Group #29513720 — subgroups

Subgroups — C₆₁×#10287 #29513720

Order 15616.

566 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 130 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	C₆₁×#3206	C₂	1	2	yes	maximal
2	C₆₁×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#1962	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1548	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1276	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#532	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
8	C₆₁×#492	—	2	2	no	—
9	C₆₁×#487	—	2	2	no	—
10	C₆₁×#461	—	2	4	no	—
11	C₆₁×#448	—	2	4	no	—
12	C₆₁×#431	C₂²	1	2	yes	—
13	C₆₁×#423	C₂²	1	1	yes	characteristic
14	C₂×#104×C₆₁	—	2	2	no	—
15	C₆₁×#391	—	2	4	no	—
16	C₆₁×#382	—	2	2	no	—
17	C₄³×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#333	—	2	4	no	—
19	C₂×#41×C₆₁	—	2	1	no	—
20	C₂²×Q₈×C₆₁	D₄	1	4	yes	—
21	C₂×SD₁₆×C₆₁	—	2	8	no	—
22	C₂×M₁₆×C₆₁	—	2	1	no	—
23	C₄⋊Q₈×C₆₁	—	2	2	no	—
24	C₄⋊Q₈×C₆₁	—	2	2	no	—
25	C₄⋊Q₈×C₆₁	—	2	2	no	—
26	C₄⋊Q₈×C₆₁	—	2	2	no	—
27	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
28	#127×C₆₁	D₄	1	1	yes	characteristic
29	#124×C₆₁	—	2	1	no	—
30	#121×C₆₁	—	2	2	no	—
31	C₄×D₄×C₆₁	—	2	2	no	—
32	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
34	C₂×C₄²×C₆₁	—	2	2	no	—
35	C₂×C₄²×C₆₁	D₄	1	2	yes	—
36	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₆₁	—	2	2	no	—
38	C₄⋊C₈×C₆₁	D₄	1	4	yes	—
39	#104×C₆₁	—	4	4	no	—
40	#103×C₆₁	—	2	8	no	—
41	C₂²⋊C₈×C₆₁	—	2	2	no	—
42	C₄×C₈×C₆₁	—	2	2	no	—
43	#95×C₆₁	—	2	8	no	—
44	#41×C₆₁	—	4	2	no	—
45	#41×C₆₁	—	4	2	no	—
46	C₂×Q₈×C₆₁	—	2	4	no	—
47	C₂×Q₈×C₆₁	—	2	1	no	—
48	C₂×Q₈×C₆₁	—	2	4	no	—
49	C₂×Q₈×C₆₁	—	4	8	no	—
50	C₂×D₄×C₆₁	—	2	2	no	—
51	C₂×D₄×C₆₁	—	2	1	no	—
52	C₂×D₄×C₆₁	—	4	1	no	—
53	C₂²×C₄×C₆₁	—	2	2	no	—
54	C₂²×C₄×C₆₁	—	2	4	no	—
55	C₂²×C₄×C₆₁	—	4	1	no	—
56	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
57	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
58	SD₁₆×C₆₁	—	8	8	no	—
59	M₁₆×C₆₁	—	4	2	no	—
60	C₂×C₈×C₆₁	—	2	4	no	—
61	C₂×C₈×C₆₁	—	4	1	no	—
62	C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₄⋊C₄×C₆₁	—	4	2	no	—
64	C₄⋊C₄×C₆₁	—	4	2	no	—
65	C₄⋊C₄×C₆₁	—	4	2	no	—
66	C₄⋊C₄×C₆₁	—	4	2	no	—
67	C₂²⋊C₄×C₆₁	—	4	2	no	—
68	C₄²×C₆₁	—	2	2	no	—
69	C₄²×C₆₁	—	4	4	no	—
70	C₄²×C₆₁	SD₁₆	1	4	yes	complemented
71	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₆₁	C₂×D₄	1	2	yes	—
73	C₄²×C₆₁	#41	1	1	yes	characteristic
74	C₂³×C₆₁	—	4	1	no	—
75	C₂³×C₆₁	#120	1	1	yes	characteristic
76	Q₈×C₆₁	—	4	8	no	—
77	Q₈×C₆₁	—	4	2	no	—
78	Q₈×C₆₁	—	8	4	no	—
79	D₄×C₆₁	—	4	4	no	—
80	D₄×C₆₁	—	4	2	no	—
81	D₄×C₆₁	—	8	2	no	—
82	C₂×C₄×C₆₁	—	2	4	no	—
83	C₂×C₄×C₆₁	—	2	4	no	—
84	C₂×C₄×C₆₁	—	4	4	no	—
85	C₂×C₄×C₆₁	—	4	8	no	—
86	C₂×C₄×C₆₁	—	4	1	no	—
87	C₂×C₄×C₆₁	—	4	4	no	—
88	C₂×C₄×C₆₁	—	8	1	no	—
89	C₂×C₄×C₆₁	—	8	1	no	—
90	C₂×C₄×C₆₁	#120	1	2	yes	—
91	C₂×C₄×C₆₁	#121	1	2	yes	—
92	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
93	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
94	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
95	C₂×C₄×C₆₁	#137	1	2	yes	—
96	C₈×C₆₁	—	4	4	no	—
97	C₈×C₆₁	—	8	1	no	—
98	#10287	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂²×C₆₁	—	2	2	no	—
100	C₂²×C₆₁	—	8	2	no	—
101	C₂²×C₆₁	—	8	1	no	—
102	C₂²×C₆₁	#392	1	1	yes	characteristic
103	C₂²×C₆₁	#448	1	2	yes	—
104	C₄×C₆₁	—	2	2	no	—
105	C₄×C₆₁	—	4	4	no	—
106	C₄×C₆₁	—	8	4	no	—
107	C₄×C₆₁	—	8	1	no	—
108	C₄×C₆₁	#455	1	4	yes	—
109	C₄×C₆₁	#461	1	2	yes	—
110	C₄×C₆₁	#492	1	1	yes	characteristic
111	C₄×C₆₁	#497	1	1	yes	characteristic
112	#3206	C₂×C₆₁	1	2	yes	—
113	#2862	C₂×C₆₁	1	1	yes	characteristic, complemented
114	#1962	C₂×C₆₁	1	1	yes	characteristic
115	#1548	C₂×C₆₁	1	2	yes	complemented
116	#1276	C₂×C₆₁	1	1	yes	characteristic, complemented
117	C₂×C₆₁	—	2	2	no	—
118	C₂×C₆₁	—	16	1	no	—
119	C₂×C₆₁	#2004	1	2	yes	—
120	C₂×C₆₁	#2013	1	1	yes	characteristic
121	#532	C₂²×C₆₁	1	1	yes	characteristic
122	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
123	#492	—	2	2	no	—
124	#487	—	2	2	no	—
125	#461	—	2	4	no	—
126	#448	—	2	4	no	—
127	#431	C₂²×C₆₁	1	2	yes	—
128	#423	C₂²×C₆₁	1	1	yes	characteristic
129	C₂×#104	—	2	2	no	—
130	#391	—	2	4	no	—
131	#382	—	2	2	no	—
132	C₄³	C₂²×C₆₁	1	1	yes	characteristic
133	#333	—	2	4	no	—
134	C₆₁	#10287	1	1	yes	characteristic, direct product factor, Sylow
135	C₂×#41	—	2	1	no	—
136	C₂²×Q₈	D₄×C₆₁	1	4	yes	—
137	C₂×SD₁₆	—	2	8	no	—
138	C₂×M₁₆	—	2	1	no	—
139	C₄⋊Q₈	—	2	2	no	—
140	C₄⋊Q₈	—	2	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
144	#127	D₄×C₆₁	1	1	yes	characteristic
145	#124	—	2	1	no	—
146	#121	—	2	2	no	—
147	C₄×D₄	—	2	2	no	—
148	C₂×C₄⋊C₄	—	2	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄²	—	2	2	no	—
151	C₂×C₄²	D₄×C₆₁	1	2	yes	—
152	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	D₄×C₆₁	1	4	yes	—
155	#104	—	4	4	no	—
156	#103	—	2	8	no	—
157	C₂²⋊C₈	—	2	2	no	—
158	C₄×C₈	—	2	2	no	—
159	#95	—	2	8	no	—
160	#41	—	4	2	no	—
161	#41	—	4	2	no	—
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	2	1	no	—
164	C₂×Q₈	—	2	4	no	—
165	C₂×Q₈	—	4	8	no	—
166	C₂×D₄	—	2	2	no	—
167	C₂×D₄	—	2	1	no	—
168	C₂×D₄	—	4	1	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	2	4	no	—
171	C₂²×C₄	—	4	1	no	—
172	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
173	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
174	SD₁₆	—	8	8	no	—
175	M₁₆	—	4	2	no	—
176	C₂×C₈	—	2	4	no	—
177	C₂×C₈	—	4	1	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄⋊C₄	—	4	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	—	4	4	no	—
186	C₄²	SD₁₆×C₆₁	1	4	yes	complemented
187	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
188	C₄²	C₂×D₄×C₆₁	1	2	yes	—
189	C₄²	#41×C₆₁	1	1	yes	characteristic
190	C₂³	—	4	1	no	—
191	C₂³	#120×C₆₁	1	1	yes	characteristic
192	Q₈	—	4	8	no	—
193	Q₈	—	4	2	no	—
194	Q₈	—	8	4	no	—
195	D₄	—	4	4	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	2	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	4	4	no	—
201	C₂×C₄	—	4	8	no	—
202	C₂×C₄	—	4	1	no	—
203	C₂×C₄	—	4	4	no	—
204	C₂×C₄	—	8	1	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	#120×C₆₁	1	2	yes	—
207	C₂×C₄	#121×C₆₁	1	2	yes	—
208	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
209	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
210	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
211	C₂×C₄	#137×C₆₁	1	2	yes	—
212	C₈	—	4	4	no	—
213	C₈	—	8	1	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	8	1	no	—
216	C₂²	—	8	2	no	—
217	C₂²	C₆₁×#392	1	1	yes	characteristic
218	C₂²	C₆₁×#448	1	2	yes	—
219	C₄	—	2	2	no	—
220	C₄	—	4	4	no	—
221	C₄	—	8	1	no	—
222	C₄	—	8	4	no	—
223	C₄	C₆₁×#455	1	4	yes	—
224	C₄	C₆₁×#461	1	2	yes	—
225	C₄	C₆₁×#492	1	1	yes	characteristic
226	C₄	C₆₁×#497	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	—	16	1	no	—
229	C₂	C₆₁×#2004	1	2	yes	—
230	C₂	C₆₁×#2013	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₆₁×#3206

C₂

yes

maximal

C₆₁×#2862

C₂

yes

maximal, characteristic, complemented

C₆₁×#1962

C₂

yes

maximal, characteristic

C₆₁×#1548

C₂

yes

maximal, complemented

C₆₁×#1276

C₂

yes

maximal, characteristic, complemented

C₆₁×#532

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₆₁

C₂²

yes

—

C₆₁×#492

—

C₆₁×#487

—

C₆₁×#461

—

C₆₁×#448

—

C₆₁×#431

C₂²

yes

—

C₆₁×#423

C₂²

yes

characteristic

C₂×#104×C₆₁

—

C₆₁×#391

—

C₆₁×#382

—

C₄³×C₆₁

C₂²

yes

characteristic

C₆₁×#333

—

C₂×#41×C₆₁

—

C₂²×Q₈×C₆₁

D₄

yes

—

C₂×SD₁₆×C₆₁

—

C₂×M₁₆×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

—

C₄⋊Q₈×C₆₁

D₄

yes

characteristic

#127×C₆₁

D₄

yes

characteristic

#124×C₆₁

—

#121×C₆₁

—

C₄×D₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄⋊C₄×C₆₁

—

C₂×C₄²×C₆₁

—

C₂×C₄²×C₆₁

D₄

yes

—

C₂×C₄²×C₆₁

C₂³

yes

characteristic

C₄⋊C₈×C₆₁

—

C₄⋊C₈×C₆₁

D₄

yes

—

#104×C₆₁

—

#103×C₆₁

—

C₂²⋊C₈×C₆₁

—

C₄×C₈×C₆₁

—

#95×C₆₁

—

#41×C₆₁

—

#41×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×Q₈×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂×D₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₂×D₄

yes

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

SD₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

SD₁₆

yes

complemented

C₄²×C₆₁

C₂×D₄

yes

characteristic

C₄²×C₆₁

C₂×D₄

yes

—

C₄²×C₆₁

#41

yes

characteristic

C₂³×C₆₁

—

C₂³×C₆₁

#120

yes

characteristic

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

D₄×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

#120

yes

—

C₂×C₄×C₆₁

#121

yes

—

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

C₂×SD₁₆

yes

—

C₂×C₄×C₆₁

#137

yes

—

C₈×C₆₁

—

C₈×C₆₁

—

#10287

C₆₁

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₆₁

—

100

C₂²×C₆₁

—

101

C₂²×C₆₁

—

102

C₂²×C₆₁

#392

yes

characteristic

103

C₂²×C₆₁

#448

yes

—

104

C₄×C₆₁

—

105

C₄×C₆₁

—

106

C₄×C₆₁

—

107

C₄×C₆₁

—

108

C₄×C₆₁

#455

yes

—

109

C₄×C₆₁

#461

yes

—

110

C₄×C₆₁

#492

yes

characteristic

111

C₄×C₆₁

#497

yes

characteristic

112

#3206

C₂×C₆₁

yes

—

113

#2862

C₂×C₆₁

yes

characteristic, complemented

114

#1962

C₂×C₆₁

yes

characteristic

115

#1548

C₂×C₆₁

yes

complemented

116

#1276

C₂×C₆₁

yes

characteristic, complemented

117

C₂×C₆₁

—

118

C₂×C₆₁

—

119

C₂×C₆₁

#2004

yes

—

120

C₂×C₆₁

#2013

yes

characteristic

121

#532

C₂²×C₆₁

yes

characteristic

122

C₂×C₄⋊Q₈

C₂²×C₆₁

yes

—

123

#492

—

124

#487

—

125

#461

—

126

#448

—

127

#431

C₂²×C₆₁

yes

—

128

#423

C₂²×C₆₁

yes

characteristic

129

C₂×#104

—

130

#391

—

131

#382

—

132

C₄³

C₂²×C₆₁

yes

characteristic

133

#333

—

134

C₆₁

#10287

yes

characteristic, direct product factor, Sylow

135

C₂×#41

—

136

C₂²×Q₈

D₄×C₆₁

yes

—

137

C₂×SD₁₆

—

138

C₂×M₁₆

—

139

C₄⋊Q₈

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

D₄×C₆₁

yes

characteristic

144

#127

D₄×C₆₁

yes

characteristic

145

#124

—

146

#121

—

147

C₄×D₄

—

148

C₂×C₄⋊C₄

—

149

C₂×C₄⋊C₄

—

150

C₂×C₄²

—

151

C₂×C₄²

D₄×C₆₁

yes

—

152

C₂×C₄²

C₂³×C₆₁

yes

characteristic

153

C₄⋊C₈

—

154

C₄⋊C₈

D₄×C₆₁

yes

—

155

#104

—

156

#103

—

157

C₂²⋊C₈

—

158

C₄×C₈

—

159

#95

—

160

#41

—

161

#41

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

169

C₂²×C₄

—

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

C₂×D₄×C₆₁

yes

—

173

C₂²×C₄

C₂×D₄×C₆₁

yes

characteristic

174

SD₁₆

—

175

M₁₆

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

—

186

C₄²

SD₁₆×C₆₁

yes

complemented

187

C₄²

C₂×D₄×C₆₁

yes

characteristic

188

C₄²

C₂×D₄×C₆₁

yes

—

189

C₄²

#41×C₆₁

yes

characteristic

190

C₂³

—

191

C₂³

#120×C₆₁

yes

characteristic

192

Q₈

—

193

Q₈

—

194

Q₈

—

195

D₄

—

196

D₄

—

197

D₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

#120×C₆₁

yes

—

207

C₂×C₄

#121×C₆₁

yes

—

208

C₂×C₄

#121×C₆₁

yes

characteristic

209

C₂×C₄

#127×C₆₁

yes

characteristic

210

C₂×C₄

C₂×SD₁₆×C₆₁

yes

—

211

C₂×C₄

#137×C₆₁

yes

—

212

C₈

—

213

C₈

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₆₁×#392

yes

characteristic

218

C₂²

C₆₁×#448

yes

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

C₆₁×#455

yes

—

224

C₄

C₆₁×#461

yes

—

225

C₄

C₆₁×#492

yes

characteristic

226

C₄

C₆₁×#497

yes

characteristic

227

C₂

—

228

C₂

—

229

C₂

C₆₁×#2004

yes

—

230

C₂

C₆₁×#2013

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₆₁×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

subgroup

G/H

center, socle

C₂²×C₆₁

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₆₁

prime radical

C₆₁×#532

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

N	H ≅ G/N	type
2. C₆₁×#2862	C₂	semidirect
4. C₆₁×#1548	C₂	semidirect
5. C₆₁×#1276	C₂	semidirect
70. C₄²×C₆₁	SD₁₆	semidirect
98. #10287	C₆₁	direct (N × H)
113. #2862	C₂×C₆₁	semidirect
115. #1548	C₂×C₆₁	semidirect
116. #1276	C₂×C₆₁	semidirect
134. C₆₁	#10287	direct (N × H)
186. C₄²	SD₁₆×C₆₁	semidirect

H ≅ G/N

type

2. C₆₁×#2862

C₂

semidirect

4. C₆₁×#1548

C₂

semidirect

5. C₆₁×#1276

C₂

semidirect

70. C₄²×C₆₁

SD₁₆

semidirect

98. #10287

C₆₁

direct (N × H)

113. #2862

C₂×C₆₁

semidirect

115. #1548

C₂×C₆₁

semidirect

116. #1276

C₂×C₆₁

semidirect

134. C₆₁

#10287

direct (N × H)

186. C₄²

SD₁₆×C₆₁

semidirect

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

subgroup	index
C₆₁×#3206	2
C₆₁×#2862	2
C₆₁×#1962	2
C₆₁×#1548	2
C₆₁×#1276	2
#10287	61

subgroup

index

C₆₁×#3206

C₆₁×#2862

C₆₁×#1962

C₆₁×#1548

C₆₁×#1276

#10287

Subgroups — C₆₁×#10287 #29513720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C61×#10287 #29513720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#10287 #29513720