Group #36707725 — subgroups

Subgroups — C₂×#26022123 #36707725

Order 22784.

670 conjugacy classes of subgroups; only the 267 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 267 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×Q₁₆×Dic₈₉	C₂	1	2	yes	maximal
2	#26022123	C₂	1	8	yes	maximal, direct product factor
3	C₂×#19151426	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151402	C₂	1	2	yes	maximal
5	C₂×#19151373	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈×Dic₈₉	—	2	2	no	—
8	C₂²×#13083549	C₂²	1	1	yes	characteristic
9	Q₁₆×Dic₈₉	—	2	4	no	—
10	Q₁₆×Dic₈₉	C₂²	1	8	yes	—
11	C₂×#15667946	C₂²	1	2	yes	—
12	C₂×#15667936	—	2	2	no	—
13	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
14	#19151426	C₂²	1	4	yes	—
15	#19151402	C₂²	1	8	yes	—
16	#19151373	C₂²	1	4	yes	—
17	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
18	C₂×Q₃₂×C₈₉	C₄	1	8	yes	complemented
19	C₂×Q₃₂×C₈₉	C₂²	1	4	yes	—
20	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×#10623494	D₄	1	1	yes	characteristic
22	Q₈×Dic₈₉	—	2	8	no	—
23	Q₈×Dic₈₉	—	4	4	no	—
24	C₂×C₄⋊Dic₈₉	—	2	2	no	—
25	C₂×C₄⋊Dic₈₉	—	4	2	no	—
26	C₂×C₄×Dic₈₉	—	4	2	no	—
27	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
28	C₂×#13083549	—	2	2	no	—
29	C₂×#13083549	C₂³	1	2	yes	—
30	#15667946	—	2	2	no	—
31	#15667946	C₂³	1	4	yes	—
32	#15667936	—	2	8	no	—
33	C₈×Dic₈₉	D₄	1	2	yes	—
34	C₈×Dic₈₉	C₂³	1	2	yes	—
35	C₂²×Q₈×C₈₉	—	2	2	no	—
36	C₂×Q₁₆×C₈₉	—	2	2	no	—
37	C₂×Q₁₆×C₈₉	—	2	4	no	—
38	C₂×Q₁₆×C₈₉	C₂×C₄	1	8	yes	—
39	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
40	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
41	Q₃₂×C₈₉	C₂×C₄	1	16	yes	complemented
42	C₂×C₁₆×C₈₉	C₂×C₄	1	4	yes	—
43	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
44	C₂²×Dic₈₉	—	4	2	no	—
45	C₂²×Dic₈₉	D₈	1	2	yes	—
46	C₂×#10623494	—	2	2	no	—
47	C₂×#10623494	C₂×D₄	1	2	yes	—
48	C₄⋊Dic₈₉	—	2	4	no	—
49	C₄⋊Dic₈₉	—	4	2	no	—
50	C₄⋊Dic₈₉	—	4	8	no	—
51	C₄×Dic₈₉	—	4	8	no	—
52	C₄×Dic₈₉	D₈	1	2	yes	—
53	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
54	#13083549	—	2	2	no	—
55	C₂×Q₈×C₈₉	—	2	8	no	—
56	C₂×Q₈×C₈₉	—	2	4	no	—
57	C₂×Q₈×C₈₉	—	4	2	no	—
58	C₂×Q₈×C₈₉	—	4	4	no	—
59	C₂²×C₄×C₈₉	—	4	2	no	—
60	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
61	Q₁₆×C₈₉	—	2	8	no	—
62	Q₁₆×C₈₉	—	2	4	no	—
63	Q₁₆×C₈₉	C₂²×C₄	1	8	yes	—
64	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₈₉	#41	1	2	yes	—
67	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
68	C₁₆×C₈₉	C₂²×C₄	1	4	yes	—
69	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
70	Q₈×C₈₉	—	2	8	no	—
71	Q₈×C₈₉	—	4	4	no	—
72	Q₈×C₈₉	—	4	8	no	—
73	C₂×C₄×C₈₉	—	4	4	no	—
74	C₂×C₄×C₈₉	—	4	8	no	—
75	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
76	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₈₉	#135	1	2	yes	—
78	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
79	C₂×Dic₈₉	—	2	4	no	—
80	C₂×Dic₈₉	—	4	4	no	—
81	C₂×Dic₈₉	—	8	4	no	—
82	C₂×Dic₈₉	C₂×D₈	1	4	yes	—
83	C₈×C₈₉	C₄×D₄	1	2	yes	—
84	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
85	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
86	#10623494	—	2	2	no	—
87	C₂²×C₈₉	C₄×D₈	1	2	yes	—
88	C₂²×C₈₉	#510	1	4	yes	—
89	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
90	C₄×C₈₉	—	4	8	no	—
91	C₄×C₈₉	C₄×D₈	1	2	yes	—
92	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
93	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
94	Dic₈₉	—	2	4	no	—
95	Dic₈₉	—	8	4	no	—
96	C₂×#2176	—	89	1	no	maximal, Sylow
97	C₂×C₈₉	#2176	1	4	yes	complemented
98	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
99	C₂×C₈₉	C₂×#510	1	2	yes	—
100	C₂²×Q₃₂	D₈₉	1	1	yes	characteristic
101	C₂×C₄×Q₁₆	—	89	2	no	—
102	#2176	—	89	8	no	—
103	C₂×#367	—	89	1	no	—
104	C₂×#358	—	89	2	no	—
105	C₂×#346	—	89	1	no	—
106	C₈₉	C₂×#2176	1	1	yes	characteristic, complemented, Sylow
107	C₂²×Q₁₆	C₂×D₈₉	1	2	yes	—
108	C₂×C₄×Q₈	—	178	2	no	—
109	C₂×Q₃₂	Dic₈₉	1	8	yes	complemented
110	C₂×Q₃₂	C₂×D₈₉	1	4	yes	—
111	C₂²×C₁₆	—	89	1	no	—
112	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
113	C₄×Q₁₆	—	89	8	no	—
114	C₄×Q₁₆	—	178	4	no	—
115	C₂×#107	—	89	2	no	—
116	C₂×#103	—	178	2	no	—
117	C₂×C₄×C₈	—	89	1	no	—
118	#367	—	89	4	no	—
119	#358	—	89	8	no	—
120	#346	—	89	4	no	—
121	C₂²×Q₈	—	2	2	no	—
122	C₂×Q₁₆	—	2	2	no	—
123	C₂×Q₁₆	—	2	4	no	—
124	C₂×Q₁₆	C₂×Dic₈₉	1	8	yes	—
125	C₂×Q₁₆	C₂²×D₈₉	1	4	yes	—
126	C₂²×C₈	—	89	1	no	—
127	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
128	C₄×Q₈	—	356	4	no	—
129	C₄×Q₈	—	178	8	no	—
130	C₂×C₄⋊C₄	—	356	2	no	—
131	C₂×C₄⋊C₄	—	178	2	no	—
132	C₂×C₄²	—	89	1	no	—
133	C₂×C₄²	—	356	2	no	—
134	Q₃₂	C₂×Dic₈₉	1	16	yes	complemented
135	C₂×C₁₆	—	89	2	no	—
136	C₂×C₁₆	—	178	2	no	—
137	C₂×C₁₆	C₂×Dic₈₉	1	4	yes	—
138	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
139	#107	—	89	4	no	—
140	#107	—	178	2	no	—
141	#103	—	178	8	no	—
142	C₄×C₈	—	89	2	no	—
143	C₄×C₈	—	89	2	no	—
144	C₂×Q₈	—	2	8	no	—
145	C₂×Q₈	—	2	4	no	—
146	C₂×Q₈	—	4	2	no	—
147	C₂×Q₈	—	4	4	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	—	89	2	no	—
150	C₂²×C₄	—	356	2	no	—
151	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
152	Q₁₆	—	2	8	no	—
153	Q₁₆	—	2	4	no	—
154	Q₁₆	C₂²×Dic₈₉	1	8	yes	—
155	C₂×C₈	—	89	2	no	—
156	C₂×C₈	—	178	2	no	—
157	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
158	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
159	C₂×C₈	#13083573	1	2	yes	—
160	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
161	C₄⋊C₄	—	356	8	no	—
162	C₄⋊C₄	—	356	2	no	—
163	C₄⋊C₄	—	178	4	no	—
164	C₄²	—	89	2	no	—
165	C₄²	—	89	2	no	—
166	C₄²	—	356	8	no	—
167	C₁₆	—	178	2	no	—
168	C₁₆	C₂²×Dic₈₉	1	4	yes	—
169	C₂³	D₈×D₈₉	1	1	yes	characteristic
170	Q₈	—	2	8	no	—
171	Q₈	—	4	8	no	—
172	Q₈	—	4	4	no	—
173	C₂×C₄	—	4	8	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	89	4	no	—
176	C₂×C₄	—	356	4	no	—
177	C₂×C₄	—	178	4	no	—
178	C₂×C₄	—	712	4	no	—
179	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
180	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
181	C₂×C₄	#15668031	1	2	yes	—
182	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
183	C₈	—	178	2	no	—
184	C₈	D₄×Dic₈₉	1	2	yes	—
185	C₈	C₂³×Dic₈₉	1	1	yes	characteristic
186	C₈	C₂×#13083573	1	1	yes	characteristic
187	C₂²	D₈×Dic₈₉	1	2	yes	—
188	C₂²	#19152040	1	4	yes	—
189	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
190	C₄	—	4	8	no	—
191	C₄	—	178	4	no	—
192	C₄	—	712	4	no	—
193	C₄	D₈×Dic₈₉	1	2	yes	—
194	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
195	C₄	C₂×#15668031	1	1	yes	characteristic
196	C₂	#26022123	1	4	yes	direct product factor
197	C₂	C₂×D₈×Dic₈₉	1	1	yes	characteristic
198	C₂	C₂×#19152040	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₁₆×Dic₈₉

C₂

yes

maximal

#26022123

C₂

yes

maximal, direct product factor

C₂×#19151426

C₂

yes

maximal, characteristic

C₂×#19151402

C₂

yes

maximal

C₂×#19151373

C₂

yes

maximal, characteristic

C₂²×Q₃₂×C₈₉

C₂

yes

maximal, characteristic

C₂×Q₈×Dic₈₉

—

C₂²×#13083549

C₂²

yes

characteristic

Q₁₆×Dic₈₉

—

Q₁₆×Dic₈₉

C₂²

yes

—

C₂×#15667946

C₂²

yes

—

C₂×#15667936

—

C₂×C₈×Dic₈₉

C₂²

yes

characteristic

#19151426

C₂²

yes

—

#19151402

C₂²

yes

—

#19151373

C₂²

yes

—

C₂²×Q₁₆×C₈₉

C₂²

yes

—

C₂×Q₃₂×C₈₉

C₄

yes

complemented

C₂×Q₃₂×C₈₉

C₂²

yes

—

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂²×#10623494

D₄

yes

characteristic

Q₈×Dic₈₉

—

Q₈×Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄×Dic₈₉

—

C₂×C₄×Dic₈₉

D₄

yes

characteristic

C₂×#13083549

—

C₂×#13083549

C₂³

yes

—

#15667946

—

#15667946

C₂³

yes

—

#15667936

—

C₈×Dic₈₉

D₄

yes

—

C₈×Dic₈₉

C₂³

yes

—

C₂²×Q₈×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

C₂×C₄

yes

—

C₂×Q₁₆×C₈₉

C₂³

yes

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

Q₃₂×C₈₉

C₂×C₄

yes

complemented

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₂×C₁₆×C₈₉

C₂³

yes

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

D₈

yes

—

C₂×#10623494

—

C₂×#10623494

C₂×D₄

yes

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

D₈

yes

—

C₄×Dic₈₉

C₂×D₄

yes

—

#13083549

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

#41

yes

—

C₂×C₈×C₈₉

C₂⁴

yes

characteristic

C₁₆×C₈₉

C₂²×C₄

yes

—

C₂³×C₈₉

C₂×D₈

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

#135

yes

—

C₂×C₄×C₈₉

C₂²×D₄

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂×D₈

yes

—

C₈×C₈₉

C₄×D₄

yes

—

C₈×C₈₉

C₂³×C₄

yes

characteristic

C₈×C₈₉

C₂×#41

yes

characteristic

#10623494

—

C₂²×C₈₉

C₄×D₈

yes

—

C₂²×C₈₉

#510

yes

—

C₂²×C₈₉

C₂²×D₈

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

C₄×D₈

yes

—

C₄×C₈₉

C₂×C₄×D₄

yes

characteristic

C₄×C₈₉

C₂×#135

yes

characteristic

Dic₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

C₂×C₄×D₈

yes

characteristic

C₂×C₈₉

C₂×#510

yes

—

100

C₂²×Q₃₂

D₈₉

yes

characteristic

101

C₂×C₄×Q₁₆

—

102

#2176

—

103

C₂×#367

—

104

C₂×#358

—

105

C₂×#346

—

106

C₈₉

C₂×#2176

yes

characteristic, complemented, Sylow

107

C₂²×Q₁₆

C₂×D₈₉

yes

—

108

C₂×C₄×Q₈

—

178

—

109

C₂×Q₃₂

Dic₈₉

yes

complemented

110

C₂×Q₃₂

C₂×D₈₉

yes

—

111

C₂²×C₁₆

—

112

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

113

C₄×Q₁₆

—

114

C₄×Q₁₆

—

178

—

115

C₂×#107

—

116

C₂×#103

—

178

—

117

C₂×C₄×C₈

—

118

#367

—

119

#358

—

120

#346

—

121

C₂²×Q₈

—

122

C₂×Q₁₆

—

123

C₂×Q₁₆

—

124

C₂×Q₁₆

C₂×Dic₈₉

yes

—

125

C₂×Q₁₆

C₂²×D₈₉

yes

—

126

C₂²×C₈

—

127

C₂²×C₈

C₂²×D₈₉

yes

characteristic

128

C₄×Q₈

—

356

—

129

C₄×Q₈

—

178

—

130

C₂×C₄⋊C₄

—

356

—

131

C₂×C₄⋊C₄

—

178

—

132

C₂×C₄²

—

133

C₂×C₄²

—

356

—

134

Q₃₂

C₂×Dic₈₉

yes

complemented

135

C₂×C₁₆

—

136

C₂×C₁₆

—

178

—

137

C₂×C₁₆

C₂×Dic₈₉

yes

—

138

C₂×C₁₆

C₂²×D₈₉

yes

—

139

#107

—

140

#107

—

178

—

141

#103

—

178

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

356

—

151

C₂²×C₄

D₄×D₈₉

yes

characteristic

152

Q₁₆

—

153

Q₁₆

—

154

Q₁₆

C₂²×Dic₈₉

yes

—

155

C₂×C₈

—

156

C₂×C₈

—

178

—

157

C₂×C₈

C₂²×Dic₈₉

yes

—

158

C₂×C₈

D₄×D₈₉

yes

characteristic

159

C₂×C₈

#13083573

yes

—

160

C₂×C₈

C₂³×D₈₉

yes

characteristic

161

C₄⋊C₄

—

356

—

162

C₄⋊C₄

—

356

—

163

C₄⋊C₄

—

178

—

164

C₄²

—

165

C₄²

—

166

C₄²

—

356

—

167

C₁₆

—

178

—

168

C₁₆

C₂²×Dic₈₉

yes

—

169

C₂³

D₈×D₈₉

yes

characteristic

170

Q₈

—

171

Q₈

—

172

Q₈

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

356

—

177

C₂×C₄

—

178

—

178

C₂×C₄

—

712

—

179

C₂×C₄

D₄×Dic₈₉

yes

—

180

C₂×C₄

D₈×D₈₉

yes

characteristic

181

C₂×C₄

#15668031

yes

—

182

C₂×C₄

C₂×D₄×D₈₉

yes

characteristic

183

C₈

—

178

—

184

C₈

D₄×Dic₈₉

yes

—

185

C₈

C₂³×Dic₈₉

yes

characteristic

186

C₈

C₂×#13083573

yes

characteristic

187

C₂²

D₈×Dic₈₉

yes

—

188

C₂²

#19152040

yes

—

189

C₂²

C₂×D₈×D₈₉

yes

characteristic

190

C₄

—

191

C₄

—

178

—

192

C₄

—

712

—

193

C₄

D₈×Dic₈₉

yes

—

194

C₄

C₂×D₄×Dic₈₉

yes

characteristic

195

C₄

C₂×#15668031

yes

characteristic

196

C₂

#26022123

yes

direct product factor

197

C₂

C₂×D₈×Dic₈₉

yes

characteristic

198

C₂

C₂×#19152040

yes

—

	subgroup	G/H
center	C₂³	D₈×D₈₉
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂²×Q₃₂×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×D₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂²×Q₃₂	D₈₉
hypocenter	C₈₉	C₂×#2176
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

subgroup

G/H

center

C₂³

D₈×D₈₉

commutator

C₈×C₈₉

C₂³×C₄

Frattini

C₂×C₈

C₂³×D₈₉

Fitting

C₂²×Q₃₂×C₈₉

C₂

socle, prime radical

C₂³×C₈₉

C₂×D₈

cosocle

C₂×C₈×C₈₉

C₂⁴

hypercenter

C₂²×Q₃₂

D₈₉

hypocenter

C₈₉

C₂×#2176

LCS

G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

N	H ≅ G/N	type
2. #26022123	C₂	direct (N × H)
18. C₂×Q₃₂×C₈₉	C₄	semidirect
41. Q₃₂×C₈₉	C₂×C₄	semidirect
97. C₂×C₈₉	#2176	semidirect
106. C₈₉	C₂×#2176	semidirect
109. C₂×Q₃₂	Dic₈₉	semidirect
134. Q₃₂	C₂×Dic₈₉	semidirect
196. C₂	#26022123	direct (N × H)

H ≅ G/N

type

2. #26022123

C₂

direct (N × H)

18. C₂×Q₃₂×C₈₉

C₄

semidirect

41. Q₃₂×C₈₉

C₂×C₄

semidirect

97. C₂×C₈₉

#2176

semidirect

106. C₈₉

C₂×#2176

semidirect

109. C₂×Q₃₂

Dic₈₉

semidirect

134. Q₃₂

C₂×Dic₈₉

semidirect

196. C₂

#26022123

direct (N × H)

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

subgroup	index
C₂×Q₁₆×Dic₈₉	2
#26022123	2
C₂×#19151426	2
C₂×#19151402	2
C₂×#19151373	2
C₂²×Q₃₂×C₈₉	2
C₂×#2176	89

subgroup

index

C₂×Q₁₆×Dic₈₉

C₂²×Q₃₂×C₈₉

Subgroups — C₂×#26022123 #36707725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#26022123 #36707725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26022123 #36707725