Group #25014996 — subgroups

Subgroups — #25014996

Order 11008.

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	C₂²×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582727	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582704	C₂	1	2	yes	maximal
4	#19135456	C₂	1	2	yes	maximal
5	C₂×C₄₃×#346	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₇₂	C₂²	1	2	yes	—
7	C₂×Dic₃₄₄	—	2	2	no	—
8	C₂×Dic₃₄₄	—	2	2	no	—
9	C₂×Dic₃₄₄	C₄	1	4	yes	complemented
10	C₂×#13063259	C₂²	1	2	yes	—
11	C₂×#13063250	—	2	2	no	—
12	#14582805	—	2	2	no	—
13	#14582727	—	2	2	no	—
14	#14582704	—	2	4	no	—
15	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#346	—	2	2	no	—
19	C₂²×Dic₈₆	—	2	2	no	—
20	C₂×Dic₁₇₂	—	2	2	no	—
21	C₂×Dic₁₇₂	—	2	2	no	—
22	C₂×Dic₁₇₂	—	2	2	no	—
23	C₂×Dic₁₇₂	—	2	2	no	—
24	C₂×Dic₁₇₂	—	2	2	no	—
25	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	—
26	C₂×C₄⋊Dic₄₃	—	2	2	no	—
27	Dic₃₄₄	—	2	8	no	—
28	#13063259	—	2	2	no	—
29	#13063259	—	2	2	no	—
30	#13063250	—	4	4	no	—
31	C₄₃⋊#95	—	4	4	no	—
32	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₄₃	—	2	1	no	—
36	C₂×C₁₆×C₄₃	—	2	1	no	—
37	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
38	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
39	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
40	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
41	C₄×C₈×C₄₃	—	2	1	no	—
42	C₄×C₈×C₄₃	—	2	1	no	—
43	C₂²×C₄×C₄₃	D₈	1	2	yes	—
44	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₄₃	—	4	2	no	—
46	C₂²×Dic₄₃	—	4	2	no	—
47	C₂×Dic₈₆	—	2	4	no	—
48	C₂×Dic₈₆	—	4	2	no	—
49	C₂×Dic₈₆	—	4	2	no	—
50	C₂×Dic₈₆	—	4	2	no	—
51	C₂×Dic₈₆	—	4	2	no	—
52	C₂×Dic₈₆	—	4	2	no	—
53	C₂×C₈×C₄₃	—	2	1	no	—
54	C₂×C₈×C₄₃	—	2	1	no	—
55	C₂×C₈×C₄₃	D₈	1	2	yes	—
56	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
61	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
62	C₄²×C₄₃	—	2	1	no	—
63	C₄²×C₄₃	—	2	1	no	—
64	C₄⋊Dic₄₃	—	4	2	no	—
65	C₄⋊Dic₄₃	—	4	2	no	—
66	Dic₁₇₂	—	2	4	no	—
67	Dic₁₇₂	—	2	4	no	—
68	Dic₁₇₂	—	4	2	no	—
69	Dic₁₇₂	—	4	2	no	—
70	C₁₆×C₄₃	—	2	2	no	—
71	C₁₆×C₄₃	C₂²⋊C₄	1	4	yes	—
72	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₄₃	—	2	2	no	—
74	C₂×C₄×C₄₃	—	2	4	no	—
75	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
77	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
78	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
80	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
81	C₂×Dic₄₃	—	4	4	no	—
82	C₂×Dic₄₃	—	8	2	no	—
83	C₂×Dic₄₃	—	8	2	no	—
84	C₂×Dic₄₃	—	8	2	no	—
85	C₂×Dic₄₃	—	8	4	no	—
86	Dic₈₆	—	4	4	no	—
87	Dic₈₆	—	4	4	no	—
88	Dic₈₆	—	8	2	no	—
89	Dic₈₆	—	8	2	no	—
90	C₈×C₄₃	—	2	2	no	—
91	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
93	C₈×C₄₃	#121	1	1	yes	characteristic
94	C₈×C₄₃	#124	1	1	yes	characteristic
95	#13240	—	43	1	no	maximal, Sylow
96	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₄₃	#466	1	1	yes	characteristic
98	C₂²×C₄₃	#493	1	1	yes	characteristic
99	C₂²×C₄₃	#510	1	4	yes	—
100	C₄×C₄₃	—	4	2	no	—
101	C₄×C₄₃	#390	1	1	yes	characteristic
102	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
103	C₄×C₄₃	#466	1	1	yes	characteristic
104	C₄×C₄₃	#495	1	1	yes	characteristic
105	Dic₄₃	—	8	4	no	—
106	Dic₄₃	—	16	2	no	—
107	C₂²×Q₃₂	—	43	1	no	—
108	C₂×#367	—	43	1	no	—
109	C₂×#358	—	43	2	no	—
110	C₂×#346	D₄₃	1	1	yes	characteristic
111	#1969	—	43	2	no	—
112	C₂×C₄₃	#1970	1	1	yes	characteristic
113	C₂×C₄₃	#2176	1	2	yes	—
114	C₂×C₄₃	#2219	1	2	yes	—
115	C₂×C₄₃	#2251	1	2	yes	—
116	C₂²×Q₁₆	—	43	2	no	—
117	C₂×Q₃₂	—	43	4	no	—
118	C₂×Q₃₂	—	86	2	no	—
119	C₂×Q₃₂	—	86	2	no	—
120	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
121	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
122	C₂×#107	—	43	2	no	—
123	C₂×#103	—	86	2	no	—
124	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
125	#391	—	86	2	no	—
126	#367	—	86	2	no	—
127	#358	—	86	4	no	—
128	#346	—	2	2	no	—
129	C₄₃	#13240	1	1	yes	characteristic, complemented, Sylow
130	C₂²×Q₈	—	86	2	no	—
131	C₂×Q₁₆	—	43	4	no	—
132	C₂×Q₁₆	—	86	2	no	—
133	C₂×Q₁₆	—	86	2	no	—
134	C₂×Q₁₆	—	86	2	no	—
135	C₂×Q₁₆	—	86	2	no	—
136	C₂×Q₁₆	—	86	2	no	—
137	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
138	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
139	C₂×C₄⋊C₄	—	86	2	no	—
140	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
141	Q₃₂	—	86	8	no	—
142	C₂×C₁₆	—	2	1	no	—
143	C₂×C₁₆	—	2	1	no	—
144	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
145	C₂×C₁₆	D₁₇₂	1	2	yes	—
146	C₂×C₁₆	D₁₇₂	1	2	yes	—
147	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
148	#107	—	86	2	no	—
149	#107	—	86	2	no	—
150	#103	—	172	4	no	—
151	C₄×C₈	—	2	1	no	—
152	C₄×C₈	—	2	1	no	—
153	#95	—	172	4	no	—
154	C₂×Q₈	—	86	4	no	—
155	C₂×Q₈	—	172	2	no	—
156	C₂×Q₈	—	172	2	no	—
157	C₂×Q₈	—	172	2	no	—
158	C₂×Q₈	—	172	2	no	—
159	C₂×Q₈	—	172	2	no	—
160	C₂²×C₄	—	172	2	no	—
161	C₂²×C₄	—	172	2	no	—
162	C₂²×C₄	D₃₄₄	1	2	yes	—
163	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
164	Q₁₆	—	86	4	no	—
165	Q₁₆	—	86	4	no	—
166	Q₁₆	—	172	2	no	—
167	Q₁₆	—	172	2	no	—
168	C₂×C₈	—	2	1	no	—
169	C₂×C₈	—	2	1	no	—
170	C₂×C₈	D₃₄₄	1	2	yes	—
171	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
172	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
173	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
174	C₂×C₈	#10621898	1	1	yes	characteristic
175	C₂×C₈	#10621898	1	1	yes	characteristic
176	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
177	C₄⋊C₄	—	172	2	no	—
178	C₄⋊C₄	—	172	2	no	—
179	C₄²	—	2	1	no	—
180	C₄²	—	2	1	no	—
181	C₁₆	—	2	2	no	—
182	C₁₆	(C₂×D₄₃)⋊C₄	1	4	yes	—
183	C₂³	C₂×D₃₄₄	1	1	yes	characteristic
184	Q₈	—	344	2	no	—
185	Q₈	—	344	2	no	—
186	Q₈	—	172	4	no	—
187	Q₈	—	172	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	344	2	no	—
191	C₂×C₄	—	344	2	no	—
192	C₂×C₄	—	344	4	no	—
193	C₂×C₄	—	344	2	no	—
194	C₂×C₄	—	172	4	no	—
195	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
196	C₂×C₄	#13063299	1	1	yes	characteristic
197	C₂×C₄	#13063322	1	1	yes	characteristic
198	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
199	C₂×C₄	#13063347	1	1	yes	characteristic
200	C₂×C₄	#13063347	1	1	yes	characteristic
201	C₈	—	2	2	no	—
202	C₈	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
203	C₈	C₄×D₁₇₂	1	1	yes	characteristic
204	C₈	#13063299	1	1	yes	characteristic
205	C₈	#13063313	1	1	yes	characteristic
206	C₂²	C₄×D₃₄₄	1	1	yes	characteristic
207	C₂²	#14583135	1	1	yes	characteristic
208	C₂²	#14583276	1	1	yes	characteristic
209	C₂²	#14583342	1	4	yes	—
210	C₄	—	4	2	no	—
211	C₄	—	344	4	no	—
212	C₄	—	688	2	no	—
213	C₄	#14582801	1	1	yes	characteristic
214	C₄	C₄×D₃₄₄	1	1	yes	characteristic
215	C₄	#14583135	1	1	yes	characteristic
216	C₄	#14583283	1	1	yes	characteristic
217	C₂	#19135461	1	1	yes	characteristic
218	C₂	#19136467	1	2	yes	—
219	C₂	#19136703	1	2	yes	—
220	C₂	#19136866	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₃₄₄

C₂

yes

maximal, characteristic

C₂×#14582727

C₂

yes

maximal, characteristic

C₂×#14582704

C₂

yes

maximal

#19135456

C₂

yes

maximal

C₂×C₄₃×#346

C₂

yes

maximal, characteristic

C₂²×Dic₁₇₂

C₂²

yes

—

C₂×Dic₃₄₄

—

C₂×Dic₃₄₄

—

C₂×Dic₃₄₄

C₄

yes

complemented

C₂×#13063259

C₂²

yes

—

—

—

—

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄₃×#346

—

C₂²×Dic₈₆

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

C₂×C₄

yes

—

C₂×C₄⋊Dic₄₃

—

Dic₃₄₄

—

#13063259

—

#13063259

—

#13063250

—

C₄₃⋊#95

—

C₂²×C₈×C₄₃

D₄

yes

characteristic

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₄²×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

—

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

—

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

D₈

yes

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₈

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×D₄

yes

C₂×C₈×C₄₃

yes

C₂×C₈×C₄₃

yes

C₄²×C₄₃

—

C₄²×C₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₁₆×C₄₃

C₂²⋊C₄

yes

—

C₂³×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×D₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₄×D₄

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

—

C₂²×C₄₃

C₄×D₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

100

C₄×C₄₃

—

101

C₄×C₄₃

#390

yes

characteristic

102

C₄×C₄₃

C₄×D₈

yes

characteristic

103

C₄×C₄₃

#466

yes

characteristic

104

C₄×C₄₃

#495

yes

characteristic

105

Dic₄₃

—

106

Dic₄₃

—

107

C₂²×Q₃₂

—

108

C₂×#367

—

109

C₂×#358

—

110

C₂×#346

D₄₃

yes

characteristic

111

#1969

—

112

C₂×C₄₃

#1970

yes

characteristic

113

C₂×C₄₃

#2176

yes

—

114

C₂×C₄₃

#2219

yes

—

115

C₂×C₄₃

#2251

yes

—

116

C₂²×Q₁₆

—

117

C₂×Q₃₂

—

118

C₂×Q₃₂

—

119

C₂×Q₃₂

—

120

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

121

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

122

C₂×#107

—

123

C₂×#103

—

124

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

125

#391

—

126

#367

—

127

#358

—

128

#346

—

129

C₄₃

#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

—

137

C₂²×C₈

D₁₇₂

yes

characteristic

138

C₂²×C₈

C₂²×D₄₃

yes

characteristic

139

C₂×C₄⋊C₄

—

140

C₂×C₄²

D₁₇₂

yes

characteristic

141

Q₃₂

—

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

C₄×D₄₃

yes

—

145

C₂×C₁₆

D₁₇₂

yes

—

146

C₂×C₁₆

D₁₇₂

yes

—

147

C₂×C₁₆

C₂²⋊D₄₃

yes

—

148

#107

—

149

#107

—

150

#103

—

172

—

151

C₄×C₈

—

152

C₄×C₈

—

153

#95

—

172

—

154

C₂×Q₈

—

155

C₂×Q₈

—

172

—

156

C₂×Q₈

—

172

—

157

C₂×Q₈

—

172

—

158

C₂×Q₈

—

172

—

159

C₂×Q₈

—

172

—

160

C₂²×C₄

—

172

—

161

C₂²×C₄

—

172

—

162

C₂²×C₄

D₃₄₄

yes

—

163

C₂²×C₄

C₂×D₁₇₂

yes

characteristic

164

Q₁₆

—

165

Q₁₆

—

166

Q₁₆

—

172

—

167

Q₁₆

—

172

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

D₃₄₄

yes

—

171

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

172

C₂×C₈

C₂×D₁₇₂

yes

characteristic

173

C₂×C₈

C₂×D₁₇₂

yes

characteristic

174

C₂×C₈

#10621898

yes

characteristic

175

C₂×C₈

#10621898

yes

characteristic

176

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

177

C₄⋊C₄

—

172

—

178

C₄⋊C₄

—

172

—

179

C₄²

—

180

C₄²

—

181

C₁₆

—

182

C₁₆

(C₂×D₄₃)⋊C₄

yes

—

183

C₂³

C₂×D₃₄₄

yes

characteristic

184

Q₈

—

344

—

185

Q₈

—

344

—

186

Q₈

—

172

—

187

Q₈

—

172

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

344

—

191

C₂×C₄

—

344

—

192

C₂×C₄

—

344

—

193

C₂×C₄

—

344

—

194

C₂×C₄

—

172

—

195

C₂×C₄

C₄×D₁₇₂

yes

characteristic

196

C₂×C₄

#13063299

yes

characteristic

197

C₂×C₄

#13063322

yes

characteristic

198

C₂×C₄

C₂×D₃₄₄

yes

characteristic

199

C₂×C₄

#13063347

yes

characteristic

200

C₂×C₄

#13063347

yes

characteristic

201

C₈

—

202

C₈

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

203

C₈

C₄×D₁₇₂

yes

characteristic

204

C₈

#13063299

yes

characteristic

205

C₈

#13063313

yes

characteristic

206

C₂²

C₄×D₃₄₄

yes

characteristic

207

C₂²

#14583135

yes

characteristic

208

C₂²

#14583276

yes

characteristic

209

C₂²

#14583342

yes

—

210

C₄

—

211

C₄

—

344

—

212

C₄

—

688

—

213

C₄

#14582801

yes

characteristic

214

C₄

C₄×D₃₄₄

yes

characteristic

215

C₄

#14583135

yes

characteristic

216

C₄

#14583283

yes

characteristic

217

C₂

#19135461

yes

characteristic

218

C₂

#19136467

yes

—

219

C₂

#19136703

yes

—

220

C₂

#19136866

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#346	C₂
socle, prime radical	C₂³×C₄₃	C₂×D₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#346	D₄₃
hypocenter	C₄₃	#13240
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂³

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#346

C₂

socle, prime radical

C₂³×C₄₃

C₂×D₈

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
9. C₂×Dic₃₄₄	C₄	semidirect
129. C₄₃	#13240	semidirect

H ≅ G/N

type

9. C₂×Dic₃₄₄

C₄

semidirect

129. C₄₃

#13240

semidirect

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

subgroup	index
C₂²×Dic₃₄₄	2
C₂×#14582727	2
C₂×#14582704	2
#19135456	2
C₂×C₄₃×#346	2
#13240	43

subgroup

index

C₂²×Dic₃₄₄

C₂×C₄₃×#346

Subgroups — #25014996

Conjugacy classes of subgroups

Complements

Maximal subgroups