Group #28488378 — subgroups

Subgroups — #28488378

Order 15104.

602 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 131 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	C₂×#16837779	C₂	1	1	yes	maximal, characteristic
2	#21424936	C₂	1	2	yes	maximal, complemented
3	#21422852	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422763	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄₇₂	C₄	1	4	yes	—
7	C₂×#14273724	C₂²	1	2	yes	—
8	#16837779	—	2	2	no	—
9	#16837779	—	2	1	no	—
10	#16837779	—	2	1	no	—
11	#16837426	C₂²	1	2	yes	—
12	C₂×#14273643	—	2	4	no	—
13	#16837153	—	2	2	no	—
14	#16837145	—	2	4	no	—
15	C₅₉×#431	C₂²	1	1	yes	characteristic
16	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#322	—	2	1	no	—
19	C₅₉×#322	—	2	1	no	—
20	C₂²×D₂₃₆	—	2	2	no	—
21	C₂²×D₂₃₆	—	2	2	no	—
22	C₂²×D₂₃₆	C₂×C₄	1	4	yes	—
23	C₂×D₄₇₂	—	2	4	no	—
24	C₂×D₄₇₂	—	2	4	no	—
25	C₂×D₄₇₂	—	4	8	no	—
26	C₂×#11745664	—	2	2	no	—
27	#14273724	—	2	2	no	—
28	#14273724	—	2	2	no	—
29	#14273724	—	2	2	no	—
30	#14273724	—	2	2	no	—
31	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
32	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
33	#14273643	—	4	8	no	—
34	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
35	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
38	C₂²⋊C₈×C₅₉	—	2	1	no	—
39	#97×C₅₉	—	2	1	no	—
40	C₄×C₈×C₅₉	—	2	1	no	—
41	C₄×C₈×C₅₉	—	2	1	no	—
42	C₄×C₈×C₅₉	D₄	1	2	yes	—
43	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
44	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
45	C₂³×D₅₉	—	2	4	no	—
46	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
49	C₂×D₂₃₆	—	2	4	no	—
50	C₂×D₂₃₆	—	2	4	no	—
51	C₂×D₂₃₆	—	4	8	no	—
52	C₂×D₂₃₆	—	4	2	no	—
53	C₂×D₂₃₆	—	4	2	no	—
54	C₂×D₂₃₆	—	4	2	no	—
55	C₂×D₂₃₆	—	4	2	no	—
56	C₂×D₂₃₆	—	4	4	no	—
57	C₂×D₂₃₆	—	4	4	no	—
58	C₂×D₂₃₆	—	8	4	no	—
59	M₁₆×C₅₉	—	2	4	no	—
60	C₂×C₈×C₅₉	—	2	4	no	—
61	C₂×C₈×C₅₉	—	2	2	no	—
62	C₂×C₈×C₅₉	—	2	2	no	—
63	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
67	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₄²×C₅₉	#41	1	1	yes	characteristic
69	#11745664	—	4	4	no	—
70	C₂×C₅₉⋊C₈	—	4	2	no	—
71	D₄₇₂	—	4	8	no	—
72	D₄₇₂	—	4	8	no	—
73	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
74	C₂²×D₅₉	—	4	4	no	—
75	C₂²×D₅₉	—	4	8	no	—
76	C₂²×D₅₉	—	8	4	no	—
77	C₂²×D₅₉	—	8	4	no	—
78	C₂×C₄×C₅₉	—	2	2	no	—
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
83	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
84	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
85	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
86	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	4	yes	—
87	D₂₃₆	—	4	8	no	—
88	D₂₃₆	—	8	4	no	—
89	D₂₃₆	—	8	4	no	—
90	D₂₃₆	—	8	4	no	—
91	D₂₃₆	—	8	4	no	—
92	D₂₃₆	—	8	2	no	—
93	D₂₃₆	—	8	2	no	—
94	C₈×C₅₉	—	2	2	no	—
95	C₈×C₅₉	—	4	2	no	—
96	C₈×C₅₉	—	4	2	no	—
97	C₈×C₅₉	#100	1	4	yes	complemented
98	C₅₉⋊C₈	—	8	2	no	—
99	#9811	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	—	2	1	no	—
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	#390	1	1	yes	characteristic
103	C₂²×C₅₉	#442	1	2	yes	—
104	C₂×D₅₉	—	8	4	no	—
105	C₂×D₅₉	—	8	4	no	—
106	C₂×D₅₉	—	8	4	no	—
107	C₂×D₅₉	—	16	8	no	—
108	C₄×C₅₉	—	2	1	no	—
109	C₄×C₅₉	—	2	1	no	—
110	C₄×C₅₉	C₂×#100	1	2	yes	—
111	C₄×C₅₉	#469	1	2	yes	—
112	C₄×C₅₉	#472	1	2	yes	—
113	C₄×C₅₉	#496	1	2	yes	—
114	C₂×#493	—	59	1	no	—
115	#1965	—	59	2	no	—
116	#1566	—	59	1	no	—
117	#1545	—	59	2	no	—
118	#1451	D₅₉	1	1	yes	characteristic, complemented
119	C₂×C₅₉	—	2	2	no	—
120	C₂×C₅₉	#1965	1	1	yes	characteristic
121	C₂×C₅₉	#1972	1	1	yes	characteristic
122	C₂×C₅₉	#1978	1	1	yes	characteristic
123	D₅₉	—	16	4	no	—
124	C₂²×D₈	—	59	4	no	—
125	C₂×#127	—	59	2	no	—
126	#493	—	118	2	no	—
127	#493	—	118	1	no	—
128	#493	—	118	1	no	—
129	#431	C₂×D₅₉	1	1	yes	characteristic
130	#423	—	59	2	no	—
131	C₂×#100	—	118	4	no	—
132	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
134	#334	—	118	2	no	—
135	#331	—	118	4	no	—
136	#322	—	2	1	no	—
137	#322	—	2	1	no	—
138	C₅₉	#9811	1	1	yes	characteristic, complemented, Sylow
139	C₂²×D₄	—	59	4	no	—
140	C₂²×D₄	—	118	2	no	—
141	C₂²×D₄	—	118	2	no	—
142	C₂×D₈	—	118	4	no	—
143	C₂×D₈	—	118	4	no	—
144	C₂×D₈	—	236	8	no	—
145	C₂×M₁₆	—	118	2	no	—
146	C₂×M₁₆	D₂₃₆	1	2	yes	—
147	C₂²×C₈	C₄×D₅₉	1	2	yes	—
148	#127	—	118	2	no	—
149	#127	—	118	2	no	—
150	#127	—	118	2	no	—
151	#127	—	118	2	no	—
152	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
153	C₄⋊C₈	—	118	2	no	—
154	C₄⋊C₈	—	118	2	no	—
155	C₄⋊C₈	D₂₃₆	1	2	yes	—
156	#100	—	236	8	no	—
157	C₂²⋊C₈	—	2	1	no	—
158	#97	—	2	1	no	—
159	C₄×C₈	—	2	1	no	—
160	C₄×C₈	—	2	1	no	—
161	C₄×C₈	D₂₃₆	1	2	yes	—
162	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
163	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
164	C₂⁴	—	118	4	no	—
165	C₂×D₄	—	118	4	no	—
166	C₂×D₄	—	118	4	no	—
167	C₂×D₄	—	472	4	no	—
168	C₂×D₄	—	236	8	no	—
169	C₂×D₄	—	236	2	no	—
170	C₂×D₄	—	236	2	no	—
171	C₂×D₄	—	236	2	no	—
172	C₂×D₄	—	236	2	no	—
173	C₂×D₄	—	236	4	no	—
174	C₂×D₄	—	236	4	no	—
175	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
176	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
177	C₂²×C₄	#11745685	1	1	yes	characteristic
178	D₈	—	236	8	no	—
179	D₈	—	236	8	no	—
180	M₁₆	—	2	4	no	—
181	M₁₆	—	236	4	no	—
182	C₂×C₈	—	2	4	no	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	236	2	no	—
186	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
187	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
188	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
189	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
190	C₄²	#11745685	1	1	yes	characteristic
191	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
192	C₂³	—	472	4	no	—
193	C₂³	—	472	4	no	—
194	C₂³	—	236	8	no	—
195	C₂³	—	236	4	no	—
196	C₂³	C₄×D₂₃₆	1	1	yes	characteristic
197	D₄	—	472	4	no	—
198	D₄	—	472	4	no	—
199	D₄	—	472	4	no	—
200	D₄	—	472	4	no	—
201	D₄	—	472	2	no	—
202	D₄	—	472	2	no	—
203	D₄	—	236	8	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
207	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
208	C₂×C₄	#14273701	1	1	yes	characteristic
209	C₂×C₄	#14273701	1	1	yes	characteristic
210	C₂×C₄	#14273715	1	1	yes	characteristic
211	C₂×C₄	#14273724	1	1	yes	characteristic
212	C₂×C₄	#14273755	1	4	yes	—
213	C₈	—	2	2	no	—
214	C₈	—	4	2	no	—
215	C₈	—	4	2	no	—
216	C₈	—	472	2	no	—
217	C₈	#14273643	1	4	yes	complemented
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	944	8	no	—
221	C₂²	—	472	4	no	—
222	C₂²	—	472	4	no	—
223	C₂²	—	472	4	no	—
224	C₂²	#16837304	1	1	yes	characteristic
225	C₂²	#16837515	1	2	yes	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	C₂×#14273643	1	2	yes	—
229	C₄	#16837655	1	2	yes	—
230	C₄	#16837672	1	2	yes	—
231	C₄	#16837791	1	2	yes	—
232	C₂	—	2	2	no	—
233	C₂	—	944	4	no	—
234	C₂	#21424936	1	1	yes	characteristic
235	C₂	#21424972	1	1	yes	characteristic
236	C₂	#21425006	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837779

C₂

yes

maximal, characteristic

#21424936

C₂

yes

maximal, complemented

#21422852

C₂

yes

maximal, characteristic, complemented

#21422763

C₂

yes

maximal, complemented

C₅₉×#1451

C₂

yes

maximal, characteristic, complemented

C₂²×D₄₇₂

C₄

yes

—

C₂×#14273724

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×#14273643

—

#16837153

—

#16837145

—

C₅₉×#431

C₂²

yes

characteristic

C₄×M₁₆×C₅₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#322

—

C₅₉×#322

—

C₂²×D₂₃₆

—

C₂²×D₂₃₆

—

C₂²×D₂₃₆

C₂×C₄

yes

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

—

—

—

—

—

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

—

#14273643

—

C₂×M₁₆×C₅₉

D₄

yes

—

C₂²×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄⋊C₈×C₅₉

D₄

yes

—

C₂²⋊C₈×C₅₉

—

#97×C₅₉

—

C₄×C₈×C₅₉

—

C₄×C₈×C₅₉

—

C₄×C₈×C₅₉

D₄

yes

—

C₄×C₈×C₅₉

D₄

yes

characteristic

C₄×C₈×C₅₉

D₄

yes

characteristic

C₂³×D₅₉

—

C₂²×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₉

#41

yes

characteristic

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

characteristic

C₄²×C₅₉

C₂×D₄

yes

C₄²×C₅₉

yes

—

C₂×C₅₉⋊C₈

—

D₄₇₂

—

D₄₇₂

—

C₂³×C₅₉

C₄×D₄

yes

characteristic

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

#100

yes

complemented

C₅₉⋊C₈

—

#9811

—

maximal, Sylow

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

#390

yes

characteristic

103

C₂²×C₅₉

#442

yes

—

104

C₂×D₅₉

—

105

C₂×D₅₉

—

106

C₂×D₅₉

—

107

C₂×D₅₉

—

108

C₄×C₅₉

—

109

C₄×C₅₉

—

110

C₄×C₅₉

C₂×#100

yes

—

111

C₄×C₅₉

#469

yes

—

112

C₄×C₅₉

#472

yes

—

113

C₄×C₅₉

#496

yes

—

114

C₂×#493

—

115

#1965

—

116

#1566

—

117

#1545

—

118

#1451

D₅₉

yes

characteristic, complemented

119

C₂×C₅₉

—

120

C₂×C₅₉

#1965

yes

characteristic

121

C₂×C₅₉

#1972

yes

characteristic

122

C₂×C₅₉

#1978

yes

characteristic

123

D₅₉

—

124

C₂²×D₈

—

125

C₂×#127

—

126

#493

—

118

—

127

#493

—

118

—

128

#493

—

118

—

129

#431

C₂×D₅₉

yes

characteristic

130

#423

—

131

C₂×#100

—

118

—

132

C₄×M₁₆

C₂×D₅₉

yes

characteristic

133

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

134

#334

—

118

—

135

#331

—

118

—

136

#322

—

137

#322

—

138

C₅₉

#9811

yes

characteristic, complemented, Sylow

139

C₂²×D₄

—

140

C₂²×D₄

—

118

—

141

C₂²×D₄

—

118

—

142

C₂×D₈

—

118

—

143

C₂×D₈

—

118

—

144

C₂×D₈

—

236

—

145

C₂×M₁₆

—

118

—

146

C₂×M₁₆

D₂₃₆

yes

—

147

C₂²×C₈

C₄×D₅₉

yes

—

148

#127

—

118

—

149

#127

—

118

—

150

#127

—

118

—

151

#127

—

118

—

152

C₂×C₄²

C₂²×D₅₉

yes

characteristic

153

C₄⋊C₈

—

118

—

154

C₄⋊C₈

—

118

—

155

C₄⋊C₈

D₂₃₆

yes

—

156

#100

—

236

—

157

C₂²⋊C₈

—

158

#97

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

D₂₃₆

yes

—

162

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

163

C₄×C₈

C₂²⋊D₅₉

yes

characteristic

164

C₂⁴

—

118

—

165

C₂×D₄

—

118

—

166

C₂×D₄

—

118

—

167

C₂×D₄

—

472

—

168

C₂×D₄

—

236

—

169

C₂×D₄

—

236

—

170

C₂×D₄

—

236

—

171

C₂×D₄

—

236

—

172

C₂×D₄

—

236

—

173

C₂×D₄

—

236

—

174

C₂×D₄

—

236

—

175

C₂²×C₄

C₂×C₄×D₅₉

yes

characteristic

176

C₂²×C₄

C₂×D₂₃₆

yes

characteristic

177

C₂²×C₄

#11745685

yes

characteristic

178

D₈

—

236

—

179

D₈

—

236

—

180

M₁₆

—

181

M₁₆

—

236

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

236

—

186

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

187

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

188

C₄²

C₂×D₂₃₆

yes

characteristic

189

C₄²

C₂×D₂₃₆

yes

characteristic

190

C₄²

#11745685

yes

characteristic

191

C₄²

C₂×C₂²⋊D₅₉

yes

characteristic

192

C₂³

—

472

—

193

C₂³

—

472

—

194

C₂³

—

236

—

195

C₂³

—

236

—

196

C₂³

C₄×D₂₃₆

yes

characteristic

197

D₄

—

472

—

198

D₄

—

472

—

199

D₄

—

472

—

200

D₄

—

472

—

201

D₄

—

472

—

202

D₄

—

472

—

203

D₄

—

236

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

207

C₂×C₄

C₄×D₂₃₆

yes

characteristic

208

C₂×C₄

#14273701

yes

characteristic

209

C₂×C₄

#14273701

yes

characteristic

210

C₂×C₄

#14273715

yes

characteristic

211

C₂×C₄

#14273724

yes

characteristic

212

C₂×C₄

#14273755

yes

—

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

472

—

217

C₈

#14273643

yes

complemented

218

C₂²

—

219

C₂²

—

220

C₂²

—

944

—

221

C₂²

—

472

—

222

C₂²

—

472

—

223

C₂²

—

472

—

224

C₂²

#16837304

yes

characteristic

225

C₂²

#16837515

yes

—

226

C₄

—

227

C₄

—

228

C₄

C₂×#14273643

yes

—

229

C₄

#16837655

yes

—

230

C₄

#16837672

yes

—

231

C₄

#16837791

yes

—

232

C₂

—

233

C₂

—

944

—

234

C₂

#21424936

yes

characteristic

235

C₂

#21424972

yes

characteristic

236

C₂

#21425006

yes

characteristic

	subgroup	G/H
center	C₂²	#16837304
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₅₉×#1451	C₂
socle	C₂²×C₅₉	#390
prime radical	C₂×#16837779	C₂
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1451	D₅₉
hypocenter	C₅₉	#9811
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1451

subgroup

G/H

center

C₂²

#16837304

commutator

C₂²×C₄×C₅₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₉

Fitting

C₅₉×#1451

C₂

C₂²×C₅₉

C₂

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1451

N	H ≅ G/N	type
2. #21424936	C₂	semidirect
3. #21422852	C₂	semidirect
4. #21422763	C₂	semidirect
5. C₅₉×#1451	C₂	semidirect
97. C₈×C₅₉	#100	semidirect
118. #1451	D₅₉	semidirect
138. C₅₉	#9811	semidirect
217. C₈	#14273643	semidirect

H ≅ G/N

type

2. #21424936

C₂

semidirect

3. #21422852

C₂

semidirect

4. #21422763

C₂

semidirect

5. C₅₉×#1451

C₂

semidirect

97. C₈×C₅₉

#100

semidirect

118. #1451

D₅₉

semidirect

138. C₅₉

#9811

semidirect

217. C₈

#14273643

semidirect

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

subgroup	index
C₂×#16837779	2
#21424936	2
#21422852	2
#21422763	2
C₅₉×#1451	2
#9811	59

subgroup

index

C₅₉×#1451

Subgroups — #28488378

Conjugacy classes of subgroups

Complements

Maximal subgroups