

yes

complemented

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

#121

yes

characteristic

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#120

yes

characteristic

C₂×C₄×C₅₉

#121

yes

—

C₂×C₄×C₅₉

#123

yes

—

C₂×C₄×C₅₉

#124

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₁₆

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

#10522

—

maximal, Sylow

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

#394

yes

characteristic

103

C₂²×C₅₉

#467

yes

characteristic

104

C₂²×C₅₉

#470

yes

characteristic

105

C₄×C₅₉

—

106

C₄×C₅₉

—

107

C₄×C₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

#453

yes

characteristic

110

C₄×C₅₉

#456

yes

characteristic

111

C₄×C₅₉

#462

yes

—

112

C₄×C₅₉

#464

yes

—

113

Dic₅₉

—

114

Dic₅₉

—

115

#3249

D₅₉

yes

characteristic

116

#1994

—

117

#1842

—

118

#1550

—

119

#1292

—

120

C₂×C₅₉

—

121

C₂×C₅₉

—

122

C₂×C₅₉

#2039

yes

characteristic

123

C₂×C₅₉

#2050

yes

characteristic

124

C₂×C₅₉

#2056

yes

characteristic

125

#533

C₂×D₅₉

yes

—

126

#477

—

127

#467

—

128

#462

—

129

#423

—

130

C₂×C₄⋊C₈

—

131

C₂×C₄⋊C₈

—

118

—

132

C₂×C₄⋊C₈

C₂×D₅₉

yes

characteristic

133

C₄³

—

134

#339

—

118

—

135

#339

—

118

—

136

#333

—

118

—

137

#332

—

118

—

138

C₅₉

#10522

yes

characteristic, complemented, Sylow

139

C₂×Q₁₆

—

140

C₂×M₁₆

—

118

—

141

C₂²×C₈

—

118

—

142

C₂²×C₈

C₂²⋊D₅₉

yes

—

143

C₄⋊Q₈

C₂²⋊D₅₉

yes

—

144

C₄⋊Q₈

C₂²⋊D₅₉

yes

—

145

#125

—

146

C₂²⋊Q₈

—

147

C₂²⋊Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

#117

—

151

C₂×C₄²

—

152

C₂×C₄²

—

153

C₂×C₄²

—

118

—

154

C₂×C₄²

—

118

—

155

C₂×C₄²

C₂²×D₅₉

yes

characteristic

156

#107

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

118

—

159

C₄⋊C₈

—

118

—

160

C₄⋊C₈

—

118

—

161

C₄⋊C₈

—

236

—

162

#103

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂²×C₄

—

118

—

166

C₂²×C₄

—

118

—

167

C₂²×C₄

D₄×D₅₉

yes

characteristic

168

C₂²×C₄

#11745687

yes

characteristic

169

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

170

Q₁₆

—

171

M₁₆

—

236

—

172

M₁₆

—

236

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

236

—

176

C₂×C₈

—

236

—

177

C₂×C₈

—

236

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₂²⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

118

—

188

C₄²

—

118

—

189

C₄²

—

118

—

190

C₄²

—

118

—

191

C₄²

—

236

—

192

C₄²

#11745687

yes

—

193

C₄²

C₂×C₂²⋊D₅₉

yes

—

194

C₂³

#14273698

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

118

—

204

C₂×C₄

—

118

—

205

C₂×C₄

—

118

—

206

C₂×C₄

—

118

—

207

C₂×C₄

—

236

—

208

C₂×C₄

—

236

—

209

C₂×C₄

#14273696

yes

characteristic

210

C₂×C₄

#14273699

yes

—

211

C₂×C₄

#14273708

yes

—

212

C₂×C₄

#14273714

yes

characteristic

213

C₂×C₄

Q₁₆×D₅₉

yes

characteristic

214

C₂×C₄

#14273750

yes

characteristic

215

C₂×C₄

#14273759

yes

—

216

C₈

—

217

C₈

—

472

—

218

C₈

—

472

—

219

C₂²

—

220

C₂²

—

221

C₂²

#16837316

yes

characteristic

222

C₂²

#16837640

yes

characteristic

223

C₂²

#16837657

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

118

—

229

C₄

—

236

—

230

C₄

#16837570

yes

characteristic

231

C₄

#16837585

yes

characteristic

232

C₄

#16837610

yes

—

233

C₄

#16837626

yes

—

234

C₂

—

235

C₂

—

236

C₂

#21425317

yes

characteristic

237

C₂

#21425380

yes

characteristic

238

C₂

#21425416

yes

characteristic

	subgroup	G/H
center	C₂²	#16837316
commutator, cosocle	C₂×C₄²×C₅₉	C₂³
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#3249	C₂
socle	C₂²×C₅₉	#394
prime radical	C₂³×C₅₉	#121
hypercenter	#3249	D₅₉
hypocenter	C₅₉	#10522
LCS	G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3249

subgroup

G/H

center

C₂²

#16837316

commutator, cosocle

C₂×C₄²×C₅₉

C₂³

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#3249

C₂

C₂²×C₅₉

C₂³×C₅₉

D₅₉

C₅₉

G ▷ C₂×C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3249

N	H ≅ G/N	type
68. C₄×Dic₅₉	Q₁₆	semidirect
138. C₅₉	#10522	semidirect

H ≅ G/N

type

68. C₄×Dic₅₉

Q₁₆

semidirect

138. C₅₉

#10522

semidirect

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

subgroup	index
#21425074	2
#21424247	2
#21422786	2
#21421971	2
C₅₉×#3249	2
#10522	59

subgroup

index

C₅₉×#3249

Subgroups — #28492814

Conjugacy classes of subgroups

Complements

Maximal subgroups