Group #29573243 — subgroups

Subgroups — #29573243

Order 15616.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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	#21454753	C₂	1	1	yes	maximal, characteristic
2	#21445950	C₂	1	1	yes	maximal, characteristic
3	#21444384	C₂	1	2	yes	maximal
4	#21443678	C₂	1	2	yes	maximal
5	C₆₁×#1564	C₂	1	1	yes	maximal, characteristic
6	#16840319	C₂²	1	1	yes	characteristic
7	#16839892	—	2	1	no	—
8	#16839892	C₄	1	2	yes	complemented
9	C₈×Dic₁₂₂	—	2	1	no	—
10	C₈×Dic₁₂₂	C₄	1	2	yes	complemented
11	#16839788	—	2	1	no	—
12	#16839786	C₂²	1	1	yes	characteristic
13	#16839717	—	2	1	no	—
14	#16839628	C₂²	1	2	yes	—
15	#16839525	—	2	1	no	—
16	#16839525	—	2	1	no	—
17	#16839500	—	2	4	no	—
18	C₆₁×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#335	—	2	1	no	—
21	C₆₁×#334	—	2	1	no	—
22	C₂×#11758194	—	2	1	no	—
23	#14519777	Q₈	1	1	yes	characteristic
24	#14519777	Q₈	1	1	yes	characteristic
25	#14519769	—	2	1	no	—
26	#14519756	—	2	1	no	—
27	#14519756	D₄	1	2	yes	—
28	C₄×Dic₁₂₂	—	2	1	no	—
29	C₄×Dic₁₂₂	C₂×C₄	1	2	yes	—
30	#14519736	—	2	1	no	—
31	C₂×C₄⋊Dic₆₁	—	2	2	no	—
32	C₄⋊#92418	—	2	1	no	—
33	C₄⋊#92418	C₂×C₄	1	2	yes	—
34	#14519706	—	2	2	no	—
35	#14519706	—	2	2	no	—
36	#14519687	—	2	2	no	—
37	C₈×Dic₆₁	—	2	2	no	—
38	#14519684	—	2	2	no	—
39	#14519684	—	2	2	no	—
40	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
43	C₄⋊C₈×C₆₁	—	2	2	no	—
44	C₂²⋊C₈×C₆₁	—	2	2	no	—
45	C₄×C₈×C₆₁	—	2	2	no	—
46	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
49	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
53	C₂²×Dic₆₁	—	4	2	no	—
54	C₂×Dic₁₂₂	—	2	1	no	—
55	C₂×Dic₁₂₂	C₄⋊C₄	1	2	yes	—
56	C₂×C₈×C₆₁	—	2	2	no	—
57	C₂×C₈×C₆₁	—	2	2	no	—
58	C₂×C₈×C₆₁	—	4	2	no	—
59	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₆₁	C₂×Q₈	1	1	yes	characteristic
66	C₄²×C₆₁	#41	1	1	yes	characteristic
67	C₂²⋊Dic₆₁	—	2	2	no	—
68	C₄⋊Dic₆₁	—	2	1	no	—
69	C₄⋊Dic₆₁	—	2	1	no	—
70	C₄⋊Dic₆₁	—	2	1	no	—
71	C₄⋊Dic₆₁	—	4	2	no	—
72	C₄⋊Dic₆₁	—	4	2	no	—
73	C₄⋊Dic₆₁	C₄⋊C₄	1	2	yes	—
74	#11758196	—	2	2	no	—
75	#11758196	—	2	2	no	—
76	C₄×Dic₆₁	—	2	2	no	—
77	#11758194	—	4	2	no	—
78	C₂×#92418	—	2	2	no	—
79	C₂³×C₆₁	#121	1	1	yes	characteristic
80	C₂×C₄×C₆₁	—	4	1	no	—
81	C₂×C₄×C₆₁	—	4	1	no	—
82	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
85	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
86	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
88	C₂×C₄×C₆₁	#135	1	2	yes	—
89	C₂×C₄×C₆₁	#137	1	2	yes	—
90	C₂×Dic₆₁	—	2	2	no	—
91	C₂×Dic₆₁	—	2	2	no	—
92	C₂×Dic₆₁	—	8	2	no	—
93	C₂×Dic₆₁	—	8	2	no	—
94	C₂×Dic₆₁	—	8	2	no	—
95	Dic₁₂₂	—	4	2	no	—
96	Dic₁₂₂	—	4	2	no	—
97	C₈×C₆₁	—	2	1	no	—
98	C₈×C₆₁	—	2	1	no	—
99	C₈×C₆₁	—	2	1	no	—
100	C₈×C₆₁	—	2	1	no	—
101	C₈×C₆₁	—	8	2	no	—
102	#92418	—	4	2	no	—
103	#8679	—	61	1	no	maximal, Sylow
104	C₂²×C₆₁	—	2	1	no	—
105	C₂²×C₆₁	—	2	1	no	—
106	C₂²×C₆₁	#380	1	1	yes	characteristic
107	C₂²×C₆₁	#464	1	2	yes	—
108	C₄×C₆₁	—	2	1	no	—
109	C₄×C₆₁	—	2	1	no	—
110	C₄×C₆₁	—	2	1	no	—
111	C₄×C₆₁	—	2	1	no	—
112	C₄×C₆₁	#416	1	1	yes	characteristic
113	C₄×C₆₁	#419	1	1	yes	characteristic
114	C₄×C₆₁	#479	1	2	yes	—
115	Dic₆₁	—	4	2	no	—
116	Dic₆₁	—	4	2	no	—
117	Dic₆₁	—	16	2	no	—
118	#2960	—	61	1	no	—
119	#1835	—	61	1	no	—
120	#1564	D₆₁	1	1	yes	characteristic
121	#1518	—	61	2	no	—
122	#1286	—	61	2	no	—
123	C₂×C₆₁	—	2	2	no	—
124	C₂×C₆₁	#1805	1	1	yes	characteristic
125	C₂×C₆₁	#1812	1	1	yes	characteristic
126	C₂×C₆₁	#1814	1	1	yes	characteristic
127	#533	—	61	1	no	—
128	#446	—	61	2	no	—
129	#446	—	122	1	no	—
130	C₈×Q₈	—	61	2	no	—
131	C₈×Q₈	—	122	1	no	—
132	#431	C₂×D₆₁	1	2	yes	—
133	#424	—	122	1	no	—
134	#423	—	61	1	no	—
135	#405	—	122	1	no	—
136	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
137	#382	—	61	2	no	—
138	#340	—	122	1	no	—
139	#340	—	122	1	no	—
140	#335	—	2	1	no	—
141	#334	—	2	1	no	—
142	#328	—	122	4	no	—
143	C₆₁	#8679	1	1	yes	characteristic, complemented, Sylow
144	C₂×M₁₆	—	122	1	no	—
145	C₂²×C₈	D₂₄₄	1	1	yes	characteristic
146	C₂²×C₈	D₂₄₄	1	1	yes	characteristic
147	C₄⋊Q₈	—	61	1	no	—
148	C₄⋊Q₈	—	61	1	no	—
149	#125	—	122	1	no	—
150	C₂²⋊Q₈	—	61	2	no	—
151	C₂²⋊Q₈	—	122	1	no	—
152	C₄×Q₈	—	61	2	no	—
153	C₄×Q₈	—	122	1	no	—
154	#117	—	122	1	no	—
155	C₂×C₄⋊C₄	—	122	2	no	—
156	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
157	C₄⋊C₈	—	2	2	no	—
158	C₄⋊C₈	—	61	2	no	—
159	C₄⋊C₈	—	122	2	no	—
160	C₄⋊C₈	—	122	2	no	—
161	C₄⋊C₈	—	122	1	no	—
162	C₂²⋊C₈	—	2	2	no	—
163	#97	—	122	2	no	—
164	C₄×C₈	—	2	2	no	—
165	C₄×C₈	—	122	2	no	—
166	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
167	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
169	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
170	#95	—	122	2	no	—
171	#95	—	122	2	no	—
172	C₂×Q₈	—	61	2	no	—
173	C₂×Q₈	—	122	1	no	—
174	C₂²×C₄	—	244	2	no	—
175	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
176	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
177	C₂²×C₄	#11758226	1	1	yes	characteristic
178	M₁₆	—	244	2	no	—
179	C₂×C₈	—	2	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	122	2	no	—
183	C₂×C₈	#11758198	1	1	yes	characteristic
184	C₂×C₈	#11758198	1	1	yes	characteristic
185	C₂×C₈	#11758198	1	1	yes	characteristic
186	C₂×C₈	#11758198	1	1	yes	characteristic
187	C₄⋊C₄	—	61	2	no	—
188	C₄⋊C₄	—	122	2	no	—
189	C₄⋊C₄	—	122	2	no	—
190	C₄⋊C₄	—	122	1	no	—
191	C₄⋊C₄	—	122	1	no	—
192	C₄⋊C₄	—	122	1	no	—
193	C₄⋊C₄	—	244	2	no	—
194	C₄⋊C₄	—	244	2	no	—
195	C₂²⋊C₄	—	122	2	no	—
196	C₄²	—	122	2	no	—
197	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
198	C₄²	#11758224	1	1	yes	characteristic
199	C₄²	Q₈×D₆₁	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
201	C₂³	#14519752	1	1	yes	characteristic
202	Q₈	—	244	2	no	—
203	Q₈	—	244	2	no	—
204	C₂×C₄	—	4	1	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	122	2	no	—
207	C₂×C₄	—	122	2	no	—
208	C₂×C₄	—	488	2	no	—
209	C₂×C₄	—	488	2	no	—
210	C₂×C₄	—	488	2	no	—
211	C₂×C₄	C₂×#11758198	1	1	yes	characteristic
212	C₂×C₄	C₄⋊C₄×D₆₁	1	1	yes	characteristic
213	C₂×C₄	#14519735	1	1	yes	characteristic
214	C₂×C₄	#14519748	1	1	yes	characteristic
215	C₂×C₄	#14519753	1	1	yes	characteristic
216	C₂×C₄	#14519757	1	1	yes	characteristic
217	C₂×C₄	#14519799	1	2	yes	—
218	C₂×C₄	#14519810	1	2	yes	—
219	C₈	—	2	1	no	—
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	8	2	no	—
224	C₈	—	244	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#16839619	1	1	yes	characteristic
228	C₂²	#16839985	1	2	yes	—
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	976	2	no	—
234	C₄	—	244	2	no	—
235	C₄	—	244	2	no	—
236	C₄	#16839759	1	1	yes	characteristic
237	C₄	#16839772	1	1	yes	characteristic
238	C₄	#16840070	1	2	yes	—
239	C₂	—	2	2	no	—
240	C₂	#21445835	1	1	yes	characteristic
241	C₂	#21445862	1	1	yes	characteristic
242	C₂	#21445874	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21454753

C₂

yes

maximal, characteristic

#21445950

C₂

yes

maximal, characteristic

#21444384

C₂

yes

maximal

#21443678

C₂

yes

maximal

C₆₁×#1564

C₂

yes

maximal, characteristic

#16840319

C₂²

yes

characteristic

#16839892

—

#16839892

C₄

yes

complemented

C₈×Dic₁₂₂

—

C₈×Dic₁₂₂

C₄

yes

complemented

#16839788

—

#16839786

C₂²

yes

characteristic

#16839717

—

#16839628

C₂²

yes

—

#16839525

—

#16839525

—

#16839500

—

C₆₁×#431

C₂²

yes

—

C₂×C₄×C₈×C₆₁

C₂²

yes

characteristic

C₆₁×#335

—

C₆₁×#334

—

C₂×#11758194

—

#14519777

Q₈

yes

characteristic

#14519777

Q₈

yes

—

—

D₄

yes

—

C₄×Dic₁₂₂

—

C₄×Dic₁₂₂

C₂×C₄

yes

—

#14519736

—

C₂×C₄⋊Dic₆₁

—

C₄⋊#92418

—

C₄⋊#92418

C₂×C₄

yes

—

#14519706

—

#14519706

—

#14519687

—

C₈×Dic₆₁

—

#14519684

—

#14519684

—

C₂²×C₈×C₆₁

D₄

yes

characteristic

C₂²×C₈×C₆₁

D₄

yes

characteristic

C₂×C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊C₈×C₆₁

—

C₂²⋊C₈×C₆₁

—

C₄×C₈×C₆₁

—

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

C₂×C₄

yes

characteristic

C₄×C₈×C₆₁

D₄

yes

characteristic

C₄×C₈×C₆₁

D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

#41

yes

characteristic

C₂²×Dic₆₁

—

C₂×Dic₁₂₂

—

C₂×Dic₁₂₂

C₄⋊C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₆₁

C₂²⋊C₄

yes

characteristic

C₄²×C₆₁

C₂²×C₄

yes

characteristic

C₄²×C₆₁

C₂×D₄

yes

characteristic

C₄²×C₆₁

C₂×Q₈

yes

characteristic

C₄²×C₆₁

#41

yes

characteristic

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₄⋊C₄

yes

—

#11758196

—

#11758196

—

C₄×Dic₆₁

—

#11758194

—

C₂×#92418

—

C₂³×C₆₁

#121

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂×C₄⋊C₄

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₆₁

#135

yes

—

C₂×C₄×C₆₁

#137

yes

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

100

C₈×C₆₁

—

101

C₈×C₆₁

—

102

#92418

—

103

#8679

—

maximal, Sylow

104

C₂²×C₆₁

—

105

C₂²×C₆₁

—

106

C₂²×C₆₁

#380

yes

characteristic

107

C₂²×C₆₁

#464

yes

—

108

C₄×C₆₁

—

109

C₄×C₆₁

—

110

C₄×C₆₁

—

111

C₄×C₆₁

—

112

C₄×C₆₁

#416

yes

characteristic

113

C₄×C₆₁

#419

yes

characteristic

114

C₄×C₆₁

#479

yes

—

115

Dic₆₁

—

116

Dic₆₁

—

117

Dic₆₁

—

118

#2960

—

119

#1835

—

120

#1564

D₆₁

yes

characteristic

121

#1518

—

122

#1286

—

123

C₂×C₆₁

—

124

C₂×C₆₁

#1805

yes

characteristic

125

C₂×C₆₁

#1812

yes

characteristic

126

C₂×C₆₁

#1814

yes

characteristic

127

#533

—

128

#446

—

129

#446

—

122

—

130

C₈×Q₈

—

131

C₈×Q₈

—

122

—

132

#431

C₂×D₆₁

yes

—

133

#424

—

122

—

134

#423

—

135

#405

—

122

—

136

C₂×C₄×C₈

C₂×D₆₁

yes

characteristic

137

#382

—

138

#340

—

122

—

139

#340

—

122

—

140

#335

—

141

#334

—

142

#328

—

122

—

143

C₆₁

#8679

yes

characteristic, complemented, Sylow

144

C₂×M₁₆

—

122

—

145

C₂²×C₈

D₂₄₄

yes

characteristic

146

C₂²×C₈

D₂₄₄

yes

characteristic

147

C₄⋊Q₈

—

148

C₄⋊Q₈

—

149

#125

—

122

—

150

C₂²⋊Q₈

—

151

C₂²⋊Q₈

—

122

—

152

C₄×Q₈

—

153

C₄×Q₈

—

122

—

154

#117

—

122

—

155

C₂×C₄⋊C₄

—

122

—

156

C₂×C₄²

C₂²×D₆₁

yes

characteristic

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

122

—

160

C₄⋊C₈

—

122

—

161

C₄⋊C₈

—

122

—

162

C₂²⋊C₈

—

163

#97

—

122

—

164

C₄×C₈

—

165

C₄×C₈

—

122

—

166

C₄×C₈

C₄×D₆₁

yes

characteristic

167

C₄×C₈

C₄×D₆₁

yes

characteristic

168

C₄×C₈

C₂²⋊D₆₁

yes

characteristic

169

C₄×C₈

C₂²⋊D₆₁

yes

characteristic

170

#95

—

122

—

171

#95

—

122

—

172

C₂×Q₈

—

173

C₂×Q₈

—

122

—

174

C₂²×C₄

—

244

—

175

C₂²×C₄

C₂×D₂₄₄

yes

characteristic

176

C₂²×C₄

D₄×D₆₁

yes

characteristic

177

C₂²×C₄

#11758226

yes

characteristic

178

M₁₆

—

244

—

179

C₂×C₈

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

122

—

183

C₂×C₈

#11758198

yes

characteristic

184

C₂×C₈

#11758198

yes

characteristic

185

C₂×C₈

#11758198

yes

characteristic

186

C₂×C₈

#11758198

yes

characteristic

187

C₄⋊C₄

—

188

C₄⋊C₄

—

122

—

189

C₄⋊C₄

—

122

—

190

C₄⋊C₄

—

122

—

191

C₄⋊C₄

—

122

—

192

C₄⋊C₄

—

122

—

193

C₄⋊C₄

—

244

—

194

C₄⋊C₄

—

244

—

195

C₂²⋊C₄

—

122

—

196

C₄²

—

122

—

197

C₄²

C₂×C₄×D₆₁

yes

characteristic

198

C₄²

#11758224

yes

characteristic

199

C₄²

Q₈×D₆₁

yes

characteristic

200

C₄²

C₂×C₂²⋊D₆₁

yes

characteristic

201

C₂³

#14519752

yes

characteristic

202

Q₈

—

244

—

203

Q₈

—

244

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

122

—

207

C₂×C₄

—

122

—

208

C₂×C₄

—

488

—

209

C₂×C₄

—

488

—

210

C₂×C₄

—

488

—

211

C₂×C₄

C₂×#11758198

yes

characteristic

212

C₂×C₄

C₄⋊C₄×D₆₁

yes

characteristic

213

C₂×C₄

#14519735

yes

characteristic

214

C₂×C₄

#14519748

yes

characteristic

215

C₂×C₄

#14519753

yes

characteristic

216

C₂×C₄

#14519757

yes

characteristic

217

C₂×C₄

#14519799

yes

—

218

C₂×C₄

#14519810

yes

—

219

C₈

—

220

C₈

—

221

C₈

—

222

C₈

—

223

C₈

—

224

C₈

—

244

—

225

C₂²

—

226

C₂²

—

227

C₂²

#16839619

yes

characteristic

228

C₂²

#16839985

yes

—

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

976

—

234

C₄

—

244

—

235

C₄

—

244

—

236

C₄

#16839759

yes

characteristic

237

C₄

#16839772

yes

characteristic

238

C₄

#16840070

yes

—

239

C₂

—

240

C₂

#21445835

yes

characteristic

241

C₂

#21445862

yes

characteristic

242

C₂

#21445874

yes

characteristic

	subgroup	G/H
center	C₂²	#16839619
commutator	C₄²×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₆₁×#1564	C₂
socle	C₂²×C₆₁	#380
prime radical	C₂³×C₆₁	#121
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	#1564	D₆₁
hypocenter	C₆₁	#8679
LCS	G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

subgroup

G/H

center

C₂²

#16839619

commutator

C₄²×C₆₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₁

Fitting

C₆₁×#1564

C₂

C₂²×C₆₁

C₂³×C₆₁

C₂×C₄²×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₄²×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

N	H ≅ G/N	type
8. #16839892	C₄	semidirect
10. C₈×Dic₁₂₂	C₄	semidirect
143. C₆₁	#8679	semidirect

H ≅ G/N

type

8. #16839892

C₄

semidirect

10. C₈×Dic₁₂₂

C₄

semidirect

143. C₆₁

#8679

semidirect

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

subgroup	index
#21454753	2
#21445950	2
#21444384	2
#21443678	2
C₆₁×#1564	2
#8679	61

subgroup

index

C₆₁×#1564

Subgroups — #29573243

Conjugacy classes of subgroups

Complements

Maximal subgroups