Group #21436967 — subgroups

Subgroups — #21436967

Order 7552.

338 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 133 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	#16838112	C₂	1	1	yes	maximal, characteristic
2	#16837801	C₂	1	2	yes	maximal, complemented
3	#16837798	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837709	C₂	1	2	yes	maximal, complemented
5	#16837699	C₂	1	2	yes	maximal
6	#16837697	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837679	C₂	1	1	yes	maximal, characteristic
8	Q₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11745671	C₂	1	1	yes	maximal, characteristic
10	C₄×#11745671	C₂	1	2	yes	maximal
11	C₅₉×#557	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11745671	C₂²	1	1	yes	characteristic
13	#14273727	C₂²	1	1	yes	characteristic
14	#14273719	C₂²	1	2	yes	—
15	#14273705	—	2	2	no	—
16	#14273703	—	2	1	no	—
17	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
18	C₄×D₂₃₆	C₂²	1	2	yes	—
19	C₄⋊C₄×D₅₉	—	2	1	no	—
20	#14273660	C₂²	1	2	yes	—
21	#14273660	C₂²	1	2	yes	—
22	#14273658	C₂²	1	2	yes	—
23	#14273658	C₂²	1	2	yes	—
24	#14273658	C₂²	1	1	yes	characteristic
25	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
27	#14273651	C₂²	1	2	yes	—
28	#14273651	C₂²	1	1	yes	characteristic
29	#14273647	C₂²	1	2	yes	—
30	#14273647	C₂²	1	1	yes	characteristic
31	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₅₉	—	2	1	no	—
34	C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
35	#125×C₅₉	—	2	2	no	—
36	#125×C₅₉	C₂²	1	2	yes	—
37	C₄×Q₈×C₅₉	—	2	1	no	—
38	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₄×Q₈×C₅₉	C₂²	1	2	yes	—
40	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₅₉	—	2	1	no	—
42	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
43	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₅₉	—	2	1	no	—
46	C₂×C₄×D₅₉	—	2	2	no	—
47	C₂×Dic₁₁₈	—	2	1	no	—
48	C₄⋊C₄×C₅₉	—	2	2	no	—
49	C₄⋊C₄×C₅₉	—	2	1	no	—
50	C₄⋊C₄×C₅₉	—	2	2	no	—
51	C₄⋊C₄×C₅₉	—	2	1	no	—
52	C₄⋊C₄×C₅₉	—	2	2	no	—
53	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
54	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
55	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
56	C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
57	C₄²×C₅₉	—	2	2	no	—
58	C₄²×C₅₉	—	2	1	no	—
59	C₄²×C₅₉	C₂³	1	2	yes	—
60	C₄²×C₅₉	C₂³	1	1	yes	characteristic
61	#11745671	Q₈	1	4	yes	complemented
62	(C₂×D₅₉)⋊C₄	—	2	2	no	—
63	(C₂×D₅₉)⋊C₄	—	2	1	no	—
64	C₄⋊Dic₅₉	—	2	1	no	—
65	C₄⋊Dic₅₉	C₂³	1	2	yes	—
66	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
67	Dic₅₉⋊C₄	—	2	2	no	—
68	Dic₅₉⋊C₄	—	2	2	no	—
69	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
71	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×D₅₉	—	2	1	no	—
73	Q₈×C₅₉	—	2	2	no	—
74	Q₈×C₅₉	—	2	1	no	—
75	Q₈×C₅₉	—	4	2	no	—
76	Q₈×C₅₉	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₅₉	—	2	1	no	—
78	C₂×C₄×C₅₉	—	2	1	no	—
79	C₂×C₄×C₅₉	—	2	2	no	—
80	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
81	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
85	C₂×Dic₅₉	—	2	1	no	—
86	C₂×Dic₅₉	—	2	2	no	—
87	D₂₃₆	—	2	1	no	—
88	D₂₃₆	C₂×Q₈	1	2	yes	—
89	C₄×D₅₉	—	4	2	no	—
90	C₄×D₅₉	—	8	2	no	—
91	Dic₁₁₈	—	8	1	no	—
92	C₅₉⋊C₈	—	2	1	no	—
93	C₅₉⋊C₈	—	2	2	no	—
94	C₅₉⋊C₈	C₂×Q₈	1	2	yes	—
95	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
96	C₂×D₅₉	—	2	2	no	—
97	C₂×D₅₉	—	4	1	no	—
98	C₂×D₅₉	—	4	1	no	—
99	C₄×C₅₉	—	2	2	no	—
100	C₄×C₅₉	—	2	2	no	—
101	C₄×C₅₉	—	2	1	no	—
102	C₄×C₅₉	—	2	2	no	—
103	C₄×C₅₉	—	4	2	no	—
104	C₄×C₅₉	—	4	1	no	—
105	C₄×C₅₉	#135	1	2	yes	—
106	C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
107	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
108	Dic₅₉	—	4	1	no	—
109	Dic₅₉	—	4	2	no	—
110	#3381	—	59	1	no	maximal, Sylow
111	C₂×C₅₉	D₄×Q₈	1	1	yes	characteristic
112	C₂×C₅₉	C₂×#135	1	1	yes	characteristic
113	C₂×C₅₉	#577	1	1	yes	characteristic
114	D₅₉	—	4	2	no	—
115	#557	D₅₉	1	1	yes	characteristic, complemented
116	#554	—	59	1	no	—
117	#499	—	59	2	no	—
118	#498	—	59	1	no	—
119	#479	—	59	2	no	—
120	#478	—	59	2	no	—
121	#477	—	59	1	no	—
122	#474	—	59	1	no	—
123	C₈×Q₈	—	59	1	no	—
124	C₄×SD₁₆	—	59	1	no	—
125	C₄×SD₁₆	—	59	2	no	—
126	C₅₉	#3381	1	1	yes	characteristic, complemented, Sylow
127	C₂×SD₁₆	—	59	1	no	—
128	C₄⋊Q₈	—	2	1	no	—
129	C₄⋊Q₈	—	59	1	no	—
130	C₄⋊Q₈	C₂×D₅₉	1	1	yes	characteristic
131	#125	—	2	2	no	—
132	#125	—	59	2	no	—
133	#125	C₂×D₅₉	1	2	yes	—
134	C₂²⋊Q₈	—	118	1	no	—
135	C₂²⋊Q₈	—	118	2	no	—
136	C₄×Q₈	—	2	1	no	—
137	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
138	C₄×Q₈	C₂×D₅₉	1	2	yes	—
139	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
140	C₄×D₄	—	59	1	no	—
141	C₄×D₄	—	59	2	no	—
142	C₂×C₄⋊C₄	—	118	1	no	—
143	#107	—	59	2	no	—
144	#107	—	59	2	no	—
145	#106	—	59	2	no	—
146	#106	—	59	1	no	—
147	#106	—	59	2	no	—
148	C₄⋊C₈	—	59	1	no	—
149	C₄⋊C₈	—	59	2	no	—
150	#103	—	59	2	no	—
151	#103	—	59	1	no	—
152	#102	—	59	2	no	—
153	#102	—	59	1	no	—
154	C₄×C₈	—	59	1	no	—
155	C₄×C₈	—	59	2	no	—
156	C₂×Q₈	—	2	1	no	—
157	C₂×Q₈	—	118	1	no	—
158	C₂×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
159	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
160	C₂×D₄	—	59	1	no	—
161	C₂²×C₄	—	118	2	no	—
162	C₂²×C₄	—	118	1	no	—
163	SD₁₆	—	59	4	no	—
164	C₂×C₈	—	59	1	no	—
165	C₂×C₈	—	59	1	no	—
166	C₂×C₈	—	59	2	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	2	1	no	—
169	C₄⋊C₄	—	2	2	no	—
170	C₄⋊C₄	—	2	1	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	59	2	no	—
173	C₄⋊C₄	—	59	1	no	—
174	C₄⋊C₄	—	118	2	no	—
175	C₄⋊C₄	—	118	1	no	—
176	C₄⋊C₄	—	118	2	no	—
177	C₄⋊C₄	C₂²⋊D₅₉	1	1	yes	characteristic
178	C₄⋊C₄	C₂²⋊D₅₉	1	2	yes	—
179	C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
180	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
181	C₂²⋊C₄	—	118	1	no	—
182	C₂²⋊C₄	—	118	2	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	C₂²×D₅₉	1	2	yes	—
186	C₄²	C₂²×D₅₉	1	1	yes	characteristic
187	C₂³	—	118	1	no	—
188	Q₈	—	2	2	no	—
189	Q₈	—	2	1	no	—
190	Q₈	—	4	2	no	—
191	Q₈	—	472	1	no	—
192	Q₈	Q₈×D₅₉	1	2	yes	—
193	D₄	—	59	2	no	—
194	D₄	—	118	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	118	1	no	—
199	C₂×C₄	—	118	2	no	—
200	C₂×C₄	—	472	2	no	—
201	C₂×C₄	—	236	2	no	—
202	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
203	C₂×C₄	C₂×C₂²⋊D₅₉	1	2	yes	—
204	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
205	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
206	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
207	C₈	—	59	2	no	—
208	C₈	—	118	1	no	—
209	C₈	—	118	2	no	—
210	C₂²	—	118	2	no	—
211	C₂²	—	236	1	no	—
212	C₂²	—	236	1	no	—
213	C₂²	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	2	no	—
216	C₄	—	2	1	no	—
217	C₄	—	2	2	no	—
218	C₄	—	4	2	no	—
219	C₄	—	4	1	no	—
220	C₄	—	236	1	no	—
221	C₄	—	236	2	no	—
222	C₄	#14273747	1	2	yes	—
223	C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
224	C₄	#14273775	1	1	yes	characteristic
225	C₂	—	236	2	no	—
226	C₂	Q₈×C₂²⋊D₅₉	1	1	yes	characteristic
227	C₂	C₂×#14273747	1	1	yes	characteristic
228	C₂	#16838210	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16838112

C₂

yes

maximal, characteristic

#16837801

C₂

yes

maximal, complemented

#16837798

C₂

yes

maximal, characteristic, complemented

#16837709

C₂

yes

maximal, complemented

#16837699

C₂

yes

maximal

#16837697

C₂

yes

maximal, characteristic, complemented

#16837679

C₂

yes

maximal, characteristic

Q₈×C₅₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄×#11745671

C₂

yes

maximal, characteristic

C₄×#11745671

C₂

yes

maximal

C₅₉×#557

C₂

yes

maximal, characteristic, complemented

C₂×#11745671

C₂²

yes

characteristic

#14273727

C₂²

yes

characteristic

#14273719

C₂²

yes

—

#14273705

—

#14273703

—

C₄×D₂₃₆

C₂²

yes

characteristic

C₄×D₂₃₆

C₂²

yes

—

C₄⋊C₄×D₅₉

—

#14273660

C₂²

yes

—

#14273660

C₂²

yes

—

#14273658

C₂²

yes

—

#14273658

C₂²

yes

—

#14273658

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₅₉⋊C₈)

C₂²

yes

—

#14273651

C₂²

yes

—

#14273651

C₂²

yes

characteristic

#14273647

C₂²

yes

—

#14273647

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

characteristic

C₄×C₅₉⋊C₈

C₂²

yes

—

C₄⋊Q₈×C₅₉

—

C₄⋊Q₈×C₅₉

C₂²

yes

characteristic

#125×C₅₉

—

#125×C₅₉

C₂²

yes

—

C₄×Q₈×C₅₉

—

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄×Q₈×C₅₉

C₂²

yes

—

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

—

C₂×Q₈×C₅₉

D₄

yes

characteristic

C₂×Q₈×C₅₉

C₂³

yes

characteristic

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

—

C₄⋊C₄×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

C₂³

yes

—

C₄²×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂³

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

#11745671

Q₈

yes

complemented

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂×C₅₉⋊C₈

C₂³

yes

—

C₂×C₅₉⋊C₈

C₂³

yes

characteristic

C₂²×D₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

—

Q₈×C₅₉

C₂×Q₈

yes

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

C₂×Q₈

yes

—

C₄×D₅₉

—

C₄×D₅₉

—

Dic₁₁₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₅₉⋊C₈

C₂×Q₈

yes

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

C₄×C₅₉

—

100

C₄×C₅₉

—

101

C₄×C₅₉

—

102

C₄×C₅₉

—

103

C₄×C₅₉

—

104

C₄×C₅₉

—

105

C₄×C₅₉

#135

yes

—

106

C₄×C₅₉

C₂²×Q₈

yes

characteristic

107

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

108

Dic₅₉

—

109

Dic₅₉

—

110

#3381

—

maximal, Sylow

111

C₂×C₅₉

D₄×Q₈

yes

characteristic

112

C₂×C₅₉

C₂×#135

yes

characteristic

113

C₂×C₅₉

#577

yes

characteristic

114

D₅₉

—

115

#557

D₅₉

yes

characteristic, complemented

116

#554

—

117

#499

—

118

#498

—

119

#479

—

120

#478

—

121

#477

—

122

#474

—

123

C₈×Q₈

—

124

C₄×SD₁₆

—

125

C₄×SD₁₆

—

126

C₅₉

#3381

yes

characteristic, complemented, Sylow

127

C₂×SD₁₆

—

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

C₂×D₅₉

yes

characteristic

131

#125

—

132

#125

—

133

#125

C₂×D₅₉

yes

—

134

C₂²⋊Q₈

—

118

—

135

C₂²⋊Q₈

—

118

—

136

C₄×Q₈

—

137

C₄×Q₈

C₂×D₅₉

yes

characteristic

138

C₄×Q₈

C₂×D₅₉

yes

—

139

C₄×Q₈

C₂×D₅₉

yes

characteristic

140

C₄×D₄

—

141

C₄×D₄

—

142

C₂×C₄⋊C₄

—

118

—

143

#107

—

144

#107

—

145

#106

—

146

#106

—

147

#106

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#103

—

151

#103

—

152

#102

—

153

#102

—

154

C₄×C₈

—

155

C₄×C₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

118

—

158

C₂×Q₈

C₂²⋊D₅₉

yes

characteristic

159

C₂×Q₈

C₂²×D₅₉

yes

characteristic

160

C₂×D₄

—

161

C₂²×C₄

—

118

—

162

C₂²×C₄

—

118

—

163

SD₁₆

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

118

—

175

C₄⋊C₄

—

118

—

176

C₄⋊C₄

—

118

—

177

C₄⋊C₄

C₂²⋊D₅₉

yes

characteristic

178

C₄⋊C₄

C₂²⋊D₅₉

yes

—

179

C₄⋊C₄

C₂²×D₅₉

yes

—

180

C₄⋊C₄

C₂²×D₅₉

yes

characteristic

181

C₂²⋊C₄

—

118

—

182

C₂²⋊C₄

—

118

—

183

C₄²

—

184

C₄²

—

185

C₄²

C₂²×D₅₉

yes

—

186

C₄²

C₂²×D₅₉

yes

characteristic

187

C₂³

—

118

—

188

Q₈

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

472

—

192

Q₈

Q₈×D₅₉

yes

—

193

D₄

—

194

D₄

—

118

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

118

—

199

C₂×C₄

—

118

—

200

C₂×C₄

—

472

—

201

C₂×C₄

—

236

—

202

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

203

C₂×C₄

C₂×C₂²⋊D₅₉

yes

—

204

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

205

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

206

C₂×C₄

C₂³×D₅₉

yes

characteristic

207

C₈

—

208

C₈

—

118

—

209

C₈

—

118

—

210

C₂²

—

118

—

211

C₂²

—

236

—

212

C₂²

—

236

—

213

C₂²

C₂²×C₂²⋊D₅₉

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

236

—

221

C₄

—

236

—

222

C₄

#14273747

yes

—

223

C₄

C₂×Q₈×D₅₉

yes

characteristic

224

C₄

#14273775

yes

characteristic

225

C₂

—

236

—

226

C₂

Q₈×C₂²⋊D₅₉

yes

characteristic

227

C₂

C₂×#14273747

yes

characteristic

228

C₂

#16838210

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#557	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#557	D₅₉
hypocenter	C₅₉	#3381
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #557

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₅₉

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#557

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #557

N	H ≅ G/N	type
2. #16837801	C₂	semidirect
3. #16837798	C₂	semidirect
4. #16837709	C₂	semidirect
6. #16837697	C₂	semidirect
8. Q₈×C₅₉⋊C₈	C₂	semidirect
11. C₅₉×#557	C₂	semidirect
61. #11745671	Q₈	semidirect
115. #557	D₅₉	semidirect
126. C₅₉	#3381	semidirect

H ≅ G/N

type

2. #16837801

C₂

semidirect

3. #16837798

C₂

semidirect

4. #16837709

C₂

semidirect

6. #16837697

C₂

semidirect

8. Q₈×C₅₉⋊C₈

C₂

semidirect

11. C₅₉×#557

C₂

semidirect

61. #11745671

Q₈

semidirect

115. #557

D₅₉

semidirect

126. C₅₉

#3381

semidirect

Subgroups — #21436967

Conjugacy classes of subgroups

Complements