Group #30602050 — subgroups

Subgroups — #30602050

Order 15616.

510 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 132 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	#21462000	C₂	1	2	yes	maximal
2	#21461946	C₂	1	2	yes	maximal
3	#21461754	C₂	1	1	yes	maximal, characteristic
4	#21461013	C₂	1	1	yes	maximal, characteristic
5	#500×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#14519845	—	2	2	no	—
7	C₂×#14519840	—	2	4	no	—
8	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
9	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
10	#16840708	C₂²	1	2	yes	—
11	#16840635	—	2	4	no	—
12	#16840603	—	2	2	no	—
13	C₄⋊Q₈×D₆₁	C₂²	1	2	yes	—
14	#16840167	C₄	1	1	yes	characteristic, complemented
15	#16840166	—	2	2	no	—
16	#16840165	C₄	1	2	yes	complemented
17	#107×D₆₁	—	2	2	no	—
18	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#500	C₄	1	1	yes	characteristic, complemented
20	C₂×D₆₁⋊C₈	D₄	1	2	yes	—
21	C₂×D₆₁⋊C₈	D₄	1	2	yes	—
22	C₂×C₄⋊#6923	—	2	2	no	—
23	C₂×C₄⋊#6923	—	2	2	no	—
24	C₂×C₄⋊#6923	—	2	2	no	—
25	#14519845	—	4	4	no	—
26	#14519840	—	4	8	no	—
27	C₄×#92420	—	2	1	no	—
28	C₄×#92420	—	2	1	no	—
29	C₄×#92420	—	2	1	no	—
30	C₄×#92420	—	2	1	no	—
31	C₂×Q₈×D₆₁	—	2	2	no	—
32	C₂×C₈×D₆₁	D₄	1	2	yes	—
33	#14519777	C₂×C₄	1	2	yes	—
34	#14519776	—	2	2	no	—
35	#14519776	—	2	2	no	—
36	#14519775	—	2	2	no	—
37	C₄⋊C₄×D₆₁	—	2	2	no	—
38	C₄⋊C₄×D₆₁	—	2	2	no	—
39	C₄²×D₆₁	C₂³	1	1	yes	characteristic
40	#14519711	—	2	2	no	—
41	#14519710	—	2	4	no	—
42	C₄×#92418	C₂×C₄	1	1	yes	characteristic
43	C₈×Dic₆₁	D₄	1	2	yes	—
44	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
45	#107×C₆₁	—	2	2	no	—
46	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂²×#6923	—	4	2	no	—
48	C₂×Q₈×C₆₁	—	2	2	no	—
49	Q₈×D₆₁	—	4	4	no	—
50	Q₈×D₆₁	—	4	4	no	—
51	C₂×C₄×D₆₁	—	4	2	no	—
52	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
53	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
54	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₁₂₂	—	2	2	no	—
56	C₂×Dic₁₂₂	—	4	2	no	—
57	C₂×#92420	—	2	2	no	—
58	C₂×#92420	—	2	2	no	—
59	C₄⋊#6923	—	4	4	no	—
60	C₄⋊#6923	—	4	4	no	—
61	C₄⋊#6923	—	4	4	no	—
62	D₆₁⋊C₈	—	2	4	no	—
63	D₆₁⋊C₈	—	2	4	no	—
64	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
65	C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₄⋊C₄×C₆₁	—	2	2	no	—
67	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
68	C₄⋊Dic₆₁	—	2	2	no	—
69	C₄⋊Dic₆₁	—	2	2	no	—
70	#11758196	—	4	2	no	—
71	#11758196	—	4	2	no	—
72	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
73	C₄×Dic₆₁	#41	1	1	yes	characteristic
74	C₄×Dic₆₁	#41	1	1	yes	characteristic
75	C₂×#92418	C₂²⋊C₄	1	2	yes	—
76	C₈×D₆₁	SD₁₆	1	4	yes	—
77	C₈×D₆₁	Q₁₆	1	4	yes	—
78	C₂²×D₆₁	#127	1	1	yes	characteristic
79	C₂×#6923	—	8	2	no	—
80	C₂×#6923	—	8	2	no	—
81	C₂×#6923	—	8	2	no	—
82	Q₈×C₆₁	—	4	4	no	—
83	C₂×C₄×C₆₁	—	4	2	no	—
84	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
87	C₂×Dic₆₁	—	4	2	no	—
88	C₂×Dic₆₁	#121	1	1	yes	characteristic
89	C₂×Dic₆₁	#121	1	1	yes	characteristic
90	C₂×Dic₆₁	#124	1	1	yes	characteristic
91	C₄×D₆₁	—	8	2	no	—
92	C₄×D₆₁	—	8	2	no	—
93	C₄×D₆₁	C₂×SD₁₆	1	2	yes	—
94	C₄×D₆₁	C₂×Q₁₆	1	2	yes	—
95	C₄×D₆₁	AGL(1,ℤ/8)	1	4	yes	—
96	C₄×D₆₁	#137	1	4	yes	—
97	Dic₁₂₂	—	4	4	no	—
98	Dic₁₂₂	—	8	4	no	—
99	#92420	—	4	2	no	—
100	#92420	—	4	2	no	—
101	C₈×C₆₁	#103	1	4	yes	complemented
102	#92418	#103	1	4	yes	complemented
103	#9836	—	61	1	no	maximal, Sylow
104	C₂²×C₆₁	#390	1	1	yes	characteristic
105	C₂×D₆₁	#492	1	1	yes	characteristic
106	C₂×D₆₁	#494	1	1	yes	characteristic
107	C₂×D₆₁	#496	1	2	yes	—
108	C₂×D₆₁	#497	1	2	yes	—
109	#6923	—	16	2	no	—
110	C₄×C₆₁	—	8	2	no	—
111	C₄×C₆₁	C₂×#103	1	2	yes	—
112	C₄×C₆₁	#441	1	2	yes	—
113	C₄×C₆₁	#442	1	2	yes	—
114	Dic₆₁	—	8	2	no	—
115	Dic₆₁	#469	1	2	yes	—
116	Dic₆₁	#470	1	2	yes	—
117	Dic₆₁	#487	1	2	yes	—
118	C₂×#500	—	61	1	no	—
119	#1990	—	61	2	no	—
120	#1956	—	61	2	no	—
121	#1844	—	61	1	no	—
122	C₂×#322	—	61	1	no	—
123	C₂×C₆₁	#1956	1	1	yes	characteristic
124	C₂×C₆₁	#1971	1	1	yes	characteristic
125	C₂×C₆₁	#1972	1	1	yes	characteristic
126	D₆₁	#1714	1	2	yes	—
127	D₆₁	#1723	1	2	yes	—
128	C₂×C₄⋊Q₈	—	61	2	no	—
129	#500	—	61	2	no	—
130	#500	—	61	1	no	—
131	#500	—	122	2	no	—
132	#500	#6923	1	1	yes	characteristic, complemented
133	C₂×#107	—	122	2	no	—
134	C₂×#106	—	122	2	no	—
135	C₂×#103	—	122	4	no	—
136	C₂×C₄×C₈	—	61	1	no	—
137	C₂×C₄×C₈	—	61	1	no	—
138	C₂×C₄×C₈	—	61	1	no	—
139	#384	—	61	2	no	—
140	#340	—	122	4	no	—
141	#322	—	122	2	no	—
142	C₆₁	#9836	1	1	yes	characteristic, complemented, Sylow
143	C₂²×Q₈	—	122	2	no	—
144	C₂²×C₈	—	61	2	no	—
145	C₂²×C₈	—	61	2	no	—
146	C₂²×C₈	—	61	2	no	—
147	C₄⋊Q₈	—	61	2	no	—
148	C₄⋊Q₈	—	122	2	no	—
149	C₄⋊Q₈	—	122	2	no	—
150	C₄⋊Q₈	—	122	2	no	—
151	C₄⋊Q₈	C₂×#6923	1	2	yes	—
152	C₂×C₄⋊C₄	—	122	2	no	—
153	C₂×C₄⋊C₄	—	122	2	no	—
154	C₂×C₄⋊C₄	—	122	2	no	—
155	C₂×C₄⋊C₄	—	122	2	no	—
156	C₂×C₄⋊C₄	—	122	2	no	—
157	C₂×C₄²	—	61	1	no	—
158	#107	—	2	2	no	—
159	#107	—	122	4	no	—
160	#107	—	122	2	no	—
161	#106	—	244	4	no	—
162	#103	—	244	8	no	—
163	C₄×C₈	—	61	2	no	—
164	C₄×C₈	—	61	1	no	—
165	C₄×C₈	—	122	1	no	—
166	C₄×C₈	—	122	1	no	—
167	C₄×C₈	—	122	1	no	—
168	C₄×C₈	—	122	1	no	—
169	C₄×C₈	C₂×#6923	1	1	yes	characteristic
170	C₂×Q₈	—	2	2	no	—
171	C₂×Q₈	—	122	2	no	—
172	C₂×Q₈	—	244	2	no	—
173	C₂×Q₈	—	244	4	no	—
174	C₂×Q₈	—	244	4	no	—
175	C₂²×C₄	—	61	1	no	—
176	C₂²×C₄	—	61	1	no	—
177	C₂²×C₄	—	61	1	no	—
178	C₂²×C₄	—	244	2	no	—
179	C₂²×C₄	—	244	2	no	—
180	C₂×C₈	—	61	2	no	—
181	C₂×C₈	—	61	4	no	—
182	C₂×C₈	—	61	4	no	—
183	C₂×C₈	—	122	2	no	—
184	C₂×C₈	—	122	2	no	—
185	C₂×C₈	—	122	4	no	—
186	C₂×C₈	—	122	4	no	—
187	C₂×C₈	C₂²⋊#6923	1	2	yes	—
188	C₄⋊C₄	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	122	2	no	—
191	C₄⋊C₄	—	122	2	no	—
192	C₄⋊C₄	—	244	2	no	—
193	C₄⋊C₄	—	244	2	no	—
194	C₄⋊C₄	—	244	4	no	—
195	C₄⋊C₄	—	244	4	no	—
196	C₄⋊C₄	—	244	4	no	—
197	C₄²	—	61	1	no	—
198	C₄²	—	61	1	no	—
199	C₄²	—	61	1	no	—
200	C₄²	C₂²×#6923	1	1	yes	characteristic
201	C₂³	—	61	1	no	—
202	Q₈	—	4	4	no	—
203	Q₈	—	488	4	no	—
204	Q₈	—	244	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	61	1	no	—
207	C₂×C₄	—	61	1	no	—
208	C₂×C₄	—	61	1	no	—
209	C₂×C₄	—	61	2	no	—
210	C₂×C₄	—	61	2	no	—
211	C₂×C₄	—	61	4	no	—
212	C₂×C₄	—	61	4	no	—
213	C₂×C₄	—	488	2	no	—
214	C₂×C₄	—	488	2	no	—
215	C₂×C₄	—	488	2	no	—
216	C₂×C₄	—	488	2	no	—
217	C₂×C₄	—	488	2	no	—
218	C₂×C₄	—	244	2	no	—
219	C₂×C₄	C₂×C₂²⋊#6923	1	1	yes	characteristic
220	C₂×C₄	D₄×#6923	1	1	yes	characteristic
221	C₂×C₄	D₄×#6923	1	1	yes	characteristic
222	C₈	—	61	4	no	—
223	C₈	—	244	2	no	—
224	C₈	—	244	2	no	—
225	C₈	#14519840	1	4	yes	complemented
226	C₂²	—	61	1	no	—
227	C₂²	—	61	1	no	—
228	C₂²	—	61	2	no	—
229	C₂²	—	61	2	no	—
230	C₂²	#16840714	1	1	yes	characteristic
231	C₄	—	8	2	no	—
232	C₄	—	61	2	no	—
233	C₄	—	61	2	no	—
234	C₄	—	61	2	no	—
235	C₄	—	976	2	no	—
236	C₄	—	488	2	no	—
237	C₄	C₂×#14519840	1	2	yes	—
238	C₄	#16840802	1	2	yes	—
239	C₄	#16840803	1	2	yes	—
240	C₂	—	61	2	no	—
241	C₂	—	61	2	no	—
242	C₂	#21461946	1	1	yes	characteristic
243	C₂	#21461967	1	1	yes	characteristic
244	C₂	#21461968	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21462000

C₂

yes

maximal

#21461946

C₂

yes

maximal

#21461754

C₂

yes

maximal, characteristic

#21461013

C₂

yes

maximal, characteristic

#500×D₆₁

C₂

yes

maximal, characteristic

C₂×#14519845

—

C₂×#14519840

—

C₄×D₆₁⋊C₈

C₂²

yes

characteristic

C₄×D₆₁⋊C₈

C₂²

yes

characteristic

#16840708

C₂²

yes

—

#16840635

—

#16840603

—

C₄⋊Q₈×D₆₁

C₂²

yes

—

#16840167

C₄

yes

characteristic, complemented

#16840166

—

#16840165

C₄

yes

complemented

#107×D₆₁

—

C₄×C₈×D₆₁

C₂²

yes

characteristic

C₆₁×#500

C₄

yes

characteristic, complemented

C₂×D₆₁⋊C₈

D₄

yes

—

C₂×D₆₁⋊C₈

D₄

yes

—

C₂×C₄⋊#6923

—

C₂×C₄⋊#6923

—

C₂×C₄⋊#6923

—

—

—

—

—

—

—

C₂×Q₈×D₆₁

—

C₂×C₈×D₆₁

D₄

yes

—

#14519777

C₂×C₄

yes

—

#14519776

—

#14519776

—

#14519775

—

C₄⋊C₄×D₆₁

—

C₄⋊C₄×D₆₁

—

C₄²×D₆₁

C₂³

yes

—

—

C₂×C₄

yes

characteristic

C₈×Dic₆₁

D₄

yes

—

C₄⋊Q₈×C₆₁

C₂×C₄

yes

—

#107×C₆₁

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂²×#6923

—

C₂×Q₈×C₆₁

—

Q₈×D₆₁

—

Q₈×D₆₁

—

C₂×C₄×D₆₁

—

C₂×C₄×D₆₁

C₂×D₄

yes

characteristic

C₂×C₄×D₆₁

C₂×D₄

yes

characteristic

C₂×C₄×D₆₁

C₂×D₄

yes

characteristic

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

—

—

—

—

—

D₆₁⋊C₈

—

D₆₁⋊C₈

—

C₂×C₈×C₆₁

C₂²⋊C₄

yes

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

#11758196

—

C₄×Dic₆₁

C₂×D₄

yes

C₄×Dic₆₁

yes

C₄×Dic₆₁

yes

C₂²⋊C₄

yes

—

C₈×D₆₁

SD₁₆

yes

—

C₈×D₆₁

Q₁₆

yes

—

C₂²×D₆₁

yes

—

—

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄×D₄

yes

characteristic

C₂×C₄×C₆₁

C₄×D₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

yes

C₂×Dic₆₁

yes

C₂×Dic₆₁

yes

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₂×SD₁₆

yes

—

C₄×D₆₁

C₂×Q₁₆

yes

—

C₄×D₆₁

AGL(1,ℤ/8)

yes

—

C₄×D₆₁

#137

yes

—

Dic₁₂₂

—

Dic₁₂₂

—

#92420

—

100

#92420

—

101

C₈×C₆₁

yes

102

yes

103

—

104

C₂²×C₆₁

#390

yes

characteristic

105

C₂×D₆₁

#492

yes

characteristic

106

C₂×D₆₁

#494

yes

characteristic

107

C₂×D₆₁

#496

yes

—

108

C₂×D₆₁

#497

yes

—

109

#6923

—

110

C₄×C₆₁

—

111

C₄×C₆₁

C₂×#103

yes

—

112

C₄×C₆₁

#441

yes

—

113

C₄×C₆₁

#442

yes

—

114

Dic₆₁

—

115

Dic₆₁

#469

yes

—

116

Dic₆₁

#470

yes

—

117

Dic₆₁

#487

yes

—

118

C₂×#500

—

119

#1990

—

120

#1956

—

121

#1844

—

122

C₂×#322

—

123

C₂×C₆₁

#1956

yes

characteristic

124

C₂×C₆₁

#1971

yes

characteristic

125

C₂×C₆₁

#1972

yes

characteristic

126

D₆₁

#1714

yes

—

127

D₆₁

#1723

yes

—

128

C₂×C₄⋊Q₈

—

129

#500

—

130

#500

—

131

#500

—

122

—

132

#500

#6923

yes

characteristic, complemented

133

C₂×#107

—

122

—

134

C₂×#106

—

122

—

135

C₂×#103

—

122

—

136

C₂×C₄×C₈

—

137

C₂×C₄×C₈

—

138

C₂×C₄×C₈

—

139

#384

—

140

#340

—

122

—

141

#322

—

122

—

142

C₆₁

#9836

yes

characteristic, complemented, Sylow

143

C₂²×Q₈

—

122

—

144

C₂²×C₈

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

122

—

149

C₄⋊Q₈

—

122

—

150

C₄⋊Q₈

—

122

—

151

C₄⋊Q₈

C₂×#6923

yes

—

152

C₂×C₄⋊C₄

—

122

—

153

C₂×C₄⋊C₄

—

122

—

154

C₂×C₄⋊C₄

—

122

—

155

C₂×C₄⋊C₄

—

122

—

156

C₂×C₄⋊C₄

—

122

—

157

C₂×C₄²

—

158

#107

—

159

#107

—

122

—

160

#107

—

122

—

161

#106

—

244

—

162

#103

—

244

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₄×C₈

—

122

—

166

C₄×C₈

—

122

—

167

C₄×C₈

—

122

—

168

C₄×C₈

—

122

—

169

C₄×C₈

C₂×#6923

yes

characteristic

170

C₂×Q₈

—

171

C₂×Q₈

—

122

—

172

C₂×Q₈

—

244

—

173

C₂×Q₈

—

244

—

174

C₂×Q₈

—

244

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂²×C₄

—

244

—

179

C₂²×C₄

—

244

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

122

—

184

C₂×C₈

—

122

—

185

C₂×C₈

—

122

—

186

C₂×C₈

—

122

—

187

C₂×C₈

C₂²⋊#6923

yes

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

122

—

191

C₄⋊C₄

—

122

—

192

C₄⋊C₄

—

244

—

193

C₄⋊C₄

—

244

—

194

C₄⋊C₄

—

244

—

195

C₄⋊C₄

—

244

—

196

C₄⋊C₄

—

244

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

C₂²×#6923

yes

characteristic

201

C₂³

—

202

Q₈

—

203

Q₈

—

488

—

204

Q₈

—

244

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

488

—

214

C₂×C₄

—

488

—

215

C₂×C₄

—

488

—

216

C₂×C₄

—

488

—

217

C₂×C₄

—

488

—

218

C₂×C₄

—

244

—

219

C₂×C₄

C₂×C₂²⋊#6923

yes

characteristic

220

C₂×C₄

D₄×#6923

yes

characteristic

221

C₂×C₄

D₄×#6923

yes

characteristic

222

C₈

—

223

C₈

—

244

—

224

C₈

—

244

—

225

C₈

#14519840

yes

complemented

226

C₂²

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

#16840714

yes

characteristic

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

976

—

236

C₄

—

488

—

237

C₄

C₂×#14519840

yes

—

238

C₄

#16840802

yes

—

239

C₄

#16840803

yes

—

240

C₂

—

241

C₂

—

242

C₂

#21461946

yes

characteristic

243

C₂

#21461967

yes

characteristic

244

C₂

#21461968

yes

characteristic

	subgroup	G/H
center	C₂²	#16840714
commutator	C₄²×C₆₁	C₂²×C₄
Frattini	C₄²	C₂²×#6923
Fitting	C₆₁×#500	C₄
socle	C₂²×C₆₁	#390
prime radical	C₂²×D₆₁	#127
cosocle	C₄²×D₆₁	C₂³
hypercenter	#500	#6923
hypocenter	C₆₁	#9836
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #500

subgroup

G/H

center

C₂²

#16840714

commutator

C₄²×C₆₁

C₂²×C₄

Frattini

C₄²

C₂²×#6923

Fitting

C₆₁×#500

C₄

C₂²×C₆₁

C₂²×D₆₁

C₄²×D₆₁

C₂³

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #500

N	H ≅ G/N	type
14. #16840167	C₄	semidirect
16. #16840165	C₄	semidirect
19. C₆₁×#500	C₄	semidirect
101. C₈×C₆₁	#103	semidirect
102. #92418	#103	semidirect
132. #500	#6923	semidirect
142. C₆₁	#9836	semidirect
225. C₈	#14519840	semidirect

H ≅ G/N

type

14. #16840167

C₄

semidirect

16. #16840165

C₄

semidirect

19. C₆₁×#500

C₄

semidirect

101. C₈×C₆₁

#103

semidirect

102. #92418

#103

semidirect

132. #500

#6923

semidirect

142. C₆₁

#9836

semidirect

225. C₈

#14519840

semidirect

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

subgroup	index
#21462000	2
#21461946	2
#21461754	2
#21461013	2
#500×D₆₁	2
#9836	61

subgroup

index

#500×D₆₁

Subgroups — #30602050

Conjugacy classes of subgroups

Complements

Maximal subgroups