Group #20252873 — subgroups

Subgroups — #20252873

Order 6016.

480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#13094054	C₂	1	1	yes	maximal, characteristic
2	C₂×#13094022	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#15689331	C₂	1	4	yes	maximal, complemented
5	#15689326	C₂	1	4	yes	maximal, complemented
6	#15689146	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689133	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689132	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#137×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
11	#13094054	—	2	4	no	—
12	C₂×#10625337	C₂²	1	2	yes	—
13	C₂×#10625335	C₂²	1	2	yes	—
14	C₂×#10625329	C₂²	1	1	yes	characteristic
15	#13094022	—	2	1	no	—
16	#13094022	—	2	1	no	—
17	#13094022	C₂²	1	4	yes	—
18	Q₈×Dic₄₇	C₂²	1	2	yes	—
19	D₄×Dic₄₇	—	2	2	no	—
20	D₄×Dic₄₇	C₂²	1	2	yes	—
21	#13093983	—	2	1	no	—
22	#13093983	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₄	—	2	2	no	—
24	C₂×C₄×Dic₄₇	—	2	1	no	—
25	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
26	Dic₄₇⋊C₈	C₂²	1	4	yes	—
27	#13093949	C₂²	1	4	yes	—
28	#13093948	C₂²	1	4	yes	—
29	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	#137×C₄₇	—	2	4	no	—
32	C₂×Q₁₆×C₄₇	C₂²	1	2	yes	—
33	C₂×SD₁₆×C₄₇	C₂²	1	2	yes	—
34	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
35	#41×C₄₇	—	2	2	no	—
36	#41×C₄₇	D₄	1	4	yes	—
37	C₂×Q₈×C₄₇	—	2	1	no	—
38	C₂×Q₈×C₄₇	—	2	2	no	—
39	C₂×Q₈×C₄₇	—	2	2	no	—
40	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
41	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×D₄×C₄₇	—	2	1	no	—
43	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	—	2	1	no	—
45	C₂²×C₄×C₄₇	—	2	1	no	—
46	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂²×Dic₄₇	—	2	1	no	—
48	C₂²×Dic₄₇	—	2	2	no	—
49	C₂²×Dic₄₇	D₄	1	2	yes	—
50	C₂×Dic₉₄	—	2	2	no	—
51	C₂×Dic₉₄	—	2	2	no	—
52	C₂×Dic₉₄	—	2	1	no	—
53	C₂×Dic₉₄	C₂³	1	2	yes	—
54	Q₁₆×C₄₇	—	2	4	no	—
55	SD₁₆×C₄₇	—	2	4	no	—
56	M₁₆×C₄₇	—	2	2	no	—
57	C₂×C₈×C₄₇	C₂³	1	2	yes	—
58	C₂²⋊Dic₄₇	—	2	1	no	—
59	C₂²⋊Dic₄₇	—	2	2	no	—
60	#10625337	—	2	4	no	—
61	#10625335	—	2	4	no	—
62	C₄⋊Dic₄₇	—	2	2	no	—
63	C₄⋊Dic₄₇	C₂³	1	2	yes	—
64	Dic₄₇⋊C₄	—	2	4	no	—
65	Dic₄₇⋊C₄	—	2	4	no	—
66	C₄×Dic₄₇	—	2	1	no	—
67	C₄×Dic₄₇	—	2	2	no	—
68	C₄×Dic₄₇	D₄	1	1	yes	characteristic
69	C₄×Dic₄₇	D₄	1	1	yes	characteristic
70	C₄×Dic₄₇	C₂³	1	2	yes	—
71	#10625329	—	2	2	no	—
72	C₂×C₄₇⋊C₈	C₂³	1	2	yes	—
73	C₂³×C₄₇	—	2	1	no	—
74	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
75	Q₈×C₄₇	—	2	1	no	—
76	Q₈×C₄₇	—	2	2	no	—
77	Q₈×C₄₇	—	2	2	no	—
78	Q₈×C₄₇	—	4	2	no	—
79	Q₈×C₄₇	C₂×D₄	1	2	yes	—
80	D₄×C₄₇	—	2	4	no	—
81	D₄×C₄₇	—	2	1	no	—
82	D₄×C₄₇	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₄₇	—	2	1	no	—
84	C₂×C₄×C₄₇	—	2	4	no	—
85	C₂×C₄×C₄₇	—	2	2	no	—
86	C₂×C₄×C₄₇	—	4	2	no	—
87	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
89	C₂×C₄×C₄₇	#41	1	2	yes	—
90	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂×Dic₄₇	—	2	4	no	—
92	C₂×Dic₄₇	—	2	2	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	4	4	no	—
96	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
97	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
98	Dic₉₄	—	2	2	no	—
99	Dic₉₄	—	2	2	no	—
100	Dic₉₄	—	4	2	no	—
101	C₈×C₄₇	—	2	2	no	—
102	C₄₇⋊C₈	—	2	2	no	—
103	C₂²×C₄₇	—	2	2	no	—
104	C₂²×C₄₇	—	2	2	no	—
105	C₂²×C₄₇	—	4	2	no	—
106	C₂²×C₄₇	#121	1	2	yes	—
107	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
108	C₄×C₄₇	—	2	2	no	—
109	C₄×C₄₇	—	4	2	no	—
110	C₄×C₄₇	#121	1	2	yes	—
111	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
112	C₄×C₄₇	C₂×#41	1	1	yes	characteristic
113	Dic₄₇	—	2	2	no	—
114	Dic₄₇	—	4	2	no	—
115	Dic₄₇	—	4	2	no	—
116	Dic₄₇	#137	1	4	yes	complemented
117	#3039	—	47	1	no	maximal, Sylow
118	C₂×C₄₇	—	2	2	no	—
119	C₂×C₄₇	—	4	2	no	—
120	C₂×C₄₇	C₂×#121	1	1	yes	characteristic
121	C₂×C₄₇	C₂×#137	1	2	yes	—
122	C₂×#137	—	47	1	no	—
123	C₂×#137	D₄₇	1	1	yes	characteristic
124	C₂×C₄⋊Q₈	—	47	1	no	—
125	C₄×#41	—	47	1	no	—
126	#462	—	47	4	no	—
127	#461	—	47	4	no	—
128	#423	—	47	1	no	—
129	#419	—	47	1	no	—
130	#419	—	47	1	no	—
131	C₄₇	#3039	1	1	yes	characteristic, complemented, Sylow
132	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
133	C₂²×Q₈	—	47	1	no	—
134	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
135	#137	—	2	4	no	—
136	#137	—	94	4	no	—
137	C₂×Q₁₆	—	47	2	no	—
138	C₂×Q₁₆	C₂×D₄₇	1	2	yes	—
139	C₂×SD₁₆	—	47	2	no	—
140	C₂×SD₁₆	C₂×D₄₇	1	2	yes	—
141	C₂×M₁₆	—	47	1	no	—
142	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
143	C₄⋊Q₈	—	47	4	no	—
144	C₄⋊Q₈	—	94	1	no	—
145	C₄⋊Q₈	—	94	1	no	—
146	C₄×Q₈	—	47	2	no	—
147	C₄×D₄	—	47	2	no	—
148	C₄×D₄	—	94	2	no	—
149	#117	—	47	1	no	—
150	#117	—	94	1	no	—
151	C₂×C₄⋊C₄	—	94	2	no	—
152	C₂×C₄²	—	47	1	no	—
153	C₂×C₄²	—	94	1	no	—
154	C₄⋊C₈	—	47	4	no	—
155	#103	—	47	4	no	—
156	#103	—	47	4	no	—
157	#41	—	2	2	no	—
158	#41	C₂²⋊D₄₇	1	4	yes	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	47	2	no	—
163	C₂×Q₈	—	94	1	no	—
164	C₂×Q₈	—	94	2	no	—
165	C₂×Q₈	—	94	2	no	—
166	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
167	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
168	C₂×D₄	—	2	1	no	—
169	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	47	2	no	—
173	C₂²×C₄	—	94	2	no	—
174	C₂²×C₄	—	94	1	no	—
175	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
176	Q₁₆	—	2	4	no	—
177	Q₁₆	—	94	4	no	—
178	SD₁₆	—	2	4	no	—
179	SD₁₆	—	94	4	no	—
180	M₁₆	—	2	2	no	—
181	M₁₆	—	94	2	no	—
182	C₂×C₈	—	47	2	no	—
183	C₂×C₈	C₂²×D₄₇	1	2	yes	—
184	C₄⋊C₄	—	47	2	no	—
185	C₄⋊C₄	—	94	4	no	—
186	C₄⋊C₄	—	94	4	no	—
187	C₄⋊C₄	—	94	2	no	—
188	C₂²⋊C₄	—	94	2	no	—
189	C₂²⋊C₄	—	94	1	no	—
190	C₄²	—	47	1	no	—
191	C₄²	—	47	1	no	—
192	C₄²	—	47	2	no	—
193	C₄²	—	94	2	no	—
194	C₄²	—	94	1	no	—
195	C₂³	—	2	1	no	—
196	C₂³	D₄×D₄₇	1	1	yes	characteristic
197	Q₈	—	2	1	no	—
198	Q₈	—	2	2	no	—
199	Q₈	—	2	2	no	—
200	Q₈	—	4	2	no	—
201	Q₈	—	94	2	no	—
202	Q₈	—	94	2	no	—
203	Q₈	—	188	2	no	—
204	Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
205	D₄	—	2	4	no	—
206	D₄	—	2	1	no	—
207	D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	47	2	no	—
213	C₂×C₄	—	47	2	no	—
214	C₂×C₄	—	94	4	no	—
215	C₂×C₄	—	94	2	no	—
216	C₂×C₄	—	94	2	no	—
217	C₂×C₄	—	188	4	no	—
218	C₂×C₄	—	188	2	no	—
219	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
220	C₂×C₄	#10625352	1	2	yes	—
221	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
222	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	94	2	no	—
225	C₂²	—	2	2	no	—
226	C₂²	—	2	2	no	—
227	C₂²	—	4	2	no	—
228	C₂²	#13093996	1	2	yes	—
229	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
230	C₄	—	2	2	no	—
231	C₄	—	4	2	no	—
232	C₄	—	47	4	no	—
233	C₄	—	94	2	no	—
234	C₄	—	188	2	no	—
235	C₄	—	188	2	no	—
236	C₄	#13093996	1	2	yes	—
237	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
238	C₄	C₂×#10625352	1	1	yes	characteristic
239	C₂	—	2	2	no	—
240	C₂	—	4	2	no	—
241	C₂	C₂×#13093996	1	1	yes	characteristic
242	C₂	#137×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094054

C₂

yes

maximal, characteristic

C₂×#13094022

C₂

yes

maximal, characteristic, complemented

#41×Dic₄₇

C₂

yes

maximal, characteristic

#15689331

C₂

yes

maximal, complemented

#15689326

C₂

yes

maximal, complemented

#15689146

C₂

yes

maximal, characteristic, complemented

#15689133

C₂

yes

maximal, characteristic, complemented

#15689132

C₂

yes

maximal, characteristic, complemented

C₂×#137×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

characteristic

#13094054

—

C₂×#10625337

C₂²

yes

—

C₂×#10625335

C₂²

yes

—

C₂×#10625329

C₂²

yes

—

—

C₂²

yes

—

Q₈×Dic₄₇

C₂²

yes

—

D₄×Dic₄₇

—

D₄×Dic₄₇

C₂²

yes

—

#13093983

—

#13093983

C₂²

yes

characteristic

C₂×Dic₄₇⋊C₄

—

C₂×C₄×Dic₄₇

—

C₂×C₄×Dic₄₇

C₂²

yes

characteristic

Dic₄₇⋊C₈

C₂²

yes

—

#13093949

C₂²

yes

—

#13093948

C₂²

yes

—

C₂×#41×C₄₇

C₂²

yes

characteristic

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

#137×C₄₇

—

C₂×Q₁₆×C₄₇

C₂²

yes

—

C₂×SD₁₆×C₄₇

C₂²

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

#41×C₄₇

D₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂³

yes

—

C₂×Q₈×C₄₇

C₂³

yes

characteristic

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₄

yes

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

C₂³

yes

—

Q₁₆×C₄₇

—

SD₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

#10625337

—

#10625335

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

C₂³

yes

—

#10625329

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

C₂×D₄

yes

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

C₂×D₄

yes

—

Dic₉₄

—

Dic₉₄

—

100

Dic₉₄

—

101

C₈×C₄₇

—

102

C₄₇⋊C₈

—

103

C₂²×C₄₇

—

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

#121

yes

—

107

C₂²×C₄₇

C₂²×D₄

yes

characteristic

108

C₄×C₄₇

—

109

C₄×C₄₇

—

110

C₄×C₄₇

#121

yes

—

111

C₄×C₄₇

C₂²×D₄

yes

characteristic

112

C₄×C₄₇

C₂×#41

yes

characteristic

113

Dic₄₇

—

114

Dic₄₇

—

115

Dic₄₇

—

116

Dic₄₇

yes

117

—

118

C₂×C₄₇

—

119

C₂×C₄₇

—

120

C₂×C₄₇

C₂×#121

yes

characteristic

121

C₂×C₄₇

C₂×#137

yes

—

122

C₂×#137

—

123

C₂×#137

D₄₇

yes

characteristic

124

C₂×C₄⋊Q₈

—

125

C₄×#41

—

126

#462

—

127

#461

—

128

#423

—

129

#419

—

130

#419

—

131

C₄₇

#3039

yes

characteristic, complemented, Sylow

132

C₂×#41

C₂×D₄₇

yes

characteristic

133

C₂²×Q₈

—

134

C₂²×Q₈

C₂×D₄₇

yes

characteristic

135

#137

—

136

#137

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

C₂×D₄₇

yes

—

139

C₂×SD₁₆

—

140

C₂×SD₁₆

C₂×D₄₇

yes

—

141

C₂×M₁₆

—

142

C₂×M₁₆

C₂×D₄₇

yes

characteristic

143

C₄⋊Q₈

—

144

C₄⋊Q₈

—

145

C₄⋊Q₈

—

146

C₄×Q₈

—

147

C₄×D₄

—

148

C₄×D₄

—

149

#117

—

150

#117

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄²

—

153

C₂×C₄²

—

154

C₄⋊C₈

—

155

#103

—

156

#103

—

157

#41

—

158

#41

C₂²⋊D₄₇

yes

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

C₂²×D₄₇

yes

—

167

C₂×Q₈

C₂²×D₄₇

yes

characteristic

168

C₂×D₄

—

169

C₂×D₄

C₂²×D₄₇

yes

characteristic

170

C₂²×C₄

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

—

175

C₂²×C₄

C₂²×D₄₇

yes

characteristic

176

Q₁₆

—

177

Q₁₆

—

178

SD₁₆

—

179

SD₁₆

—

180

M₁₆

—

181

M₁₆

—

182

C₂×C₈

—

183

C₂×C₈

C₂²×D₄₇

yes

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₂²⋊C₄

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

—

194

C₄²

—

195

C₂³

—

196

C₂³

D₄×D₄₇

yes

characteristic

197

Q₈

—

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

Q₈

—

188

—

204

Q₈

C₂×C₂²⋊D₄₇

yes

—

205

D₄

—

206

D₄

—

207

D₄

C₂×C₂²⋊D₄₇

yes

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

188

—

218

C₂×C₄

—

188

—

219

C₂×C₄

D₄×D₄₇

yes

characteristic

220

C₂×C₄

#10625352

yes

—

221

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

222

C₂×C₄

C₂³×D₄₇

yes

characteristic

223

C₈

—

224

C₈

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

#13093996

yes

—

229

C₂²

C₂×D₄×D₄₇

yes

characteristic

230

C₄

—

231

C₄

—

232

C₄

—

233

C₄

—

234

C₄

—

188

—

235

C₄

—

188

—

236

C₄

#13093996

yes

—

237

C₄

C₂²×C₂²⋊D₄₇

yes

characteristic

238

C₄

C₂×#10625352

yes

characteristic

239

C₂

—

240

C₂

—

241

C₂

C₂×#13093996

yes

characteristic

242

C₂

#137×D₄₇

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×#137×C₄₇	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	C₂×#137	D₄₇
hypocenter	C₄₇	#3039
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

subgroup

G/H

center

C₂²

C₂×D₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×#137×C₄₇

C₂

socle

C₂²×C₄₇

C₂²×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#137

N	H ≅ G/N	type
2. C₂×#13094022	C₂	semidirect
4. #15689331	C₂	semidirect
5. #15689326	C₂	semidirect
6. #15689146	C₂	semidirect
7. #15689133	C₂	semidirect
8. #15689132	C₂	semidirect
116. Dic₄₇	#137	semidirect
131. C₄₇	#3039	semidirect

H ≅ G/N

type

2. C₂×#13094022

C₂

semidirect

4. #15689331

C₂

semidirect

5. #15689326

C₂

semidirect

6. #15689146

C₂

semidirect

7. #15689133

C₂

semidirect

8. #15689132

C₂

semidirect

116. Dic₄₇

#137

semidirect

131. C₄₇

#3039

semidirect

Subgroups — #20252873

Conjugacy classes of subgroups

Complements