Group #29579913 — subgroups

Subgroups — #29579913

Order 15616.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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	C₆₁×#1744	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	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₄³×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#336	—	2	2	no	—
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	1	no	—
41	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₆₁	D₄	1	2	yes	—
44	C₄×C₈×C₆₁	D₄	1	2	yes	—
45	C₂²×C₄×C₆₁	—	2	2	no	—
46	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
49	C₂×Dic₁₂₂	—	2	2	no	—
50	C₂×Dic₁₂₂	—	2	2	no	—
51	C₂×C₈×C₆₁	—	2	2	no	—
52	C₂×C₈×C₆₁	—	4	2	no	—
53	C₂×C₈×C₆₁	—	4	2	no	—
54	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₆₁	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₆₁	—	2	2	no	—
57	C₄²×C₆₁	—	4	2	no	—
58	C₄²×C₆₁	—	4	2	no	—
59	C₄²×C₆₁	Q₁₆	1	4	yes	complemented
60	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₆₁	#41	1	1	yes	characteristic
64	C₂²⋊Dic₆₁	—	4	2	no	—
65	C₄⋊Dic₆₁	—	2	2	no	—
66	C₄⋊Dic₆₁	—	2	2	no	—
67	C₄⋊Dic₆₁	—	2	2	no	—
68	C₄⋊Dic₆₁	—	2	2	no	—
69	#11758196	—	4	2	no	—
70	#11758196	—	4	2	no	—
71	C₄×Dic₆₁	—	4	2	no	—
72	#11758194	—	4	4	no	—
73	C₂×#92418	—	4	2	no	—
74	Dic₂₄₄	—	4	4	no	—
75	C₂³×C₆₁	#121	1	1	yes	characteristic
76	C₂×C₄×C₆₁	—	2	2	no	—
77	C₂×C₄×C₆₁	—	2	2	no	—
78	C₂×C₄×C₆₁	—	2	4	no	—
79	C₂×C₄×C₆₁	—	4	2	no	—
80	C₂×C₄×C₆₁	—	4	2	no	—
81	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
85	C₂×C₄×C₆₁	#124	1	1	yes	characteristic
86	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
87	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₆₁	#135	1	2	yes	—
89	C₂×Dic₆₁	—	4	2	no	—
90	C₂×Dic₆₁	—	4	2	no	—
91	Dic₁₂₂	—	4	4	no	—
92	Dic₁₂₂	—	4	4	no	—
93	C₈×C₆₁	—	2	2	no	—
94	C₈×C₆₁	—	2	2	no	—
95	C₈×C₆₁	—	4	2	no	—
96	#92418	—	8	2	no	—
97	#9848	—	61	1	no	maximal, Sylow
98	C₂²×C₆₁	—	2	1	no	—
99	C₂²×C₆₁	—	2	1	no	—
100	C₂²×C₆₁	#390	1	1	yes	characteristic
101	C₂²×C₆₁	#467	1	2	yes	—
102	C₄×C₆₁	—	2	1	no	—
103	C₄×C₆₁	—	2	1	no	—
104	C₄×C₆₁	—	4	4	no	—
105	C₄×C₆₁	#421	1	2	yes	—
106	C₄×C₆₁	C₄×Q₁₆	1	2	yes	—
107	C₄×C₆₁	#444	1	2	yes	—
108	C₄×C₆₁	#494	1	1	yes	characteristic
109	C₄×C₆₁	#495	1	1	yes	characteristic
110	Dic₆₁	—	8	2	no	—
111	Dic₆₁	—	8	2	no	—
112	#3170	—	61	1	no	—
113	#1994	—	61	2	no	—
114	#1744	D₆₁	1	1	yes	characteristic
115	#1567	—	61	1	no	—
116	#1493	—	61	2	no	—
117	C₂×C₆₁	—	2	2	no	—
118	C₂×C₆₁	#1963	1	1	yes	characteristic
119	C₂×C₆₁	#1969	1	1	yes	characteristic
120	C₂×C₆₁	#1975	1	1	yes	characteristic
121	#533	—	61	2	no	—
122	#500	—	61	1	no	—
123	#494	—	61	1	no	—
124	#487	—	61	2	no	—
125	#467	—	122	2	no	—
126	C₄×Q₁₆	—	122	2	no	—
127	#423	—	61	2	no	—
128	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
129	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
130	C₄³	C₂×D₆₁	1	1	yes	characteristic
131	#339	—	122	4	no	—
132	#336	—	2	2	no	—
133	#335	—	122	2	no	—
134	Q₈⋊C₈	—	122	4	no	—
135	C₆₁	#9848	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	122	2	no	—
137	C₂×M₁₆	—	122	2	no	—
138	C₂²×C₈	—	2	1	no	—
139	C₂²×C₈	C₂²⋊D₆₁	1	2	yes	—
140	C₄⋊Q₈	—	61	2	no	—
141	C₄⋊Q₈	—	61	2	no	—
142	#125	—	122	2	no	—
143	C₂²⋊Q₈	—	122	2	no	—
144	C₂²⋊Q₈	—	122	2	no	—
145	C₄×Q₈	—	122	2	no	—
146	C₄×Q₈	—	122	2	no	—
147	#117	—	122	2	no	—
148	C₂×C₄²	—	2	1	no	—
149	C₂×C₄²	—	2	1	no	—
150	C₂×C₄²	D₂₄₄	1	2	yes	—
151	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
152	#107	—	122	2	no	—
153	C₄⋊C₈	—	122	2	no	—
154	C₄⋊C₈	—	122	2	no	—
155	#103	—	122	4	no	—
156	C₄×C₈	—	2	1	no	—
157	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
158	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
159	C₄×C₈	D₂₄₄	1	2	yes	—
160	C₄×C₈	D₂₄₄	1	2	yes	—
161	C₂×Q₈	—	122	2	no	—
162	C₂×Q₈	—	122	2	no	—
163	C₂²×C₄	—	2	2	no	—
164	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
165	C₂²×C₄	#11758222	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
167	Q₁₆	—	244	4	no	—
168	M₁₆	—	244	4	no	—
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	4	2	no	—
172	C₂×C₈	—	244	2	no	—
173	C₂×C₈	#11758198	1	2	yes	—
174	C₂×C₈	#11758198	1	2	yes	—
175	C₄⋊C₄	—	122	2	no	—
176	C₄⋊C₄	—	122	2	no	—
177	C₄⋊C₄	—	122	2	no	—
178	C₄⋊C₄	—	122	2	no	—
179	C₄⋊C₄	—	244	2	no	—
180	C₄⋊C₄	—	244	2	no	—
181	C₂²⋊C₄	—	244	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	—	4	2	no	—
184	C₄²	—	4	2	no	—
185	C₄²	—	244	2	no	—
186	C₄²	Dic₂₄₄	1	4	yes	complemented
187	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
188	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
189	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
190	C₄²	#11758222	1	1	yes	characteristic
191	C₂³	#14519751	1	1	yes	characteristic
192	Q₈	—	244	4	no	—
193	Q₈	—	244	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	244	2	no	—
200	C₂×C₄	—	244	2	no	—
201	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
202	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
203	C₂×C₄	C₄×D₂₄₄	1	1	yes	characteristic
204	C₂×C₄	#14519751	1	1	yes	characteristic
205	C₂×C₄	#14519765	1	1	yes	characteristic
206	C₂×C₄	#14519774	1	1	yes	characteristic
207	C₂×C₄	C₂×Dic₂₄₄	1	2	yes	—
208	C₂×C₄	#14519799	1	2	yes	—
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	4	2	no	—
212	C₈	—	488	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#16839664	1	1	yes	characteristic
216	C₂²	#16840003	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	4	4	no	—
220	C₄	—	488	2	no	—
221	C₄	—	488	2	no	—
222	C₄	#16839780	1	2	yes	—
223	C₄	C₄×Dic₂₄₄	1	2	yes	—
224	C₄	#16839885	1	2	yes	—
225	C₄	#16840142	1	1	yes	characteristic
226	C₄	#16840146	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#21446651	1	1	yes	characteristic
229	C₂	#21446680	1	1	yes	characteristic
230	C₂	#21446712	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

C₆₁×#1744

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

C₂²

yes

characteristic

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₄³×C₆₁

C₂²

yes

characteristic

C₆₁×#336

—

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

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

—

#92418

—

#9848

—

maximal, Sylow

C₂²×C₆₁

—

C₂²×C₆₁

—

100

C₂²×C₆₁

#390

yes

characteristic

101

C₂²×C₆₁

#467

yes

—

102

C₄×C₆₁

—

103

C₄×C₆₁

—

104

C₄×C₆₁

—

105

C₄×C₆₁

#421

yes

—

106

C₄×C₆₁

C₄×Q₁₆

yes

—

107

C₄×C₆₁

#444

yes

—

108

C₄×C₆₁

#494

yes

characteristic

109

C₄×C₆₁

#495

yes

characteristic

110

Dic₆₁

—

111

Dic₆₁

—

112

#3170

—

113

#1994

—

114

#1744

D₆₁

yes

characteristic

115

#1567

—

116

#1493

—

117

C₂×C₆₁

—

118

C₂×C₆₁

#1963

yes

characteristic

119

C₂×C₆₁

#1969

yes

characteristic

120

C₂×C₆₁

#1975

yes

characteristic

121

#533

—

122

#500

—

123

#494

—

124

#487

—

125

#467

—

122

—

126

C₄×Q₁₆

—

122

—

127

#423

—

128

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

129

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

130

C₄³

C₂×D₆₁

yes

characteristic

131

#339

—

122

—

132

#336

—

133

#335

—

122

—

134

Q₈⋊C₈

—

122

—

135

C₆₁

#9848

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

122

—

137

C₂×M₁₆

—

122

—

138

C₂²×C₈

—

139

C₂²×C₈

C₂²⋊D₆₁

yes

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

#125

—

122

—

143

C₂²⋊Q₈

—

122

—

144

C₂²⋊Q₈

—

122

—

145

C₄×Q₈

—

122

—

146

C₄×Q₈

—

122

—

147

#117

—

122

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

D₂₄₄

yes

—

151

C₂×C₄²

C₂²×D₆₁

yes

characteristic

152

#107

—

122

—

153

C₄⋊C₈

—

122

—

154

C₄⋊C₈

—

122

—

155

#103

—

122

—

156

C₄×C₈

—

157

C₄×C₈

C₄×D₆₁

yes

characteristic

158

C₄×C₈

C₄×D₆₁

yes

characteristic

159

C₄×C₈

D₂₄₄

yes

—

160

C₄×C₈

D₂₄₄

yes

—

161

C₂×Q₈

—

122

—

162

C₂×Q₈

—

122

—

163

C₂²×C₄

—

164

C₂²×C₄

C₂×D₂₄₄

yes

characteristic

165

C₂²×C₄

#11758222

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

167

Q₁₆

—

244

—

168

M₁₆

—

244

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

244

—

173

C₂×C₈

#11758198

yes

—

174

C₂×C₈

#11758198

yes

—

175

C₄⋊C₄

—

122

—

176

C₄⋊C₄

—

122

—

177

C₄⋊C₄

—

122

—

178

C₄⋊C₄

—

122

—

179

C₄⋊C₄

—

244

—

180

C₄⋊C₄

—

244

—

181

C₂²⋊C₄

—

244

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

244

—

186

C₄²

Dic₂₄₄

yes

complemented

187

C₄²

C₂×C₄×D₆₁

yes

characteristic

188

C₄²

C₂×D₂₄₄

yes

characteristic

189

C₄²

C₂×D₂₄₄

yes

characteristic

190

C₄²

#11758222

yes

characteristic

191

C₂³

#14519751

yes

characteristic

192

Q₈

—

244

—

193

Q₈

—

244

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

244

—

200

C₂×C₄

—

244

—

201

C₂×C₄

C₂×#11758198

yes

characteristic

202

C₂×C₄

C₄×D₂₄₄

yes

characteristic

203

C₂×C₄

C₄×D₂₄₄

yes

characteristic

204

C₂×C₄

#14519751

yes

characteristic

205

C₂×C₄

#14519765

yes

characteristic

206

C₂×C₄

#14519774

yes

characteristic

207

C₂×C₄

C₂×Dic₂₄₄

yes

—

208

C₂×C₄

#14519799

yes

—

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

488

—

213

C₂²

—

214

C₂²

—

215

C₂²

#16839664

yes

characteristic

216

C₂²

#16840003

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

488

—

221

C₄

—

488

—

222

C₄

#16839780

yes

—

223

C₄

C₄×Dic₂₄₄

yes

—

224

C₄

#16839885

yes

—

225

C₄

#16840142

yes

characteristic

226

C₄

#16840146

yes

characteristic

227

C₂

—

228

C₂

#21446651

yes

characteristic

229

C₂

#21446680

yes

characteristic

230

C₂

#21446712

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14519774
commutator	C₄²×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₆₁×#1744	C₂
socle	C₂²×C₆₁	#390
prime radical	C₂³×C₆₁	#121
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	#1744	D₆₁
hypocenter	C₆₁	#9848
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1744

subgroup

G/H

center

C₂×C₄

#14519774

commutator

C₄²×C₆₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₁

Fitting

C₆₁×#1744

C₂

C₂²×C₆₁

C₂³×C₆₁

C₂×C₄²×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1744

N	H ≅ G/N	type
7. #16840167	C₄	semidirect
8. #16840142	C₄	semidirect
9. #16840113	C₄	semidirect
59. C₄²×C₆₁	Q₁₆	semidirect
135. C₆₁	#9848	semidirect
186. C₄²	Dic₂₄₄	semidirect

H ≅ G/N

type

7. #16840167

C₄

semidirect

8. #16840142

C₄

semidirect

9. #16840113

C₄

semidirect

59. C₄²×C₆₁

Q₁₆

semidirect

135. C₆₁

#9848

semidirect

186. 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
C₆₁×#1744	2
#9848	61

subgroup

index

C₆₁×#1744

Subgroups — #29579913

Conjugacy classes of subgroups

Complements

Maximal subgroups