Group #29577394 — subgroups

Subgroups — #29577394

Order 15616.

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

normal subgroups only

This group has 470 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	#21454900	C₂	1	1	yes	maximal, characteristic
2	#21445815	C₂	1	1	yes	maximal, characteristic
3	#21444504	C₂	1	2	yes	maximal
4	#21443722	C₂	1	2	yes	maximal
5	C₆₁×#2568	C₂	1	1	yes	maximal, characteristic
6	Q₈×#92418	—	2	4	no	—
7	#16839815	—	2	2	no	—
8	#16839815	C₂²	1	2	yes	—
9	#16839786	C₂²	1	2	yes	—
10	C₂×#14519696	—	2	1	no	—
11	#16839531	—	2	1	no	—
12	#16839508	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#400	C₄	1	4	yes	—
16	C₆₁×#391	—	2	1	no	—
17	C₆₁×#391	—	2	2	no	—
18	C₆₁×#382	—	2	1	no	—
19	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#11758194	—	2	2	no	—
21	C₄⋊#92418	—	2	4	no	—
22	C₄⋊#92418	—	2	2	no	—
23	C₄⋊#92418	—	2	2	no	—
24	C₄⋊#92418	D₄	1	4	yes	—
25	#14519696	—	4	2	no	—
26	C₂²⋊#92418	—	2	2	no	—
27	C₄×#92418	—	2	4	no	—
28	C₄×#92418	—	2	2	no	—
29	C₂²×Q₈×C₆₁	—	2	1	no	—
30	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
31	C₄⋊Q₈×C₆₁	—	2	2	no	—
32	C₄⋊Q₈×C₆₁	—	2	2	no	—
33	C₄×Q₈×C₆₁	—	2	2	no	—
34	C₄×Q₈×C₆₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
37	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
38	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₆₁	—	2	1	no	—
41	C₂×C₄²×C₆₁	D₄	1	2	yes	—
42	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
43	#95×C₆₁	—	2	4	no	—
44	#95×C₆₁	—	2	4	no	—
45	#95×C₆₁	C₂×C₄	1	2	yes	—
46	C₂×Q₈×C₆₁	—	2	2	no	—
47	C₂×Q₈×C₆₁	—	2	2	no	—
48	C₂×Q₈×C₆₁	—	4	4	no	—
49	C₂×Q₈×C₆₁	—	4	1	no	—
50	C₂×Q₈×C₆₁	—	4	1	no	—
51	C₂×Q₈×C₆₁	SD₁₆	1	2	yes	—
52	C₂×Q₈×C₆₁	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₆₁	—	2	2	no	—
54	C₂²×C₄×C₆₁	—	2	2	no	—
55	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
60	C₄⋊C₄×C₆₁	—	2	4	no	—
61	C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₄⋊C₄×C₆₁	—	2	4	no	—
63	C₄⋊C₄×C₆₁	—	4	2	no	—
64	C₄⋊C₄×C₆₁	—	4	2	no	—
65	C₄²×C₆₁	—	2	2	no	—
66	C₄²×C₆₁	—	2	2	no	—
67	C₄²×C₆₁	—	4	2	no	—
68	C₄²×C₆₁	C₂×D₄	1	2	yes	—
69	C₄²×C₆₁	#41	1	2	yes	—
70	#11758194	—	4	2	no	—
71	#11758194	—	4	2	no	—
72	C₂×#92418	—	2	4	no	—
73	C₂×#92418	—	4	2	no	—
74	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	Q₈×C₆₁	—	2	4	no	—
76	Q₈×C₆₁	—	2	4	no	—
77	Q₈×C₆₁	—	8	2	no	—
78	Q₈×C₆₁	—	8	2	no	—
79	C₂×C₄×C₆₁	—	2	2	no	—
80	C₂×C₄×C₆₁	—	2	2	no	—
81	C₂×C₄×C₆₁	—	2	2	no	—
82	C₂×C₄×C₆₁	—	2	2	no	—
83	C₂×C₄×C₆₁	—	4	1	no	—
84	C₂×C₄×C₆₁	—	4	2	no	—
85	C₂×C₄×C₆₁	—	4	2	no	—
86	C₂×C₄×C₆₁	—	4	2	no	—
87	C₂×C₄×C₆₁	—	4	4	no	—
88	C₂×C₄×C₆₁	—	4	2	no	—
89	C₂×C₄×C₆₁	—	4	2	no	—
90	C₂×C₄×C₆₁	#103	1	4	yes	—
91	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
92	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
93	C₂×C₄×C₆₁	#121	1	2	yes	—
94	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
95	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
97	C₂×C₄×C₆₁	#135	1	2	yes	—
98	#92418	—	4	4	no	—
99	#92418	—	8	2	no	—
100	#9396	—	61	1	no	maximal, Sylow
101	C₂²×C₆₁	—	2	1	no	—
102	C₂²×C₆₁	—	2	1	no	—
103	C₂²×C₆₁	#386	1	1	yes	characteristic
104	C₂²×C₆₁	C₂×#103	1	1	yes	characteristic
105	C₂²×C₆₁	#416	1	1	yes	characteristic
106	C₄×C₆₁	—	2	1	no	—
107	C₄×C₆₁	—	2	4	no	—
108	C₄×C₆₁	—	2	2	no	—
109	C₄×C₆₁	—	4	2	no	—
110	C₄×C₆₁	—	8	2	no	—
111	C₄×C₆₁	—	8	2	no	—
112	C₄×C₆₁	#454	1	2	yes	—
113	C₄×C₆₁	#465	1	2	yes	—
114	C₄×C₆₁	#467	1	2	yes	—
115	#2982	—	61	1	no	—
116	#2568	D₆₁	1	1	yes	characteristic
117	#1801	—	61	1	no	—
118	#1549	—	61	2	no	—
119	#1303	—	61	2	no	—
120	C₂×C₆₁	—	2	1	no	—
121	C₂×C₆₁	—	2	1	no	—
122	C₂×C₆₁	#1888	1	1	yes	characteristic
123	C₂×C₆₁	#1892	1	1	yes	characteristic
124	C₂×C₆₁	#1915	1	1	yes	characteristic
125	C₂×C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
126	C₂×C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
127	C₈×Q₈	—	122	4	no	—
128	#431	—	61	2	no	—
129	#431	—	122	2	no	—
130	#423	—	61	2	no	—
131	C₂×#101	—	122	1	no	—
132	#400	Dic₆₁	1	4	yes	—
133	#391	—	2	1	no	—
134	#391	—	2	2	no	—
135	#382	—	2	1	no	—
136	C₄×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
137	#343	—	122	1	no	—
138	#332	—	122	4	no	—
139	C₆₁	#9396	1	1	yes	characteristic, complemented, Sylow
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×Q₈	C₂²⋊D₆₁	1	1	yes	characteristic
142	C₂×M₁₆	—	122	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	C₂×Dic₆₁	1	2	yes	—
150	C₂×C₄⋊C₄	C₂×Dic₆₁	1	2	yes	—
151	C₂×C₄⋊C₄	C₂²⋊D₆₁	1	1	yes	characteristic
152	C₂×C₄²	—	2	1	no	—
153	C₂×C₄²	C₂²⋊D₆₁	1	2	yes	—
154	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
155	C₄⋊C₈	—	61	4	no	—
156	C₄⋊C₈	—	122	4	no	—
157	C₄⋊C₈	—	122	2	no	—
158	C₄⋊C₈	—	122	2	no	—
159	#101	—	244	2	no	—
160	C₂²⋊C₈	—	122	2	no	—
161	C₄×C₈	—	122	4	no	—
162	C₄×C₈	—	122	2	no	—
163	#95	—	2	4	no	—
164	#95	—	2	4	no	—
165	#95	C₂×Dic₆₁	1	2	yes	—
166	C₂×Q₈	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	4	4	no	—
169	C₂×Q₈	—	4	1	no	—
170	C₂×Q₈	—	4	1	no	—
171	C₂×Q₈	#11758201	1	2	yes	—
172	C₂×Q₈	#11758202	1	2	yes	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	—	2	2	no	—
175	C₂²×C₄	C₂²⋊Dic₆₁	1	2	yes	—
176	C₂²×C₄	C₂²⋊Dic₆₁	1	2	yes	—
177	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
178	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
179	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
180	M₁₆	—	244	2	no	—
181	M₁₆	—	244	2	no	—
182	C₂×C₈	—	122	4	no	—
183	C₂×C₈	—	244	2	no	—
184	C₄⋊C₄	—	2	4	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	2	4	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₄⋊C₄	—	4	2	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	2	2	no	—
191	C₄²	—	4	2	no	—
192	C₄²	D₄×D₆₁	1	2	yes	—
193	C₄²	#11758224	1	2	yes	—
194	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
195	Q₈	—	2	4	no	—
196	Q₈	—	2	4	no	—
197	Q₈	—	8	2	no	—
198	Q₈	—	8	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	2	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	2	no	—
210	C₂×C₄	#14519701	1	4	yes	—
211	C₂×C₄	D₄×Dic₆₁	1	2	yes	—
212	C₂×C₄	#14519745	1	1	yes	characteristic
213	C₂×C₄	#14519749	1	2	yes	—
214	C₂×C₄	#14519758	1	1	yes	characteristic
215	C₂×C₄	C₂×#11758201	1	1	yes	characteristic
216	C₂×C₄	C₂×#11758202	1	1	yes	characteristic
217	C₂×C₄	#14519797	1	2	yes	—
218	C₈	—	488	2	no	—
219	C₈	—	244	4	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	#16839642	1	1	yes	characteristic
223	C₂²	C₂×#14519701	1	1	yes	characteristic
224	C₂²	#16839758	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	4	no	—
227	C₄	—	2	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	8	2	no	—
230	C₄	—	8	2	no	—
231	C₄	#16839934	1	2	yes	—
232	C₄	#16839993	1	2	yes	—
233	C₄	#16840001	1	2	yes	—
234	C₂	—	2	1	no	—
235	C₂	—	2	1	no	—
236	C₂	#21446223	1	1	yes	characteristic
237	C₂	#21446243	1	1	yes	characteristic
238	C₂	#21446372	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#21454900

C₂

yes

maximal, characteristic

#21445815

C₂

yes

maximal, characteristic

#21444504

C₂

yes

maximal

#21443722

C₂

yes

maximal

C₆₁×#2568

C₂

yes

maximal, characteristic

Q₈×#92418

—

#16839815

—

#16839815

C₂²

yes

—

#16839786

C₂²

yes

—

C₂×#14519696

—

#16839531

—

#16839508

—

C₂×C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

C₂×C₄×Q₈×C₆₁

C₂²

yes

characteristic

C₆₁×#400

C₄

yes

—

C₆₁×#391

—

C₆₁×#391

—

C₆₁×#382

—

C₄×C₄⋊C₄×C₆₁

C₂²

yes

—

—

—

—

D₄

yes

—

—

—

—

—

C₂²×Q₈×C₆₁

—

C₂²×Q₈×C₆₁

D₄

yes

characteristic

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₄×Q₈×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₆₁

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

D₄

yes

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

#95×C₆₁

—

#95×C₆₁

—

#95×C₆₁

C₂×C₄

yes

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

SD₁₆

yes

—

C₂×Q₈×C₆₁

Q₁₆

yes

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₁

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

C₂×D₄

yes

—

C₄²×C₆₁

#41

yes

—

—

—

—

—

C₂³×C₆₁

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

#103

yes

—

C₂×C₄×C₆₁

C₄×D₄

yes

—

C₂×C₄×C₆₁

#120

yes

characteristic

C₂×C₄×C₆₁

#121

yes

—

C₂×C₄×C₆₁

#123

yes

characteristic

C₂×C₄×C₆₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₆₁

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₆₁

#135

yes

—

#92418

—

#92418

—

100

#9396

—

maximal, Sylow

101

C₂²×C₆₁

—

102

C₂²×C₆₁

—

103

C₂²×C₆₁

#386

yes

characteristic

104

C₂²×C₆₁

C₂×#103

yes

characteristic

105

C₂²×C₆₁

#416

yes

characteristic

106

C₄×C₆₁

—

107

C₄×C₆₁

—

108

C₄×C₆₁

—

109

C₄×C₆₁

—

110

C₄×C₆₁

—

111

C₄×C₆₁

—

112

C₄×C₆₁

#454

yes

—

113

C₄×C₆₁

#465

yes

—

114

C₄×C₆₁

#467

yes

—

115

#2982

—

116

#2568

D₆₁

yes

characteristic

117

#1801

—

118

#1549

—

119

#1303

—

120

C₂×C₆₁

—

121

C₂×C₆₁

—

122

C₂×C₆₁

#1888

yes

characteristic

123

C₂×C₆₁

#1892

yes

characteristic

124

C₂×C₆₁

#1915

yes

characteristic

125

C₂×C₄⋊Q₈

C₂×D₆₁

yes

characteristic

126

C₂×C₄×Q₈

C₂×D₆₁

yes

characteristic

127

C₈×Q₈

—

122

—

128

#431

—

129

#431

—

122

—

130

#423

—

131

C₂×#101

—

122

—

132

#400

Dic₆₁

yes

—

133

#391

—

134

#391

—

135

#382

—

136

C₄×C₄⋊C₄

C₂×D₆₁

yes

characteristic

137

#343

—

122

—

138

#332

—

122

—

139

C₆₁

#9396

yes

characteristic, complemented, Sylow

140

C₂²×Q₈

—

141

C₂²×Q₈

C₂²⋊D₆₁

yes

characteristic

142

C₂×M₁₆

—

122

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

C₂×Dic₆₁

yes

—

150

C₂×C₄⋊C₄

C₂×Dic₆₁

yes

—

151

C₂×C₄⋊C₄

C₂²⋊D₆₁

yes

characteristic

152

C₂×C₄²

—

153

C₂×C₄²

C₂²⋊D₆₁

yes

—

154

C₂×C₄²

C₂²×D₆₁

yes

characteristic

155

C₄⋊C₈

—

156

C₄⋊C₈

—

122

—

157

C₄⋊C₈

—

122

—

158

C₄⋊C₈

—

122

—

159

#101

—

244

—

160

C₂²⋊C₈

—

122

—

161

C₄×C₈

—

122

—

162

C₄×C₈

—

122

—

163

#95

—

164

#95

—

165

#95

C₂×Dic₆₁

yes

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

#11758201

yes

—

172

C₂×Q₈

#11758202

yes

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²⋊Dic₆₁

yes

—

176

C₂²×C₄

C₂²⋊Dic₆₁

yes

—

177

C₂²×C₄

C₂²×Dic₆₁

yes

characteristic

178

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

179

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

180

M₁₆

—

244

—

181

M₁₆

—

244

—

182

C₂×C₈

—

122

—

183

C₂×C₈

—

244

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

D₄×D₆₁

yes

—

193

C₄²

#11758224

yes

—

194

C₂³

C₂×C₂²⋊Dic₆₁

yes

characteristic

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

#14519701

yes

—

211

C₂×C₄

D₄×Dic₆₁

yes

—

212

C₂×C₄

#14519745

yes

characteristic

213

C₂×C₄

#14519749

yes

—

214

C₂×C₄

#14519758

yes

characteristic

215

C₂×C₄

C₂×#11758201

yes

characteristic

216

C₂×C₄

C₂×#11758202

yes

characteristic

217

C₂×C₄

#14519797

yes

—

218

C₈

—

488

—

219

C₈

—

244

—

220

C₂²

—

221

C₂²

—

222

C₂²

#16839642

yes

characteristic

223

C₂²

C₂×#14519701

yes

characteristic

224

C₂²

#16839758

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

—

230

C₄

—

231

C₄

#16839934

yes

—

232

C₄

#16839993

yes

—

233

C₄

#16840001

yes

—

234

C₂

—

235

C₂

—

236

C₂

#21446223

yes

characteristic

237

C₂

#21446243

yes

characteristic

238

C₂

#21446372

yes

characteristic

	subgroup	G/H
center	C₂²	#16839642
commutator	C₂²×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₁
Fitting	C₆₁×#2568	C₂
socle	C₂²×C₆₁	#386
prime radical	C₂³×C₆₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₆₁	C₂³
hypercenter	#2568	D₆₁
hypocenter	C₆₁	#9396
LCS	G ▷ C₂²×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2568

subgroup

G/H

center

C₂²

#16839642

commutator

C₂²×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₁

Fitting

C₆₁×#2568

C₂

socle

C₂²×C₆₁

#386

prime radical

C₂³×C₆₁

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₂²×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2568

N	H ≅ G/N	type
139. C₆₁	#9396	semidirect

H ≅ G/N

type

139. C₆₁

#9396

semidirect

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

subgroup	index
#21454900	2
#21445815	2
#21444504	2
#21443722	2
C₆₁×#2568	2
#9396	61

subgroup

index

C₆₁×#2568

Subgroups — #29577394

Conjugacy classes of subgroups

Complements

Maximal subgroups