Group #21437008 — subgroups

Subgroups — #21437008

Order 7552.

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

normal subgroups only

This group has 340 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	Q₈×Dic₁₁₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#16838112	C₂	1	1	yes	maximal, characteristic
3	#16837811	C₂	1	2	yes	maximal, complemented
4	#16837807	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837710	C₂	1	2	yes	maximal, complemented
6	#16837698	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837693	C₂	1	1	yes	maximal, characteristic
8	#16837683	C₂	1	2	yes	maximal
9	#16837504	C₂	1	2	yes	maximal
10	C₄×#11745660	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#446	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11745660	C₂²	1	1	yes	characteristic
13	#14273727	C₂²	1	2	yes	—
14	#14273727	C₂²	1	1	yes	characteristic
15	#14273727	C₂²	1	1	yes	characteristic
16	#14273726	—	2	1	no	—
17	#14273726	—	2	2	no	—
18	#14273719	C₂²	1	2	yes	—
19	#14273705	—	2	2	no	—
20	#14273703	—	2	1	no	—
21	Q₈×Dic₅₉	—	2	1	no	—
22	C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
23	C₄×Dic₁₁₈	C₂²	1	2	yes	—
24	C₄×D₂₃₆	C₂²	1	2	yes	—
25	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×D₅₉	—	2	1	no	—
27	#14273661	C₂²	1	2	yes	—
28	#14273661	C₂²	1	2	yes	—
29	#14273661	C₂²	1	2	yes	—
30	#14273659	C₂²	1	2	yes	—
31	#14273659	C₂²	1	1	yes	characteristic
32	#14273652	C₂²	1	2	yes	—
33	#14273652	C₂²	1	1	yes	characteristic
34	#14273649	C₂²	1	1	yes	characteristic
35	#14273649	C₂²	1	2	yes	—
36	C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
38	C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
39	#97×C₅₉	C₂²	1	2	yes	—
40	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
42	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
43	C₂×C₄×D₅₉	—	2	1	no	—
44	C₂×C₄×D₅₉	—	2	2	no	—
45	C₂×Dic₁₁₈	—	2	1	no	—
46	C₂×Dic₁₁₈	—	2	2	no	—
47	C₂×Dic₁₁₈	—	2	1	no	—
48	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
49	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₅₉	C₂³	1	2	yes	—
51	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
52	C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
53	C₄⋊C₄×C₅₉	D₄	1	2	yes	—
54	C₄²×C₅₉	C₂³	1	1	yes	characteristic
55	C₄²×C₅₉	C₂³	1	2	yes	—
56	(C₂×D₅₉)⋊C₄	—	2	2	no	—
57	(C₂×D₅₉)⋊C₄	—	2	1	no	—
58	C₄⋊Dic₅₉	—	2	1	no	—
59	C₄⋊Dic₅₉	—	2	2	no	—
60	C₄⋊Dic₅₉	—	2	1	no	—
61	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
62	C₄⋊Dic₅₉	C₂³	1	2	yes	—
63	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₅₉	C₂³	1	2	yes	—
65	Dic₅₉⋊C₄	—	2	2	no	—
66	Dic₅₉⋊C₄	—	2	2	no	—
67	Dic₅₉⋊C₄	—	2	1	no	—
68	Dic₅₉⋊C₄	—	2	2	no	—
69	C₄×Dic₅₉	—	2	2	no	—
70	C₄×Dic₅₉	—	2	1	no	—
71	#11745660	Q₈	1	4	yes	complemented
72	C₂²×D₅₉	—	2	1	no	—
73	Q₈×C₅₉	—	2	2	no	—
74	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
79	C₂×Dic₅₉	—	2	1	no	—
80	C₂×Dic₅₉	—	2	2	no	—
81	C₂×Dic₅₉	—	2	1	no	—
82	C₂×Dic₅₉	—	2	1	no	—
83	C₂×Dic₅₉	—	2	2	no	—
84	D₂₃₆	—	2	1	no	—
85	D₂₃₆	C₂×Q₈	1	2	yes	—
86	C₄×D₅₉	—	4	2	no	—
87	C₄×D₅₉	—	8	2	no	—
88	Dic₁₁₈	—	2	1	no	—
89	Dic₁₁₈	—	8	1	no	—
90	Dic₁₁₈	—	8	2	no	—
91	Dic₁₁₈	—	8	1	no	—
92	Dic₁₁₈	C₂×Q₈	1	2	yes	—
93	C₈×C₅₉	—	2	1	no	—
94	C₈×C₅₉	—	2	2	no	—
95	C₈×C₅₉	C₂×Q₈	1	2	yes	—
96	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
97	C₂×D₅₉	—	2	2	no	—
98	C₂×D₅₉	—	4	1	no	—
99	C₂×D₅₉	—	4	1	no	—
100	C₄×C₅₉	—	2	2	no	—
101	C₄×C₅₉	—	2	1	no	—
102	C₄×C₅₉	—	2	2	no	—
103	C₄×C₅₉	#137	1	2	yes	—
104	C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
105	C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
106	Dic₅₉	—	2	2	no	—
107	Dic₅₉	—	4	1	no	—
108	Dic₅₉	—	4	2	no	—
109	Dic₅₉	—	4	1	no	—
110	Dic₅₉	—	4	2	no	—
111	#3385	—	59	1	no	maximal, Sylow
112	C₂×C₅₉	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₅₉	C₂×#137	1	1	yes	characteristic
114	C₂×C₅₉	#576	1	1	yes	characteristic
115	D₅₉	—	4	2	no	—
116	Q₈²	—	59	1	no	—
117	#554	—	59	1	no	—
118	#501	—	59	2	no	—
119	#500	—	59	1	no	—
120	#479	—	59	2	no	—
121	#477	—	59	1	no	—
122	#476	—	59	1	no	—
123	#474	—	59	2	no	—
124	#446	D₅₉	1	1	yes	characteristic, complemented
125	#440	—	59	2	no	—
126	C₄×SD₁₆	—	59	1	no	—
127	C₅₉	#3385	1	1	yes	characteristic, complemented, Sylow
128	C₂×SD₁₆	—	59	1	no	—
129	C₄⋊Q₈	—	59	1	no	—
130	C₄⋊Q₈	—	59	2	no	—
131	C₄⋊Q₈	—	59	1	no	—
132	C₄⋊Q₈	—	118	1	no	—
133	C₄⋊Q₈	—	118	2	no	—
134	#125	—	59	2	no	—
135	C₂²⋊Q₈	—	118	1	no	—
136	C₂²⋊Q₈	—	118	2	no	—
137	C₄×Q₈	—	59	1	no	—
138	C₄×Q₈	—	59	2	no	—
139	C₄×Q₈	—	118	1	no	—
140	C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
141	C₄×D₄	—	59	1	no	—
142	C₄×D₄	—	59	2	no	—
143	C₂×C₄⋊C₄	—	118	1	no	—
144	#107	—	59	2	no	—
145	#107	—	59	2	no	—
146	#107	—	59	2	no	—
147	#106	—	59	1	no	—
148	#106	—	59	2	no	—
149	C₄⋊C₈	C₂×D₅₉	1	2	yes	—
150	C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
151	#103	—	59	1	no	—
152	#103	—	59	2	no	—
153	#102	—	59	1	no	—
154	#102	—	59	2	no	—
155	#97	C₂×D₅₉	1	2	yes	—
156	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
157	C₂×Q₈	—	59	1	no	—
158	C₂×Q₈	—	118	1	no	—
159	C₂×Q₈	—	118	1	no	—
160	C₂×Q₈	—	118	2	no	—
161	C₂×Q₈	D₂₃₆	1	1	yes	characteristic
162	C₂×D₄	—	59	1	no	—
163	C₂²×C₄	—	118	2	no	—
164	C₂²×C₄	—	118	1	no	—
165	SD₁₆	—	59	4	no	—
166	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
167	C₂×C₈	C₂²×D₅₉	1	2	yes	—
168	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
169	C₄⋊C₄	—	59	1	no	—
170	C₄⋊C₄	—	59	2	no	—
171	C₄⋊C₄	—	59	1	no	—
172	C₄⋊C₄	—	59	2	no	—
173	C₄⋊C₄	—	118	2	no	—
174	C₄⋊C₄	—	118	1	no	—
175	C₄⋊C₄	—	118	1	no	—
176	C₄⋊C₄	—	118	2	no	—
177	C₄⋊C₄	—	118	2	no	—
178	C₄⋊C₄	—	118	1	no	—
179	C₄⋊C₄	—	118	2	no	—
180	C₄⋊C₄	D₂₃₆	1	1	yes	characteristic
181	C₄⋊C₄	D₂₃₆	1	2	yes	—
182	C₂²⋊C₄	—	118	1	no	—
183	C₂²⋊C₄	—	118	2	no	—
184	C₄²	—	118	2	no	—
185	C₄²	—	118	1	no	—
186	C₄²	C₂²×D₅₉	1	1	yes	characteristic
187	C₄²	C₂²×D₅₉	1	2	yes	—
188	C₂³	—	118	1	no	—
189	Q₈	—	2	2	no	—
190	Q₈	—	59	2	no	—
191	Q₈	—	118	1	no	—
192	Q₈	—	472	2	no	—
193	Q₈	—	472	1	no	—
194	Q₈	—	472	1	no	—
195	D₄	—	59	2	no	—
196	D₄	—	118	1	no	—
197	C₂×C₄	—	118	1	no	—
198	C₂×C₄	—	118	2	no	—
199	C₂×C₄	—	118	1	no	—
200	C₂×C₄	—	118	1	no	—
201	C₂×C₄	—	118	2	no	—
202	C₂×C₄	—	472	2	no	—
203	C₂×C₄	—	236	2	no	—
204	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
205	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
206	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
207	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	2	2	no	—
211	C₈	Q₈×D₅₉	1	2	yes	—
212	C₂²	—	118	2	no	—
213	C₂²	—	236	1	no	—
214	C₂²	—	236	1	no	—
215	C₂²	C₂²×D₂₃₆	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	2	no	—
218	C₄	—	2	1	no	—
219	C₄	—	118	2	no	—
220	C₄	—	236	1	no	—
221	C₄	—	236	2	no	—
222	C₄	—	236	1	no	—
223	C₄	—	236	2	no	—
224	C₄	#14273760	1	2	yes	—
225	C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
226	C₄	#14273774	1	1	yes	characteristic
227	C₂	—	236	2	no	—
228	C₂	Q₈×D₂₃₆	1	1	yes	characteristic
229	C₂	C₂×#14273760	1	1	yes	characteristic
230	C₂	#16838207	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₁₁₈

C₂

yes

maximal, characteristic, complemented

#16838112

C₂

yes

maximal, characteristic

#16837811

C₂

yes

maximal, complemented

#16837807

C₂

yes

maximal, characteristic, complemented

#16837710

C₂

yes

maximal, complemented

#16837698

C₂

yes

maximal, characteristic, complemented

#16837693

C₂

yes

maximal, characteristic

#16837683

C₂

yes

maximal

#16837504

C₂

yes

maximal

C₄×#11745660

C₂

yes

maximal, characteristic

C₅₉×#446

C₂

yes

maximal, characteristic, complemented

C₂×#11745660

C₂²

yes

characteristic

#14273727

C₂²

yes

—

#14273727

C₂²

yes

characteristic

#14273727

C₂²

yes

—

—

C₂²

yes

—

#14273705

—

#14273703

—

Q₈×Dic₅₉

—

C₄×Dic₁₁₈

C₂²

yes

characteristic

C₄×Dic₁₁₈

C₂²

yes

—

C₄×D₂₃₆

C₂²

yes

—

C₄×D₂₃₆

C₂²

yes

characteristic

C₄⋊C₄×D₅₉

—

#14273661

C₂²

yes

—

#14273661

C₂²

yes

—

#14273661

C₂²

yes

—

#14273659

C₂²

yes

—

#14273659

C₂²

yes

characteristic

#14273652

C₂²

yes

—

#14273652

C₂²

yes

characteristic

#14273649

C₂²

yes

characteristic

#14273649

C₂²

yes

—

C₄×Q₈×C₅₉

C₂²

yes

characteristic

C₄⋊C₈×C₅₉

C₂²

yes

—

C₄⋊C₈×C₅₉

C₂²

yes

characteristic

#97×C₅₉

C₂²

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×Q₈×C₅₉

D₄

yes

characteristic

C₂×D₂₃₆

C₂³

yes

characteristic

C₂×C₄×D₅₉

—

C₂×C₄×D₅₉

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

—

C₂×Dic₁₁₈

C₂³

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₂×C₈×C₅₉

C₂³

yes

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

characteristic

C₄⋊C₄×C₅₉

D₄

yes

—

C₄²×C₅₉

C₂³

yes

characteristic

C₄²×C₅₉

C₂³

yes

—

(C₂×D₅₉)⋊C₄

—

(C₂×D₅₉)⋊C₄

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

C₂³

yes

—

C₄⋊Dic₅₉

C₂³

yes

characteristic

C₄⋊Dic₅₉

C₂³

yes

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

Dic₅₉⋊C₄

—

C₄×Dic₅₉

—

C₄×Dic₅₉

—

#11745660

Q₈

yes

complemented

C₂²×D₅₉

—

Q₈×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

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

D₂₃₆

—

D₂₃₆

C₂×Q₈

yes

—

C₄×D₅₉

—

C₄×D₅₉

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

—

Dic₁₁₈

C₂×Q₈

yes

—

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

C₂×Q₈

yes

—

C₂²×C₅₉

C₂²×D₄

yes

characteristic

C₂×D₅₉

—

C₂×D₅₉

—

C₂×D₅₉

—

100

C₄×C₅₉

—

101

C₄×C₅₉

—

102

C₄×C₅₉

—

103

C₄×C₅₉

#137

yes

—

104

C₄×C₅₉

C₂²×Q₈

yes

characteristic

105

C₄×C₅₉

2₋¹⁺⁴

yes

characteristic

106

Dic₅₉

—

107

Dic₅₉

—

108

Dic₅₉

—

109

Dic₅₉

—

110

Dic₅₉

—

111

#3385

—

maximal, Sylow

112

C₂×C₅₉

D₄×Q₈

yes

characteristic

113

C₂×C₅₉

C₂×#137

yes

characteristic

114

C₂×C₅₉

#576

yes

characteristic

115

D₅₉

—

116

Q₈²

—

117

#554

—

118

#501

—

119

#500

—

120

#479

—

121

#477

—

122

#476

—

123

#474

—

124

#446

D₅₉

yes

characteristic, complemented

125

#440

—

126

C₄×SD₁₆

—

127

C₅₉

#3385

yes

characteristic, complemented, Sylow

128

C₂×SD₁₆

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

118

—

133

C₄⋊Q₈

—

118

—

134

#125

—

135

C₂²⋊Q₈

—

118

—

136

C₂²⋊Q₈

—

118

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

118

—

140

C₄×Q₈

C₂×D₅₉

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

—

143

C₂×C₄⋊C₄

—

118

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

—

149

C₄⋊C₈

C₂×D₅₉

yes

—

150

C₄⋊C₈

C₂×D₅₉

yes

characteristic

151

#103

—

152

#103

—

153

#102

—

154

#102

—

155

#97

C₂×D₅₉

yes

—

156

C₄×C₈

C₂×D₅₉

yes

characteristic

157

C₂×Q₈

—

158

C₂×Q₈

—

118

—

159

C₂×Q₈

—

118

—

160

C₂×Q₈

—

118

—

161

C₂×Q₈

D₂₃₆

yes

characteristic

162

C₂×D₄

—

163

C₂²×C₄

—

118

—

164

C₂²×C₄

—

118

—

165

SD₁₆

—

166

C₂×C₈

C₂²×D₅₉

yes

characteristic

167

C₂×C₈

C₂²×D₅₉

yes

—

168

C₂×C₈

C₂²×D₅₉

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

118

—

174

C₄⋊C₄

—

118

—

175

C₄⋊C₄

—

118

—

176

C₄⋊C₄

—

118

—

177

C₄⋊C₄

—

118

—

178

C₄⋊C₄

—

118

—

179

C₄⋊C₄

—

118

—

180

C₄⋊C₄

D₂₃₆

yes

characteristic

181

C₄⋊C₄

D₂₃₆

yes

—

182

C₂²⋊C₄

—

118

—

183

C₂²⋊C₄

—

118

—

184

C₄²

—

118

—

185

C₄²

—

118

—

186

C₄²

C₂²×D₅₉

yes

characteristic

187

C₄²

C₂²×D₅₉

yes

—

188

C₂³

—

118

—

189

Q₈

—

190

Q₈

—

191

Q₈

—

118

—

192

Q₈

—

472

—

193

Q₈

—

472

—

194

Q₈

—

472

—

195

D₄

—

196

D₄

—

118

—

197

C₂×C₄

—

118

—

198

C₂×C₄

—

118

—

199

C₂×C₄

—

118

—

200

C₂×C₄

—

118

—

201

C₂×C₄

—

118

—

202

C₂×C₄

—

472

—

203

C₂×C₄

—

236

—

204

C₂×C₄

C₂×D₂₃₆

yes

—

205

C₂×C₄

C₂×D₂₃₆

yes

characteristic

206

C₂×C₄

C₂×D₂₃₆

yes

—

207

C₂×C₄

C₂×D₂₃₆

yes

characteristic

208

C₂×C₄

C₂³×D₅₉

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

Q₈×D₅₉

yes

—

212

C₂²

—

118

—

213

C₂²

—

236

—

214

C₂²

—

236

—

215

C₂²

C₂²×D₂₃₆

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

118

—

220

C₄

—

236

—

221

C₄

—

236

—

222

C₄

—

236

—

223

C₄

—

236

—

224

C₄

#14273760

yes

—

225

C₄

C₂×Q₈×D₅₉

yes

characteristic

226

C₄

#14273774

yes

characteristic

227

C₂

—

236

—

228

C₂

Q₈×D₂₃₆

yes

characteristic

229

C₂

C₂×#14273760

yes

characteristic

230

C₂

#16838207

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#446	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#446	D₅₉
hypocenter	C₅₉	#3385
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

subgroup

G/H

center

C₂²

C₂²×D₂₃₆

commutator

C₂×C₄×C₅₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₉

Fitting

C₅₉×#446

C₂

socle

C₂²×C₅₉

C₂²×D₄

D₅₉

C₅₉

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #446

N	H ≅ G/N	type
1. Q₈×Dic₁₁₈	C₂	semidirect
3. #16837811	C₂	semidirect
4. #16837807	C₂	semidirect
5. #16837710	C₂	semidirect
6. #16837698	C₂	semidirect
11. C₅₉×#446	C₂	semidirect
71. #11745660	Q₈	semidirect
124. #446	D₅₉	semidirect
127. C₅₉	#3385	semidirect

H ≅ G/N

type

1. Q₈×Dic₁₁₈

C₂

semidirect

3. #16837811

C₂

semidirect

4. #16837807

C₂

semidirect

5. #16837710

C₂

semidirect

6. #16837698

C₂

semidirect

11. C₅₉×#446

C₂

semidirect

71. #11745660

Q₈

semidirect

124. #446

D₅₉

semidirect

127. C₅₉

#3385

semidirect

Subgroups — #21437008

Conjugacy classes of subgroups

Complements