Group #26134678 — subgroups

Subgroups — #26134678

Order 12032.

430 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 139 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×#15688951	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688927	C₂	1	2	yes	maximal
3	C₂×#15688898	C₂	1	1	yes	maximal, characteristic
4	#20244250	C₂	1	2	yes	maximal
5	C₂²×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#13093958	C₂²	1	2	yes	—
8	C₂×#13093948	—	2	2	no	—
9	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
10	#15689030	—	2	2	no	—
11	#15688951	—	2	2	no	—
12	#15688927	—	2	4	no	—
13	#15688898	—	2	2	no	—
14	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂×Q₃₂×C₄₇	—	2	2	no	—
16	C₂×Q₃₂×C₄₇	—	2	2	no	—
17	C₂×Q₃₂×C₄₇	C₄	1	4	yes	complemented
18	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₄₇	—	2	2	no	—
21	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
22	C₂×C₄₇⋊C₁₆	—	2	1	no	—
23	C₂×C₄₇⋊C₁₆	—	2	1	no	—
24	C₂×C₄₇⋊C₁₆	D₄	1	2	yes	—
25	#13093958	—	2	2	no	—
26	#13093958	—	2	2	no	—
27	#13093948	—	4	4	no	—
28	C₈×Dic₄₇	—	2	1	no	—
29	C₈×Dic₄₇	—	2	1	no	—
30	C₄₇⋊#95	—	4	4	no	—
31	C₂²×Q₈×C₄₇	—	2	2	no	—
32	C₂×Q₁₆×C₄₇	—	2	2	no	—
33	C₂×Q₁₆×C₄₇	—	2	2	no	—
34	C₂×Q₁₆×C₄₇	—	2	2	no	—
35	C₂×Q₁₆×C₄₇	—	2	2	no	—
36	C₂×Q₁₆×C₄₇	—	2	2	no	—
37	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
39	Q₃₂×C₄₇	—	2	8	no	—
40	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
42	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
43	C₂×Q₈×C₄₇	—	2	4	no	—
44	C₂×Q₈×C₄₇	—	4	2	no	—
45	C₂×Q₈×C₄₇	—	4	2	no	—
46	C₂×Q₈×C₄₇	—	4	2	no	—
47	C₂×Q₈×C₄₇	—	4	2	no	—
48	C₂×Q₈×C₄₇	—	4	2	no	—
49	C₂²×C₄×C₄₇	—	4	2	no	—
50	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₄₇	—	4	2	no	—
52	C₂²×Dic₄₇	D₈	1	2	yes	—
53	Q₁₆×C₄₇	—	2	4	no	—
54	Q₁₆×C₄₇	—	2	4	no	—
55	Q₁₆×C₄₇	—	4	2	no	—
56	Q₁₆×C₄₇	—	4	2	no	—
57	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
62	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
63	C₄⋊Dic₄₇	—	4	2	no	—
64	C₄⋊Dic₄₇	—	4	2	no	—
65	C₄×Dic₄₇	—	2	1	no	—
66	C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄₇⋊C₈	—	2	1	no	—
68	C₂×C₄₇⋊C₈	—	2	1	no	—
69	C₂×C₄₇⋊C₈	D₈	1	2	yes	—
70	C₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
71	C₄₇⋊C₁₆	—	2	2	no	—
72	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₄₇	—	4	4	no	—
74	Q₈×C₄₇	—	4	4	no	—
75	Q₈×C₄₇	—	8	2	no	—
76	Q₈×C₄₇	—	8	2	no	—
77	C₂×C₄×C₄₇	—	4	4	no	—
78	C₂×C₄×C₄₇	—	8	2	no	—
79	C₂×C₄×C₄₇	—	8	2	no	—
80	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
82	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
83	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
85	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
86	C₂×Dic₄₇	—	2	2	no	—
87	C₂×Dic₄₇	—	2	4	no	—
88	C₂×Dic₄₇	—	8	2	no	—
89	C₂×Dic₄₇	—	8	4	no	—
90	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
92	C₈×C₄₇	#121	1	1	yes	characteristic
93	C₈×C₄₇	#124	1	1	yes	characteristic
94	C₄₇⋊C₈	—	2	2	no	—
95	#13240	—	47	1	no	maximal, Sylow
96	C₂²×C₄₇	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₄₇	#466	1	1	yes	characteristic
98	C₂²×C₄₇	#493	1	1	yes	characteristic
99	C₂²×C₄₇	#510	1	4	yes	—
100	C₄×C₄₇	—	8	4	no	—
101	C₄×C₄₇	#390	1	1	yes	characteristic
102	C₄×C₄₇	C₄×D₈	1	1	yes	characteristic
103	C₄×C₄₇	#466	1	1	yes	characteristic
104	C₄×C₄₇	#495	1	1	yes	characteristic
105	Dic₄₇	—	4	2	no	—
106	Dic₄₇	—	16	2	no	—
107	C₂²×Q₃₂	D₄₇	1	1	yes	characteristic
108	C₂×#367	—	47	1	no	—
109	C₂×#358	—	47	2	no	—
110	C₂×#346	—	47	1	no	—
111	#1969	—	47	2	no	—
112	C₂×C₄₇	#1970	1	1	yes	characteristic
113	C₂×C₄₇	#2176	1	2	yes	—
114	C₂×C₄₇	#2219	1	2	yes	—
115	C₂×C₄₇	#2251	1	2	yes	—
116	C₂²×Q₁₆	C₂×D₄₇	1	2	yes	—
117	C₂×Q₃₂	—	2	2	no	—
118	C₂×Q₃₂	—	2	2	no	—
119	C₂×Q₃₂	Dic₄₇	1	4	yes	complemented
120	C₂²×C₁₆	—	47	1	no	—
121	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
122	C₂×#107	—	47	2	no	—
123	C₂×#103	—	94	2	no	—
124	C₂×C₄×C₈	—	47	1	no	—
125	#391	—	94	2	no	—
126	#367	—	94	2	no	—
127	#358	—	94	4	no	—
128	#346	—	94	2	no	—
129	C₄₇	#13240	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₈	—	2	2	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
137	C₂²×C₈	—	47	1	no	—
138	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	94	2	no	—
140	C₂×C₄²	—	47	1	no	—
141	Q₃₂	—	2	8	no	—
142	C₂×C₁₆	—	47	2	no	—
143	C₂×C₁₆	—	94	1	no	—
144	C₂×C₁₆	—	94	1	no	—
145	C₂×C₁₆	C₂×Dic₄₇	1	2	yes	—
146	C₂×C₁₆	C₂²⋊D₄₇	1	2	yes	—
147	C₂×C₁₆	C₂²⋊D₄₇	1	2	yes	—
148	#107	—	94	2	no	—
149	#107	—	94	2	no	—
150	#103	—	188	4	no	—
151	C₄×C₈	—	94	1	no	—
152	C₄×C₈	—	94	1	no	—
153	#95	—	188	4	no	—
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	2	no	—
157	C₂×Q₈	—	4	2	no	—
158	C₂×Q₈	—	4	2	no	—
159	C₂×Q₈	—	4	2	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	—	47	2	no	—
162	C₂²×C₄	—	188	2	no	—
163	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
164	Q₁₆	—	2	4	no	—
165	Q₁₆	—	2	4	no	—
166	Q₁₆	—	4	2	no	—
167	Q₁₆	—	4	2	no	—
168	C₂×C₈	—	47	2	no	—
169	C₂×C₈	—	94	1	no	—
170	C₂×C₈	—	94	1	no	—
171	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
172	C₂×C₈	#10625352	1	1	yes	characteristic
173	C₂×C₈	#10625352	1	1	yes	characteristic
174	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
175	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
176	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
177	C₄⋊C₄	—	188	2	no	—
178	C₄⋊C₄	—	188	2	no	—
179	C₄²	—	94	1	no	—
180	C₄²	—	94	1	no	—
181	C₁₆	—	94	2	no	—
182	C₁₆	C₂²⋊Dic₄₇	1	4	yes	—
183	C₂³	D₈×D₄₇	1	1	yes	characteristic
184	Q₈	—	4	4	no	—
185	Q₈	—	4	4	no	—
186	Q₈	—	8	2	no	—
187	Q₈	—	8	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	—	94	4	no	—
192	C₂×C₄	—	94	2	no	—
193	C₂×C₄	—	376	2	no	—
194	C₂×C₄	—	376	4	no	—
195	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
196	C₂×C₄	#13093995	1	1	yes	characteristic
197	C₂×C₄	#13094020	1	1	yes	characteristic
198	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
199	C₂×C₄	#13094043	1	1	yes	characteristic
200	C₂×C₄	#13094043	1	1	yes	characteristic
201	C₈	—	94	2	no	—
202	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
203	C₈	D₄×Dic₄₇	1	1	yes	characteristic
204	C₈	#13093995	1	1	yes	characteristic
205	C₈	#13094011	1	1	yes	characteristic
206	C₂²	D₈×Dic₄₇	1	1	yes	characteristic
207	C₂²	#15689356	1	1	yes	characteristic
208	C₂²	#15689498	1	1	yes	characteristic
209	C₂²	#15689565	1	4	yes	—
210	C₄	—	8	4	no	—
211	C₄	—	188	2	no	—
212	C₄	—	752	2	no	—
213	C₄	#15689026	1	1	yes	characteristic
214	C₄	D₈×Dic₄₇	1	1	yes	characteristic
215	C₄	#15689356	1	1	yes	characteristic
216	C₄	#15689506	1	1	yes	characteristic
217	C₂	#20244255	1	1	yes	characteristic
218	C₂	#20245259	1	2	yes	—
219	C₂	#20245493	1	2	yes	—
220	C₂	#20245656	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15688951

C₂

yes

maximal, characteristic

C₂×#15688927

C₂

yes

maximal

C₂×#15688898

C₂

yes

maximal, characteristic

#20244250

C₂

yes

maximal

C₂²×Q₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×#13093958

C₂²

yes

—

C₂×#13093948

—

C₂×C₈×Dic₄₇

C₂²

yes

—

—

—

—

C₂²×Q₁₆×C₄₇

C₂²

yes

—

C₂×Q₃₂×C₄₇

—

C₂×Q₃₂×C₄₇

—

C₂×Q₃₂×C₄₇

C₄

yes

complemented

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₂²×C₄₇⋊C₈

D₄

yes

characteristic

C₂×C₄⋊Dic₄₇

—

C₂×C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

—

C₂×C₄₇⋊C₁₆

D₄

yes

—

#13093958

—

#13093958

—

#13093948

—

C₈×Dic₄₇

—

C₈×Dic₄₇

—

C₄₇⋊#95

—

C₂²×Q₈×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

C₂×C₄

yes

—

C₂²×C₈×C₄₇

C₂³

yes

characteristic

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₁₆×C₄₇

D₄

yes

—

C₂×C₁₆×C₄₇

D₄

yes

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

D₈

yes

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

characteristic

C₂×C₈×C₄₇

C₂×D₄

yes

C₂×C₈×C₄₇

yes

C₂×C₈×C₄₇

yes

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₈

yes

—

C₁₆×C₄₇

C₂²⋊C₄

yes

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄×D₄

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

C₂×D₈

yes

C₂×C₄×C₄₇

yes

C₂×C₄×C₄₇

yes

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₄₇

C₄×D₄

yes

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

—

#13240

—

maximal, Sylow

C₂²×C₄₇

C₄×D₈

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

100

C₄×C₄₇

—

101

C₄×C₄₇

#390

yes

characteristic

102

C₄×C₄₇

C₄×D₈

yes

characteristic

103

C₄×C₄₇

#466

yes

characteristic

104

C₄×C₄₇

#495

yes

characteristic

105

Dic₄₇

—

106

Dic₄₇

—

107

C₂²×Q₃₂

D₄₇

yes

characteristic

108

C₂×#367

—

109

C₂×#358

—

110

C₂×#346

—

111

#1969

—

112

C₂×C₄₇

#1970

yes

characteristic

113

C₂×C₄₇

#2176

yes

—

114

C₂×C₄₇

#2219

yes

—

115

C₂×C₄₇

#2251

yes

—

116

C₂²×Q₁₆

C₂×D₄₇

yes

—

117

C₂×Q₃₂

—

118

C₂×Q₃₂

—

119

C₂×Q₃₂

Dic₄₇

yes

complemented

120

C₂²×C₁₆

—

121

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

122

C₂×#107

—

123

C₂×#103

—

124

C₂×C₄×C₈

—

125

#391

—

126

#367

—

127

#358

—

128

#346

—

129

C₄₇

#13240

yes

characteristic, complemented, Sylow

130

C₂²×Q₈

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

C₂×Dic₄₇

yes

—

137

C₂²×C₈

—

138

C₂²×C₈

C₂²×D₄₇

yes

characteristic

139

C₂×C₄⋊C₄

—

140

C₂×C₄²

—

141

Q₃₂

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

—

145

C₂×C₁₆

C₂×Dic₄₇

yes

—

146

C₂×C₁₆

C₂²⋊D₄₇

yes

—

147

C₂×C₁₆

C₂²⋊D₄₇

yes

—

148

#107

—

149

#107

—

150

#103

—

188

—

151

C₄×C₈

—

152

C₄×C₈

—

153

#95

—

188

—

154

C₂×Q₈

—

155

C₂×Q₈

—

156

C₂×Q₈

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

188

—

163

C₂²×C₄

D₄×D₄₇

yes

characteristic

164

Q₁₆

—

165

Q₁₆

—

166

Q₁₆

—

167

Q₁₆

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

D₄×D₄₇

yes

characteristic

172

C₂×C₈

#10625352

yes

characteristic

173

C₂×C₈

#10625352

yes

characteristic

174

C₂×C₈

C₂²×Dic₄₇

yes

characteristic

175

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

176

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

177

C₄⋊C₄

—

188

—

178

C₄⋊C₄

—

188

—

179

C₄²

—

180

C₄²

—

181

C₁₆

—

182

C₁₆

C₂²⋊Dic₄₇

yes

—

183

C₂³

D₈×D₄₇

yes

characteristic

184

Q₈

—

185

Q₈

—

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

376

—

194

C₂×C₄

—

376

—

195

C₂×C₄

D₄×Dic₄₇

yes

characteristic

196

C₂×C₄

#13093995

yes

characteristic

197

C₂×C₄

#13094020

yes

characteristic

198

C₂×C₄

D₈×D₄₇

yes

characteristic

199

C₂×C₄

#13094043

yes

characteristic

200

C₂×C₄

#13094043

yes

characteristic

201

C₈

—

202

C₈

C₂×C₂²⋊Dic₄₇

yes

characteristic

203

C₈

D₄×Dic₄₇

yes

characteristic

204

C₈

#13093995

yes

characteristic

205

C₈

#13094011

yes

characteristic

206

C₂²

D₈×Dic₄₇

yes

characteristic

207

C₂²

#15689356

yes

characteristic

208

C₂²

#15689498

yes

characteristic

209

C₂²

#15689565

yes

—

210

C₄

—

211

C₄

—

188

—

212

C₄

—

752

—

213

C₄

#15689026

yes

characteristic

214

C₄

D₈×Dic₄₇

yes

characteristic

215

C₄

#15689356

yes

characteristic

216

C₄

#15689506

yes

characteristic

217

C₂

#20244255

yes

characteristic

218

C₂

#20245259

yes

—

219

C₂

#20245493

yes

—

220

C₂

#20245656

yes

—

	subgroup	G/H
center	C₂³	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂²×Q₃₂×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×D₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂²×Q₃₂	D₄₇
hypocenter	C₄₇	#13240
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂²×Q₃₂×C₄₇

C₂

socle, prime radical

C₂³×C₄₇

C₂×D₈

cosocle

C₂²×C₈×C₄₇

C₂³

hypercenter

C₂²×Q₃₂

D₄₇

hypocenter

C₄₇

#13240

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
17. C₂×Q₃₂×C₄₇	C₄	semidirect
119. C₂×Q₃₂	Dic₄₇	semidirect
129. C₄₇	#13240	semidirect

H ≅ G/N

type

17. C₂×Q₃₂×C₄₇

C₄

semidirect

119. C₂×Q₃₂

Dic₄₇

semidirect

129. C₄₇

#13240

semidirect

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

subgroup	index
C₂×#15688951	2
C₂×#15688927	2
C₂×#15688898	2
#20244250	2
C₂²×Q₃₂×C₄₇	2
#13240	47

subgroup

index

C₂²×Q₃₂×C₄₇

Subgroups — #26134678

Conjugacy classes of subgroups

Complements

Maximal subgroups