Group #28500258 — subgroups

Subgroups — #28500258

Order 15104.

270 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 115 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	#21425850	C₂	1	2	yes	maximal
2	C₈²×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#21422166	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422165	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14273666	—	2	2	no	—
7	C₄×C₈×D₅₉	C₄	1	1	yes	characteristic
8	C₄×C₈×D₅₉	C₄	1	1	yes	characteristic
9	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
10	C₄⋊(C₅₉⋊C₁₆)	C₂²	1	2	yes	—
11	Dic₅₉⋊C₁₆	—	2	2	no	—
12	C₈×C₅₉⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₅₉⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₅₉×C₄⋊C₁₆	C₂²	1	2	yes	—
16	C₈²×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₅₉	—	2	1	no	—
18	C₂×C₈×D₅₉	C₈	1	1	yes	characteristic
19	C₂×C₈×D₅₉	C₈	1	1	yes	characteristic
20	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
21	C₂×C₈×D₅₉	Q₈	1	1	yes	characteristic
22	C₄²×D₅₉	C₂×C₄	1	1	yes	characteristic
23	#14273666	—	4	4	no	—
24	C₂×C₅₉⋊C₁₆	—	2	2	no	—
25	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₅₉	—	2	1	no	—
29	C₈×Dic₅₉	C₈	1	1	yes	characteristic
30	C₈×Dic₅₉	C₈	1	1	yes	characteristic
31	C₈×Dic₅₉	D₄	1	1	yes	characteristic
32	C₈×Dic₅₉	Q₈	1	1	yes	characteristic
33	C₂×C₁₆×C₅₉	—	2	2	no	—
34	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
37	C₂×C₄×D₅₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×D₅₉	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×D₅₉	M₁₆	1	1	yes	characteristic
40	C₂×C₈×C₅₉	—	2	1	no	—
41	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
46	C₄×Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
47	C₄×Dic₅₉	C₂×C₈	1	1	yes	characteristic
48	C₄×Dic₅₉	M₁₆	1	1	yes	characteristic
49	C₂×C₅₉⋊C₈	—	2	1	no	—
50	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₅₉⋊C₈	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
53	C₂×C₅₉⋊C₈	C₂×C₈	1	1	yes	characteristic
54	C₈×D₅₉	—	2	4	no	—
55	C₈×D₅₉	—	2	2	no	—
56	C₈×D₅₉	—	2	2	no	—
57	C₈×D₅₉	—	2	2	no	—
58	C₈×D₅₉	D₈	1	2	yes	—
59	C₈×D₅₉	Q₁₆	1	2	yes	—
60	C₁₆×C₅₉	—	4	2	no	—
61	C₅₉⋊C₁₆	—	4	2	no	—
62	C₂²×D₅₉	C₄⋊C₈	1	1	yes	characteristic
63	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
65	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
66	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
67	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
68	C₂×Dic₅₉	C₄⋊C₈	1	1	yes	characteristic
69	C₄×D₅₉	—	2	1	no	—
70	C₄×D₅₉	—	2	1	no	—
71	C₄×D₅₉	—	2	2	no	—
72	C₄×D₅₉	#107	1	2	yes	—
73	C₄×D₅₉	#108	1	2	yes	—
74	C₈×C₅₉	—	2	2	no	—
75	C₈×C₅₉	—	2	1	no	—
76	C₈×C₅₉	—	2	1	no	—
77	C₈×C₅₉	M₃₂	1	2	yes	complemented
78	C₈×C₅₉	C₂×D₈	1	1	yes	characteristic
79	C₈×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
80	C₅₉⋊C₈	—	2	2	no	—
81	C₅₉⋊C₈	—	2	1	no	—
82	C₅₉⋊C₈	—	2	1	no	—
83	C₅₉⋊C₈	#107	1	2	yes	—
84	C₅₉⋊C₈	M₃₂	1	2	yes	complemented
85	#12004	—	59	1	no	maximal, Sylow
86	C₂²×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
87	C₂×D₅₉	—	2	1	no	—
88	C₂×D₅₉	—	2	1	no	—
89	C₂×D₅₉	#335	1	2	yes	—
90	C₄×C₅₉	—	2	1	no	—
91	C₄×C₅₉	C₂×#107	1	1	yes	characteristic
92	C₄×C₅₉	C₂×#108	1	1	yes	characteristic
93	C₄×C₅₉	C₂×M₃₂	1	1	yes	characteristic
94	C₄×C₅₉	C₂×M₃₂	1	1	yes	characteristic
95	Dic₅₉	—	2	1	no	—
96	Dic₅₉	#335	1	2	yes	—
97	Dic₅₉	#364	1	2	yes	—
98	#2150	—	59	2	no	—
99	C₂×C₈²	—	59	1	no	—
100	#1370	—	59	2	no	—
101	#1370	—	59	1	no	—
102	#1370	D₅₉	1	1	yes	characteristic, complemented
103	C₂×C₅₉	C₂×#335	1	1	yes	characteristic
104	C₂×C₅₉	#2150	1	1	yes	characteristic
105	C₂×C₅₉	C₂×#364	1	1	yes	characteristic
106	D₅₉	—	2	2	no	—
107	C₂×M₃₂	—	118	2	no	—
108	C₂×C₄×C₈	—	59	1	no	—
109	C₂×C₄×C₈	—	59	1	no	—
110	C₂×C₄×C₈	—	59	1	no	—
111	C₄⋊C₁₆	—	59	2	no	—
112	C₄⋊C₁₆	—	118	2	no	—
113	C₄⋊C₁₆	C₂×D₅₉	1	2	yes	—
114	C₈²	—	59	1	no	—
115	C₈²	—	59	1	no	—
116	C₈²	—	59	1	no	—
117	C₈²	C₂×D₅₉	1	1	yes	characteristic
118	C₅₉	#12004	1	1	yes	characteristic, complemented, Sylow
119	C₂²×C₈	—	59	1	no	—
120	C₂²×C₈	—	59	1	no	—
121	C₂²×C₈	—	59	1	no	—
122	C₂²×C₈	—	59	1	no	—
123	C₂²×C₈	—	118	1	no	—
124	C₂×C₄²	—	59	1	no	—
125	M₃₂	—	236	4	no	—
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	118	2	no	—
128	C₄×C₈	—	59	1	no	—
129	C₄×C₈	—	59	1	no	—
130	C₄×C₈	—	59	1	no	—
131	C₄×C₈	—	59	1	no	—
132	C₄×C₈	—	59	1	no	—
133	C₄×C₈	—	59	1	no	—
134	C₄×C₈	—	59	1	no	—
135	C₄×C₈	—	118	1	no	—
136	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
137	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
138	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
139	C₂²×C₄	—	59	1	no	—
140	C₂²×C₄	—	59	1	no	—
141	C₂²×C₄	—	59	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	59	1	no	—
144	C₂×C₈	—	59	1	no	—
145	C₂×C₈	—	59	2	no	—
146	C₂×C₈	—	59	2	no	—
147	C₂×C₈	—	59	1	no	—
148	C₂×C₈	—	59	1	no	—
149	C₂×C₈	—	118	2	no	—
150	C₂×C₈	—	118	2	no	—
151	C₂×C₈	—	118	4	no	—
152	C₂×C₈	—	118	1	no	—
153	C₂×C₈	—	118	2	no	—
154	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
155	C₂×C₈	C₈×D₅₉	1	1	yes	characteristic
156	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
157	C₂×C₈	Q₈×D₅₉	1	1	yes	characteristic
158	C₄²	—	59	1	no	—
159	C₄²	—	59	1	no	—
160	C₄²	—	59	1	no	—
161	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
162	C₁₆	—	4	2	no	—
163	C₁₆	—	236	2	no	—
164	C₂³	—	59	1	no	—
165	C₂×C₄	—	59	1	no	—
166	C₂×C₄	—	59	1	no	—
167	C₂×C₄	—	59	2	no	—
168	C₂×C₄	—	59	2	no	—
169	C₂×C₄	—	59	1	no	—
170	C₂×C₄	—	118	2	no	—
171	C₂×C₄	—	118	1	no	—
172	C₂×C₄	—	118	1	no	—
173	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
174	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
175	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	2	1	no	—
178	C₈	—	2	1	no	—
179	C₈	—	59	2	no	—
180	C₈	—	59	2	no	—
181	C₈	—	118	2	no	—
182	C₈	—	118	1	no	—
183	C₈	—	118	1	no	—
184	C₈	#14273666	1	2	yes	complemented
185	C₈	D₈×D₅₉	1	1	yes	characteristic
186	C₈	Q₁₆×D₅₉	1	1	yes	characteristic
187	C₂²	—	59	2	no	—
188	C₂²	—	118	1	no	—
189	C₂²	—	118	1	no	—
190	C₂²	C₄⋊C₈×D₅₉	1	1	yes	characteristic
191	C₄	—	2	1	no	—
192	C₄	—	59	2	no	—
193	C₄	—	59	2	no	—
194	C₄	—	118	1	no	—
195	C₄	#107×D₅₉	1	1	yes	characteristic
196	C₄	#108×D₅₉	1	1	yes	characteristic
197	C₄	M₃₂×D₅₉	1	1	yes	characteristic
198	C₄	C₂×#14273666	1	1	yes	characteristic
199	C₂	—	118	2	no	—
200	C₂	#335×D₅₉	1	1	yes	characteristic
201	C₂	#21425850	1	1	yes	characteristic
202	C₂	#364×D₅₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21425850

C₂

yes

maximal

C₈²×D₅₉

C₂

yes

maximal, characteristic

#21422166

C₂

yes

maximal, characteristic, complemented

#21422165

C₂

yes

maximal, complemented

C₅₉×#1370

C₂

yes

maximal, characteristic, complemented

C₂×#14273666

—

C₄×C₈×D₅₉

C₄

yes

characteristic

C₄×C₈×D₅₉

C₄

yes

characteristic

C₄×C₈×D₅₉

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₁₆)

C₂²

yes

—

Dic₅₉⋊C₁₆

—

C₈×C₅₉⋊C₈

C₄

yes

characteristic

C₈×C₅₉⋊C₈

C₄

yes

characteristic

C₈×C₅₉⋊C₈

C₂²

yes

characteristic

C₅₉×C₄⋊C₁₆

C₂²

yes

—

C₈²×C₅₉

C₂²

yes

characteristic

C₂×C₈×D₅₉

—

C₂×C₈×D₅₉

C₈

yes

characteristic

C₂×C₈×D₅₉

C₈

yes

characteristic

C₂×C₈×D₅₉

D₄

yes

characteristic

C₂×C₈×D₅₉

Q₈

yes

characteristic

C₄²×D₅₉

C₂×C₄

yes

characteristic

#14273666

—

C₂×C₅₉⋊C₁₆

—

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₄×C₅₉⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₅₉

—

C₈×Dic₅₉

C₈

yes

characteristic

C₈×Dic₅₉

C₈

yes

characteristic

C₈×Dic₅₉

D₄

yes

characteristic

C₈×Dic₅₉

Q₈

yes

characteristic

C₂×C₁₆×C₅₉

—

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂×C₄

yes

characteristic

C₄×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₄×D₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×D₅₉

C₂×C₈

yes

characteristic

C₂×C₄×D₅₉

M₁₆

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₈

yes

characteristic

C₂×C₈×C₅₉

C₂×C₈

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×Q₈

yes

characteristic

C₄²×C₅₉

C₂²×C₄

yes

characteristic

C₄×Dic₅₉

C₄⋊C₄

yes

characteristic

C₄×Dic₅₉

C₂×C₈

yes

characteristic

C₄×Dic₅₉

M₁₆

yes

characteristic

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₈

yes

characteristic

C₂×C₅₉⋊C₈

C₂×C₈

yes

characteristic

C₈×D₅₉

—

C₈×D₅₉

—

C₈×D₅₉

—

C₈×D₅₉

—

C₈×D₅₉

D₈

yes

—

C₈×D₅₉

Q₁₆

yes

—

C₁₆×C₅₉

—

C₅₉⋊C₁₆

—

C₂²×D₅₉

C₄⋊C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×M₁₆

yes

characteristic

C₂×Dic₅₉

C₄⋊C₈

yes

characteristic

C₂×Dic₅₉

C₄⋊C₈

yes

characteristic

C₂×Dic₅₉

C₄⋊C₈

yes

characteristic

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

—

C₄×D₅₉

#107

yes

—

C₄×D₅₉

#108

yes

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

M₃₂

yes

complemented

C₈×C₅₉

C₂×D₈

yes

characteristic

C₈×C₅₉

C₂×Q₁₆

yes

characteristic

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

#107

yes

—

C₅₉⋊C₈

M₃₂

yes

complemented

#12004

—

maximal, Sylow

C₂²×C₅₉

C₂×C₄⋊C₈

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

#335

yes

—

C₄×C₅₉

—

C₄×C₅₉

yes

C₄×C₅₉

yes

C₄×C₅₉

C₂×M₃₂

yes

characteristic

C₄×C₅₉

C₂×M₃₂

yes

characteristic

Dic₅₉

—

Dic₅₉

#335

yes

—

Dic₅₉

#364

yes

—

#2150

—

C₂×C₈²

—

100

#1370

—

101

#1370

—

102

#1370

D₅₉

yes

characteristic, complemented

103

C₂×C₅₉

C₂×#335

yes

characteristic

104

C₂×C₅₉

#2150

yes

characteristic

105

C₂×C₅₉

C₂×#364

yes

characteristic

106

D₅₉

—

107

C₂×M₃₂

—

118

—

108

C₂×C₄×C₈

—

109

C₂×C₄×C₈

—

110

C₂×C₄×C₈

—

111

C₄⋊C₁₆

—

112

C₄⋊C₁₆

—

118

—

113

C₄⋊C₁₆

C₂×D₅₉

yes

—

114

C₈²

—

115

C₈²

—

116

C₈²

—

117

C₈²

C₂×D₅₉

yes

characteristic

118

C₅₉

#12004

yes

characteristic, complemented, Sylow

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

—

118

—

124

C₂×C₄²

—

125

M₃₂

—

236

—

126

C₂×C₁₆

—

127

C₂×C₁₆

—

118

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₄×C₈

—

134

C₄×C₈

—

135

C₄×C₈

—

118

—

136

C₄×C₈

C₄×D₅₉

yes

characteristic

137

C₄×C₈

C₄×D₅₉

yes

characteristic

138

C₄×C₈

C₂²×D₅₉

yes

characteristic

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

118

—

150

C₂×C₈

—

118

—

151

C₂×C₈

—

118

—

152

C₂×C₈

—

118

—

153

C₂×C₈

—

118

—

154

C₂×C₈

C₈×D₅₉

yes

characteristic

155

C₂×C₈

C₈×D₅₉

yes

characteristic

156

C₂×C₈

D₄×D₅₉

yes

characteristic

157

C₂×C₈

Q₈×D₅₉

yes

characteristic

158

C₄²

—

159

C₄²

—

160

C₄²

—

161

C₄²

C₂×C₄×D₅₉

yes

characteristic

162

C₁₆

—

163

C₁₆

—

236

—

164

C₂³

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

118

—

171

C₂×C₄

—

118

—

172

C₂×C₄

—

118

—

173

C₂×C₄

C₄⋊C₄×D₅₉

yes

characteristic

174

C₂×C₄

C₂×C₈×D₅₉

yes

characteristic

175

C₂×C₄

M₁₆×D₅₉

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

118

—

182

C₈

—

118

—

183

C₈

—

118

—

184

C₈

#14273666

yes

complemented

185

C₈

D₈×D₅₉

yes

characteristic

186

C₈

Q₁₆×D₅₉

yes

characteristic

187

C₂²

—

188

C₂²

—

118

—

189

C₂²

—

118

—

190

C₂²

C₄⋊C₈×D₅₉

yes

characteristic

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

118

—

195

C₄

#107×D₅₉

yes

characteristic

196

C₄

#108×D₅₉

yes

characteristic

197

C₄

M₃₂×D₅₉

yes

characteristic

198

C₄

C₂×#14273666

yes

characteristic

199

C₂

—

118

—

200

C₂

#335×D₅₉

yes

characteristic

201

C₂

#21425850

yes

characteristic

202

C₂

#364×D₅₉

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₅₉
Fitting	C₅₉×#1370	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₈
prime radical	C₂²×D₅₉	C₄⋊C₈
cosocle	C₄×C₈×C₅₉	C₂³
hypercenter	#1370	D₅₉
hypocenter	C₅₉	#12004
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₅₉

commutator

C₂×C₄×C₅₉

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₅₉

Fitting

C₅₉×#1370

C₂

socle

C₂²×C₅₉

C₂×C₄⋊C₈

prime radical

C₂²×D₅₉

C₄⋊C₈

cosocle

C₄×C₈×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
3. #21422166	C₂	semidirect
4. #21422165	C₂	semidirect
5. C₅₉×#1370	C₂	semidirect
77. C₈×C₅₉	M₃₂	semidirect
84. C₅₉⋊C₈	M₃₂	semidirect
102. #1370	D₅₉	semidirect
118. C₅₉	#12004	semidirect
184. C₈	#14273666	semidirect

H ≅ G/N

type

3. #21422166

C₂

semidirect

4. #21422165

C₂

semidirect

5. C₅₉×#1370

C₂

semidirect

77. C₈×C₅₉

M₃₂

semidirect

84. C₅₉⋊C₈

M₃₂

semidirect

102. #1370

D₅₉

semidirect

118. C₅₉

#12004

semidirect

184. C₈

#14273666

semidirect

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

subgroup	index
#21425850	2
C₈²×D₅₉	2
#21422166	2
#21422165	2
C₅₉×#1370	2
#12004	59

subgroup

index

C₈²×D₅₉

C₅₉×#1370

Subgroups — #28500258

Conjugacy classes of subgroups

Complements

Maximal subgroups