Group #26134698 — subgroups

Subgroups — #26134698

Order 12032.

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

normal subgroups only

This group has 402 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	C₂×#15688953	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688939	C₂	1	2	yes	maximal
3	#20244984	C₂	1	1	yes	maximal, characteristic
4	#20244304	C₂	1	2	yes	maximal
5	C₂²×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093964	C₂²	1	1	yes	characteristic
7	C₂×#13093960	C₂²	1	2	yes	—
8	#15689132	—	2	2	no	—
9	C₂×#13093943	—	2	2	no	—
10	#15689078	C₂²	1	1	yes	characteristic
11	#15688953	—	2	2	no	—
12	#15688939	—	2	4	no	—
13	#15688898	—	2	1	no	—
14	C₁₆×Dic₄₇	—	2	1	no	—
15	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂×Q₃₂×C₄₇	—	2	1	no	—
17	C₂×Q₃₂×C₄₇	—	2	1	no	—
18	C₂×Q₃₂×C₄₇	—	2	2	no	—
19	C₂×Q₃₂×C₄₇	C₄	1	4	yes	complemented
20	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#10625329	—	2	2	no	—
22	C₂×#10625329	D₄	1	1	yes	characteristic
23	#13093983	D₄	1	1	yes	characteristic
24	#13093964	—	2	1	no	—
25	#13093964	D₄	1	2	yes	—
26	C₂×C₄₇⋊C₁₆	—	2	1	no	—
27	#13093960	—	2	2	no	—
28	#13093960	—	2	2	no	—
29	#13093948	—	4	4	no	—
30	#13093943	—	4	4	no	—
31	#13093934	—	2	1	no	—
32	C₈×Dic₄₇	—	2	1	no	—
33	C₂²×Q₈×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	—	2	2	no	—
38	C₂×Q₁₆×C₄₇	—	2	2	no	—
39	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
41	Q₃₂×C₄₇	—	2	4	no	—
42	Q₃₂×C₄₇	—	2	4	no	—
43	C₂×C₁₆×C₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
45	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
46	C₂×C₁₆×C₄₇	D₄	1	2	yes	—
47	C₂×Q₈×C₄₇	—	2	4	no	—
48	C₂×Q₈×C₄₇	—	4	2	no	—
49	C₂×Q₈×C₄₇	—	4	2	no	—
50	C₂×Q₈×C₄₇	—	4	2	no	—
51	C₂×Q₈×C₄₇	—	4	2	no	—
52	C₂×Q₈×C₄₇	—	4	2	no	—
53	C₂²×C₄×C₄₇	—	4	2	no	—
54	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
55	Q₁₆×C₄₇	—	2	4	no	—
56	Q₁₆×C₄₇	—	2	4	no	—
57	Q₁₆×C₄₇	—	4	2	no	—
58	Q₁₆×C₄₇	—	4	2	no	—
59	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
63	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
64	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
65	C₂²⋊Dic₄₇	—	2	1	no	—
66	C₄⋊Dic₄₇	D₈	1	2	yes	—
67	C₄×Dic₄₇	—	2	1	no	—
68	#10625329	—	2	1	no	—
69	#10625329	—	4	2	no	—
70	#10625329	—	4	2	no	—
71	#10625329	D₈	1	2	yes	—
72	C₂×C₄₇⋊C₈	—	2	1	no	—
73	C₂×C₄₇⋊C₈	—	4	2	no	—
74	C₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
75	C₁₆×C₄₇	C₂²⋊C₄	1	2	yes	—
76	C₄₇⋊C₁₆	—	2	2	no	—
77	C₂³×C₄₇	#135	1	1	yes	characteristic
78	Q₈×C₄₇	—	4	4	no	—
79	Q₈×C₄₇	—	4	4	no	—
80	Q₈×C₄₇	—	8	2	no	—
81	Q₈×C₄₇	—	8	2	no	—
82	C₂×C₄×C₄₇	—	4	4	no	—
83	C₂×C₄×C₄₇	—	8	2	no	—
84	C₂×C₄×C₄₇	—	8	2	no	—
85	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
87	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
88	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
90	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
91	C₂×Dic₄₇	—	2	2	no	—
92	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
94	C₈×C₄₇	#121	1	1	yes	characteristic
95	C₈×C₄₇	#124	1	1	yes	characteristic
96	C₄₇⋊C₈	—	2	2	no	—
97	C₄₇⋊C₈	—	8	2	no	—
98	#13244	—	47	1	no	maximal, Sylow
99	C₂²×C₄₇	—	2	2	no	—
100	C₂²×C₄₇	C₄×D₈	1	1	yes	characteristic
101	C₂²×C₄₇	#466	1	1	yes	characteristic
102	C₂²×C₄₇	#495	1	1	yes	characteristic
103	C₄×C₄₇	—	8	4	no	—
104	C₄×C₄₇	#390	1	1	yes	characteristic
105	C₄×C₄₇	C₄×D₈	1	1	yes	characteristic
106	C₄×C₄₇	#466	1	1	yes	characteristic
107	C₄×C₄₇	#493	1	1	yes	characteristic
108	Dic₄₇	—	4	2	no	—
109	C₂²×Q₃₂	D₄₇	1	1	yes	characteristic
110	C₂×#368	—	47	1	no	—
111	C₂×#362	—	47	2	no	—
112	#2108	—	47	1	no	—
113	#1979	—	47	2	no	—
114	C₂×C₄₇	—	2	1	no	—
115	C₂×C₄₇	—	2	1	no	—
116	C₂×C₄₇	#1970	1	1	yes	characteristic
117	C₂×C₄₇	#2222	1	2	yes	—
118	C₂²×Q₁₆	C₂×D₄₇	1	2	yes	—
119	C₂×Q₃₂	—	2	1	no	—
120	C₂×Q₃₂	—	2	1	no	—
121	C₂×Q₃₂	—	2	2	no	—
122	C₂×Q₃₂	Dic₄₇	1	4	yes	complemented
123	C₂×M₃₂	—	47	1	no	—
124	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
125	C₂×#108	—	47	2	no	—
126	#419	—	94	2	no	—
127	C₂×#101	—	94	2	no	—
128	#405	—	47	1	no	—
129	#368	—	94	2	no	—
130	#362	—	94	4	no	—
131	#346	—	94	1	no	—
132	C₄×C₁₆	—	94	1	no	—
133	C₄₇	#13244	1	1	yes	characteristic, complemented, Sylow
134	C₂²×Q₈	—	2	2	no	—
135	C₂×Q₁₆	—	2	2	no	—
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×Q₁₆	—	2	2	no	—
138	C₂×Q₁₆	—	2	2	no	—
139	C₂×Q₁₆	—	2	2	no	—
140	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
141	C₂×M₁₆	—	47	1	no	—
142	C₂×M₁₆	—	94	2	no	—
143	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
144	#117	—	47	1	no	—
145	Q₃₂	—	2	4	no	—
146	Q₃₂	—	2	4	no	—
147	M₃₂	—	47	2	no	—
148	M₃₂	—	94	1	no	—
149	C₂×C₁₆	—	94	1	no	—
150	C₂×C₁₆	C₂×Dic₄₇	1	2	yes	—
151	C₂×C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
152	C₂×C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
153	C₂×C₁₆	C₂²⋊D₄₇	1	2	yes	—
154	#108	—	94	2	no	—
155	#108	—	94	2	no	—
156	#103	—	188	4	no	—
157	#101	—	188	4	no	—
158	#97	—	94	1	no	—
159	C₄×C₈	—	94	1	no	—
160	C₂×Q₈	—	2	4	no	—
161	C₂×Q₈	—	4	2	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	2	no	—
164	C₂×Q₈	—	4	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂²×C₄	—	4	2	no	—
167	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
168	Q₁₆	—	2	4	no	—
169	Q₁₆	—	2	4	no	—
170	Q₁₆	—	4	2	no	—
171	Q₁₆	—	4	2	no	—
172	M₁₆	—	47	2	no	—
173	M₁₆	—	94	1	no	—
174	M₁₆	—	188	2	no	—
175	M₁₆	—	188	2	no	—
176	C₂×C₈	—	94	1	no	—
177	C₂×C₈	—	188	2	no	—
178	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
179	C₂×C₈	#10625352	1	1	yes	characteristic
180	C₂×C₈	#10625352	1	1	yes	characteristic
181	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
182	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
183	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
184	C₄⋊C₄	—	47	2	no	—
185	C₂²⋊C₄	—	94	1	no	—
186	C₄²	—	94	1	no	—
187	C₁₆	—	94	2	no	—
188	C₁₆	C₂²⋊Dic₄₇	1	2	yes	—
189	C₁₆	C₂²⋊Dic₄₇	1	2	yes	—
190	C₂³	#13094043	1	1	yes	characteristic
191	Q₈	—	4	4	no	—
192	Q₈	—	4	4	no	—
193	Q₈	—	8	2	no	—
194	Q₈	—	8	2	no	—
195	C₂×C₄	—	4	4	no	—
196	C₂×C₄	—	8	2	no	—
197	C₂×C₄	—	8	2	no	—
198	C₂×C₄	—	94	2	no	—
199	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
200	C₂×C₄	#13093995	1	1	yes	characteristic
201	C₂×C₄	#13094020	1	1	yes	characteristic
202	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
203	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
204	C₂×C₄	#13094043	1	1	yes	characteristic
205	C₈	—	94	2	no	—
206	C₈	—	376	2	no	—
207	C₈	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
208	C₈	D₄×Dic₄₇	1	1	yes	characteristic
209	C₈	#13093995	1	1	yes	characteristic
210	C₈	#13094011	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	D₈×Dic₄₇	1	1	yes	characteristic
213	C₂²	#15689356	1	1	yes	characteristic
214	C₂²	#15689506	1	1	yes	characteristic
215	C₄	—	8	4	no	—
216	C₄	—	188	2	no	—
217	C₄	#15689026	1	1	yes	characteristic
218	C₄	D₈×Dic₄₇	1	1	yes	characteristic
219	C₄	#15689356	1	1	yes	characteristic
220	C₄	#15689498	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#20244255	1	1	yes	characteristic
224	C₂	#20245510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15688953

C₂

yes

maximal, characteristic

C₂×#15688939

C₂

yes

maximal

#20244984

C₂

yes

maximal, characteristic

#20244304

C₂

yes

maximal

C₂²×Q₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂×#13093964

C₂²

yes

characteristic

C₂×#13093960

C₂²

yes

—

#15689132

—

C₂×#13093943

—

#15689078

C₂²

yes

—

—

—

C₁₆×Dic₄₇

—

C₂²×Q₁₆×C₄₇

C₂²

yes

—

C₂×Q₃₂×C₄₇

—

C₂×Q₃₂×C₄₇

—

C₂×Q₃₂×C₄₇

—

C₂×Q₃₂×C₄₇

C₄

yes

complemented

C₂²×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×#10625329

—

C₂×#10625329

D₄

yes

characteristic

#13093983

D₄

yes

characteristic

#13093964

—

#13093964

D₄

yes

—

C₂×C₄₇⋊C₁₆

—

—

—

—

—

—

C₈×Dic₄₇

—

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

—

Q₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂×C₄

yes

—

C₂×C₁₆×C₄₇

D₄

yes

characteristic

C₂×C₁₆×C₄₇

D₄

yes

characteristic

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

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

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

D₈

yes

—

C₄×Dic₄₇

—

—

—

—

D₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₁₆×C₄₇

C₂²⋊C₄

yes

—

C₁₆×C₄₇

C₂²⋊C₄

yes

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

#135

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

characteristic

C₂×C₄×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

#135

yes

characteristic

C₂×Dic₄₇

—

C₈×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₄₇

C₄×D₄

yes

C₈×C₄₇

yes

C₈×C₄₇

yes

C₄₇⋊C₈

—

C₄₇⋊C₈

—

#13244

—

maximal, Sylow

C₂²×C₄₇

—

100

C₂²×C₄₇

C₄×D₈

yes

characteristic

101

C₂²×C₄₇

#466

yes

characteristic

102

C₂²×C₄₇

#495

yes

characteristic

103

C₄×C₄₇

—

104

C₄×C₄₇

#390

yes

characteristic

105

C₄×C₄₇

C₄×D₈

yes

characteristic

106

C₄×C₄₇

#466

yes

characteristic

107

C₄×C₄₇

#493

yes

characteristic

108

Dic₄₇

—

109

C₂²×Q₃₂

D₄₇

yes

characteristic

110

C₂×#368

—

111

C₂×#362

—

112

#2108

—

113

#1979

—

114

C₂×C₄₇

—

115

C₂×C₄₇

—

116

C₂×C₄₇

#1970

yes

characteristic

117

C₂×C₄₇

#2222

yes

—

118

C₂²×Q₁₆

C₂×D₄₇

yes

—

119

C₂×Q₃₂

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

—

122

C₂×Q₃₂

Dic₄₇

yes

complemented

123

C₂×M₃₂

—

124

C₂²×C₁₆

C₂×D₄₇

yes

characteristic

125

C₂×#108

—

126

#419

—

127

C₂×#101

—

128

#405

—

129

#368

—

130

#362

—

131

#346

—

132

C₄×C₁₆

—

133

C₄₇

#13244

yes

characteristic, complemented, Sylow

134

C₂²×Q₈

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

—

139

C₂×Q₁₆

—

140

C₂×Q₁₆

C₂×Dic₄₇

yes

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

143

C₂²×C₈

C₂²×D₄₇

yes

characteristic

144

#117

—

145

Q₃₂

—

146

Q₃₂

—

147

M₃₂

—

148

M₃₂

—

149

C₂×C₁₆

—

150

C₂×C₁₆

C₂×Dic₄₇

yes

—

151

C₂×C₁₆

C₂²⋊D₄₇

yes

characteristic

152

C₂×C₁₆

C₂²⋊D₄₇

yes

characteristic

153

C₂×C₁₆

C₂²⋊D₄₇

yes

—

154

#108

—

155

#108

—

156

#103

—

188

—

157

#101

—

188

—

158

#97

—

159

C₄×C₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂²×C₄

—

167

C₂²×C₄

D₄×D₄₇

yes

characteristic

168

Q₁₆

—

169

Q₁₆

—

170

Q₁₆

—

171

Q₁₆

—

172

M₁₆

—

173

M₁₆

—

174

M₁₆

—

188

—

175

M₁₆

—

188

—

176

C₂×C₈

—

177

C₂×C₈

—

188

—

178

C₂×C₈

D₄×D₄₇

yes

characteristic

179

C₂×C₈

#10625352

yes

characteristic

180

C₂×C₈

#10625352

yes

characteristic

181

C₂×C₈

C₂²×Dic₄₇

yes

characteristic

182

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

183

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

186

C₄²

—

187

C₁₆

—

188

C₁₆

C₂²⋊Dic₄₇

yes

—

189

C₁₆

C₂²⋊Dic₄₇

yes

—

190

C₂³

#13094043

yes

characteristic

191

Q₈

—

192

Q₈

—

193

Q₈

—

194

Q₈

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

D₄×Dic₄₇

yes

characteristic

200

C₂×C₄

#13093995

yes

characteristic

201

C₂×C₄

#13094020

yes

characteristic

202

C₂×C₄

D₈×D₄₇

yes

characteristic

203

C₂×C₄

D₈×D₄₇

yes

characteristic

204

C₂×C₄

#13094043

yes

characteristic

205

C₈

—

206

C₈

—

376

—

207

C₈

C₂×C₂²⋊Dic₄₇

yes

characteristic

208

C₈

D₄×Dic₄₇

yes

characteristic

209

C₈

#13093995

yes

characteristic

210

C₈

#13094011

yes

characteristic

211

C₂²

—

212

C₂²

D₈×Dic₄₇

yes

characteristic

213

C₂²

#15689356

yes

characteristic

214

C₂²

#15689506

yes

characteristic

215

C₄

—

216

C₄

—

188

—

217

C₄

#15689026

yes

characteristic

218

C₄

D₈×Dic₄₇

yes

characteristic

219

C₄

#15689356

yes

characteristic

220

C₄

#15689498

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#20244255

yes

characteristic

224

C₂

#20245510

yes

—

	subgroup	G/H
center	C₂²	#15689356
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂²×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	#466
prime radical	C₂³×C₄₇	#135
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂²×Q₃₂	D₄₇
hypocenter	C₄₇	#13244
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂²

#15689356

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂²×Q₃₂×C₄₇

C₂

C₂²×C₄₇

C₂³×C₄₇

C₂²×C₈×C₄₇

C₂³

hypercenter

C₂²×Q₃₂

D₄₇

hypocenter

C₄₇

#13244

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
19. C₂×Q₃₂×C₄₇	C₄	semidirect
122. C₂×Q₃₂	Dic₄₇	semidirect
133. C₄₇	#13244	semidirect

H ≅ G/N

type

19. C₂×Q₃₂×C₄₇

C₄

semidirect

122. C₂×Q₃₂

Dic₄₇

semidirect

133. C₄₇

#13244

semidirect

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

subgroup	index
C₂×#15688953	2
C₂×#15688939	2
#20244984	2
#20244304	2
C₂²×Q₃₂×C₄₇	2
#13244	47

subgroup

index

C₂²×Q₃₂×C₄₇

Subgroups — #26134698

Conjugacy classes of subgroups

Complements

Maximal subgroups