Group #29596574 — subgroups

Subgroups — #29596574

Order 15616.

414 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₂×#16839800	C₂	1	1	yes	maximal, characteristic
2	C₂×#16839586	C₂	1	2	yes	maximal, complemented
3	#21447430	C₂	1	1	yes	maximal, characteristic
4	#21443919	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1810	C₂	1	1	yes	maximal, characteristic
6	C₂×#14519736	—	2	1	no	—
7	C₂×#14519717	C₂²	1	2	yes	—
8	#16839800	—	2	4	no	—
9	C₂×#14519711	—	2	1	no	—
10	C₂×#14519709	C₂²	1	2	yes	—
11	#16839586	—	2	4	no	—
12	C₂²⋊#11758185	C₄	1	4	yes	complemented
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#108×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#407	—	2	1	no	—
17	C₆₁×#341	—	2	1	no	—
18	#14519736	—	2	4	no	—
19	#14519736	—	4	2	no	—
20	C₂×C₄⋊Dic₆₁	—	2	2	no	—
21	C₂×C₂²⋊Dic₆₁	—	4	1	no	—
22	C₂×C₄×Dic₆₁	—	4	1	no	—
23	#14519717	—	2	2	no	—
24	#14519717	—	2	2	no	—
25	C₂×#11758185	C₂×C₄	1	4	yes	—
26	#14519711	—	2	4	no	—
27	#14519709	—	2	2	no	—
28	#14519709	D₄	1	4	yes	—
29	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₆₁	—	2	1	no	—
31	C₂×M₁₆×C₆₁	—	2	1	no	—
32	C₂²×C₈×C₆₁	—	2	2	no	—
33	C₂²×C₈×C₆₁	—	2	2	no	—
34	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₆₁	Q₈	1	2	yes	—
37	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
38	#108×C₆₁	—	2	2	no	—
39	#108×C₆₁	—	2	2	no	—
40	C₂²⋊C₈×C₆₁	—	4	2	no	—
41	C₂⁴×C₆₁	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₆₁	—	2	1	no	—
43	C₂²×C₄×C₆₁	—	2	1	no	—
44	C₂²×C₄×C₆₁	—	2	1	no	—
45	C₂²×C₄×C₆₁	—	2	1	no	—
46	C₂²×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₆₁	SD₁₆	1	2	yes	—
49	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₆₁	—	4	2	no	—
51	M₁₆×C₆₁	—	4	1	no	—
52	M₁₆×C₆₁	—	4	1	no	—
53	M₁₆×C₆₁	—	4	1	no	—
54	M₁₆×C₆₁	—	4	1	no	—
55	C₂×C₈×C₆₁	—	2	1	no	—
56	C₂×C₈×C₆₁	—	2	1	no	—
57	C₂×C₈×C₆₁	—	2	4	no	—
58	C₂×C₈×C₆₁	—	2	4	no	—
59	C₂×C₈×C₆₁	—	4	1	no	—
60	C₂×C₈×C₆₁	—	4	1	no	—
61	C₂×C₈×C₆₁	C₄⋊C₄	1	2	yes	—
62	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
64	C₂×C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₆₁	#41	1	2	yes	—
66	C₂²⋊Dic₆₁	—	4	4	no	—
67	C₄⋊Dic₆₁	—	2	4	no	—
68	C₄⋊Dic₆₁	—	4	2	no	—
69	C₄×Dic₆₁	—	4	4	no	—
70	#11758185	—	2	4	no	—
71	C₂³×C₆₁	—	2	1	no	—
72	C₂³×C₆₁	—	2	1	no	—
73	C₂³×C₆₁	—	4	2	no	—
74	C₂³×C₆₁	#106	1	2	yes	—
75	C₂³×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₆₁	—	2	1	no	—
77	C₂×C₄×C₆₁	—	2	1	no	—
78	C₂×C₄×C₆₁	—	2	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	#106	1	2	yes	—
83	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
85	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
86	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
89	C₂×Dic₆₁	—	4	4	no	—
90	C₂×Dic₆₁	—	8	4	no	—
91	C₈×C₆₁	—	2	2	no	—
92	C₈×C₆₁	—	8	1	no	—
93	C₈×C₆₁	—	8	1	no	—
94	C₈×C₆₁	C₄×D₄	1	2	yes	—
95	C₈×C₆₁	C₂²⋊Q₈	1	2	yes	—
96	#12930	—	61	1	no	maximal, Sylow
97	C₂²×C₆₁	—	2	2	no	—
98	C₂²×C₆₁	—	2	2	no	—
99	C₂²×C₆₁	—	2	4	no	—
100	C₂²×C₆₁	—	4	2	no	—
101	C₂²×C₆₁	—	4	2	no	—
102	C₂²×C₆₁	C₂×#106	1	1	yes	characteristic
103	C₂²×C₆₁	#450	1	1	yes	characteristic
104	C₂²×C₆₁	#483	1	1	yes	characteristic
105	C₄×C₆₁	—	2	2	no	—
106	C₄×C₆₁	#385	1	1	yes	characteristic
107	C₄×C₆₁	#428	1	1	yes	characteristic
108	C₄×C₆₁	#448	1	1	yes	characteristic
109	C₄×C₆₁	#481	1	1	yes	characteristic
110	Dic₆₁	—	8	4	no	—
111	C₂×#427	—	61	1	no	—
112	C₂×#365	—	61	2	no	—
113	#2112	—	61	1	no	—
114	#1810	D₆₁	1	1	yes	characteristic
115	#1383	—	61	2	no	—
116	C₂×C₆₁	—	2	1	no	—
117	C₂×C₆₁	—	2	1	no	—
118	C₂×C₆₁	—	4	2	no	—
119	C₂×C₆₁	#1853	1	1	yes	characteristic
120	C₂×C₆₁	#2155	1	2	yes	—
121	C₂³×C₈	C₂×D₆₁	1	1	yes	characteristic
122	C₂×#117	—	122	1	no	—
123	C₂×M₃₂	—	61	2	no	—
124	C₂×#108	C₂×D₆₁	1	1	yes	characteristic
125	C₂×#108	C₂×D₆₁	1	1	yes	characteristic
126	#427	—	122	4	no	—
127	C₂×#107	—	122	1	no	—
128	C₂×#106	—	61	2	no	—
129	#407	—	2	1	no	—
130	#365	—	122	4	no	—
131	C₂²⋊C₁₆	—	61	4	no	—
132	#341	—	2	1	no	—
133	C₆₁	#12930	1	1	yes	characteristic, complemented, Sylow
134	C₂³×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₁₂₂	1	2	yes	—
140	C₂²×C₈	C₄×D₆₁	1	2	yes	—
141	C₂²×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
143	#117	—	122	4	no	—
144	#117	—	244	2	no	—
145	C₂×C₄⋊C₄	—	122	2	no	—
146	C₂×C₂²⋊C₄	—	244	1	no	—
147	C₂×C₄²	—	244	1	no	—
148	M₃₂	—	122	2	no	—
149	M₃₂	—	122	2	no	—
150	C₂×C₁₆	—	61	4	no	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#107	—	122	4	no	—
154	#106	—	61	4	no	—
155	#106	—	122	2	no	—
156	C₂²⋊C₈	—	4	2	no	—
157	C₂⁴	#11758201	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	244	2	no	—
163	C₂²×C₄	#11758196	1	2	yes	—
164	C₂²×C₄	#11758200	1	2	yes	—
165	C₂²×C₄	#11758201	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
167	M₁₆	—	4	1	no	—
168	M₁₆	—	4	1	no	—
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	#11758196	1	2	yes	—
178	C₂×C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
179	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
180	C₂×C₈	D₄×D₆₁	1	2	yes	—
181	C₂×C₈	#11758224	1	2	yes	—
182	C₄⋊C₄	—	122	4	no	—
183	C₄⋊C₄	—	244	2	no	—
184	C₂²⋊C₄	—	244	4	no	—
185	C₄²	—	244	4	no	—
186	C₁₆	—	122	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#14519708	1	2	yes	—
191	C₂³	C₂×#11758201	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	488	4	no	—
199	C₂×C₄	—	244	4	no	—
200	C₂×C₄	#14519708	1	2	yes	—
201	C₂×C₄	C₂×#11758196	1	1	yes	characteristic
202	C₂×C₄	#14519745	1	1	yes	characteristic
203	C₂×C₄	#14519758	1	1	yes	characteristic
204	C₂×C₄	C₂×#11758200	1	1	yes	characteristic
205	C₂×C₄	#14519802	1	1	yes	characteristic
206	C₂×C₄	#14519807	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	8	1	no	—
209	C₈	—	8	1	no	—
210	C₈	#14519737	1	2	yes	—
211	C₈	#14519754	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	2	no	—
214	C₂²	—	2	4	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#14519708	1	1	yes	characteristic
218	C₂²	#16839912	1	1	yes	characteristic
219	C₂²	#16840090	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	488	4	no	—
222	C₄	#16839634	1	1	yes	characteristic
223	C₄	#16839805	1	1	yes	characteristic
224	C₄	#16839900	1	1	yes	characteristic
225	C₄	#16840078	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#21446011	1	1	yes	characteristic
230	C₂	#21447593	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16839800

C₂

yes

maximal, characteristic

C₂×#16839586

C₂

yes

maximal, complemented

#21447430

C₂

yes

maximal, characteristic

#21443919

C₂

yes

maximal, complemented

C₆₁×#1810

C₂

yes

maximal, characteristic

C₂×#14519736

—

C₂×#14519717

C₂²

yes

—

#16839800

—

C₂×#14519711

—

C₂×#14519709

C₂²

yes

—

#16839586

—

C₂²⋊#11758185

C₄

yes

complemented

C₂³×C₈×C₆₁

C₂²

yes

characteristic

C₂×#108×C₆₁

C₂²

yes

characteristic

C₂×#108×C₆₁

C₂²

yes

characteristic

C₆₁×#407

—

C₆₁×#341

—

#14519736

—

#14519736

—

C₂×C₄⋊Dic₆₁

—

C₂×C₂²⋊Dic₆₁

—

C₂×C₄×Dic₆₁

—

#14519717

—

#14519717

—

C₂×#11758185

C₂×C₄

yes

—

#14519711

—

#14519709

—

#14519709

D₄

yes

—

C₂³×C₄×C₆₁

D₄

yes

characteristic

C₂×M₁₆×C₆₁

—

C₂×M₁₆×C₆₁

—

C₂²×C₈×C₆₁

—

C₂²×C₈×C₆₁

—

C₂²×C₈×C₆₁

C₂×C₄

yes

—

C₂²×C₈×C₆₁

D₄

yes

characteristic

C₂²×C₈×C₆₁

Q₈

yes

—

C₂²×C₈×C₆₁

C₂³

yes

characteristic

#108×C₆₁

—

#108×C₆₁

—

C₂²⋊C₈×C₆₁

—

C₂⁴×C₆₁

SD₁₆

yes

characteristic

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

—

C₂²×C₄×C₆₁

C₄⋊C₄

yes

—

C₂²×C₄×C₆₁

SD₁₆

yes

characteristic

C₂²×C₄×C₆₁

SD₁₆

yes

—

C₂²×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂²×Dic₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

M₁₆×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₄⋊C₄

yes

—

C₂×C₈×C₆₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×D₄

yes

—

C₂×C₈×C₆₁

C₂×Q₈

yes

characteristic

C₂×C₈×C₆₁

#41

yes

—

C₂²⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄×Dic₆₁

—

#11758185

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

—

C₂³×C₆₁

#106

yes

—

C₂³×C₆₁

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

#106

yes

—

C₂×C₄×C₆₁

C₂×C₄⋊C₄

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

C₂×SD₁₆

yes

C₂×C₄×C₆₁

yes

C₂×C₄×C₆₁

yes

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

—

C₈×C₆₁

C₄×D₄

yes

—

C₈×C₆₁

C₂²⋊Q₈

yes

—

#12930

—

maximal, Sylow

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

—

100

C₂²×C₆₁

—

101

C₂²×C₆₁

—

102

C₂²×C₆₁

C₂×#106

yes

characteristic

103

C₂²×C₆₁

#450

yes

characteristic

104

C₂²×C₆₁

#483

yes

characteristic

105

C₄×C₆₁

—

106

C₄×C₆₁

#385

yes

characteristic

107

C₄×C₆₁

#428

yes

characteristic

108

C₄×C₆₁

#448

yes

characteristic

109

C₄×C₆₁

#481

yes

characteristic

110

Dic₆₁

—

111

C₂×#427

—

112

C₂×#365

—

113

#2112

—

114

#1810

D₆₁

yes

characteristic

115

#1383

—

116

C₂×C₆₁

—

117

C₂×C₆₁

—

118

C₂×C₆₁

—

119

C₂×C₆₁

#1853

yes

characteristic

120

C₂×C₆₁

#2155

yes

—

121

C₂³×C₈

C₂×D₆₁

yes

characteristic

122

C₂×#117

—

122

—

123

C₂×M₃₂

—

124

C₂×#108

C₂×D₆₁

yes

characteristic

125

C₂×#108

C₂×D₆₁

yes

characteristic

126

#427

—

122

—

127

C₂×#107

—

122

—

128

C₂×#106

—

129

#407

—

130

#365

—

122

—

131

C₂²⋊C₁₆

—

132

#341

—

133

C₆₁

#12930

yes

characteristic, complemented, Sylow

134

C₂³×C₄

C₂²⋊D₆₁

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₁₂₂

yes

—

140

C₂²×C₈

C₄×D₆₁

yes

—

141

C₂²×C₈

C₂²⋊D₆₁

yes

characteristic

142

C₂²×C₈

C₂²×D₆₁

yes

characteristic

143

#117

—

122

—

144

#117

—

244

—

145

C₂×C₄⋊C₄

—

122

—

146

C₂×C₂²⋊C₄

—

244

—

147

C₂×C₄²

—

244

—

148

M₃₂

—

122

—

149

M₃₂

—

122

—

150

C₂×C₁₆

—

151

#108

—

152

#108

—

153

#107

—

122

—

154

#106

—

155

#106

—

122

—

156

C₂²⋊C₈

—

157

C₂⁴

#11758201

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

244

—

163

C₂²×C₄

#11758196

yes

—

164

C₂²×C₄

#11758200

yes

—

165

C₂²×C₄

#11758201

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

#11758196

yes

—

178

C₂×C₈

C₂×Dic₁₂₂

yes

characteristic

179

C₂×C₈

C₂×C₄×D₆₁

yes

characteristic

180

C₂×C₈

D₄×D₆₁

yes

—

181

C₂×C₈

#11758224

yes

—

182

C₄⋊C₄

—

122

—

183

C₄⋊C₄

—

244

—

184

C₂²⋊C₄

—

244

—

185

C₄²

—

244

—

186

C₁₆

—

122

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#14519708

yes

—

191

C₂³

C₂×#11758201

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

488

—

199

C₂×C₄

—

244

—

200

C₂×C₄

#14519708

yes

—

201

C₂×C₄

C₂×#11758196

yes

characteristic

202

C₂×C₄

#14519745

yes

characteristic

203

C₂×C₄

#14519758

yes

characteristic

204

C₂×C₄

C₂×#11758200

yes

characteristic

205

C₂×C₄

#14519802

yes

characteristic

206

C₂×C₄

#14519807

yes

characteristic

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

#14519737

yes

—

211

C₈

#14519754

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#14519708

yes

characteristic

218

C₂²

#16839912

yes

characteristic

219

C₂²

#16840090

yes

characteristic

220

C₄

—

221

C₄

—

488

—

222

C₄

#16839634

yes

characteristic

223

C₄

#16839805

yes

characteristic

224

C₄

#16839900

yes

characteristic

225

C₄

#16840078

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#21446011

yes

characteristic

230

C₂

#21447593

yes

—

	subgroup	G/H
center	C₂²	C₂×#14519708
commutator	C₂×C₈×C₆₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₁
Fitting	C₆₁×#1810	C₂
socle	C₂²×C₆₁	C₂×#106
prime radical	C₂⁴×C₆₁	SD₁₆
cosocle	C₂²×C₈×C₆₁	C₂³
hypercenter	#1810	D₆₁
hypocenter	C₆₁	#12930
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂²

C₂×#14519708

commutator

C₂×C₈×C₆₁

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₁

Fitting

C₆₁×#1810

C₂

socle

C₂²×C₆₁

C₂×#106

prime radical

C₂⁴×C₆₁

SD₁₆

cosocle

C₂²×C₈×C₆₁

C₂³

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
2. C₂×#16839586	C₂	semidirect
4. #21443919	C₂	semidirect
12. C₂²⋊#11758185	C₄	semidirect
133. C₆₁	#12930	semidirect

H ≅ G/N

type

2. C₂×#16839586

C₂

semidirect

4. #21443919

C₂

semidirect

12. C₂²⋊#11758185

C₄

semidirect

133. C₆₁

#12930

semidirect

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

subgroup	index
C₂×#16839800	2
C₂×#16839586	2
#21447430	2
#21443919	2
C₆₁×#1810	2
#12930	61

subgroup

index

C₆₁×#1810

Subgroups — #29596574

Conjugacy classes of subgroups

Complements

Maximal subgroups