Group #28506920 — subgroups

Subgroups — #28506920

Order 15104.

590 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 159 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	C₂×#16837202	C₂	1	4	yes	maximal, complemented
3	C₂×#16837178	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1846	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄₇₂	—	2	1	no	—
6	C₂²×D₄₇₂	C₂²	1	2	yes	—
7	C₂×#14273724	—	2	1	no	—
8	C₂²×C₅₉⋊C₁₆	C₂²	1	2	yes	—
9	#16837779	—	2	2	no	—
10	#16837779	C₄	1	4	yes	complemented
11	#16837202	—	2	8	no	—
12	#16837178	—	2	2	no	—
13	C₂×#107×C₅₉	C₂²	1	2	yes	—
14	C₂×#106×C₅₉	—	2	1	no	—
15	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#382	—	2	1	no	—
17	C₂²×D₂₃₆	—	2	2	no	—
18	C₂²×D₂₃₆	—	4	2	no	—
19	C₂×D₄₇₂	—	2	4	no	—
20	C₂×D₄₇₂	—	2	4	no	—
21	C₂×D₄₇₂	—	2	4	no	—
22	C₂×D₄₇₂	—	2	2	no	—
23	C₂×D₄₇₂	—	4	2	no	—
24	C₂×D₄₇₂	—	4	2	no	—
25	C₂×D₄₇₂	C₂×C₄	1	4	yes	—
26	#14273724	—	2	4	no	—
27	#14273724	—	4	2	no	—
28	C₂×C₅₉⋊C₁₆	—	2	2	no	—
29	C₂×C₅₉⋊C₁₆	—	2	2	no	—
30	C₂×C₅₉⋊C₁₆	D₄	1	4	yes	complemented
31	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
32	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
34	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
35	#107×C₅₉	—	2	4	no	—
36	#106×C₅₉	—	4	2	no	—
37	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₅₉	D₄	1	2	yes	—
39	#95×C₅₉	—	4	2	no	—
40	C₂³×D₅₉	—	4	2	no	—
41	C₂²×C₄×C₅₉	—	4	2	no	—
42	C₂²×C₄×C₅₉	D₈	1	2	yes	—
43	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
44	C₂×D₂₃₆	—	2	4	no	—
45	C₂×D₂₃₆	—	4	2	no	—
46	C₂×D₂₃₆	—	4	2	no	—
47	C₂×D₂₃₆	—	4	2	no	—
48	C₂×D₂₃₆	—	4	2	no	—
49	C₂×D₂₃₆	—	4	8	no	—
50	C₂×D₂₃₆	—	4	2	no	—
51	C₂×D₂₃₆	—	8	8	no	—
52	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
53	C₂×C₈×C₅₉	D₈	1	2	yes	—
54	C₂×C₈×C₅₉	SD₁₆	1	2	yes	—
55	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₅₉	#41	1	2	yes	—
59	C₄⋊C₄×C₅₉	—	4	2	no	—
60	C₄⋊C₄×C₅₉	—	4	2	no	—
61	C₄²×C₅₉	C₂²⋊C₄	1	2	yes	—
62	C₄²×C₅₉	SD₁₆	1	2	yes	—
63	D₄₇₂	—	2	8	no	—
64	D₄₇₂	—	4	8	no	—
65	D₄₇₂	—	4	4	no	—
66	C₅₉⋊C₁₆	—	2	4	no	—
67	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
68	C₂²×D₅₉	—	4	4	no	—
69	C₂²×D₅₉	—	8	2	no	—
70	C₂²×D₅₉	—	8	2	no	—
71	C₂²×D₅₉	—	8	8	no	—
72	C₂×C₄×C₅₉	—	2	4	no	—
73	C₂×C₄×C₅₉	—	8	2	no	—
74	C₂×C₄×C₅₉	—	8	4	no	—
75	C₂×C₄×C₅₉	#102	1	4	yes	—
76	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
78	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
79	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
82	D₂₃₆	—	4	4	no	—
83	D₂₃₆	—	4	4	no	—
84	D₂₃₆	—	8	16	no	—
85	D₂₃₆	—	8	2	no	—
86	D₂₃₆	—	8	2	no	—
87	C₈×C₅₉	#102	1	4	yes	—
88	C₈×C₅₉	C₄×D₄	1	2	yes	—
89	C₈×C₅₉	#121	1	2	yes	—
90	#13206	—	59	1	no	maximal, Sylow
91	C₂²×C₅₉	C₂×#102	1	1	yes	characteristic
92	C₂²×C₅₉	#486	1	1	yes	characteristic
93	C₂²×C₅₉	#493	1	1	yes	characteristic
94	C₂²×C₅₉	#509	1	4	yes	—
95	C₂×D₅₉	—	8	8	no	—
96	C₂×D₅₉	—	8	4	no	—
97	C₂×D₅₉	—	16	4	no	—
98	C₂×D₅₉	—	16	4	no	—
99	C₄×C₅₉	—	2	4	no	—
100	C₄×C₅₉	—	16	2	no	—
101	C₄×C₅₉	#390	1	1	yes	characteristic
102	C₄×C₅₉	C₂×#102	1	1	yes	characteristic
103	C₄×C₅₉	#486	1	1	yes	characteristic
104	C₄×C₅₉	#492	1	1	yes	characteristic
105	C₂×#493	—	59	1	no	—
106	C₂×#357	—	59	4	no	—
107	C₂×#346	—	59	1	no	—
108	#1846	D₅₉	1	1	yes	characteristic, complemented
109	C₂×C₅₉	#1957	1	1	yes	characteristic
110	C₂×C₅₉	#2140	1	2	yes	—
111	C₂×C₅₉	#2244	1	2	yes	—
112	C₂×C₅₉	#2250	1	2	yes	—
113	D₅₉	—	16	4	no	—
114	C₂²×D₈	—	59	2	no	—
115	C₂²×D₈	—	118	1	no	—
116	C₂×#127	—	118	1	no	—
117	C₂²×C₁₆	—	59	2	no	—
118	#493	—	59	4	no	—
119	#493	—	118	2	no	—
120	C₂×#107	C₂×D₅₉	1	2	yes	—
121	C₂×#106	—	2	1	no	—
122	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
123	#382	—	2	1	no	—
124	#357	—	118	8	no	—
125	#346	—	118	2	no	—
126	C₅₉	#13206	1	1	yes	characteristic, complemented, Sylow
127	C₂²×D₄	—	118	2	no	—
128	C₂²×D₄	—	236	2	no	—
129	C₂×D₈	—	59	4	no	—
130	C₂×D₈	—	118	4	no	—
131	C₂×D₈	—	118	2	no	—
132	C₂×D₈	—	118	4	no	—
133	C₂×D₈	—	118	4	no	—
134	C₂×D₈	—	236	2	no	—
135	C₂×D₈	—	236	2	no	—
136	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
137	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
138	#127	—	118	4	no	—
139	#127	—	236	2	no	—
140	C₂×C₄⋊C₄	—	2	2	no	—
141	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
142	C₂×C₁₆	—	59	4	no	—
143	C₂×C₁₆	—	118	2	no	—
144	C₂×C₁₆	—	118	2	no	—
145	#107	—	2	4	no	—
146	#106	—	4	2	no	—
147	C₄×C₈	C₄×D₅₉	1	2	yes	—
148	C₄×C₈	D₂₃₆	1	2	yes	—
149	#95	—	4	2	no	—
150	C₂⁴	—	236	2	no	—
151	C₂×D₄	—	118	4	no	—
152	C₂×D₄	—	472	8	no	—
153	C₂×D₄	—	236	8	no	—
154	C₂×D₄	—	236	2	no	—
155	C₂×D₄	—	236	2	no	—
156	C₂×D₄	—	236	2	no	—
157	C₂×D₄	—	236	2	no	—
158	C₂×D₄	—	236	2	no	—
159	C₂²×C₄	—	4	2	no	—
160	C₂²×C₄	#11745669	1	2	yes	—
161	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
162	D₈	—	118	8	no	—
163	D₈	—	236	8	no	—
164	D₈	—	236	4	no	—
165	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
166	C₂×C₈	#11745669	1	2	yes	—
167	C₂×C₈	#11745671	1	2	yes	—
168	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
169	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
170	C₂×C₈	D₄×D₅₉	1	2	yes	—
171	C₂×C₈	#11745689	1	2	yes	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	2	no	—
174	C₄²	(C₂×D₅₉)⋊C₄	1	2	yes	—
175	C₄²	#11745671	1	2	yes	—
176	C₁₆	—	118	4	no	—
177	C₂³	—	472	2	no	—
178	C₂³	—	472	2	no	—
179	C₂³	—	472	8	no	—
180	C₂³	—	236	4	no	—
181	C₂³	C₂×#11745669	1	1	yes	characteristic
182	D₄	—	472	16	no	—
183	D₄	—	472	2	no	—
184	D₄	—	472	2	no	—
185	D₄	—	236	4	no	—
186	D₄	—	236	4	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	8	2	no	—
189	C₂×C₄	—	8	4	no	—
190	C₂×C₄	#14273647	1	4	yes	—
191	C₂×C₄	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#14273716	1	1	yes	characteristic
193	C₂×C₄	#14273723	1	1	yes	characteristic
194	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
195	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
196	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
197	C₈	#14273647	1	4	yes	—
198	C₈	#14273689	1	2	yes	—
199	C₈	#14273702	1	2	yes	—
200	C₂²	—	944	4	no	—
201	C₂²	—	944	4	no	—
202	C₂²	—	472	4	no	—
203	C₂²	—	472	8	no	—
204	C₂²	C₂×#14273647	1	1	yes	characteristic
205	C₂²	#16837750	1	1	yes	characteristic
206	C₂²	#16837778	1	1	yes	characteristic
207	C₂²	#16837837	1	4	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	16	2	no	—
210	C₄	#16837303	1	1	yes	characteristic
211	C₄	C₂×#14273647	1	1	yes	characteristic
212	C₄	#16837750	1	1	yes	characteristic
213	C₄	#16837776	1	1	yes	characteristic
214	C₂	—	944	4	no	—
215	C₂	#21424901	1	1	yes	characteristic
216	C₂	#21425811	1	2	yes	—
217	C₂	#21426339	1	2	yes	—
218	C₂	#21426363	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837779

C₂

yes

maximal, characteristic

C₂×#16837202

C₂

yes

maximal, complemented

C₂×#16837178

C₂

yes

maximal, characteristic, complemented

C₅₉×#1846

C₂

yes

maximal, characteristic, complemented

C₂²×D₄₇₂

—

C₂²×D₄₇₂

C₂²

yes

—

C₂×#14273724

—

C₂²×C₅₉⋊C₁₆

C₂²

yes

—

#16837779

—

#16837779

C₄

yes

complemented

#16837202

—

#16837178

—

C₂×#107×C₅₉

C₂²

yes

—

C₂×#106×C₅₉

—

C₂×C₄×C₈×C₅₉

C₂²

yes

characteristic

C₅₉×#382

—

C₂²×D₂₃₆

—

C₂²×D₂₃₆

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

—

C₂×D₄₇₂

C₂×C₄

yes

—

#14273724

—

#14273724

—

C₂×C₅₉⋊C₁₆

—

C₂×C₅₉⋊C₁₆

—

C₂×C₅₉⋊C₁₆

D₄

yes

complemented

C₂²×C₈×C₅₉

D₄

yes

characteristic

C₂²×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄²×C₅₉

D₄

yes

characteristic

#107×C₅₉

—

#106×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

—

C₄×C₈×C₅₉

D₄

yes

—

#95×C₅₉

—

C₂³×D₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

D₈

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×D₂₃₆

—

C₂×C₈×C₅₉

C₂²⋊C₄

yes

—

C₂×C₈×C₅₉

D₈

yes

—

C₂×C₈×C₅₉

SD₁₆

yes

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

—

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

#41

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

C₂²⋊C₄

yes

—

C₄²×C₅₉

SD₁₆

yes

—

D₄₇₂

—

D₄₇₂

—

D₄₇₂

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

C₂×D₈

yes

characteristic

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂²×D₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#102

yes

—

C₂×C₄×C₅₉

C₂×C₂²⋊C₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×D₈

yes

characteristic

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₉

C₂×SD₁₆

yes

characteristic

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

D₂₃₆

—

C₈×C₅₉

#102

yes

—

C₈×C₅₉

C₄×D₄

yes

—

C₈×C₅₉

#121

yes

—

—

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

C₂²×C₅₉

yes

—

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

100

C₄×C₅₉

—

101

C₄×C₅₉

#390

yes

characteristic

102

C₄×C₅₉

C₂×#102

yes

characteristic

103

C₄×C₅₉

#486

yes

characteristic

104

C₄×C₅₉

#492

yes

characteristic

105

C₂×#493

—

106

C₂×#357

—

107

C₂×#346

—

108

#1846

D₅₉

yes

characteristic, complemented

109

C₂×C₅₉

#1957

yes

characteristic

110

C₂×C₅₉

#2140

yes

—

111

C₂×C₅₉

#2244

yes

—

112

C₂×C₅₉

#2250

yes

—

113

D₅₉

—

114

C₂²×D₈

—

115

C₂²×D₈

—

118

—

116

C₂×#127

—

118

—

117

C₂²×C₁₆

—

118

#493

—

119

#493

—

118

—

120

C₂×#107

C₂×D₅₉

yes

—

121

C₂×#106

—

122

C₂×C₄×C₈

C₂×D₅₉

yes

characteristic

123

#382

—

124

#357

—

118

—

125

#346

—

118

—

126

C₅₉

#13206

yes

characteristic, complemented, Sylow

127

C₂²×D₄

—

118

—

128

C₂²×D₄

—

236

—

129

C₂×D₈

—

130

C₂×D₈

—

118

—

131

C₂×D₈

—

118

—

132

C₂×D₈

—

118

—

133

C₂×D₈

—

118

—

134

C₂×D₈

—

236

—

135

C₂×D₈

—

236

—

136

C₂²×C₈

C₂²⋊D₅₉

yes

characteristic

137

C₂²×C₈

C₂²×D₅₉

yes

characteristic

138

#127

—

118

—

139

#127

—

236

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄²

C₂²⋊D₅₉

yes

characteristic

142

C₂×C₁₆

—

143

C₂×C₁₆

—

118

—

144

C₂×C₁₆

—

118

—

145

#107

—

146

#106

—

147

C₄×C₈

C₄×D₅₉

yes

—

148

C₄×C₈

D₂₃₆

yes

—

149

#95

—

150

C₂⁴

—

236

—

151

C₂×D₄

—

118

—

152

C₂×D₄

—

472

—

153

C₂×D₄

—

236

—

154

C₂×D₄

—

236

—

155

C₂×D₄

—

236

—

156

C₂×D₄

—

236

—

157

C₂×D₄

—

236

—

158

C₂×D₄

—

236

—

159

C₂²×C₄

—

160

C₂²×C₄

#11745669

yes

—

161

C₂²×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

162

D₈

—

118

—

163

D₈

—

236

—

164

D₈

—

236

—

165

C₂×C₈

(C₂×D₅₉)⋊C₄

yes

—

166

C₂×C₈

#11745669

yes

—

167

C₂×C₈

#11745671

yes

—

168

C₂×C₈

C₂×C₄×D₅₉

yes

characteristic

169

C₂×C₈

C₂×D₂₃₆

yes

characteristic

170

C₂×C₈

D₄×D₅₉

yes

—

171

C₂×C₈

#11745689

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄²

(C₂×D₅₉)⋊C₄

yes

—

175

C₄²

#11745671

yes

—

176

C₁₆

—

118

—

177

C₂³

—

472

—

178

C₂³

—

472

—

179

C₂³

—

472

—

180

C₂³

—

236

—

181

C₂³

C₂×#11745669

yes

characteristic

182

D₄

—

472

—

183

D₄

—

472

—

184

D₄

—

472

—

185

D₄

—

236

—

186

D₄

—

236

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

#14273647

yes

—

191

C₂×C₄

C₂×(C₂×D₅₉)⋊C₄

yes

characteristic

192

C₂×C₄

#14273716

yes

characteristic

193

C₂×C₄

#14273723

yes

characteristic

194

C₂×C₄

C₂×#11745669

yes

characteristic

195

C₂×C₄

C₂×#11745671

yes

characteristic

196

C₂×C₄

C₂×#11745671

yes

characteristic

197

C₈

#14273647

yes

—

198

C₈

#14273689

yes

—

199

C₈

#14273702

yes

—

200

C₂²

—

944

—

201

C₂²

—

944

—

202

C₂²

—

472

—

203

C₂²

—

472

—

204

C₂²

C₂×#14273647

yes

characteristic

205

C₂²

#16837750

yes

characteristic

206

C₂²

#16837778

yes

characteristic

207

C₂²

#16837837

yes

—

208

C₄

—

209

C₄

—

210

C₄

#16837303

yes

characteristic

211

C₄

C₂×#14273647

yes

characteristic

212

C₄

#16837750

yes

characteristic

213

C₄

#16837776

yes

characteristic

214

C₂

—

944

—

215

C₂

#21424901

yes

characteristic

216

C₂

#21425811

yes

—

217

C₂

#21426339

yes

—

218

C₂

#21426363

yes

—

	subgroup	G/H
center	C₂³	C₂×#11745669
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting	C₅₉×#1846	C₂
socle	C₂³×C₅₉	C₂×D₈
prime radical	C₂×#16837779	C₂
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1846	D₅₉
hypocenter	C₅₉	#13206
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1846

subgroup

G/H

center

C₂³

C₂×#11745669

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting

C₅₉×#1846

C₂

socle

C₂³×C₅₉

C₂×D₈

prime radical

C₂×#16837779

C₂

cosocle

C₂²×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1846

N	H ≅ G/N	type
2. C₂×#16837202	C₂	semidirect
3. C₂×#16837178	C₂	semidirect
4. C₅₉×#1846	C₂	semidirect
10. #16837779	C₄	semidirect
30. C₂×C₅₉⋊C₁₆	D₄	semidirect
108. #1846	D₅₉	semidirect
126. C₅₉	#13206	semidirect

H ≅ G/N

type

2. C₂×#16837202

C₂

semidirect

3. C₂×#16837178

C₂

semidirect

4. C₅₉×#1846

C₂

semidirect

10. #16837779

C₄

semidirect

30. C₂×C₅₉⋊C₁₆

D₄

semidirect

108. #1846

D₅₉

semidirect

126. C₅₉

#13206

semidirect

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

subgroup	index
C₂×#16837779	2
C₂×#16837202	2
C₂×#16837178	2
C₅₉×#1846	2
#13206	59

subgroup

index

C₅₉×#1846

Subgroups — #28506920

Conjugacy classes of subgroups

Complements

Maximal subgroups