Group #26133727 — subgroups

Subgroups — #26133727

Order 12032.

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

normal subgroups only

This group has 490 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	#20253036	C₂	1	1	yes	maximal, characteristic
2	#20245105	C₂	1	2	yes	maximal, complemented
3	#20243434	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241490	C₂	1	2	yes	maximal, complemented
5	C₄₇×#3407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
7	#15689687	—	2	1	no	—
8	#15689376	C₄	1	4	yes	complemented
9	#15689359	—	2	2	no	—
10	#15689161	C₂²	1	2	yes	—
11	#15689161	C₂²	1	1	yes	characteristic
12	#15689129	—	2	1	no	—
13	#15689097	—	2	1	no	—
14	#15688925	—	2	4	no	—
15	#15688880	—	2	1	no	—
16	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#504	—	2	4	no	—
18	C₂×M₃₂×C₄₇	—	2	2	no	—
19	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
20	C₂²×D₁₈₈	—	2	1	no	—
21	C₂×D₃₇₆	—	2	2	no	—
22	C₂×D₃₇₆	—	2	2	no	—
23	C₂×D₃₇₆	—	2	1	no	—
24	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
25	#13094020	—	4	1	no	—
26	#13094013	—	4	1	no	—
27	#13093998	—	2	4	no	—
28	#13093992	—	4	2	no	—
29	#13093983	—	2	1	no	—
30	#13093983	—	2	2	no	—
31	#13093958	—	2	1	no	—
32	#13093958	—	2	2	no	—
33	#13093956	—	2	2	no	—
34	#13093956	C₂×C₄	1	2	yes	—
35	#13093946	—	2	4	no	—
36	#13093939	—	4	2	no	—
37	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
38	#131×C₄₇	—	2	2	no	—
39	#131×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	D₄	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	M₃₂×C₄₇	—	2	4	no	—
45	M₃₂×C₄₇	—	2	2	no	—
46	M₃₂×C₄₇	—	2	2	no	—
47	C₂×C₁₆×C₄₇	—	2	4	no	—
48	C₂×C₁₆×C₄₇	D₄	1	4	yes	complemented
49	C₂³×D₄₇	—	4	1	no	—
50	#41×C₄₇	—	2	2	no	—
51	#41×C₄₇	—	2	2	no	—
52	C₂×Q₈×C₄₇	SD₁₆	1	1	yes	characteristic
53	C₂×D₄×C₄₇	D₈	1	2	yes	—
54	C₂×D₄×C₄₇	SD₁₆	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂×C₂²⋊D₄₇	—	4	4	no	—
58	C₂×D₁₈₈	—	2	2	no	—
59	C₂×D₁₈₈	—	4	2	no	—
60	C₂×D₁₈₈	—	4	2	no	—
61	C₂×D₁₈₈	—	4	1	no	—
62	M₁₆×C₄₇	—	2	2	no	—
63	M₁₆×C₄₇	—	2	4	no	—
64	C₂×C₈×C₄₇	—	2	2	no	—
65	C₂×C₈×C₄₇	—	2	2	no	—
66	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₄₇	#41	1	2	yes	—
71	C₂²⋊Dic₄₇	—	4	1	no	—
72	C₂²⋊Dic₄₇	—	4	2	no	—
73	(C₂×D₄₇)⋊C₄	—	4	4	no	—
74	C₄⋊Dic₄₇	—	2	2	no	—
75	C₄⋊Dic₄₇	—	4	2	no	—
76	C₄×Dic₄₇	—	4	1	no	—
77	C₄×Dic₄₇	—	4	2	no	—
78	D₃₇₆	—	2	4	no	—
79	D₃₇₆	—	4	1	no	—
80	D₃₇₆	—	4	1	no	—
81	C₁₆×C₄₇	—	2	4	no	—
82	C₂³×C₄₇	#102	1	2	yes	—
83	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
84	C₂²×D₄₇	—	4	2	no	—
85	C₂²×D₄₇	—	8	2	no	—
86	C₂²×D₄₇	—	16	2	no	—
87	Q₈×C₄₇	—	2	2	no	—
88	D₄×C₄₇	—	2	4	no	—
89	D₄×C₄₇	—	2	2	no	—
90	C₂×C₄×C₄₇	—	2	2	no	—
91	C₂×C₄×C₄₇	—	2	2	no	—
92	C₂×C₄×C₄₇	#102	1	2	yes	—
93	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₄₇	#121	1	2	yes	—
95	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
96	C₂×C₄×C₄₇	#135	1	2	yes	—
97	C₂²⋊D₄₇	—	16	4	no	—
98	C₂×Dic₄₇	—	4	2	no	—
99	C₂×Dic₄₇	—	8	2	no	—
100	D₁₈₈	—	4	2	no	—
101	D₁₈₈	—	4	2	no	—
102	D₁₈₈	—	8	2	no	—
103	C₈×C₄₇	—	2	2	no	—
104	C₈×C₄₇	C₄×D₄	1	2	yes	—
105	C₈×C₄₇	#120	1	1	yes	characteristic
106	C₈×C₄₇	#123	1	1	yes	characteristic
107	#13074	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	—	2	2	no	—
109	C₂²×C₄₇	—	4	1	no	—
110	C₂²×C₄₇	—	4	2	no	—
111	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
112	C₂²×C₄₇	#466	1	2	yes	—
113	C₂×D₄₇	—	8	4	no	—
114	C₂×D₄₇	—	8	2	no	—
115	C₂×D₄₇	—	16	4	no	—
116	C₄×C₄₇	—	2	2	no	—
117	C₄×C₄₇	#386	1	1	yes	characteristic
118	C₄×C₄₇	#416	1	1	yes	characteristic
119	C₄×C₄₇	#465	1	2	yes	—
120	Dic₄₇	—	8	2	no	—
121	Dic₄₇	—	16	2	no	—
122	#3407	D₄₇	1	1	yes	characteristic, complemented
123	#3058	—	47	1	no	—
124	#2140	—	47	2	no	—
125	#1812	—	47	1	no	—
126	#1384	—	47	2	no	—
127	C₂×C₄₇	—	2	1	no	—
128	C₂×C₄₇	—	2	2	no	—
129	C₂×C₄₇	—	4	2	no	—
130	C₂×C₄₇	#1893	1	1	yes	characteristic
131	D₄₇	—	16	2	no	—
132	C₂²×D₈	—	47	1	no	—
133	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
134	#535	—	94	1	no	—
135	#504	—	2	4	no	—
136	C₂×M₃₂	—	2	2	no	—
137	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
138	#469	—	47	4	no	—
139	#466	—	94	2	no	—
140	#427	—	47	1	no	—
141	#427	—	47	2	no	—
142	#418	—	94	1	no	—
143	#410	—	94	1	no	—
144	#357	—	94	4	no	—
145	H(3,ℤ/4)	—	94	1	no	—
146	C₄₇	#13074	1	1	yes	characteristic, complemented, Sylow
147	C₂×#41	D₁₈₈	1	1	yes	characteristic
148	C₂²×D₄	—	94	1	no	—
149	C₂×D₈	—	47	2	no	—
150	C₂×D₈	—	94	2	no	—
151	C₂×D₈	—	94	2	no	—
152	C₂×D₈	—	94	1	no	—
153	#131	—	2	2	no	—
154	#131	—	2	2	no	—
155	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
156	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
157	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
158	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
159	#127	—	188	1	no	—
160	#124	—	188	1	no	—
161	#121	—	94	4	no	—
162	#120	—	188	2	no	—
163	#117	—	94	1	no	—
164	#117	—	94	2	no	—
165	M₃₂	—	2	4	no	—
166	M₃₂	—	2	2	no	—
167	M₃₂	—	2	2	no	—
168	C₂×C₁₆	—	2	4	no	—
169	C₂×C₁₆	C₂²⋊D₄₇	1	4	yes	complemented
170	#107	—	94	1	no	—
171	#107	—	94	2	no	—
172	#106	—	47	2	no	—
173	#106	—	94	2	no	—
174	#102	—	94	4	no	—
175	#99	—	188	2	no	—
176	C₂⁴	—	188	1	no	—
177	#41	—	2	2	no	—
178	#41	—	2	2	no	—
179	C₂×Q₈	#10625325	1	1	yes	characteristic
180	C₂×D₄	—	94	2	no	—
181	C₂×D₄	—	188	4	no	—
182	C₂×D₄	—	188	2	no	—
183	C₂×D₄	—	188	1	no	—
184	C₂×D₄	—	188	2	no	—
185	C₂×D₄	#10625325	1	1	yes	characteristic
186	C₂×D₄	D₃₇₆	1	2	yes	—
187	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
188	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
189	D₈	—	94	4	no	—
190	D₈	—	188	1	no	—
191	D₈	—	188	1	no	—
192	M₁₆	—	2	2	no	—
193	M₁₆	—	2	4	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
198	C₂×C₈	#10625350	1	2	yes	—
199	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
200	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	C₄⋊C₄	—	94	2	no	—
202	C₄⋊C₄	—	188	2	no	—
203	C₂²⋊C₄	—	188	2	no	—
204	C₂²⋊C₄	—	188	1	no	—
205	C₂²⋊C₄	—	188	4	no	—
206	C₄²	—	188	2	no	—
207	C₄²	—	188	1	no	—
208	C₁₆	—	2	4	no	—
209	C₂³	—	376	2	no	—
210	C₂³	—	188	2	no	—
211	C₂³	—	752	2	no	—
212	C₂³	#13093946	1	2	yes	—
213	C₂³	C₂×D₃₇₆	1	1	yes	characteristic
214	Q₈	—	2	2	no	—
215	D₄	—	2	4	no	—
216	D₄	—	2	2	no	—
217	D₄	—	376	2	no	—
218	D₄	—	188	2	no	—
219	D₄	—	188	2	no	—
220	D₄	—	752	4	no	—
221	C₂×C₄	—	2	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	376	2	no	—
224	C₂×C₄	—	188	2	no	—
225	C₂×C₄	#13093946	1	2	yes	—
226	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
227	C₂×C₄	#13093998	1	2	yes	—
228	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
229	C₂×C₄	#13094046	1	2	yes	—
230	C₈	—	2	2	no	—
231	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
232	C₈	#13093993	1	1	yes	characteristic
233	C₈	#13094007	1	1	yes	characteristic
234	C₂²	—	2	2	no	—
235	C₂²	—	4	1	no	—
236	C₂²	—	4	2	no	—
237	C₂²	—	376	4	no	—
238	C₂²	—	376	2	no	—
239	C₂²	—	752	4	no	—
240	C₂²	C₂×#13093946	1	1	yes	characteristic
241	C₂²	#15689359	1	2	yes	—
242	C₄	—	2	2	no	—
243	C₄	—	376	2	no	—
244	C₄	—	752	2	no	—
245	C₄	#15689002	1	1	yes	characteristic
246	C₄	#15689120	1	1	yes	characteristic
247	C₄	#15689352	1	2	yes	—
248	C₂	—	2	1	no	—
249	C₂	—	2	2	no	—
250	C₂	—	4	2	no	—
251	C₂	—	752	2	no	—
252	C₂	#20243816	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20253036

C₂

yes

maximal, characteristic

#20245105

C₂

yes

maximal, complemented

#20243434

C₂

yes

maximal, characteristic, complemented

#20241490

C₂

yes

maximal, complemented

C₄₇×#3407

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₇₆

C₂²

yes

characteristic

#15689687

—

#15689376

C₄

yes

complemented

#15689359

—

#15689161

C₂²

yes

—

#15689161

C₂²

yes

—

—

—

—

C₂×#131×C₄₇

C₂²

yes

characteristic

C₄₇×#504

—

C₂×M₃₂×C₄₇

—

C₂×M₃₂×C₄₇

C₂²

yes

—

C₂²×D₁₈₈

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂×C₄

yes

—

—

—

—

—

—

—

—

—

—

C₂×C₄

yes

—

#13093946

—

#13093939

—

C₂×#41×C₄₇

D₄

yes

characteristic

#131×C₄₇

—

#131×C₄₇

—

C₂×M₁₆×C₄₇

C₂×C₄

yes

—

C₂×M₁₆×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

D₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

D₄

yes

complemented

C₂³×D₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

SD₁₆

yes

characteristic

C₂×D₄×C₄₇

D₈

yes

—

C₂×D₄×C₄₇

SD₁₆

yes

characteristic

C₂²×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂²⋊C₄

yes

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

—

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

#41

yes

—

C₂²⋊Dic₄₇

—

C₂²⋊Dic₄₇

—

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

C₁₆×C₄₇

—

C₂³×C₄₇

#102

yes

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

#135

yes

—

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

100

D₁₈₈

—

101

D₁₈₈

—

102

D₁₈₈

—

103

C₈×C₄₇

—

104

C₈×C₄₇

C₄×D₄

yes

—

105

C₈×C₄₇

#120

yes

characteristic

106

C₈×C₄₇

yes

107

—

108

C₂²×C₄₇

—

109

C₂²×C₄₇

—

110

C₂²×C₄₇

—

111

C₂²×C₄₇

C₂×#102

yes

characteristic

112

C₂²×C₄₇

#466

yes

—

113

C₂×D₄₇

—

114

C₂×D₄₇

—

115

C₂×D₄₇

—

116

C₄×C₄₇

—

117

C₄×C₄₇

#386

yes

characteristic

118

C₄×C₄₇

#416

yes

characteristic

119

C₄×C₄₇

#465

yes

—

120

Dic₄₇

—

121

Dic₄₇

—

122

#3407

D₄₇

yes

characteristic, complemented

123

#3058

—

124

#2140

—

125

#1812

—

126

#1384

—

127

C₂×C₄₇

—

128

C₂×C₄₇

—

129

C₂×C₄₇

—

130

C₂×C₄₇

#1893

yes

characteristic

131

D₄₇

—

132

C₂²×D₈

—

133

C₂×#131

C₂×D₄₇

yes

characteristic

134

#535

—

135

#504

—

136

C₂×M₃₂

—

137

C₂×M₃₂

C₂×D₄₇

yes

—

138

#469

—

139

#466

—

140

#427

—

141

#427

—

142

#418

—

143

#410

—

144

#357

—

145

H(3,ℤ/4)

—

146

C₄₇

#13074

yes

characteristic, complemented, Sylow

147

C₂×#41

D₁₈₈

yes

characteristic

148

C₂²×D₄

—

149

C₂×D₈

—

150

C₂×D₈

—

151

C₂×D₈

—

152

C₂×D₈

—

153

#131

—

154

#131

—

155

C₂×M₁₆

C₄×D₄₇

yes

—

156

C₂×M₁₆

D₁₈₈

yes

characteristic

157

C₂²×C₈

C₂²⋊D₄₇

yes

—

158

C₂²×C₈

C₂²×D₄₇

yes

characteristic

159

#127

—

188

—

160

#124

—

188

—

161

#121

—

162

#120

—

188

—

163

#117

—

164

#117

—

165

M₃₂

—

166

M₃₂

—

167

M₃₂

—

168

C₂×C₁₆

—

169

C₂×C₁₆

C₂²⋊D₄₇

yes

complemented

170

#107

—

171

#107

—

172

#106

—

173

#106

—

174

#102

—

175

#99

—

188

—

176

C₂⁴

—

188

—

177

#41

—

178

#41

—

179

C₂×Q₈

#10625325

yes

characteristic

180

C₂×D₄

—

181

C₂×D₄

—

188

—

182

C₂×D₄

—

188

—

183

C₂×D₄

—

188

—

184

C₂×D₄

—

188

—

185

C₂×D₄

#10625325

yes

characteristic

186

C₂×D₄

D₃₇₆

yes

—

187

C₂²×C₄

(C₂×D₄₇)⋊C₄

yes

—

188

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

189

D₈

—

190

D₈

—

188

—

191

D₈

—

188

—

192

M₁₆

—

193

M₁₆

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

197

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

198

C₂×C₈

#10625350

yes

—

199

C₂×C₈

C₂×C₂²⋊D₄₇

yes

—

200

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

201

C₄⋊C₄

—

202

C₄⋊C₄

—

188

—

203

C₂²⋊C₄

—

188

—

204

C₂²⋊C₄

—

188

—

205

C₂²⋊C₄

—

188

—

206

C₄²

—

188

—

207

C₄²

—

188

—

208

C₁₆

—

209

C₂³

—

376

—

210

C₂³

—

188

—

211

C₂³

—

752

—

212

C₂³

#13093946

yes

—

213

C₂³

C₂×D₃₇₆

yes

characteristic

214

Q₈

—

215

D₄

—

216

D₄

—

217

D₄

—

376

—

218

D₄

—

188

—

219

D₄

—

188

—

220

D₄

—

752

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

376

—

224

C₂×C₄

—

188

—

225

C₂×C₄

#13093946

yes

—

226

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

227

C₂×C₄

#13093998

yes

—

228

C₂×C₄

C₂×#10625325

yes

characteristic

229

C₂×C₄

#13094046

yes

—

230

C₈

—

231

C₈

C₄×C₂²⋊D₄₇

yes

—

232

C₈

#13093993

yes

characteristic

233

C₈

#13094007

yes

characteristic

234

C₂²

—

235

C₂²

—

236

C₂²

—

237

C₂²

—

376

—

238

C₂²

—

376

—

239

C₂²

—

752

—

240

C₂²

C₂×#13093946

yes

characteristic

241

C₂²

#15689359

yes

—

242

C₄

—

243

C₄

—

376

—

244

C₄

—

752

—

245

C₄

#15689002

yes

characteristic

246

C₄

#15689120

yes

characteristic

247

C₄

#15689352

yes

—

248

C₂

—

249

C₂

—

250

C₂

—

251

C₂

—

752

—

252

C₂

#20243816

yes

characteristic

	subgroup	G/H
center	C₂	#20243816
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#3407	C₂
socle	C₂×C₄₇	#1893
prime radical	#20253036	C₂
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#3407	D₄₇
hypocenter	C₄₇	#13074
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

subgroup

G/H

center

C₂

#20243816

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#3407

C₂

C₂×C₄₇

C₂

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#131 ◁ #3407

N	H ≅ G/N	type
2. #20245105	C₂	semidirect
3. #20243434	C₂	semidirect
4. #20241490	C₂	semidirect
5. C₄₇×#3407	C₂	semidirect
8. #15689376	C₄	semidirect
48. C₂×C₁₆×C₄₇	D₄	semidirect
122. #3407	D₄₇	semidirect
146. C₄₇	#13074	semidirect
169. C₂×C₁₆	C₂²⋊D₄₇	semidirect

H ≅ G/N

type

2. #20245105

C₂

semidirect

3. #20243434

C₂

semidirect

4. #20241490

C₂

semidirect

5. C₄₇×#3407

C₂

semidirect

8. #15689376

C₄

semidirect

48. C₂×C₁₆×C₄₇

D₄

semidirect

122. #3407

D₄₇

semidirect

146. C₄₇

#13074

semidirect

169. C₂×C₁₆

C₂²⋊D₄₇

semidirect

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

subgroup	index
#20253036	2
#20245105	2
#20243434	2
#20241490	2
C₄₇×#3407	2
#13074	47

subgroup

index

C₄₇×#3407

Subgroups — #26133727

Conjugacy classes of subgroups

Complements

Maximal subgroups