Group #21458803 — subgroups

Subgroups — #21458803

Order 7808.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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	#16840485	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840144	C₂	1	2	yes	maximal
3	#16840141	C₂	1	1	yes	maximal, characteristic, complemented
4	#16839984	C₂	1	2	yes	maximal, complemented
5	#16839981	C₂	1	2	yes	maximal, complemented
6	#16839967	C₂	1	1	yes	maximal, characteristic, complemented
7	#16839964	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#11758202	C₂	1	2	yes	maximal, complemented
10	C₄×#11758199	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11758202	C₂²	1	2	yes	—
13	C₂×#11758202	C₂²	1	2	yes	—
14	C₂×#11758200	C₂²	1	2	yes	—
15	C₂×#11758201	C₂²	1	2	yes	—
16	C₂×#11758199	C₂²	1	1	yes	characteristic
17	#14519777	C₂²	1	1	yes	characteristic
18	#14519772	—	2	2	no	—
19	#14519765	C₂²	1	2	yes	—
20	#14519753	—	2	1	no	—
21	C₄×Dic₁₂₂	C₂²	1	2	yes	—
22	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
23	#14519735	—	2	1	no	—
24	#14519710	C₂²	1	1	yes	characteristic
25	C₄⋊#92418	C₂²	1	1	yes	characteristic
26	C₄⋊#92418	C₂²	1	2	yes	—
27	#14519701	C₂²	1	2	yes	—
28	#14519700	C₂²	1	2	yes	—
29	#14519698	C₂²	1	1	yes	characteristic
30	#14519697	C₂²	1	1	yes	characteristic
31	C₄×#92418	C₂²	1	1	yes	characteristic
32	C₄×#92418	C₂²	1	2	yes	—
33	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
34	#126×C₆₁	—	2	2	no	—
35	#124×C₆₁	C₂²	1	2	yes	—
36	C₂²⋊Q₈×C₆₁	—	2	1	no	—
37	C₄×Q₈×C₆₁	C₂²	1	2	yes	—
38	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	#117×C₆₁	—	2	1	no	—
41	C₂×Q₈×C₆₁	D₄	1	1	yes	characteristic
42	C₂×Q₈×C₆₁	C₂³	1	2	yes	—
43	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₆₁	—	2	1	no	—
45	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
46	C₂×C₄×D₆₁	—	2	1	no	—
47	C₂×Dic₁₂₂	C₂³	1	2	yes	—
48	C₄⋊C₄×C₆₁	—	2	1	no	—
49	C₄⋊C₄×C₆₁	—	2	2	no	—
50	C₄⋊C₄×C₆₁	—	2	1	no	—
51	C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
52	C₄⋊C₄×C₆₁	D₄	1	2	yes	—
53	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²⋊C₄×C₆₁	—	2	2	no	—
55	C₂²⋊C₄×C₆₁	—	2	1	no	—
56	C₂²⋊C₄×C₆₁	—	2	2	no	—
57	C₄²×C₆₁	—	2	2	no	—
58	C₄²×C₆₁	C₂³	1	1	yes	characteristic
59	C₄²×C₆₁	C₂³	1	2	yes	—
60	#11758202	—	2	4	no	—
61	#11758202	—	4	2	no	—
62	#11758201	—	4	2	no	—
63	#11758200	—	4	2	no	—
64	#11758199	—	2	2	no	—
65	#11758198	—	2	2	no	—
66	#11758198	—	2	1	no	—
67	#11758198	—	2	2	no	—
68	C₄⋊Dic₆₁	—	2	1	no	—
69	C₄⋊Dic₆₁	—	2	1	no	—
70	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
71	#11758196	—	2	2	no	—
72	C₄×Dic₆₁	—	2	2	no	—
73	C₂×#92418	C₂³	1	1	yes	characteristic
74	C₂×#92418	C₂³	1	2	yes	—
75	C₂×#92418	C₂³	1	1	yes	characteristic
76	C₂³×C₆₁	—	2	1	no	—
77	C₂²×D₆₁	—	2	1	no	—
78	Q₈×C₆₁	—	2	2	no	—
79	Q₈×C₆₁	—	2	2	no	—
80	Q₈×C₆₁	—	2	2	no	—
81	D₄×C₆₁	—	2	1	no	—
82	D₄×C₆₁	—	2	1	no	—
83	C₂×C₄×C₆₁	—	2	1	no	—
84	C₂×C₄×C₆₁	—	2	2	no	—
85	C₂×C₄×C₆₁	—	4	2	no	—
86	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
87	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
88	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₆₁	—	2	1	no	—
92	C₂×Dic₆₁	—	2	2	no	—
93	D₂₄₄	—	2	1	no	—
94	D₂₄₄	—	2	1	no	—
95	C₄×D₆₁	—	4	2	no	—
96	Dic₁₂₂	—	2	2	no	—
97	Dic₁₂₂	—	2	2	no	—
98	#92418	—	2	2	no	—
99	#92418	—	2	1	no	—
100	#92418	#41	1	2	yes	—
101	C₂²×C₆₁	—	4	1	no	—
102	C₂²×C₆₁	—	4	1	no	—
103	C₂²×C₆₁	—	4	1	no	—
104	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
105	C₂×D₆₁	—	4	1	no	—
106	C₂×D₆₁	—	4	1	no	—
107	C₂×D₆₁	—	4	1	no	—
108	C₄×C₆₁	—	2	2	no	—
109	C₄×C₆₁	—	2	2	no	—
110	C₄×C₆₁	—	2	1	no	—
111	C₄×C₆₁	—	4	2	no	—
112	C₄×C₆₁	—	4	1	no	—
113	C₄×C₆₁	#135	1	2	yes	—
114	C₄×C₆₁	C₂×#41	1	1	yes	characteristic
115	C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
116	Dic₆₁	—	4	2	no	—
117	Dic₆₁	—	4	1	no	—
118	#3393	—	61	1	no	maximal, Sylow
119	C₂×C₆₁	—	8	1	no	—
120	C₂×C₆₁	#550	1	1	yes	characteristic
121	C₂×C₆₁	C₂×#135	1	1	yes	characteristic
122	C₂×C₆₁	#578	1	1	yes	characteristic
123	D₆₁	—	8	1	no	—
124	#556	—	61	1	no	—
125	#556	D₆₁	1	1	yes	characteristic, complemented
126	#495	—	61	2	no	—
127	#494	—	61	1	no	—
128	#464	—	61	2	no	—
129	#464	—	61	2	no	—
130	#461	—	61	1	no	—
131	#461	—	61	1	no	—
132	C₈×Q₈	—	61	1	no	—
133	C₄×Q₁₆	—	61	2	no	—
134	C₄×D₈	—	61	1	no	—
135	C₆₁	#3393	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	61	2	no	—
137	C₂×Q₁₆	—	61	2	no	—
138	C₂×SD₁₆	—	61	2	no	—
139	C₂×SD₁₆	—	61	2	no	—
140	C₂×D₈	—	61	1	no	—
141	C₄⋊Q₈	—	61	1	no	—
142	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
143	#126	—	2	2	no	—
144	#126	—	122	2	no	—
145	#124	—	61	2	no	—
146	#124	C₂×D₆₁	1	2	yes	—
147	C₂²⋊Q₈	—	2	1	no	—
148	C₂²⋊Q₈	—	122	1	no	—
149	C₄×Q₈	—	61	2	no	—
150	C₄×Q₈	C₂×D₆₁	1	2	yes	—
151	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic
152	C₄×D₄	—	61	1	no	—
153	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
154	#117	—	2	1	no	—
155	#117	—	122	1	no	—
156	#107	—	61	1	no	—
157	C₄⋊C₈	—	61	1	no	—
158	C₄⋊C₈	—	61	2	no	—
159	#103	—	61	2	no	—
160	#103	—	61	2	no	—
161	#102	—	61	1	no	—
162	#102	—	61	1	no	—
163	C₄×C₈	—	61	1	no	—
164	C₄×C₈	—	61	2	no	—
165	C₂×Q₈	—	61	2	no	—
166	C₂×Q₈	C₂²⋊D₆₁	1	1	yes	characteristic
167	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
168	C₂×D₄	—	61	1	no	—
169	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	122	1	no	—
172	Q₁₆	—	122	4	no	—
173	Q₁₆	—	244	2	no	—
174	SD₁₆	—	244	2	no	—
175	SD₁₆	—	244	2	no	—
176	D₈	—	122	2	no	—
177	C₂×C₈	—	61	1	no	—
178	C₂×C₈	—	61	1	no	—
179	C₂×C₈	—	61	2	no	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	1	no	—
183	C₄⋊C₄	—	61	1	no	—
184	C₄⋊C₄	—	122	2	no	—
185	C₄⋊C₄	—	122	1	no	—
186	C₄⋊C₄	—	122	1	no	—
187	C₄⋊C₄	C₂²⋊D₆₁	1	1	yes	characteristic
188	C₄⋊C₄	C₂²⋊D₆₁	1	2	yes	—
189	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
190	C₂²⋊C₄	—	2	2	no	—
191	C₂²⋊C₄	—	2	1	no	—
192	C₂²⋊C₄	—	2	2	no	—
193	C₂²⋊C₄	—	122	2	no	—
194	C₂²⋊C₄	—	122	1	no	—
195	C₂²⋊C₄	—	122	2	no	—
196	C₄²	—	2	2	no	—
197	C₄²	—	122	2	no	—
198	C₄²	C₂²×D₆₁	1	1	yes	characteristic
199	C₄²	C₂²×D₆₁	1	2	yes	—
200	C₂³	—	2	1	no	—
201	C₂³	—	122	1	no	—
202	Q₈	—	2	2	no	—
203	Q₈	—	2	2	no	—
204	Q₈	—	2	2	no	—
205	Q₈	—	122	2	no	—
206	Q₈	—	122	2	no	—
207	D₄	—	2	1	no	—
208	D₄	—	2	1	no	—
209	D₄	—	122	1	no	—
210	D₄	—	122	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	122	1	no	—
215	C₂×C₄	—	122	2	no	—
216	C₂×C₄	—	244	2	no	—
217	C₂×C₄	C₂×C₂²⋊D₆₁	1	2	yes	—
218	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
219	C₂×C₄	C₂×C₂²⋊D₆₁	1	2	yes	—
220	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
221	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
222	C₈	—	61	2	no	—
223	C₈	—	122	2	no	—
224	C₈	—	122	1	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	244	1	no	—
229	C₂²	—	244	1	no	—
230	C₂²	—	244	1	no	—
231	C₂²	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	1	no	—
236	C₄	—	4	2	no	—
237	C₄	—	244	1	no	—
238	C₄	—	244	2	no	—
239	C₄	#14519797	1	2	yes	—
240	C₄	#41×D₆₁	1	1	yes	characteristic
241	C₄	#14519823	1	1	yes	characteristic
242	C₂	—	8	1	no	—
243	C₂	—	488	1	no	—
244	C₂	#16840431	1	1	yes	characteristic
245	C₂	C₂×#14519797	1	1	yes	characteristic
246	C₂	#16840577	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840485

C₂

yes

maximal, characteristic, complemented

#16840144

C₂

yes

maximal

#16840141

C₂

yes

maximal, characteristic, complemented

#16839984

C₂

yes

maximal, complemented

#16839981

C₂

yes

maximal, complemented

#16839967

C₂

yes

maximal, characteristic, complemented

#16839964

C₂

yes

maximal, characteristic, complemented

Q₈×#92418

C₂

yes

maximal, characteristic, complemented

C₄×#11758202

C₂

yes

maximal, complemented

C₄×#11758199

C₂

yes

maximal, characteristic

C₆₁×#556

C₂

yes

maximal, characteristic, complemented

C₂×#11758202

C₂²

yes

—

C₂×#11758202

C₂²

yes

—

C₂×#11758200

C₂²

yes

—

C₂×#11758201

C₂²

yes

—

C₂×#11758199

C₂²

yes

characteristic

#14519777

C₂²

yes

characteristic

#14519772

—

#14519765

C₂²

yes

—

#14519753

—

C₄×Dic₁₂₂

C₂²

yes

—

C₄×D₂₄₄

C₂²

yes

characteristic

#14519735

—

#14519710

C₂²

yes

characteristic

C₄⋊#92418

C₂²

yes

characteristic

C₄⋊#92418

C₂²

yes

—

#14519701

C₂²

yes

—

#14519700

C₂²

yes

—

#14519698

C₂²

yes

characteristic

#14519697

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

characteristic

C₄×#92418

C₂²

yes

—

C₄⋊Q₈×C₆₁

C₂²

yes

characteristic

#126×C₆₁

—

#124×C₆₁

C₂²

yes

—

C₂²⋊Q₈×C₆₁

—

C₄×Q₈×C₆₁

C₂²

yes

—

C₄×Q₈×C₆₁

C₂²

yes

characteristic

C₄×D₄×C₆₁

C₂²

yes

characteristic

#117×C₆₁

—

C₂×Q₈×C₆₁

D₄

yes

characteristic

C₂×Q₈×C₆₁

C₂³

yes

—

C₂×D₄×C₆₁

C₂³

yes

characteristic

C₂²×C₄×C₆₁

—

C₂×D₂₄₄

C₂³

yes

characteristic

C₂×C₄×D₆₁

—

C₂×Dic₁₂₂

C₂³

yes

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

D₄

yes

characteristic

C₄⋊C₄×C₆₁

D₄

yes

—

C₄⋊C₄×C₆₁

C₂³

yes

characteristic

C₂²⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₂²⋊C₄×C₆₁

—

C₄²×C₆₁

—

C₄²×C₆₁

C₂³

yes

characteristic

C₄²×C₆₁

C₂³

yes

—

—

—

—

—

—

—

—

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

—

C₄⋊Dic₆₁

C₂³

yes

characteristic

#11758196

—

C₄×Dic₆₁

—

C₂×#92418

C₂³

yes

characteristic

C₂×#92418

C₂³

yes

—

C₂×#92418

C₂³

yes

characteristic

C₂³×C₆₁

—

C₂²×D₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

Q₈×C₆₁

—

D₄×C₆₁

—

D₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

—

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

C₂×C₄×C₆₁

C₂⁴

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

D₂₄₄

—

D₂₄₄

—

C₄×D₆₁

—

Dic₁₂₂

—

Dic₁₂₂

—

#92418

—

#92418

—

100

#92418

#41

yes

—

101

C₂²×C₆₁

—

102

C₂²×C₆₁

—

103

C₂²×C₆₁

—

104

C₂²×C₆₁

C₂²×D₄

yes

characteristic

105

C₂×D₆₁

—

106

C₂×D₆₁

—

107

C₂×D₆₁

—

108

C₄×C₆₁

—

109

C₄×C₆₁

—

110

C₄×C₆₁

—

111

C₄×C₆₁

—

112

C₄×C₆₁

—

113

C₄×C₆₁

#135

yes

—

114

C₄×C₆₁

C₂×#41

yes

characteristic

115

C₄×C₆₁

H(5,𝔽₂)

yes

characteristic

116

Dic₆₁

—

117

Dic₆₁

—

118

#3393

—

maximal, Sylow

119

C₂×C₆₁

—

120

C₂×C₆₁

#550

yes

characteristic

121

C₂×C₆₁

C₂×#135

yes

characteristic

122

C₂×C₆₁

#578

yes

characteristic

123

D₆₁

—

124

#556

—

125

#556

D₆₁

yes

characteristic, complemented

126

#495

—

127

#494

—

128

#464

—

129

#464

—

130

#461

—

131

#461

—

132

C₈×Q₈

—

133

C₄×Q₁₆

—

134

C₄×D₈

—

135

C₆₁

#3393

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×SD₁₆

—

139

C₂×SD₁₆

—

140

C₂×D₈

—

141

C₄⋊Q₈

—

142

C₄⋊Q₈

C₂×D₆₁

yes

characteristic

143

#126

—

144

#126

—

122

—

145

#124

—

146

#124

C₂×D₆₁

yes

—

147

C₂²⋊Q₈

—

148

C₂²⋊Q₈

—

122

—

149

C₄×Q₈

—

150

C₄×Q₈

C₂×D₆₁

yes

—

151

C₄×Q₈

C₂×D₆₁

yes

characteristic

152

C₄×D₄

—

153

C₄×D₄

C₂×D₆₁

yes

characteristic

154

#117

—

155

#117

—

122

—

156

#107

—

157

C₄⋊C₈

—

158

C₄⋊C₈

—

159

#103

—

160

#103

—

161

#102

—

162

#102

—

163

C₄×C₈

—

164

C₄×C₈

—

165

C₂×Q₈

—

166

C₂×Q₈

C₂²⋊D₆₁

yes

characteristic

167

C₂×Q₈

C₂²×D₆₁

yes

—

168

C₂×D₄

—

169

C₂×D₄

C₂²×D₆₁

yes

characteristic

170

C₂²×C₄

—

171

C₂²×C₄

—

122

—

172

Q₁₆

—

122

—

173

Q₁₆

—

244

—

174

SD₁₆

—

244

—

175

SD₁₆

—

244

—

176

D₈

—

122

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

122

—

185

C₄⋊C₄

—

122

—

186

C₄⋊C₄

—

122

—

187

C₄⋊C₄

C₂²⋊D₆₁

yes

characteristic

188

C₄⋊C₄

C₂²⋊D₆₁

yes

—

189

C₄⋊C₄

C₂²×D₆₁

yes

characteristic

190

C₂²⋊C₄

—

191

C₂²⋊C₄

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

122

—

194

C₂²⋊C₄

—

122

—

195

C₂²⋊C₄

—

122

—

196

C₄²

—

197

C₄²

—

122

—

198

C₄²

C₂²×D₆₁

yes

characteristic

199

C₄²

C₂²×D₆₁

yes

—

200

C₂³

—

201

C₂³

—

122

—

202

Q₈

—

203

Q₈

—

204

Q₈

—

205

Q₈

—

122

—

206

Q₈

—

122

—

207

D₄

—

208

D₄

—

209

D₄

—

122

—

210

D₄

—

122

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

122

—

215

C₂×C₄

—

122

—

216

C₂×C₄

—

244

—

217

C₂×C₄

C₂×C₂²⋊D₆₁

yes

—

218

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

219

C₂×C₄

C₂×C₂²⋊D₆₁

yes

—

220

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

221

C₂×C₄

C₂³×D₆₁

yes

characteristic

222

C₈

—

223

C₈

—

122

—

224

C₈

—

122

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

—

244

—

229

C₂²

—

244

—

230

C₂²

—

244

—

231

C₂²

C₂²×C₂²⋊D₆₁

yes

characteristic

232

C₄

—

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

244

—

238

C₄

—

244

—

239

C₄

#14519797

yes

—

240

C₄

#41×D₆₁

yes

characteristic

241

C₄

#14519823

yes

characteristic

242

C₂

—

243

C₂

—

488

—

244

C₂

#16840431

yes

characteristic

245

C₂

C₂×#14519797

yes

characteristic

246

C₂

#16840577

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₆₁
Fitting	C₆₁×#556	C₂
socle	C₂²×C₆₁	C₂²×D₄
hypercenter	#556	D₆₁
hypocenter	C₆₁	#3393
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

subgroup

G/H

center

C₂²

C₂²×C₂²⋊D₆₁

commutator

C₂×C₄×C₆₁

C₂⁴

Frattini

C₂×C₄

C₂³×D₆₁

Fitting

C₆₁×#556

C₂

socle

C₂²×C₆₁

C₂²×D₄

D₆₁

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #556

N	H ≅ G/N	type
1. #16840485	C₂	semidirect
3. #16840141	C₂	semidirect
4. #16839984	C₂	semidirect
5. #16839981	C₂	semidirect
6. #16839967	C₂	semidirect
7. #16839964	C₂	semidirect
8. Q₈×#92418	C₂	semidirect
9. C₄×#11758202	C₂	semidirect
11. C₆₁×#556	C₂	semidirect
125. #556	D₆₁	semidirect
135. C₆₁	#3393	semidirect

H ≅ G/N

type

1. #16840485

C₂

semidirect

3. #16840141

C₂

semidirect

4. #16839984

C₂

semidirect

5. #16839981

C₂

semidirect

6. #16839967

C₂

semidirect

7. #16839964

C₂

semidirect

8. Q₈×#92418

C₂

semidirect

9. C₄×#11758202

C₂

semidirect

11. C₆₁×#556

C₂

semidirect

125. #556

D₆₁

semidirect

135. C₆₁

#3393

semidirect

Subgroups — #21458803

Conjugacy classes of subgroups

Complements