Group #26134748 — subgroups

Subgroups — #26134748

Order 12032.

494 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 159 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×#15689503	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688928	C₂	1	4	yes	maximal
3	C₄×#13093958	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₈₈	—	2	1	no	—
6	C₂²×Dic₁₈₈	C₂²	1	2	yes	—
7	C₂×#13094024	—	2	1	no	—
8	#15689503	—	2	2	no	—
9	#15689503	C₄	1	4	yes	complemented
10	C₂×#13093958	C₂²	1	2	yes	—
11	C₄×C₄⋊Dic₄₇	—	2	1	no	—
12	#15688928	—	2	8	no	—
13	#15688886	—	2	1	no	—
14	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×C₄⋊C₁₆	—	2	2	no	—
17	C₂²×Dic₉₄	—	2	2	no	—
18	C₂×Dic₁₈₈	—	2	4	no	—
19	C₂×Dic₁₈₈	—	2	4	no	—
20	C₂×Dic₁₈₈	—	2	4	no	—
21	C₂×Dic₁₈₈	—	2	2	no	—
22	C₂×Dic₁₈₈	—	4	4	no	—
23	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
24	#13094024	—	2	4	no	—
25	#13094024	—	4	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	4	1	no	—
28	C₂×C₄⋊Dic₄₇	—	4	1	no	—
29	C₂×C₄×Dic₄₇	—	4	1	no	—
30	#13093958	—	2	2	no	—
31	#13093958	D₄	1	4	yes	—
32	C₄₇⋊#95	—	4	1	no	—
33	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
36	C₂×C₁₆×C₄₇	—	2	2	no	—
37	C₂×C₁₆×C₄₇	—	2	4	no	—
38	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₄₇	D₄	1	2	yes	—
40	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
41	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₄₇	—	4	2	no	—
44	C₂²×Dic₄₇	—	4	2	no	—
45	C₂×Dic₉₄	—	2	4	no	—
46	C₂×Dic₉₄	—	4	4	no	—
47	C₂×Dic₉₄	—	4	4	no	—
48	C₂×Dic₉₄	—	4	2	no	—
49	C₂×C₈×C₄₇	—	2	2	no	—
50	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
51	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₄₇	#41	1	2	yes	—
55	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₄₇	SD₁₆	1	2	yes	—
57	C₄⋊Dic₄₇	—	2	4	no	—
58	C₄⋊Dic₄₇	—	4	4	no	—
59	C₄⋊Dic₄₇	—	4	4	no	—
60	C₄⋊Dic₄₇	—	4	2	no	—
61	C₄×Dic₄₇	—	8	2	no	—
62	Dic₁₈₈	—	2	8	no	—
63	Dic₁₈₈	—	4	8	no	—
64	Dic₁₈₈	—	4	2	no	—
65	Dic₁₈₈	—	4	2	no	—
66	C₁₆×C₄₇	—	4	2	no	—
67	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₄₇	—	2	2	no	—
69	C₂×C₄×C₄₇	#102	1	2	yes	—
70	C₂×C₄×C₄₇	#102	1	2	yes	—
71	C₂×C₄×C₄₇	SD₃₂	1	2	yes	—
72	C₂×C₄×C₄₇	Q₃₂	1	2	yes	—
73	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₄₇	#121	1	2	yes	—
75	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
77	C₂×Dic₄₇	—	4	4	no	—
78	C₂×Dic₄₇	—	4	4	no	—
79	C₂×Dic₄₇	—	8	4	no	—
80	C₂×Dic₄₇	—	8	2	no	—
81	C₂×Dic₄₇	—	8	2	no	—
82	Dic₉₄	—	4	4	no	—
83	Dic₉₄	—	4	4	no	—
84	Dic₉₄	—	8	4	no	—
85	C₈×C₄₇	—	2	2	no	—
86	C₈×C₄₇	C₄×D₄	1	2	yes	—
87	C₈×C₄₇	#124	1	1	yes	characteristic
88	C₈×C₄₇	#127	1	1	yes	characteristic
89	#13253	—	47	1	no	maximal, Sylow
90	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
91	C₂²×C₄₇	#459	1	2	yes	—
92	C₂²×C₄₇	C₂×SD₃₂	1	1	yes	characteristic
93	C₂²×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
94	C₂²×C₄₇	#510	1	2	yes	—
95	C₄×C₄₇	—	2	2	no	—
96	C₄×C₄₇	#358	1	4	yes	complemented
97	C₄×C₄₇	#390	1	1	yes	characteristic
98	C₄×C₄₇	#418	1	1	yes	characteristic
99	C₄×C₄₇	#460	1	2	yes	—
100	Dic₄₇	—	8	4	no	—
101	Dic₄₇	—	8	4	no	—
102	C₂×#494	—	47	1	no	—
103	C₂×C₄⋊C₁₆	D₄₇	1	1	yes	characteristic
104	C₂×#358	—	47	4	no	—
105	C₄×#107	—	47	1	no	—
106	C₂×C₄₇	#1982	1	1	yes	characteristic
107	C₂×C₄₇	C₂×#358	1	1	yes	characteristic
108	C₂×C₄₇	#2141	1	1	yes	characteristic
109	C₂×C₄₇	#2208	1	2	yes	—
110	C₂×C₄₇	#2209	1	2	yes	—
111	C₂²×Q₁₆	—	47	2	no	—
112	C₂²×Q₁₆	—	94	1	no	—
113	C₂×C₄⋊Q₈	—	94	1	no	—
114	C₂²×C₁₆	C₂×D₄₇	1	2	yes	—
115	#494	—	47	4	no	—
116	#494	—	94	2	no	—
117	C₂×#107	—	47	2	no	—
118	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
119	C₄×C₄⋊C₄	—	94	1	no	—
120	C₄⋊C₁₆	—	2	2	no	—
121	#358	—	94	8	no	—
122	#340	—	94	1	no	—
123	C₄₇	#13253	1	1	yes	characteristic, complemented, Sylow
124	C₂²×Q₈	—	94	2	no	—
125	C₂×Q₁₆	—	47	4	no	—
126	C₂×Q₁₆	—	94	4	no	—
127	C₂×Q₁₆	—	94	4	no	—
128	C₂×Q₁₆	—	94	4	no	—
129	C₂×Q₁₆	—	94	2	no	—
130	C₂×Q₁₆	—	188	4	no	—
131	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
132	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
133	C₄⋊Q₈	—	94	4	no	—
134	C₄⋊Q₈	—	188	2	no	—
135	C₂×C₄⋊C₄	—	94	2	no	—
136	C₂×C₄⋊C₄	—	188	1	no	—
137	C₂×C₄⋊C₄	—	188	1	no	—
138	C₂×C₄²	—	188	1	no	—
139	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
140	C₂×C₁₆	—	2	4	no	—
141	C₂×C₁₆	—	2	2	no	—
142	#107	—	47	4	no	—
143	#107	—	94	2	no	—
144	C₄×C₈	C₄×D₄₇	1	2	yes	—
145	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
146	#95	—	188	1	no	—
147	C₂×Q₈	—	94	4	no	—
148	C₂×Q₈	—	188	4	no	—
149	C₂×Q₈	—	188	4	no	—
150	C₂×Q₈	—	188	2	no	—
151	C₂²×C₄	—	188	2	no	—
152	C₂²×C₄	—	188	2	no	—
153	C₂²×C₄	D₃₇₆	1	1	yes	characteristic
154	C₂²×C₄	D₃₇₆	1	1	yes	characteristic
155	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
156	Q₁₆	—	94	8	no	—
157	Q₁₆	—	188	8	no	—
158	Q₁₆	—	188	2	no	—
159	Q₁₆	—	188	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
162	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
163	C₂×C₈	D₄×D₄₇	1	2	yes	—
164	C₂×C₈	#10625354	1	2	yes	—
165	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
166	C₄⋊C₄	—	94	4	no	—
167	C₄⋊C₄	—	188	4	no	—
168	C₄⋊C₄	—	188	4	no	—
169	C₄⋊C₄	—	188	2	no	—
170	C₄²	—	376	2	no	—
171	C₄²	#10625325	1	2	yes	—
172	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
173	C₁₆	—	4	2	no	—
174	C₂³	C₂×D₃₇₆	1	1	yes	characteristic
175	Q₈	—	376	4	no	—
176	Q₈	—	188	4	no	—
177	Q₈	—	188	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	376	2	no	—
180	C₂×C₄	—	376	2	no	—
181	C₂×C₄	—	376	4	no	—
182	C₂×C₄	—	188	4	no	—
183	C₂×C₄	—	188	4	no	—
184	C₂×C₄	#13093946	1	2	yes	—
185	C₂×C₄	#13093946	1	2	yes	—
186	C₂×C₄	#13093969	1	2	yes	—
187	C₂×C₄	Dic₃₇₆	1	2	yes	—
188	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
189	C₂×C₄	#13093999	1	2	yes	—
190	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
191	C₂×C₄	#13094052	1	2	yes	—
192	C₈	—	2	2	no	—
193	C₈	#13093986	1	2	yes	—
194	C₈	#13094013	1	1	yes	characteristic
195	C₈	#13094020	1	1	yes	characteristic
196	C₂²	C₂×#13093946	1	1	yes	characteristic
197	C₂²	#15689319	1	2	yes	—
198	C₂²	C₂×#13093969	1	1	yes	characteristic
199	C₂²	C₂×Dic₃₇₆	1	1	yes	characteristic
200	C₂²	#15689566	1	2	yes	—
201	C₄	—	2	2	no	—
202	C₄	—	376	4	no	—
203	C₄	—	376	4	no	—
204	C₄	#15688928	1	4	yes	complemented
205	C₄	#15689024	1	1	yes	characteristic
206	C₄	#15689129	1	1	yes	characteristic
207	C₄	#15689324	1	2	yes	—
208	C₂	#20244314	1	1	yes	characteristic
209	C₂	C₂×#15688928	1	1	yes	characteristic
210	C₂	#20245109	1	1	yes	characteristic
211	C₂	#20245434	1	2	yes	—
212	C₂	#20245439	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15689503

C₂

yes

maximal, characteristic

C₂×#15688928

C₂

yes

maximal

C₄×#13093958

C₂

yes

maximal, characteristic

C₂×C₄₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×Dic₁₈₈

—

C₂²×Dic₁₈₈

C₂²

yes

—

C₂×#13094024

—

#15689503

—

#15689503

C₄

yes

complemented

C₂×#13093958

C₂²

yes

—

C₄×C₄⋊Dic₄₇

—

#15688928

—

#15688886

—

C₂²×C₁₆×C₄₇

C₂²

yes

—

C₂×C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄₇×C₄⋊C₁₆

—

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂×C₄

yes

—

#13094024

—

#13094024

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄×Dic₄₇

—

#13093958

—

#13093958

D₄

yes

—

C₄₇⋊#95

—

C₂²×C₈×C₄₇

D₄

yes

characteristic

C₂²×C₈×C₄₇

C₂³

yes

characteristic

C₂×C₄²×C₄₇

D₄

yes

characteristic

C₂×C₁₆×C₄₇

—

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

C₂×C₄

yes

—

C₄×C₈×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

D₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

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

SD₁₆

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

C₁₆×C₄₇

—

C₂³×C₄₇

C₂×D₈

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

#102

yes

—

C₂×C₄×C₄₇

SD₃₂

yes

—

C₂×C₄×C₄₇

Q₃₂

yes

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×C₄×C₄₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₄×D₄

yes

—

C₈×C₄₇

yes

C₈×C₄₇

yes

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

—

C₂²×C₄₇

C₂×SD₃₂

yes

characteristic

C₂²×C₄₇

C₂×Q₃₂

yes

characteristic

C₂²×C₄₇

#510

yes

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

100

Dic₄₇

—

101

Dic₄₇

—

102

C₂×#494

—

103

C₂×C₄⋊C₁₆

D₄₇

yes

characteristic

104

C₂×#358

—

105

C₄×#107

—

106

C₂×C₄₇

#1982

yes

characteristic

107

C₂×C₄₇

C₂×#358

yes

characteristic

108

C₂×C₄₇

#2141

yes

characteristic

109

C₂×C₄₇

#2208

yes

—

110

C₂×C₄₇

#2209

yes

—

111

C₂²×Q₁₆

—

112

C₂²×Q₁₆

—

113

C₂×C₄⋊Q₈

—

114

C₂²×C₁₆

C₂×D₄₇

yes

—

115

#494

—

116

#494

—

117

C₂×#107

—

118

C₂×C₄×C₈

C₂×D₄₇

yes

characteristic

119

C₄×C₄⋊C₄

—

120

C₄⋊C₁₆

—

121

#358

—

122

#340

—

123

C₄₇

#13253

yes

characteristic, complemented, Sylow

124

C₂²×Q₈

—

125

C₂×Q₁₆

—

126

C₂×Q₁₆

—

127

C₂×Q₁₆

—

128

C₂×Q₁₆

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

188

—

131

C₂²×C₈

D₁₈₈

yes

characteristic

132

C₂²×C₈

C₂²×D₄₇

yes

characteristic

133

C₄⋊Q₈

—

134

C₄⋊Q₈

—

188

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

188

—

137

C₂×C₄⋊C₄

—

188

—

138

C₂×C₄²

—

188

—

139

C₂×C₄²

D₁₈₈

yes

characteristic

140

C₂×C₁₆

—

141

C₂×C₁₆

—

142

#107

—

143

#107

—

144

C₄×C₈

C₄×D₄₇

yes

—

145

C₄×C₈

C₂²⋊D₄₇

yes

—

146

#95

—

188

—

147

C₂×Q₈

—

148

C₂×Q₈

—

188

—

149

C₂×Q₈

—

188

—

150

C₂×Q₈

—

188

—

151

C₂²×C₄

—

188

—

152

C₂²×C₄

—

188

—

153

C₂²×C₄

D₃₇₆

yes

characteristic

154

C₂²×C₄

D₃₇₆

yes

characteristic

155

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

156

Q₁₆

—

157

Q₁₆

—

188

—

158

Q₁₆

—

188

—

159

Q₁₆

—

188

—

160

C₂×C₈

—

161

C₂×C₈

(C₂×D₄₇)⋊C₄

yes

—

162

C₂×C₈

C₂×C₄×D₄₇

yes

characteristic

163

C₂×C₈

D₄×D₄₇

yes

—

164

C₂×C₈

#10625354

yes

—

165

C₂×C₈

C₂×C₂²⋊D₄₇

yes

characteristic

166

C₄⋊C₄

—

167

C₄⋊C₄

—

188

—

168

C₄⋊C₄

—

188

—

169

C₄⋊C₄

—

188

—

170

C₄²

—

376

—

171

C₄²

#10625325

yes

—

172

C₄²

(C₂×D₄₇)⋊C₄

yes

—

173

C₁₆

—

174

C₂³

C₂×D₃₇₆

yes

characteristic

175

Q₈

—

376

—

176

Q₈

—

188

—

177

Q₈

—

188

—

178

C₂×C₄

—

179

C₂×C₄

—

376

—

180

C₂×C₄

—

376

—

181

C₂×C₄

—

376

—

182

C₂×C₄

—

188

—

183

C₂×C₄

—

188

—

184

C₂×C₄

#13093946

yes

—

185

C₂×C₄

#13093946

yes

—

186

C₂×C₄

#13093969

yes

—

187

C₂×C₄

Dic₃₇₆

yes

—

188

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

189

C₂×C₄

#13093999

yes

—

190

C₂×C₄

C₂×#10625325

yes

characteristic

191

C₂×C₄

#13094052

yes

—

192

C₈

—

193

C₈

#13093986

yes

—

194

C₈

#13094013

yes

characteristic

195

C₈

#13094020

yes

characteristic

196

C₂²

C₂×#13093946

yes

characteristic

197

C₂²

#15689319

yes

—

198

C₂²

C₂×#13093969

yes

characteristic

199

C₂²

C₂×Dic₃₇₆

yes

characteristic

200

C₂²

#15689566

yes

—

201

C₄

—

202

C₄

—

376

—

203

C₄

—

376

—

204

C₄

#15688928

yes

complemented

205

C₄

#15689024

yes

characteristic

206

C₄

#15689129

yes

characteristic

207

C₄

#15689324

yes

—

208

C₂

#20244314

yes

characteristic

209

C₂

C₂×#15688928

yes

characteristic

210

C₂

#20245109

yes

characteristic

211

C₂

#20245434

yes

—

212

C₂

#20245439

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₂×C₄₇×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₄₇	C₂×D₈
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#13253
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

subgroup

G/H

center

C₂³

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₇

Fitting

C₂×C₄₇×C₄⋊C₁₆

C₂

socle, prime radical

C₂³×C₄₇

C₂×D₈

cosocle

C₂²×C₈×C₄₇

C₂³

hypercenter

C₂×C₄⋊C₁₆

D₄₇

hypocenter

C₄₇

#13253

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

N	H ≅ G/N	type
9. #15689503	C₄	semidirect
96. C₄×C₄₇	#358	semidirect
123. C₄₇	#13253	semidirect
204. C₄	#15688928	semidirect

H ≅ G/N

type

9. #15689503

C₄

semidirect

96. C₄×C₄₇

#358

semidirect

123. C₄₇

#13253

semidirect

204. C₄

#15688928

semidirect

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

subgroup	index
C₂×#15689503	2
C₂×#15688928	2
C₄×#13093958	2
C₂×C₄₇×C₄⋊C₁₆	2
#13253	47

subgroup

index

C₂×C₄₇×C₄⋊C₁₆

Subgroups — #26134748

Conjugacy classes of subgroups

Complements

Maximal subgroups