Group #29579896 — subgroups

Subgroups — #29579896

Order 15616.

478 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 139 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	#21456405	C₂	1	1	yes	maximal, characteristic
2	#21446796	C₂	1	2	yes	maximal
3	#21444578	C₂	1	1	yes	maximal, characteristic
4	#21444275	C₂	1	2	yes	maximal
5	C₄²×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic
6	#16840319	C₂²	1	2	yes	—
7	#16840167	C₄	1	1	yes	characteristic, complemented
8	#16840142	C₄	1	1	yes	characteristic, complemented
9	#16840113	C₄	1	2	yes	complemented
10	#16840003	—	2	2	no	—
11	C₄×Dic₂₄₄	—	2	2	no	—
12	#16839786	C₂²	1	2	yes	—
13	#16839522	—	2	4	no	—
14	#16839515	—	2	2	no	—
15	#16839494	—	2	4	no	—
16	C₂×C₄×C₈×C₆₁	—	2	2	no	—
17	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₄³×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×Dic₂₄₄	—	2	2	no	—
21	C₂×#11758194	—	2	2	no	—
22	#14519777	C₂×C₄	1	2	yes	—
23	#14519777	C₂×C₄	1	2	yes	—
24	#14519769	—	2	2	no	—
25	#14519756	—	2	2	no	—
26	#14519756	—	2	2	no	—
27	C₄×Dic₁₂₂	—	2	2	no	—
28	C₄×Dic₁₂₂	—	2	2	no	—
29	#14519736	—	2	2	no	—
30	#14519711	—	2	2	no	—
31	C₄⋊#92418	—	2	2	no	—
32	C₄⋊#92418	—	2	2	no	—
33	#14519702	—	2	4	no	—
34	C₂²×C₈×C₆₁	—	2	1	no	—
35	C₂²×C₈×C₆₁	D₄	1	2	yes	—
36	C₂×C₄²×C₆₁	—	2	1	no	—
37	C₂×C₄²×C₆₁	—	2	1	no	—
38	C₂×C₄²×C₆₁	D₄	1	2	yes	—
39	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
40	C₄×C₈×C₆₁	—	2	8	no	—
41	C₄×C₈×C₆₁	—	2	1	no	—
42	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₆₁	D₄	1	2	yes	—
45	C₄×C₈×C₆₁	D₄	1	2	yes	—
46	C₂²×C₄×C₆₁	—	2	2	no	—
47	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
50	C₂×Dic₁₂₂	—	2	2	no	—
51	C₂×Dic₁₂₂	—	2	2	no	—
52	C₂×C₈×C₆₁	—	2	4	no	—
53	C₂×C₈×C₆₁	—	2	2	no	—
54	C₂×C₈×C₆₁	—	2	4	no	—
55	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
57	C₄²×C₆₁	—	2	4	no	—
58	C₄²×C₆₁	—	2	4	no	—
59	C₄²×C₆₁	—	2	2	no	—
60	C₄²×C₆₁	Q₁₆	1	4	yes	complemented
61	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₆₁	#41	1	1	yes	characteristic
65	C₂²⋊Dic₆₁	—	4	2	no	—
66	C₄⋊Dic₆₁	—	2	2	no	—
67	C₄⋊Dic₆₁	—	2	2	no	—
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	—	4	2	no	—
73	#11758194	—	4	4	no	—
74	C₂×#92418	—	4	2	no	—
75	Dic₂₄₄	—	4	4	no	—
76	C₂³×C₆₁	#121	1	1	yes	characteristic
77	C₂×C₄×C₆₁	—	2	4	no	—
78	C₂×C₄×C₆₁	—	2	4	no	—
79	C₂×C₄×C₆₁	—	2	4	no	—
80	C₂×C₄×C₆₁	—	2	2	no	—
81	C₂×C₄×C₆₁	—	2	2	no	—
82	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
86	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
87	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
88	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₆₁	#135	1	2	yes	—
90	C₂×Dic₆₁	—	4	2	no	—
91	C₂×Dic₆₁	—	4	2	no	—
92	Dic₁₂₂	—	4	4	no	—
93	Dic₁₂₂	—	4	4	no	—
94	C₈×C₆₁	—	2	4	no	—
95	C₈×C₆₁	—	2	2	no	—
96	C₈×C₆₁	#104	1	4	yes	—
97	#92418	—	8	2	no	—
98	#9845	—	61	1	no	maximal, Sylow
99	C₂²×C₆₁	—	2	1	no	—
100	C₂²×C₆₁	—	2	1	no	—
101	C₂²×C₆₁	#390	1	1	yes	characteristic
102	C₂²×C₆₁	#467	1	2	yes	—
103	C₄×C₆₁	—	2	8	no	—
104	C₄×C₆₁	—	2	1	no	—
105	C₄×C₆₁	—	2	1	no	—
106	C₄×C₆₁	C₂×#104	1	2	yes	—
107	C₄×C₆₁	C₄×Q₁₆	1	2	yes	—
108	C₄×C₆₁	#443	1	2	yes	—
109	C₄×C₆₁	#494	1	1	yes	characteristic
110	C₄×C₆₁	#495	1	1	yes	characteristic
111	Dic₆₁	—	8	2	no	—
112	Dic₆₁	—	8	2	no	—
113	#3170	—	61	1	no	—
114	#1994	—	61	2	no	—
115	C₄²×C₈	D₆₁	1	1	yes	characteristic
116	#1567	—	61	1	no	—
117	#1493	—	61	2	no	—
118	C₂×C₆₁	—	2	2	no	—
119	C₂×C₆₁	#1962	1	1	yes	characteristic
120	C₂×C₆₁	#1969	1	1	yes	characteristic
121	C₂×C₆₁	#1974	1	1	yes	characteristic
122	#533	—	61	2	no	—
123	#500	—	61	1	no	—
124	#494	—	61	1	no	—
125	#487	—	61	2	no	—
126	#467	—	122	2	no	—
127	C₄×Q₁₆	—	122	2	no	—
128	#423	—	61	2	no	—
129	C₂×C₄×C₈	—	2	2	no	—
130	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
131	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
132	C₄³	C₂×D₆₁	1	1	yes	characteristic
133	#339	—	122	4	no	—
134	#335	—	122	2	no	—
135	Q₈⋊C₈	—	122	4	no	—
136	C₆₁	#9845	1	1	yes	characteristic, complemented, Sylow
137	C₂×Q₁₆	—	122	2	no	—
138	C₂×M₁₆	—	122	2	no	—
139	C₂²×C₈	—	2	1	no	—
140	C₂²×C₈	C₂²⋊D₆₁	1	2	yes	—
141	C₄⋊Q₈	—	61	2	no	—
142	C₄⋊Q₈	—	61	2	no	—
143	#125	—	122	2	no	—
144	C₂²⋊Q₈	—	122	2	no	—
145	C₂²⋊Q₈	—	122	2	no	—
146	C₄×Q₈	—	122	2	no	—
147	C₄×Q₈	—	122	2	no	—
148	#117	—	122	2	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	—	2	1	no	—
151	C₂×C₄²	D₂₄₄	1	2	yes	—
152	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
153	#107	—	122	2	no	—
154	C₄⋊C₈	—	122	2	no	—
155	C₄⋊C₈	—	122	2	no	—
156	#103	—	122	4	no	—
157	C₄×C₈	—	2	8	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
160	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
161	C₄×C₈	D₂₄₄	1	2	yes	—
162	C₄×C₈	D₂₄₄	1	2	yes	—
163	C₂×Q₈	—	122	2	no	—
164	C₂×Q₈	—	122	2	no	—
165	C₂²×C₄	—	2	2	no	—
166	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
167	C₂²×C₄	#11758222	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
169	Q₁₆	—	244	4	no	—
170	M₁₆	—	244	4	no	—
171	C₂×C₈	—	2	4	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	244	2	no	—
175	C₂×C₈	#11758198	1	2	yes	—
176	C₂×C₈	#11758198	1	2	yes	—
177	C₄⋊C₄	—	122	2	no	—
178	C₄⋊C₄	—	122	2	no	—
179	C₄⋊C₄	—	122	2	no	—
180	C₄⋊C₄	—	122	2	no	—
181	C₄⋊C₄	—	244	2	no	—
182	C₄⋊C₄	—	244	2	no	—
183	C₂²⋊C₄	—	244	2	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	4	no	—
186	C₄²	—	2	2	no	—
187	C₄²	—	244	2	no	—
188	C₄²	Dic₂₄₄	1	4	yes	complemented
189	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
190	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
191	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
192	C₄²	#11758222	1	1	yes	characteristic
193	C₂³	#14519751	1	1	yes	characteristic
194	Q₈	—	244	4	no	—
195	Q₈	—	244	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	244	2	no	—
202	C₂×C₄	—	244	2	no	—
203	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
204	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
205	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
206	C₂×C₄	#14519751	1	1	yes	characteristic
207	C₂×C₄	#14519765	1	1	yes	characteristic
208	C₂×C₄	#14519774	1	1	yes	characteristic
209	C₂×C₄	C₂×Dic₂₄₄	1	2	yes	—
210	C₂×C₄	#14519799	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	2	2	no	—
213	C₈	—	488	2	no	—
214	C₈	#14519705	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	#16839664	1	1	yes	characteristic
218	C₂²	#16840003	1	2	yes	—
219	C₄	—	2	8	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	488	2	no	—
223	C₄	—	488	2	no	—
224	C₄	C₂×#14519705	1	2	yes	—
225	C₄	C₄×Dic₂₄₄	1	2	yes	—
226	C₄	#16839880	1	2	yes	—
227	C₄	#16840142	1	1	yes	characteristic
228	C₄	#16840146	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	#21446647	1	1	yes	characteristic
231	C₂	#21446680	1	1	yes	characteristic
232	C₂	#21446707	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21456405

C₂

yes

maximal, characteristic

#21446796

C₂

yes

maximal

#21444578

C₂

yes

maximal, characteristic

#21444275

C₂

yes

maximal

C₄²×C₈×C₆₁

C₂

yes

maximal, characteristic

#16840319

C₂²

yes

—

#16840167

C₄

yes

characteristic, complemented

#16840142

C₄

yes

characteristic, complemented

#16840113

C₄

yes

complemented

#16840003

—

C₄×Dic₂₄₄

—

#16839786

C₂²

yes

—

#16839522

—

#16839515

—

#16839494

—

C₂×C₄×C₈×C₆₁

—

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄³×C₆₁

C₂²

yes

characteristic

C₂×Dic₂₄₄

—

C₂×#11758194

—

#14519777

C₂×C₄

yes

—

#14519777

C₂×C₄

yes

—

#14519769

—

#14519756

—

#14519756

—

C₄×Dic₁₂₂

—

C₄×Dic₁₂₂

—

—

—

—

—

—

C₂²×C₈×C₆₁

—

C₂²×C₈×C₆₁

D₄

yes

—

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

D₄

yes

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

C₄×C₈×C₆₁

—

C₄×C₈×C₆₁

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

D₄

yes

—

C₄×C₈×C₆₁

D₄

yes

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

#41

yes

characteristic

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂²⋊C₄

yes

—

C₂×C₈×C₆₁

C₂²⋊C₄

yes

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

Q₁₆

yes

complemented

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄²×C₆₁

C₂×D₄

yes

characteristic

C₄²×C₆₁

C₂×D₄

yes

characteristic

C₄²×C₆₁

#41

yes

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

#11758196

—

#11758196

—

C₄×Dic₆₁

—

#11758194

—

C₂×#92418

—

Dic₂₄₄

—

C₂³×C₆₁

#121

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×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

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

C₂×Q₁₆

yes

—

C₂×C₄×C₆₁

#135

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

#104

yes

—

#92418

—

#9845

—

maximal, Sylow

C₂²×C₆₁

—

100

C₂²×C₆₁

—

101

C₂²×C₆₁

#390

yes

characteristic

102

C₂²×C₆₁

#467

yes

—

103

C₄×C₆₁

—

104

C₄×C₆₁

—

105

C₄×C₆₁

—

106

C₄×C₆₁

C₂×#104

yes

—

107

C₄×C₆₁

C₄×Q₁₆

yes

—

108

C₄×C₆₁

#443

yes

—

109

C₄×C₆₁

#494

yes

characteristic

110

C₄×C₆₁

#495

yes

characteristic

111

Dic₆₁

—

112

Dic₆₁

—

113

#3170

—

114

#1994

—

115

C₄²×C₈

D₆₁

yes

characteristic

116

#1567

—

117

#1493

—

118

C₂×C₆₁

—

119

C₂×C₆₁

#1962

yes

characteristic

120

C₂×C₆₁

#1969

yes

characteristic

121

C₂×C₆₁

#1974

yes

characteristic

122

#533

—

123

#500

—

124

#494

—

125

#487

—

126

#467

—

122

—

127

C₄×Q₁₆

—

122

—

128

#423

—

129

C₂×C₄×C₈

—

130

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

131

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

132

C₄³

C₂×D₆₁

yes

characteristic

133

#339

—

122

—

134

#335

—

122

—

135

Q₈⋊C₈

—

122

—

136

C₆₁

#9845

yes

characteristic, complemented, Sylow

137

C₂×Q₁₆

—

122

—

138

C₂×M₁₆

—

122

—

139

C₂²×C₈

—

140

C₂²×C₈

C₂²⋊D₆₁

yes

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

#125

—

122

—

144

C₂²⋊Q₈

—

122

—

145

C₂²⋊Q₈

—

122

—

146

C₄×Q₈

—

122

—

147

C₄×Q₈

—

122

—

148

#117

—

122

—

149

C₂×C₄²

—

150

C₂×C₄²

—

151

C₂×C₄²

D₂₄₄

yes

—

152

C₂×C₄²

C₂²×D₆₁

yes

characteristic

153

#107

—

122

—

154

C₄⋊C₈

—

122

—

155

C₄⋊C₈

—

122

—

156

#103

—

122

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

C₄×D₆₁

yes

characteristic

160

C₄×C₈

C₄×D₆₁

yes

characteristic

161

C₄×C₈

D₂₄₄

yes

—

162

C₄×C₈

D₂₄₄

yes

—

163

C₂×Q₈

—

122

—

164

C₂×Q₈

—

122

—

165

C₂²×C₄

—

166

C₂²×C₄

C₂×D₂₄₄

yes

characteristic

167

C₂²×C₄

#11758222

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

169

Q₁₆

—

244

—

170

M₁₆

—

244

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

244

—

175

C₂×C₈

#11758198

yes

—

176

C₂×C₈

#11758198

yes

—

177

C₄⋊C₄

—

122

—

178

C₄⋊C₄

—

122

—

179

C₄⋊C₄

—

122

—

180

C₄⋊C₄

—

122

—

181

C₄⋊C₄

—

244

—

182

C₄⋊C₄

—

244

—

183

C₂²⋊C₄

—

244

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

244

—

188

C₄²

Dic₂₄₄

yes

complemented

189

C₄²

C₂×C₄×D₆₁

yes

characteristic

190

C₄²

C₂×D₂₄₄

yes

characteristic

191

C₄²

C₂×D₂₄₄

yes

characteristic

192

C₄²

#11758222

yes

characteristic

193

C₂³

#14519751

yes

characteristic

194

Q₈

—

244

—

195

Q₈

—

244

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

244

—

202

C₂×C₄

—

244

—

203

C₂×C₄

C₂×#11758198

yes

characteristic

204

C₂×C₄

C₄×D₂₄₄

yes

characteristic

205

C₂×C₄

C₄×D₂₄₄

yes

characteristic

206

C₂×C₄

#14519751

yes

characteristic

207

C₂×C₄

#14519765

yes

characteristic

208

C₂×C₄

#14519774

yes

characteristic

209

C₂×C₄

C₂×Dic₂₄₄

yes

—

210

C₂×C₄

#14519799

yes

—

211

C₈

—

212

C₈

—

213

C₈

—

488

—

214

C₈

#14519705

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

#16839664

yes

characteristic

218

C₂²

#16840003

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

488

—

223

C₄

—

488

—

224

C₄

C₂×#14519705

yes

—

225

C₄

C₄×Dic₂₄₄

yes

—

226

C₄

#16839880

yes

—

227

C₄

#16840142

yes

characteristic

228

C₄

#16840146

yes

characteristic

229

C₂

—

230

C₂

#21446647

yes

characteristic

231

C₂

#21446680

yes

characteristic

232

C₂

#21446707

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14519774
commutator	C₄²×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₄²×C₈×C₆₁	C₂
socle	C₂²×C₆₁	#390
prime radical	C₂³×C₆₁	#121
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	C₄²×C₈	D₆₁
hypocenter	C₆₁	#9845
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

subgroup

G/H

center

C₂×C₄

#14519774

commutator

C₄²×C₆₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₁

Fitting

C₄²×C₈×C₆₁

C₂

C₂²×C₆₁

C₂³×C₆₁

C₂×C₄²×C₆₁

C₂³

hypercenter

C₄²×C₈

D₆₁

hypocenter

C₆₁

#9845

LCS

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄²×C₈

N	H ≅ G/N	type
7. #16840167	C₄	semidirect
8. #16840142	C₄	semidirect
9. #16840113	C₄	semidirect
60. C₄²×C₆₁	Q₁₆	semidirect
136. C₆₁	#9845	semidirect
188. C₄²	Dic₂₄₄	semidirect

H ≅ G/N

type

7. #16840167

C₄

semidirect

8. #16840142

C₄

semidirect

9. #16840113

C₄

semidirect

60. C₄²×C₆₁

Q₁₆

semidirect

136. C₆₁

#9845

semidirect

188. C₄²

Dic₂₄₄

semidirect

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

subgroup	index
#21456405	2
#21446796	2
#21444578	2
#21444275	2
C₄²×C₈×C₆₁	2
#9845	61

subgroup

index

C₄²×C₈×C₆₁

Subgroups — #29579896

Conjugacy classes of subgroups

Complements

Maximal subgroups