Group #25015019 — subgroups

Subgroups — #25015019

Order 11008.

442 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 115 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×D₆₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582711	C₂	1	2	yes	maximal, complemented
3	#19136191	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135503	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₄₄	C₂²	1	2	yes	—
7	C₂×D₆₈₈	—	2	1	no	—
8	C₂×D₆₈₈	—	2	1	no	—
9	C₂×D₆₈₈	—	2	2	no	—
10	C₂×D₆₈₈	C₄	1	4	yes	complemented
11	C₂×#13063265	C₂²	1	1	yes	characteristic
12	#14582905	—	2	2	no	—
13	C₂×#13063241	—	2	2	no	—
14	#14582854	C₂²	1	1	yes	characteristic
15	#14582711	—	2	4	no	—
16	#14582674	—	2	1	no	—
17	C₁₆×Dic₄₃	—	2	1	no	—
18	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#108×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#368	—	2	2	no	—
21	C₂²×D₁₇₂	—	2	2	no	—
22	C₂×D₃₄₄	—	2	2	no	—
23	C₂×D₃₄₄	—	2	2	no	—
24	C₂×D₃₄₄	—	2	2	no	—
25	C₂×D₃₄₄	—	2	2	no	—
26	C₂×D₃₄₄	—	2	2	no	—
27	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
28	C₂×#10621877	D₄	1	1	yes	characteristic
29	#13063284	D₄	1	1	yes	characteristic
30	D₆₈₈	—	2	4	no	—
31	D₆₈₈	—	2	4	no	—
32	#13063265	—	2	1	no	—
33	#13063265	D₄	1	2	yes	—
34	C₂×C₄₃⋊C₁₆	—	2	1	no	—
35	#13063247	—	4	4	no	—
36	#13063241	—	4	4	no	—
37	#13063235	—	2	1	no	—
38	C₈×Dic₄₃	—	2	1	no	—
39	C₂×M₁₆×C₄₃	—	2	2	no	—
40	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
42	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
43	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
45	#108×C₄₃	—	2	2	no	—
46	#108×C₄₃	—	2	2	no	—
47	C₂³×D₄₃	—	4	2	no	—
48	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
49	C₂×D₁₇₂	—	2	4	no	—
50	C₂×D₁₇₂	—	4	2	no	—
51	C₂×D₁₇₂	—	4	2	no	—
52	C₂×D₁₇₂	—	4	2	no	—
53	C₂×D₁₇₂	—	4	2	no	—
54	C₂×D₁₇₂	—	4	2	no	—
55	M₁₆×C₄₃	—	4	2	no	—
56	M₁₆×C₄₃	—	4	2	no	—
57	C₂×C₈×C₄₃	—	4	2	no	—
58	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
63	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
64	C₂²⋊Dic₄₃	—	2	1	no	—
65	C₄⋊Dic₄₃	D₈	1	2	yes	—
66	C₄×Dic₄₃	—	2	1	no	—
67	#10621877	—	2	1	no	—
68	#10621877	D₈	1	2	yes	—
69	C₂×C₄₃⋊C₈	—	2	1	no	—
70	D₃₄₄	—	2	4	no	—
71	D₃₄₄	—	2	4	no	—
72	D₃₄₄	—	4	2	no	—
73	D₃₄₄	—	4	2	no	—
74	C₁₆×C₄₃	C₂²⋊C₄	1	2	yes	—
75	C₁₆×C₄₃	C₂²⋊C₄	1	2	yes	—
76	C₄₃⋊C₁₆	—	2	2	no	—
77	C₂³×C₄₃	#135	1	1	yes	characteristic
78	C₂²×D₄₃	—	4	4	no	—
79	C₂²×D₄₃	—	8	2	no	—
80	C₂²×D₄₃	—	8	2	no	—
81	C₂²×D₄₃	—	16	4	no	—
82	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
84	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
85	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
88	C₂×Dic₄₃	—	2	2	no	—
89	D₁₇₂	—	4	4	no	—
90	D₁₇₂	—	4	4	no	—
91	D₁₇₂	—	8	2	no	—
92	D₁₇₂	—	8	2	no	—
93	C₈×C₄₃	—	8	2	no	—
94	C₈×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
96	C₈×C₄₃	#121	1	1	yes	characteristic
97	C₈×C₄₃	#124	1	1	yes	characteristic
98	C₄₃⋊C₈	—	2	2	no	—
99	#13245	—	43	1	no	maximal, Sylow
100	C₂²×C₄₃	—	2	2	no	—
101	C₂²×C₄₃	C₄×D₈	1	1	yes	characteristic
102	C₂²×C₄₃	#466	1	1	yes	characteristic
103	C₂²×C₄₃	#495	1	1	yes	characteristic
104	C₂×D₄₃	—	8	4	no	—
105	C₂×D₄₃	—	16	4	no	—
106	C₂×D₄₃	—	16	4	no	—
107	C₂×D₄₃	—	16	4	no	—
108	C₄×C₄₃	#390	1	1	yes	characteristic
109	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
110	C₄×C₄₃	#466	1	1	yes	characteristic
111	C₄×C₄₃	#493	1	1	yes	characteristic
112	Dic₄₃	—	4	2	no	—
113	C₂²×D₁₆	—	43	1	no	—
114	C₂×#368	D₄₃	1	1	yes	characteristic, complemented
115	C₂×#361	—	43	2	no	—
116	#2108	—	43	1	no	—
117	#1978	—	43	2	no	—
118	C₂×C₄₃	—	2	1	no	—
119	C₂×C₄₃	—	2	1	no	—
120	C₂×C₄₃	#1970	1	1	yes	characteristic
121	C₂×C₄₃	#2221	1	2	yes	—
122	D₄₃	—	16	4	no	—
123	C₂²×D₈	—	43	2	no	—
124	C₂×D₁₆	—	43	4	no	—
125	C₂×D₁₆	—	86	1	no	—
126	C₂×D₁₆	—	86	1	no	—
127	C₂×D₁₆	—	86	2	no	—
128	C₂×M₃₂	—	43	1	no	—
129	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
130	C₂×#108	C₂×D₄₃	1	2	yes	—
131	#418	—	86	2	no	—
132	C₂×#100	—	86	2	no	—
133	#405	—	43	1	no	—
134	#368	—	2	2	no	—
135	#361	—	86	4	no	—
136	#346	—	86	1	no	—
137	C₄×C₁₆	—	86	1	no	—
138	C₄₃	#13245	1	1	yes	characteristic, complemented, Sylow
139	C₂²×D₄	—	86	2	no	—
140	C₂×D₈	—	43	4	no	—
141	C₂×D₈	—	86	2	no	—
142	C₂×D₈	—	86	2	no	—
143	C₂×D₈	—	86	2	no	—
144	C₂×D₈	—	86	2	no	—
145	C₂×D₈	—	86	2	no	—
146	C₂×M₁₆	—	2	2	no	—
147	C₂×M₁₆	—	43	1	no	—
148	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
149	#117	—	43	1	no	—
150	D₁₆	—	86	4	no	—
151	D₁₆	—	86	4	no	—
152	M₃₂	—	43	2	no	—
153	M₃₂	—	86	1	no	—
154	C₂×C₁₆	—	86	1	no	—
155	C₂×C₁₆	C₄×D₄₃	1	2	yes	—
156	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
157	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
158	C₂×C₁₆	C₂²⋊D₄₃	1	2	yes	—
159	#108	—	2	2	no	—
160	#108	—	2	2	no	—
161	#102	—	172	4	no	—
162	#100	—	172	4	no	—
163	#97	—	86	1	no	—
164	C₄×C₈	—	86	1	no	—
165	C₂⁴	—	172	2	no	—
166	C₂×D₄	—	86	4	no	—
167	C₂×D₄	—	172	2	no	—
168	C₂×D₄	—	172	2	no	—
169	C₂×D₄	—	172	2	no	—
170	C₂×D₄	—	172	2	no	—
171	C₂×D₄	—	172	2	no	—
172	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
173	D₈	—	86	4	no	—
174	D₈	—	86	4	no	—
175	D₈	—	172	2	no	—
176	D₈	—	172	2	no	—
177	M₁₆	—	4	2	no	—
178	M₁₆	—	4	2	no	—
179	M₁₆	—	43	2	no	—
180	M₁₆	—	86	1	no	—
181	C₂×C₈	—	4	2	no	—
182	C₂×C₈	—	86	1	no	—
183	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
184	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
185	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
186	C₂×C₈	#10621902	1	1	yes	characteristic
187	C₂×C₈	#10621902	1	1	yes	characteristic
188	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
189	C₄⋊C₄	—	43	2	no	—
190	C₂²⋊C₄	—	86	1	no	—
191	C₄²	—	86	1	no	—
192	C₁₆	—	86	2	no	—
193	C₁₆	(C₂×D₄₃)⋊C₄	1	2	yes	—
194	C₁₆	(C₂×D₄₃)⋊C₄	1	2	yes	—
195	C₂³	—	344	2	no	—
196	C₂³	—	344	2	no	—
197	C₂³	—	172	4	no	—
198	C₂³	—	688	4	no	—
199	C₂³	#13063348	1	1	yes	characteristic
200	D₄	—	344	2	no	—
201	D₄	—	344	2	no	—
202	D₄	—	172	4	no	—
203	D₄	—	172	4	no	—
204	C₂×C₄	—	86	2	no	—
205	C₂×C₄	#13063287	1	1	yes	characteristic
206	C₂×C₄	#13063300	1	1	yes	characteristic
207	C₂×C₄	#13063321	1	1	yes	characteristic
208	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
209	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
210	C₂×C₄	#13063348	1	1	yes	characteristic
211	C₈	—	8	2	no	—
212	C₈	—	86	2	no	—
213	C₈	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
214	C₈	#13063287	1	1	yes	characteristic
215	C₈	#13063300	1	1	yes	characteristic
216	C₈	#13063314	1	1	yes	characteristic
217	C₂²	—	2	2	no	—
218	C₂²	—	344	4	no	—
219	C₂²	—	688	4	no	—
220	C₂²	—	688	4	no	—
221	C₂²	—	688	4	no	—
222	C₂²	#14582981	1	1	yes	characteristic
223	C₂²	#14583136	1	1	yes	characteristic
224	C₂²	#14583284	1	1	yes	characteristic
225	C₄	—	172	2	no	—
226	C₄	#14582800	1	1	yes	characteristic
227	C₄	#14582981	1	1	yes	characteristic
228	C₄	#14583136	1	1	yes	characteristic
229	C₄	#14583274	1	1	yes	characteristic
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	—	688	4	no	—
233	C₂	#19135459	1	1	yes	characteristic
234	C₂	#19136716	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₆₈₈

C₂

yes

maximal, characteristic

C₂×#14582711

C₂

yes

maximal, complemented

#19136191

C₂

yes

maximal, characteristic, complemented

#19135503

C₂

yes

maximal, complemented

C₂×C₄₃×#368

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₄₄

C₂²

yes

—

C₂×D₆₈₈

—

C₂×D₆₈₈

—

C₂×D₆₈₈

—

C₂×D₆₈₈

C₄

yes

complemented

C₂×#13063265

C₂²

yes

—

—

C₂²

yes

characteristic

#14582711

—

#14582674

—

C₁₆×Dic₄₃

—

C₂²×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×#108×C₄₃

C₂²

yes

—

C₄₃×#368

—

C₂²×D₁₇₂

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂×C₄

yes

—

C₂×#10621877

D₄

yes

characteristic

#13063284

D₄

yes

characteristic

D₆₈₈

—

D₆₈₈

—

#13063265

—

#13063265

D₄

yes

—

C₂×C₄₃⋊C₁₆

—

#13063247

—

#13063241

—

#13063235

—

C₈×Dic₄₃

—

C₂×M₁₆×C₄₃

—

C₂²×C₈×C₄₃

C₂³

yes

characteristic

C₂×C₁₆×C₄₃

C₂×C₄

yes

—

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

characteristic

C₂×C₁₆×C₄₃

D₄

yes

—

#108×C₄₃

—

#108×C₄₃

—

C₂³×D₄₃

—

C₂²×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

M₁₆×C₄₃

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

—

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

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

D₈

yes

—

C₄×Dic₄₃

—

#10621877

—

#10621877

D₈

yes

—

C₂×C₄₃⋊C₈

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

C₁₆×C₄₃

C₂²⋊C₄

yes

—

C₁₆×C₄₃

C₂²⋊C₄

yes

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

#135

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

C₄×D₄

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₈

yes

characteristic

C₂×C₄×C₄₃

#135

yes

characteristic

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₄₃

C₄×D₄

yes

C₈×C₄₃

yes

C₈×C₄₃

yes

C₄₃⋊C₈

—

#13245

—

maximal, Sylow

100

C₂²×C₄₃

—

101

C₂²×C₄₃

C₄×D₈

yes

characteristic

102

C₂²×C₄₃

#466

yes

characteristic

103

C₂²×C₄₃

#495

yes

characteristic

104

C₂×D₄₃

—

105

C₂×D₄₃

—

106

C₂×D₄₃

—

107

C₂×D₄₃

—

108

C₄×C₄₃

#390

yes

characteristic

109

C₄×C₄₃

C₄×D₈

yes

characteristic

110

C₄×C₄₃

#466

yes

characteristic

111

C₄×C₄₃

#493

yes

characteristic

112

Dic₄₃

—

113

C₂²×D₁₆

—

114

C₂×#368

D₄₃

yes

characteristic, complemented

115

C₂×#361

—

116

#2108

—

117

#1978

—

118

C₂×C₄₃

—

119

C₂×C₄₃

—

120

C₂×C₄₃

#1970

yes

characteristic

121

C₂×C₄₃

#2221

yes

—

122

D₄₃

—

123

C₂²×D₈

—

124

C₂×D₁₆

—

125

C₂×D₁₆

—

126

C₂×D₁₆

—

127

C₂×D₁₆

—

128

C₂×M₃₂

—

129

C₂²×C₁₆

C₂×D₄₃

yes

characteristic

130

C₂×#108

C₂×D₄₃

yes

—

131

#418

—

132

C₂×#100

—

133

#405

—

134

#368

—

135

#361

—

136

#346

—

137

C₄×C₁₆

—

138

C₄₃

#13245

yes

characteristic, complemented, Sylow

139

C₂²×D₄

—

140

C₂×D₈

—

141

C₂×D₈

—

142

C₂×D₈

—

143

C₂×D₈

—

144

C₂×D₈

—

145

C₂×D₈

—

146

C₂×M₁₆

—

147

C₂×M₁₆

—

148

C₂²×C₈

C₂²×D₄₃

yes

characteristic

149

#117

—

150

D₁₆

—

151

D₁₆

—

152

M₃₂

—

153

M₃₂

—

154

C₂×C₁₆

—

155

C₂×C₁₆

C₄×D₄₃

yes

—

156

C₂×C₁₆

D₁₇₂

yes

characteristic

157

C₂×C₁₆

D₁₇₂

yes

characteristic

158

C₂×C₁₆

C₂²⋊D₄₃

yes

—

159

#108

—

160

#108

—

161

#102

—

172

—

162

#100

—

172

—

163

#97

—

164

C₄×C₈

—

165

C₂⁴

—

172

—

166

C₂×D₄

—

167

C₂×D₄

—

172

—

168

C₂×D₄

—

172

—

169

C₂×D₄

—

172

—

170

C₂×D₄

—

172

—

171

C₂×D₄

—

172

—

172

C₂²×C₄

D₄×D₄₃

yes

characteristic

173

D₈

—

174

D₈

—

175

D₈

—

172

—

176

D₈

—

172

—

177

M₁₆

—

178

M₁₆

—

179

M₁₆

—

180

M₁₆

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

C₂×C₄×D₄₃

yes

characteristic

184

C₂×C₈

C₂×D₁₇₂

yes

characteristic

185

C₂×C₈

D₄×D₄₃

yes

characteristic

186

C₂×C₈

#10621902

yes

characteristic

187

C₂×C₈

#10621902

yes

characteristic

188

C₂×C₈

C₂×C₂²⋊D₄₃

yes

characteristic

189

C₄⋊C₄

—

190

C₂²⋊C₄

—

191

C₄²

—

192

C₁₆

—

193

C₁₆

(C₂×D₄₃)⋊C₄

yes

—

194

C₁₆

(C₂×D₄₃)⋊C₄

yes

—

195

C₂³

—

344

—

196

C₂³

—

344

—

197

C₂³

—

172

—

198

C₂³

—

688

—

199

C₂³

#13063348

yes

characteristic

200

D₄

—

344

—

201

D₄

—

344

—

202

D₄

—

172

—

203

D₄

—

172

—

204

C₂×C₄

—

205

C₂×C₄

#13063287

yes

characteristic

206

C₂×C₄

#13063300

yes

characteristic

207

C₂×C₄

#13063321

yes

characteristic

208

C₂×C₄

D₈×D₄₃

yes

characteristic

209

C₂×C₄

D₈×D₄₃

yes

characteristic

210

C₂×C₄

#13063348

yes

characteristic

211

C₈

—

212

C₈

—

213

C₈

C₂×(C₂×D₄₃)⋊C₄

yes

characteristic

214

C₈

#13063287

yes

characteristic

215

C₈

#13063300

yes

characteristic

216

C₈

#13063314

yes

characteristic

217

C₂²

—

218

C₂²

—

344

—

219

C₂²

—

688

—

220

C₂²

—

688

—

221

C₂²

—

688

—

222

C₂²

#14582981

yes

characteristic

223

C₂²

#14583136

yes

characteristic

224

C₂²

#14583284

yes

characteristic

225

C₄

—

172

—

226

C₄

#14582800

yes

characteristic

227

C₄

#14582981

yes

characteristic

228

C₄

#14583136

yes

characteristic

229

C₄

#14583274

yes

characteristic

230

C₂

—

231

C₂

—

232

C₂

—

688

—

233

C₂

#19135459

yes

characteristic

234

C₂

#19136716

yes

—

	subgroup	G/H
center	C₂²	#14583136
commutator	C₂×C₈×C₄₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#368	C₂
socle	C₂²×C₄₃	#466
prime radical	C₂²×D₆₈₈	C₂
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#368	D₄₃
hypocenter	C₄₃	#13245
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂²

#14583136

commutator

C₂×C₈×C₄₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₄₃

Fitting

C₂×C₄₃×#368

C₂

socle

C₂²×C₄₃

#466

prime radical

C₂²×D₆₈₈

C₂

cosocle

C₂²×C₈×C₄₃

C₂³

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
2. C₂×#14582711	C₂	semidirect
3. #19136191	C₂	semidirect
4. #19135503	C₂	semidirect
5. C₂×C₄₃×#368	C₂	semidirect
10. C₂×D₆₈₈	C₄	semidirect
114. C₂×#368	D₄₃	semidirect
138. C₄₃	#13245	semidirect

H ≅ G/N

type

2. C₂×#14582711

C₂

semidirect

3. #19136191

C₂

semidirect

4. #19135503

C₂

semidirect

5. C₂×C₄₃×#368

C₂

semidirect

10. C₂×D₆₈₈

C₄

semidirect

114. C₂×#368

D₄₃

semidirect

138. C₄₃

#13245

semidirect

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

subgroup	index
C₂²×D₆₈₈	2
C₂×#14582711	2
#19136191	2
#19135503	2
C₂×C₄₃×#368	2
#13245	43

subgroup

index

C₂²×D₆₈₈

C₂×C₄₃×#368

Subgroups — #25015019

Conjugacy classes of subgroups

Complements

Maximal subgroups