Group #26134769 — subgroups

Subgroups — #26134769

Order 12032.

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

normal subgroups only

This group has 482 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×#15689507	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688940	C₂	1	2	yes	maximal, complemented
3	C₂×#15688937	C₂	1	2	yes	maximal
4	C₄×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	C₂²×#10625325	—	2	1	no	—
8	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
9	C₂×#13094012	—	2	1	no	—
10	#15689507	—	2	2	no	—
11	#15689507	C₄	1	4	yes	—
12	C₂×#13093960	C₂²	1	2	yes	—
13	C₄×#10625329	—	2	1	no	—
14	#15688940	—	2	4	no	—
15	#15688937	—	2	4	no	—
16	#15688888	—	2	1	no	—
17	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×C₄⋊C₁₆	—	2	2	no	—
20	C₂²×Dic₉₄	—	2	1	no	—
21	C₂²×D₁₈₈	—	2	1	no	—
22	C₂×Dic₁₈₈	—	2	2	no	—
23	C₂×Dic₁₈₈	—	2	2	no	—
24	C₂×Dic₁₈₈	—	2	1	no	—
25	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
26	C₂×#10625325	—	2	4	no	—
27	C₂×#10625325	—	4	4	no	—
28	C₂×D₃₇₆	—	2	2	no	—
29	C₂×D₃₇₆	—	2	2	no	—
30	C₂×D₃₇₆	—	2	1	no	—
31	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
32	C₂×#10625329	—	2	2	no	—
33	#13094012	—	2	4	no	—
34	#13094012	—	4	1	no	—
35	#13094012	—	4	1	no	—
36	C₂×(C₂×D₄₇)⋊C₄	—	4	2	no	—
37	#13093960	—	2	2	no	—
38	#13093960	D₄	1	4	yes	—
39	#13093935	—	4	1	no	—
40	C₄×C₄₇⋊C₈	—	4	1	no	—
41	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
43	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
44	M₃₂×C₄₇	—	2	2	no	—
45	M₃₂×C₄₇	—	2	2	no	—
46	C₂×C₁₆×C₄₇	—	2	2	no	—
47	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
48	C₄×C₈×C₄₇	D₄	1	2	yes	—
49	C₂³×D₄₇	—	4	1	no	—
50	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
51	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₄₇	—	4	1	no	—
53	C₂×D₁₈₈	—	2	2	no	—
54	C₂×D₁₈₈	—	4	2	no	—
55	C₂×D₁₈₈	—	4	2	no	—
56	C₂×D₁₈₈	—	4	1	no	—
57	C₂×Dic₉₄	—	2	2	no	—
58	C₂×Dic₉₄	—	4	2	no	—
59	C₂×Dic₉₄	—	4	2	no	—
60	C₂×Dic₉₄	—	4	1	no	—
61	C₂×C₈×C₄₇	—	2	2	no	—
62	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
65	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₄₇	#41	1	2	yes	—
67	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₄₇	D₈	1	1	yes	characteristic
69	C₄²×C₄₇	D₈	1	1	yes	characteristic
70	(C₂×D₄₇)⋊C₄	—	4	4	no	—
71	(C₂×D₄₇)⋊C₄	—	4	4	no	—
72	#10625329	—	2	4	no	—
73	#10625329	—	4	2	no	—
74	C₂×C₄₇⋊C₈	—	4	2	no	—
75	Dic₁₈₈	—	2	4	no	—
76	Dic₁₈₈	—	4	1	no	—
77	Dic₁₈₈	—	4	1	no	—
78	D₃₇₆	—	2	4	no	—
79	D₃₇₆	—	4	1	no	—
80	D₃₇₆	—	4	1	no	—
81	#10625325	—	4	8	no	—
82	C₁₆×C₄₇	—	4	2	no	—
83	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
84	C₂²×D₄₇	—	4	2	no	—
85	C₂²×D₄₇	—	8	4	no	—
86	C₂²×D₄₇	—	8	2	no	—
87	C₂×C₄×C₄₇	—	4	2	no	—
88	C₂×C₄×C₄₇	#102	1	2	yes	—
89	C₂×C₄×C₄₇	#102	1	2	yes	—
90	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₄₇	#121	1	2	yes	—
92	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
93	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
94	C₂×Dic₄₇	—	4	2	no	—
95	C₂×Dic₄₇	—	8	2	no	—
96	D₁₈₈	—	4	2	no	—
97	D₁₈₈	—	4	2	no	—
98	D₁₈₈	—	8	2	no	—
99	Dic₉₄	—	4	2	no	—
100	Dic₉₄	—	4	2	no	—
101	Dic₉₄	—	8	2	no	—
102	C₈×C₄₇	—	2	2	no	—
103	C₈×C₄₇	C₄×D₄	1	2	yes	—
104	C₈×C₄₇	#124	1	1	yes	characteristic
105	C₈×C₄₇	#127	1	1	yes	characteristic
106	C₄₇⋊C₈	—	4	4	no	—
107	#13258	—	47	1	no	maximal, Sylow
108	C₂²×C₄₇	—	2	2	no	—
109	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
110	C₂²×C₄₇	#460	1	2	yes	—
111	C₂×D₄₇	—	8	4	no	—
112	C₂×D₄₇	—	8	2	no	—
113	C₂×D₄₇	—	16	4	no	—
114	C₄×C₄₇	—	2	2	no	—
115	C₄×C₄₇	—	2	2	no	—
116	C₄×C₄₇	#390	1	1	yes	characteristic
117	C₄×C₄₇	#418	1	1	yes	characteristic
118	C₄×C₄₇	#459	1	2	yes	—
119	Dic₄₇	—	8	2	no	—
120	C₂×#495	—	47	1	no	—
121	#2150	D₄₇	1	1	yes	characteristic, complemented
122	C₂×#362	—	47	2	no	—
123	C₂×#361	—	47	2	no	—
124	C₄×#108	—	47	1	no	—
125	C₂×C₄₇	—	2	2	no	—
126	C₂×C₄₇	#1982	1	1	yes	characteristic
127	C₂×C₄₇	#2148	1	2	yes	—
128	D₄₇	—	16	2	no	—
129	C₂²×Q₁₆	—	47	1	no	—
130	C₂²×SD₁₆	—	94	1	no	—
131	C₂²×D₈	—	47	1	no	—
132	C₂×#124	—	94	1	no	—
133	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
134	#495	—	47	4	no	—
135	#495	—	94	2	no	—
136	C₂×#108	—	47	2	no	—
137	C₄×M₁₆	—	94	1	no	—
138	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
139	C₄⋊C₁₆	—	2	2	no	—
140	#362	—	94	4	no	—
141	#361	—	94	4	no	—
142	#341	—	94	1	no	—
143	C₄₇	#13258	1	1	yes	characteristic, complemented, Sylow
144	C₂²×Q₈	—	94	1	no	—
145	C₂²×D₄	—	94	1	no	—
146	C₂×Q₁₆	—	47	2	no	—
147	C₂×Q₁₆	—	94	2	no	—
148	C₂×Q₁₆	—	94	2	no	—
149	C₂×Q₁₆	—	94	1	no	—
150	C₂×SD₁₆	—	94	4	no	—
151	C₂×SD₁₆	—	188	4	no	—
152	C₂×D₈	—	47	2	no	—
153	C₂×D₈	—	94	2	no	—
154	C₂×D₈	—	94	2	no	—
155	C₂×D₈	—	94	1	no	—
156	C₂×M₁₆	—	94	2	no	—
157	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
158	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
159	#124	—	94	4	no	—
160	#124	—	188	1	no	—
161	#124	—	188	1	no	—
162	C₂×C₂²⋊C₄	—	188	2	no	—
163	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
164	M₃₂	—	2	2	no	—
165	M₃₂	—	2	2	no	—
166	C₂×C₁₆	—	2	2	no	—
167	#108	—	47	4	no	—
168	#108	—	94	2	no	—
169	#97	—	188	1	no	—
170	C₄×C₈	—	188	1	no	—
171	C₄×C₈	C₄×D₄₇	1	2	yes	—
172	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
173	C₂⁴	—	188	1	no	—
174	C₂×Q₈	—	94	2	no	—
175	C₂×Q₈	—	188	2	no	—
176	C₂×Q₈	—	188	2	no	—
177	C₂×Q₈	—	188	1	no	—
178	C₂×D₄	—	94	2	no	—
179	C₂×D₄	—	188	2	no	—
180	C₂×D₄	—	188	1	no	—
181	C₂×D₄	—	188	2	no	—
182	C₂²×C₄	—	188	1	no	—
183	C₂²×C₄	#10625325	1	2	yes	—
184	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
185	Q₁₆	—	94	4	no	—
186	Q₁₆	—	188	1	no	—
187	Q₁₆	—	188	1	no	—
188	SD₁₆	—	188	8	no	—
189	D₈	—	94	4	no	—
190	D₈	—	188	1	no	—
191	D₈	—	188	1	no	—
192	M₁₆	—	94	4	no	—
193	M₁₆	—	188	2	no	—
194	C₂×C₈	—	2	2	no	—
195	C₂×C₈	—	188	2	no	—
196	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
197	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
198	C₂×C₈	D₄×D₄₇	1	2	yes	—
199	C₂×C₈	#10625354	1	2	yes	—
200	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
201	C₂²⋊C₄	—	188	4	no	—
202	C₂²⋊C₄	—	188	4	no	—
203	C₄²	D₃₇₆	1	1	yes	characteristic
204	C₄²	D₃₇₆	1	1	yes	characteristic
205	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
206	C₁₆	—	4	2	no	—
207	C₂³	—	376	4	no	—
208	C₂³	—	376	2	no	—
209	C₂³	—	188	2	no	—
210	C₂³	C₂×#10625325	1	1	yes	characteristic
211	Q₈	—	376	2	no	—
212	Q₈	—	188	2	no	—
213	Q₈	—	188	2	no	—
214	D₄	—	376	2	no	—
215	D₄	—	188	2	no	—
216	D₄	—	188	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	376	2	no	—
219	C₂×C₄	—	188	2	no	—
220	C₂×C₄	#13093946	1	2	yes	—
221	C₂×C₄	#13093946	1	2	yes	—
222	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
223	C₂×C₄	#13093999	1	2	yes	—
224	C₂×C₄	C₂×D₃₇₆	1	1	yes	characteristic
225	C₂×C₄	#13094052	1	2	yes	—
226	C₈	—	2	2	no	—
227	C₈	—	188	4	no	—
228	C₈	#13093986	1	2	yes	—
229	C₈	#13094013	1	1	yes	characteristic
230	C₈	#13094020	1	1	yes	characteristic
231	C₂²	—	2	2	no	—
232	C₂²	—	376	2	no	—
233	C₂²	—	376	4	no	—
234	C₂²	—	752	4	no	—
235	C₂²	C₂×#13093946	1	1	yes	characteristic
236	C₂²	#15689324	1	2	yes	—
237	C₄	—	2	2	no	—
238	C₄	—	2	2	no	—
239	C₄	—	376	2	no	—
240	C₄	#15689024	1	1	yes	characteristic
241	C₄	#15689129	1	1	yes	characteristic
242	C₄	#15689319	1	2	yes	—
243	C₂	—	2	2	no	—
244	C₂	—	752	2	no	—
245	C₂	#20244314	1	1	yes	characteristic
246	C₂	#20245138	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689507

C₂

yes

maximal, characteristic

C₂×#15688940

C₂

yes

maximal, complemented

C₂×#15688937

C₂

yes

maximal

C₄×#13093960

C₂

yes

maximal, characteristic, complemented

C₄₇×#2150

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₈₈

C₂²

yes

characteristic

C₂²×#10625325

—

C₂²×D₃₇₆

C₂²

yes

—

—

C₄

yes

—

C₂×#13093960

C₂²

yes

—

—

—

—

—

C₂×M₃₂×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×C₄⋊C₁₆

—

C₂²×Dic₉₄

—

C₂²×D₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

C₂×#10625325

—

C₂×#10625325

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂×C₄

yes

—

—

—

—

—

C₂×(C₂×D₄₇)⋊C₄

—

#13093960

—

#13093960

D₄

yes

—

#13093935

—

C₄×C₄₇⋊C₈

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

M₃₂×C₄₇

—

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

C₂³×D₄₇

—

C₂²×C₄×C₄₇

SD₁₆

yes

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

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

—

C₄²×C₄₇

C₂²⋊C₄

yes

—

C₄²×C₄₇

D₈

yes

characteristic

C₄²×C₄₇

D₈

yes

characteristic

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

D₃₇₆

—

D₃₇₆

—

D₃₇₆

—

#10625325

—

C₁₆×C₄₇

—

C₂³×C₄₇

C₂×SD₁₆

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

100

Dic₉₄

—

101

Dic₉₄

—

102

C₈×C₄₇

—

103

C₈×C₄₇

C₄×D₄

yes

—

104

C₈×C₄₇

#124

yes

characteristic

105

C₈×C₄₇

#127

yes

characteristic

106

C₄₇⋊C₈

—

107

#13258

—

maximal, Sylow

108

C₂²×C₄₇

—

109

C₂²×C₄₇

C₂×#102

yes

characteristic

110

C₂²×C₄₇

#460

yes

—

111

C₂×D₄₇

—

112

C₂×D₄₇

—

113

C₂×D₄₇

—

114

C₄×C₄₇

—

115

C₄×C₄₇

—

116

C₄×C₄₇

#390

yes

characteristic

117

C₄×C₄₇

#418

yes

characteristic

118

C₄×C₄₇

#459

yes

—

119

Dic₄₇

—

120

C₂×#495

—

121

#2150

D₄₇

yes

characteristic, complemented

122

C₂×#362

—

123

C₂×#361

—

124

C₄×#108

—

125

C₂×C₄₇

—

126

C₂×C₄₇

#1982

yes

characteristic

127

C₂×C₄₇

#2148

yes

—

128

D₄₇

—

129

C₂²×Q₁₆

—

130

C₂²×SD₁₆

—

131

C₂²×D₈

—

132

C₂×#124

—

133

C₂×M₃₂

C₂×D₄₇

yes

—

134

#495

—

135

#495

—

136

C₂×#108

—

137

C₄×M₁₆

—

138

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

139

C₄⋊C₁₆

—

140

#362

—

141

#361

—

142

#341

—

143

C₄₇

#13258

yes

characteristic, complemented, Sylow

144

C₂²×Q₈

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂×Q₁₆

—

150

C₂×SD₁₆

—

151

C₂×SD₁₆

—

188

—

152

C₂×D₈

—

153

C₂×D₈

—

154

C₂×D₈

—

155

C₂×D₈

—

156

C₂×M₁₆

—

157

C₂²×C₈

D₁₈₈

yes

characteristic

158

C₂²×C₈

C₂²×D₄₇

yes

characteristic

159

#124

—

160

#124

—

188

—

161

#124

—

188

—

162

C₂×C₂²⋊C₄

—

188

—

163

C₂×C₄²

D₁₈₈

yes

characteristic

164

M₃₂

—

165

M₃₂

—

166

C₂×C₁₆

—

167

#108

—

168

#108

—

169

#97

—

188

—

170

C₄×C₈

—

188

—

171

C₄×C₈

C₄×D₄₇

yes

—

172

C₄×C₈

C₂²⋊D₄₇

yes

—

173

C₂⁴

—

188

—

174

C₂×Q₈

—

175

C₂×Q₈

—

188

—

176

C₂×Q₈

—

188

—

177

C₂×Q₈

—

188

—

178

C₂×D₄

—

179

C₂×D₄

—

188

—

180

C₂×D₄

—

188

—

181

C₂×D₄

—

188

—

182

C₂²×C₄

—

188

—

183

C₂²×C₄

#10625325

yes

—

184

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

185

Q₁₆

—

186

Q₁₆

—

188

—

187

Q₁₆

—

188

—

188

SD₁₆

—

188

—

189

D₈

—

190

D₈

—

188

—

191

D₈

—

188

—

192

M₁₆

—

193

M₁₆

—

188

—

194

C₂×C₈

—

195

C₂×C₈

—

188

—

196

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

197

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

198

C₂×C₈

D₄×D₄₇

yes

—

199

C₂×C₈

#10625354

yes

—

200

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

201

C₂²⋊C₄

—

188

—

202

C₂²⋊C₄

—

188

—

203

C₄²

D₃₇₆

yes

characteristic

204

C₄²

D₃₇₆

yes

characteristic

205

C₄²

(C₂×D₄₇)⋊C₄

yes

—

206

C₁₆

—

207

C₂³

—

376

—

208

C₂³

—

376

—

209

C₂³

—

188

—

210

C₂³

C₂×#10625325

yes

characteristic

211

Q₈

—

376

—

212

Q₈

—

188

—

213

Q₈

—

188

—

214

D₄

—

376

—

215

D₄

—

188

—

216

D₄

—

188

—

217

C₂×C₄

—

218

C₂×C₄

—

376

—

219

C₂×C₄

—

188

—

220

C₂×C₄

#13093946

yes

—

221

C₂×C₄

#13093946

yes

—

222

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

223

C₂×C₄

#13093999

yes

—

224

C₂×C₄

C₂×D₃₇₆

yes

characteristic

225

C₂×C₄

#13094052

yes

—

226

C₈

—

227

C₈

—

188

—

228

C₈

#13093986

yes

—

229

C₈

#13094013

yes

characteristic

230

C₈

#13094020

yes

characteristic

231

C₂²

—

232

C₂²

—

376

—

233

C₂²

—

376

—

234

C₂²

—

752

—

235

C₂²

C₂×#13093946

yes

characteristic

236

C₂²

#15689324

yes

—

237

C₄

—

238

C₄

—

239

C₄

—

376

—

240

C₄

#15689024

yes

characteristic

241

C₄

#15689129

yes

characteristic

242

C₄

#15689319

yes

—

243

C₂

—

244

C₂

—

752

—

245

C₂

#20244314

yes

characteristic

246

C₂

#20245138

yes

—

	subgroup	G/H
center	C₂²	C₂×#13093946
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#2150	C₂
socle	C₂²×C₄₇	C₂×#102
prime radical	C₂²×D₃₇₆	C₂²
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#2150	D₄₇
hypocenter	C₄₇	#13258
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

subgroup

G/H

center

C₂²

C₂×#13093946

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₄₇×#2150

C₂

socle

C₂²×C₄₇

C₂×#102

prime radical

C₂²×D₃₇₆

C₂²

cosocle

C₂²×C₈×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

N	H ≅ G/N	type
2. C₂×#15688940	C₂	semidirect
4. C₄×#13093960	C₂	semidirect
5. C₄₇×#2150	C₂	semidirect
121. #2150	D₄₇	semidirect
143. C₄₇	#13258	semidirect

H ≅ G/N

type

2. C₂×#15688940

C₂

semidirect

4. C₄×#13093960

C₂

semidirect

5. C₄₇×#2150

C₂

semidirect

121. #2150

D₄₇

semidirect

143. C₄₇

#13258

semidirect

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

subgroup	index
C₂×#15689507	2
C₂×#15688940	2
C₂×#15688937	2
C₄×#13093960	2
C₄₇×#2150	2
#13258	47

subgroup

index

C₄₇×#2150

Subgroups — #26134769

Conjugacy classes of subgroups

Complements

Maximal subgroups