Group #28507114 — subgroups

Subgroups — #28507114

Order 15104.

442 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16837232	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16837215	C₂	1	2	yes	maximal, complemented
3	#21425692	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425007	C₂	1	2	yes	maximal, complemented
5	C₂²×D₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14273667	C₂²	1	1	yes	characteristic
7	C₂×#14273663	C₂²	1	2	yes	—
8	#16837407	—	2	2	no	—
9	C₂×#14273644	—	2	2	no	—
10	#16837357	C₂²	1	1	yes	characteristic
11	#16837232	—	2	2	no	—
12	#16837215	—	2	4	no	—
13	#16837177	—	2	1	no	—
14	C₁₆×Dic₅₉	—	2	1	no	—
15	C₂²×D₈×C₅₉	C₂²	1	2	yes	—
16	C₂×D₁₆×C₅₉	—	2	1	no	—
17	C₂×D₁₆×C₅₉	—	2	1	no	—
18	C₂×D₁₆×C₅₉	—	2	2	no	—
19	C₂×D₁₆×C₅₉	C₄	1	4	yes	complemented
20	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#11745664	—	2	2	no	—
22	C₂×#11745664	D₄	1	1	yes	characteristic
23	#14273686	D₄	1	1	yes	characteristic
24	#14273667	—	2	1	no	—
25	#14273667	D₄	1	2	yes	—
26	C₂×C₅₉⋊C₁₆	—	2	1	no	—
27	#14273663	—	2	2	no	—
28	#14273663	—	2	2	no	—
29	#14273648	—	4	4	no	—
30	#14273644	—	4	4	no	—
31	#14273637	—	2	1	no	—
32	C₈×Dic₅₉	—	2	1	no	—
33	C₂²×D₄×C₅₉	—	2	2	no	—
34	C₂×D₈×C₅₉	—	2	2	no	—
35	C₂×D₈×C₅₉	—	2	2	no	—
36	C₂×D₈×C₅₉	—	2	2	no	—
37	C₂×D₈×C₅₉	—	2	2	no	—
38	C₂×D₈×C₅₉	—	2	2	no	—
39	C₂×D₈×C₅₉	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
41	D₁₆×C₅₉	—	2	4	no	—
42	D₁₆×C₅₉	—	2	4	no	—
43	C₂×C₁₆×C₅₉	C₂×C₄	1	2	yes	—
44	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
45	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₅₉	D₄	1	2	yes	—
47	C₂⁴×C₅₉	—	4	2	no	—
48	C₂×D₄×C₅₉	—	2	4	no	—
49	C₂×D₄×C₅₉	—	4	2	no	—
50	C₂×D₄×C₅₉	—	4	2	no	—
51	C₂×D₄×C₅₉	—	4	2	no	—
52	C₂×D₄×C₅₉	—	4	2	no	—
53	C₂×D₄×C₅₉	—	4	2	no	—
54	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
55	D₈×C₅₉	—	2	4	no	—
56	D₈×C₅₉	—	2	4	no	—
57	D₈×C₅₉	—	4	2	no	—
58	D₈×C₅₉	—	4	2	no	—
59	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
64	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
65	C₂²⋊Dic₅₉	—	2	1	no	—
66	C₄⋊Dic₅₉	D₈	1	2	yes	—
67	C₄×Dic₅₉	—	2	1	no	—
68	#11745664	—	2	1	no	—
69	#11745664	—	4	2	no	—
70	#11745664	—	4	2	no	—
71	#11745664	D₈	1	2	yes	—
72	C₂×C₅₉⋊C₈	—	2	1	no	—
73	C₂×C₅₉⋊C₈	—	4	2	no	—
74	C₁₆×C₅₉	C₂²⋊C₄	1	2	yes	—
75	C₁₆×C₅₉	C₂²⋊C₄	1	2	yes	—
76	C₅₉⋊C₁₆	—	2	2	no	—
77	C₂³×C₅₉	—	4	4	no	—
78	C₂³×C₅₉	—	8	2	no	—
79	C₂³×C₅₉	—	8	2	no	—
80	C₂³×C₅₉	—	16	4	no	—
81	C₂³×C₅₉	#135	1	1	yes	characteristic
82	D₄×C₅₉	—	4	4	no	—
83	D₄×C₅₉	—	4	4	no	—
84	D₄×C₅₉	—	8	2	no	—
85	D₄×C₅₉	—	8	2	no	—
86	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
88	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
89	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
92	C₂×Dic₅₉	—	2	2	no	—
93	C₈×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
95	C₈×C₅₉	#121	1	1	yes	characteristic
96	C₈×C₅₉	#124	1	1	yes	characteristic
97	C₅₉⋊C₈	—	2	2	no	—
98	C₅₉⋊C₈	—	8	2	no	—
99	#13245	—	59	1	no	maximal, Sylow
100	C₂²×C₅₉	—	2	2	no	—
101	C₂²×C₅₉	—	8	4	no	—
102	C₂²×C₅₉	—	16	4	no	—
103	C₂²×C₅₉	—	16	4	no	—
104	C₂²×C₅₉	—	16	4	no	—
105	C₂²×C₅₉	C₄×D₈	1	1	yes	characteristic
106	C₂²×C₅₉	#466	1	1	yes	characteristic
107	C₂²×C₅₉	#495	1	1	yes	characteristic
108	C₄×C₅₉	#390	1	1	yes	characteristic
109	C₄×C₅₉	C₄×D₈	1	1	yes	characteristic
110	C₄×C₅₉	#466	1	1	yes	characteristic
111	C₄×C₅₉	#493	1	1	yes	characteristic
112	Dic₅₉	—	4	2	no	—
113	C₂²×D₁₆	D₅₉	1	1	yes	characteristic
114	C₂×#368	—	59	1	no	—
115	C₂×#361	—	59	2	no	—
116	#2108	—	59	1	no	—
117	#1978	—	59	2	no	—
118	C₂×C₅₉	—	2	1	no	—
119	C₂×C₅₉	—	2	1	no	—
120	C₂×C₅₉	—	16	4	no	—
121	C₂×C₅₉	#1970	1	1	yes	characteristic
122	C₂×C₅₉	#2221	1	2	yes	—
123	C₂²×D₈	C₂×D₅₉	1	2	yes	—
124	C₂×D₁₆	—	2	1	no	—
125	C₂×D₁₆	—	2	1	no	—
126	C₂×D₁₆	—	2	2	no	—
127	C₂×D₁₆	Dic₅₉	1	4	yes	complemented
128	C₂×M₃₂	—	59	1	no	—
129	C₂²×C₁₆	C₂×D₅₉	1	1	yes	characteristic
130	C₂×#108	—	59	2	no	—
131	#418	—	118	2	no	—
132	C₂×#100	—	118	2	no	—
133	#405	—	59	1	no	—
134	#368	—	118	2	no	—
135	#361	—	118	4	no	—
136	#346	—	118	1	no	—
137	C₄×C₁₆	—	118	1	no	—
138	C₅₉	#13245	1	1	yes	characteristic, complemented, Sylow
139	C₂²×D₄	—	2	2	no	—
140	C₂×D₈	—	2	2	no	—
141	C₂×D₈	—	2	2	no	—
142	C₂×D₈	—	2	2	no	—
143	C₂×D₈	—	2	2	no	—
144	C₂×D₈	—	2	2	no	—
145	C₂×D₈	C₂×Dic₅₉	1	4	yes	—
146	C₂×M₁₆	—	59	1	no	—
147	C₂×M₁₆	—	118	2	no	—
148	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
149	#117	—	59	1	no	—
150	D₁₆	—	2	4	no	—
151	D₁₆	—	2	4	no	—
152	M₃₂	—	59	2	no	—
153	M₃₂	—	118	1	no	—
154	C₂×C₁₆	—	118	1	no	—
155	C₂×C₁₆	C₂×Dic₅₉	1	2	yes	—
156	C₂×C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
157	C₂×C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
158	C₂×C₁₆	C₂²⋊D₅₉	1	2	yes	—
159	#108	—	118	2	no	—
160	#108	—	118	2	no	—
161	#102	—	236	4	no	—
162	#100	—	236	4	no	—
163	#97	—	118	1	no	—
164	C₄×C₈	—	118	1	no	—
165	C₂⁴	—	4	2	no	—
166	C₂×D₄	—	2	4	no	—
167	C₂×D₄	—	4	2	no	—
168	C₂×D₄	—	4	2	no	—
169	C₂×D₄	—	4	2	no	—
170	C₂×D₄	—	4	2	no	—
171	C₂×D₄	—	4	2	no	—
172	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
173	D₈	—	2	4	no	—
174	D₈	—	2	4	no	—
175	D₈	—	4	2	no	—
176	D₈	—	4	2	no	—
177	M₁₆	—	59	2	no	—
178	M₁₆	—	118	1	no	—
179	M₁₆	—	236	2	no	—
180	M₁₆	—	236	2	no	—
181	C₂×C₈	—	118	1	no	—
182	C₂×C₈	—	236	2	no	—
183	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
184	C₂×C₈	#11745687	1	1	yes	characteristic
185	C₂×C₈	#11745687	1	1	yes	characteristic
186	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
187	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
188	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
189	C₄⋊C₄	—	59	2	no	—
190	C₂²⋊C₄	—	118	1	no	—
191	C₄²	—	118	1	no	—
192	C₁₆	—	118	2	no	—
193	C₁₆	C₂²⋊Dic₅₉	1	2	yes	—
194	C₁₆	C₂²⋊Dic₅₉	1	2	yes	—
195	C₂³	—	4	4	no	—
196	C₂³	—	8	2	no	—
197	C₂³	—	8	2	no	—
198	C₂³	—	16	4	no	—
199	C₂³	#14273746	1	1	yes	characteristic
200	D₄	—	4	4	no	—
201	D₄	—	4	4	no	—
202	D₄	—	8	2	no	—
203	D₄	—	8	2	no	—
204	C₂×C₄	—	118	2	no	—
205	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
206	C₂×C₄	#14273698	1	1	yes	characteristic
207	C₂×C₄	#14273723	1	1	yes	characteristic
208	C₂×C₄	D₈×D₅₉	1	1	yes	characteristic
209	C₂×C₄	D₈×D₅₉	1	1	yes	characteristic
210	C₂×C₄	#14273746	1	1	yes	characteristic
211	C₈	—	118	2	no	—
212	C₈	—	472	2	no	—
213	C₈	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
214	C₈	D₄×Dic₅₉	1	1	yes	characteristic
215	C₈	#14273698	1	1	yes	characteristic
216	C₈	#14273714	1	1	yes	characteristic
217	C₂²	—	2	2	no	—
218	C₂²	—	8	4	no	—
219	C₂²	—	16	4	no	—
220	C₂²	—	16	4	no	—
221	C₂²	—	16	4	no	—
222	C₂²	D₈×Dic₅₉	1	1	yes	characteristic
223	C₂²	#16837635	1	1	yes	characteristic
224	C₂²	#16837785	1	1	yes	characteristic
225	C₄	—	236	2	no	—
226	C₄	#16837305	1	1	yes	characteristic
227	C₄	D₈×Dic₅₉	1	1	yes	characteristic
228	C₄	#16837635	1	1	yes	characteristic
229	C₄	#16837777	1	1	yes	characteristic
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	—	16	4	no	—
233	C₂	#21424963	1	1	yes	characteristic
234	C₂	#21426213	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16837232

C₂

yes

maximal, characteristic, complemented

C₂×#16837215

C₂

yes

maximal, complemented

#21425692

C₂

yes

maximal, characteristic, complemented

#21425007

C₂

yes

maximal, complemented

C₂²×D₁₆×C₅₉

C₂

yes

maximal, characteristic

C₂×#14273667

C₂²

yes

characteristic

C₂×#14273663

C₂²

yes

—

#16837407

—

C₂×#14273644

—

#16837357

C₂²

yes

—

—

—

C₁₆×Dic₅₉

—

C₂²×D₈×C₅₉

C₂²

yes

—

C₂×D₁₆×C₅₉

—

C₂×D₁₆×C₅₉

—

C₂×D₁₆×C₅₉

—

C₂×D₁₆×C₅₉

C₄

yes

complemented

C₂²×C₁₆×C₅₉

C₂²

yes

characteristic

C₂×#11745664

—

C₂×#11745664

D₄

yes

characteristic

#14273686

D₄

yes

characteristic

#14273667

—

#14273667

D₄

yes

—

C₂×C₅₉⋊C₁₆

—

—

—

—

—

—

C₈×Dic₅₉

—

C₂²×D₄×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

—

C₂×D₈×C₅₉

C₂×C₄

yes

—

C₂²×C₈×C₅₉

C₂³

yes

characteristic

D₁₆×C₅₉

—

D₁₆×C₅₉

—

C₂×C₁₆×C₅₉

C₂×C₄

yes

—

C₂×C₁₆×C₅₉

D₄

yes

characteristic

C₂×C₁₆×C₅₉

D₄

yes

characteristic

C₂×C₁₆×C₅₉

D₄

yes

—

C₂⁴×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

characteristic

D₈×C₅₉

—

D₈×C₅₉

—

D₈×C₅₉

—

D₈×C₅₉

—

C₂×C₈×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

characteristic

C₂×C₈×C₅₉

C₂×D₄

yes

C₂×C₈×C₅₉

yes

C₂×C₈×C₅₉

yes

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

D₈

yes

—

C₄×Dic₅₉

—

—

—

—

D₈

yes

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₁₆×C₅₉

C₂²⋊C₄

yes

—

C₁₆×C₅₉

C₂²⋊C₄

yes

—

C₅₉⋊C₁₆

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

—

C₂³×C₅₉

#135

yes

characteristic

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

C₄×D₄

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

yes

C₂×C₄×C₅₉

C₂×D₈

yes

characteristic

C₂×C₄×C₅₉

C₂×D₈

yes

characteristic

C₂×C₄×C₅₉

#135

yes

characteristic

C₂×Dic₅₉

—

C₈×C₅₉

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₅₉

C₄×D₄

yes

C₈×C₅₉

yes

C₈×C₅₉

yes

C₅₉⋊C₈

—

C₅₉⋊C₈

—

#13245

—

maximal, Sylow

100

C₂²×C₅₉

—

101

C₂²×C₅₉

—

102

C₂²×C₅₉

—

103

C₂²×C₅₉

—

104

C₂²×C₅₉

—

105

C₂²×C₅₉

C₄×D₈

yes

characteristic

106

C₂²×C₅₉

#466

yes

characteristic

107

C₂²×C₅₉

#495

yes

characteristic

108

C₄×C₅₉

#390

yes

characteristic

109

C₄×C₅₉

C₄×D₈

yes

characteristic

110

C₄×C₅₉

#466

yes

characteristic

111

C₄×C₅₉

#493

yes

characteristic

112

Dic₅₉

—

113

C₂²×D₁₆

D₅₉

yes

characteristic

114

C₂×#368

—

115

C₂×#361

—

116

#2108

—

117

#1978

—

118

C₂×C₅₉

—

119

C₂×C₅₉

—

120

C₂×C₅₉

—

121

C₂×C₅₉

#1970

yes

characteristic

122

C₂×C₅₉

#2221

yes

—

123

C₂²×D₈

C₂×D₅₉

yes

—

124

C₂×D₁₆

—

125

C₂×D₁₆

—

126

C₂×D₁₆

—

127

C₂×D₁₆

Dic₅₉

yes

complemented

128

C₂×M₃₂

—

129

C₂²×C₁₆

C₂×D₅₉

yes

characteristic

130

C₂×#108

—

131

#418

—

118

—

132

C₂×#100

—

118

—

133

#405

—

134

#368

—

118

—

135

#361

—

118

—

136

#346

—

118

—

137

C₄×C₁₆

—

118

—

138

C₅₉

#13245

yes

characteristic, complemented, Sylow

139

C₂²×D₄

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

C₂×Dic₅₉

yes

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

118

—

148

C₂²×C₈

C₂²×D₅₉

yes

characteristic

149

#117

—

150

D₁₆

—

151

D₁₆

—

152

M₃₂

—

153

M₃₂

—

118

—

154

C₂×C₁₆

—

118

—

155

C₂×C₁₆

C₂×Dic₅₉

yes

—

156

C₂×C₁₆

C₂²⋊D₅₉

yes

characteristic

157

C₂×C₁₆

C₂²⋊D₅₉

yes

characteristic

158

C₂×C₁₆

C₂²⋊D₅₉

yes

—

159

#108

—

118

—

160

#108

—

118

—

161

#102

—

236

—

162

#100

—

236

—

163

#97

—

118

—

164

C₄×C₈

—

118

—

165

C₂⁴

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂²×C₄

D₄×D₅₉

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

176

D₈

—

177

M₁₆

—

178

M₁₆

—

118

—

179

M₁₆

—

236

—

180

M₁₆

—

236

—

181

C₂×C₈

—

118

—

182

C₂×C₈

—

236

—

183

C₂×C₈

D₄×D₅₉

yes

characteristic

184

C₂×C₈

#11745687

yes

characteristic

185

C₂×C₈

#11745687

yes

characteristic

186

C₂×C₈

C₂²×Dic₅₉

yes

characteristic

187

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

188

C₂×C₈

C₂×C₂²⋊D₅₉

yes

characteristic

189

C₄⋊C₄

—

190

C₂²⋊C₄

—

118

—

191

C₄²

—

118

—

192

C₁₆

—

118

—

193

C₁₆

C₂²⋊Dic₅₉

yes

—

194

C₁₆

C₂²⋊Dic₅₉

yes

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

199

C₂³

#14273746

yes

characteristic

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

118

—

205

C₂×C₄

D₄×Dic₅₉

yes

characteristic

206

C₂×C₄

#14273698

yes

characteristic

207

C₂×C₄

#14273723

yes

characteristic

208

C₂×C₄

D₈×D₅₉

yes

characteristic

209

C₂×C₄

D₈×D₅₉

yes

characteristic

210

C₂×C₄

#14273746

yes

characteristic

211

C₈

—

118

—

212

C₈

—

472

—

213

C₈

C₂×C₂²⋊Dic₅₉

yes

characteristic

214

C₈

D₄×Dic₅₉

yes

characteristic

215

C₈

#14273698

yes

characteristic

216

C₈

#14273714

yes

characteristic

217

C₂²

—

218

C₂²

—

219

C₂²

—

220

C₂²

—

221

C₂²

—

222

C₂²

D₈×Dic₅₉

yes

characteristic

223

C₂²

#16837635

yes

characteristic

224

C₂²

#16837785

yes

characteristic

225

C₄

—

236

—

226

C₄

#16837305

yes

characteristic

227

C₄

D₈×Dic₅₉

yes

characteristic

228

C₄

#16837635

yes

characteristic

229

C₄

#16837777

yes

characteristic

230

C₂

—

231

C₂

—

232

C₂

—

233

C₂

#21424963

yes

characteristic

234

C₂

#21426213

yes

—

	subgroup	G/H
center	C₂²	#16837635
commutator	C₂×C₈×C₅₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₉
Fitting, prime radical	C₂²×D₁₆×C₅₉	C₂
socle	C₂²×C₅₉	#466
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	C₂²×D₁₆	D₅₉
hypocenter	C₅₉	#13245
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

subgroup

G/H

center

C₂²

#16837635

commutator

C₂×C₈×C₅₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₉

Fitting, prime radical

C₂²×D₁₆×C₅₉

C₂

socle

C₂²×C₅₉

#466

cosocle

C₂²×C₈×C₅₉

C₂³

hypercenter

C₂²×D₁₆

D₅₉

hypocenter

C₅₉

#13245

LCS

G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

N	H ≅ G/N	type
1. C₂×#16837232	C₂	semidirect
2. C₂×#16837215	C₂	semidirect
3. #21425692	C₂	semidirect
4. #21425007	C₂	semidirect
19. C₂×D₁₆×C₅₉	C₄	semidirect
127. C₂×D₁₆	Dic₅₉	semidirect
138. C₅₉	#13245	semidirect

H ≅ G/N

type

1. C₂×#16837232

C₂

semidirect

2. C₂×#16837215

C₂

semidirect

3. #21425692

C₂

semidirect

4. #21425007

C₂

semidirect

19. C₂×D₁₆×C₅₉

C₄

semidirect

127. C₂×D₁₆

Dic₅₉

semidirect

138. C₅₉

#13245

semidirect

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

subgroup	index
C₂×#16837232	2
C₂×#16837215	2
#21425692	2
#21425007	2
C₂²×D₁₆×C₅₉	2
#13245	59

subgroup

index

C₂²×D₁₆×C₅₉

Subgroups — #28507114

Conjugacy classes of subgroups

Complements

Maximal subgroups