Group #36473192 — subgroups

Subgroups — #36473192

Order 22784.

516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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×Dic₇₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19151873	C₂	1	2	yes	maximal
3	C₂×#19151415	C₂	1	2	yes	maximal, complemented
4	#26018346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2113	C₂	1	1	yes	maximal, characteristic
6	C₂×#15668042	—	2	2	no	—
7	C₂²×Dic₃₅₆	C₂²	1	2	yes	—
8	C₂×Dic₇₁₂	—	2	2	no	—
9	C₂×Dic₇₁₂	—	2	4	no	—
10	#19151873	—	2	4	no	—
11	#19151873	—	2	4	no	—
12	C₂×#15667948	C₂²	1	2	yes	—
13	C₂×#15667930	—	2	2	no	—
14	#19151415	—	2	4	no	—
15	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₁₆×C₈₉	—	2	2	no	—
19	C₂²×Dic₁₇₈	—	2	2	no	—
20	#15668042	—	2	8	no	—
21	#15668042	—	4	4	no	—
22	C₂×Dic₃₅₆	—	2	2	no	—
23	C₂×Dic₃₅₆	—	2	2	no	—
24	C₂×Dic₃₅₆	—	2	2	no	—
25	C₂×Dic₃₅₆	—	2	2	no	—
26	C₂×Dic₃₅₆	—	2	2	no	—
27	C₂×Dic₃₅₆	D₄	1	4	yes	—
28	C₂×#13083564	—	4	2	no	—
29	C₂×#13083562	—	4	2	no	—
30	C₂×#13083558	—	2	2	no	—
31	Dic₇₁₂	—	2	8	no	—
32	#15667948	—	2	2	no	—
33	#15667948	D₄	1	4	yes	—
34	#15667930	—	2	8	no	—
35	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
36	#131×C₈₉	—	2	2	no	—
37	#131×C₈₉	—	2	2	no	—
38	C₂×M₁₆×C₈₉	—	2	1	no	—
39	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₈₉	—	2	1	no	—
41	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
42	M₃₂×C₈₉	—	2	2	no	—
43	C₂×C₁₆×C₈₉	—	2	2	no	—
44	C₂×C₁₆×C₈₉	—	2	1	no	—
45	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
46	C₂×Dic₁₇₈	—	2	4	no	—
47	C₂×Dic₁₇₈	—	4	2	no	—
48	C₂×Dic₁₇₈	—	4	2	no	—
49	C₂×Dic₁₇₈	—	4	2	no	—
50	C₂×Dic₁₇₈	—	4	2	no	—
51	C₂×Dic₁₇₈	—	4	2	no	—
52	C₂²×Dic₈₉	—	4	2	no	—
53	Dic₃₅₆	—	2	4	no	—
54	Dic₃₅₆	—	2	4	no	—
55	Dic₃₅₆	—	4	2	no	—
56	Dic₃₅₆	—	4	2	no	—
57	#13083564	—	4	8	no	—
58	#13083562	—	4	8	no	—
59	#13083558	—	2	4	no	—
60	#13083558	—	4	2	no	—
61	C₂×#10623494	—	4	2	no	—
62	#41×C₈₉	—	2	2	no	—
63	#41×C₈₉	—	2	2	no	—
64	C₂×Q₈×C₈₉	D₈	1	1	yes	characteristic
65	C₂×D₄×C₈₉	—	2	1	no	—
66	C₂×D₄×C₈₉	D₈	1	1	yes	characteristic
67	C₂²×C₄×C₈₉	—	2	1	no	—
68	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
69	M₁₆×C₈₉	—	2	2	no	—
70	M₁₆×C₈₉	—	4	2	no	—
71	C₂×C₈×C₈₉	—	2	1	no	—
72	C₂×C₈×C₈₉	—	4	1	no	—
73	C₂×C₈×C₈₉	—	4	1	no	—
74	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
75	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
77	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
78	C₁₆×C₈₉	—	2	2	no	—
79	C₁₆×C₈₉	—	4	1	no	—
80	C₂³×C₈₉	—	2	1	no	—
81	C₂³×C₈₉	#135	1	1	yes	characteristic
82	Q₈×C₈₉	—	2	2	no	—
83	D₄×C₈₉	—	2	2	no	—
84	D₄×C₈₉	—	4	2	no	—
85	C₂×C₄×C₈₉	—	2	1	no	—
86	C₂×C₄×C₈₉	—	4	1	no	—
87	C₂×C₄×C₈₉	—	4	1	no	—
88	C₂×C₄×C₈₉	#120	1	2	yes	—
89	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
90	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×Dic₈₉	—	4	4	no	—
93	C₂×Dic₈₉	—	8	2	no	—
94	C₂×Dic₈₉	—	8	2	no	—
95	Dic₁₇₈	—	4	4	no	—
96	Dic₁₇₈	—	4	4	no	—
97	Dic₁₇₈	—	8	2	no	—
98	Dic₁₇₈	—	8	2	no	—
99	C₈×C₈₉	—	4	1	no	—
100	C₈×C₈₉	#120	1	1	yes	characteristic
101	C₈×C₈₉	#121	1	2	yes	—
102	C₈×C₈₉	#127	1	1	yes	characteristic
103	#10623494	—	4	4	no	—
104	C₂²×C₈₉	—	2	2	no	—
105	C₂²×C₈₉	—	4	2	no	—
106	C₂²×C₈₉	—	4	1	no	—
107	C₂²×C₈₉	#449	1	2	yes	—
108	C₂²×C₈₉	#466	1	1	yes	characteristic
109	C₄×C₈₉	—	4	1	no	—
110	C₄×C₈₉	#392	1	1	yes	characteristic
111	C₄×C₈₉	#447	1	2	yes	—
112	C₄×C₈₉	#469	1	1	yes	characteristic
113	Dic₈₉	—	8	4	no	—
114	#13315	—	89	1	no	maximal, Sylow
115	C₂×C₈₉	—	2	2	no	—
116	C₂×C₈₉	—	8	1	no	—
117	C₂×C₈₉	#1999	1	1	yes	characteristic
118	C₂×C₈₉	#2222	1	2	yes	—
119	C₂²×Q₃₂	—	89	1	no	—
120	C₂×#473	—	89	2	no	—
121	C₂×#362	—	89	2	no	—
122	#2113	D₈₉	1	1	yes	characteristic
123	#1381	—	89	1	no	—
124	C₈₉	#13315	1	1	yes	characteristic, complemented, Sylow
125	C₂×#137	—	178	2	no	—
126	C₂²×Q₁₆	—	89	2	no	—
127	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
128	C₂×Q₃₂	—	178	4	no	—
129	C₂×Q₃₂	—	178	2	no	—
130	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
131	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
132	#473	—	178	4	no	—
133	#473	—	178	4	no	—
134	C₂×#108	—	89	2	no	—
135	C₂×#101	—	178	2	no	—
136	#362	—	178	4	no	—
137	C₂²⋊C₁₆	—	2	2	no	—
138	C₂×#41	D₃₅₆	1	1	yes	characteristic
139	C₂²×Q₈	—	178	2	no	—
140	#137	—	356	4	no	—
141	#137	—	178	8	no	—
142	C₂×Q₁₆	—	89	4	no	—
143	C₂×Q₁₆	—	356	2	no	—
144	C₂×Q₁₆	—	178	2	no	—
145	C₂×Q₁₆	—	178	2	no	—
146	C₂×Q₁₆	—	178	2	no	—
147	C₂×Q₁₆	—	178	2	no	—
148	C₂×Q₁₆	—	178	2	no	—
149	C₂×SD₁₆	—	356	2	no	—
150	#131	—	2	2	no	—
151	#131	—	2	2	no	—
152	C₂×M₁₆	—	2	1	no	—
153	C₂×M₁₆	—	178	2	no	—
154	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
155	C₂²×C₈	—	2	1	no	—
156	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
157	Q₃₂	—	178	8	no	—
158	M₃₂	—	2	2	no	—
159	C₂×C₁₆	—	2	2	no	—
160	C₂×C₁₆	—	2	1	no	—
161	C₂×C₁₆	C₂²⋊D₈₉	1	2	yes	—
162	#108	—	89	4	no	—
163	#108	—	178	2	no	—
164	#101	—	178	8	no	—
165	#41	—	2	2	no	—
166	#41	—	2	2	no	—
167	C₂×Q₈	—	356	2	no	—
168	C₂×Q₈	—	356	2	no	—
169	C₂×Q₈	—	356	2	no	—
170	C₂×Q₈	—	356	2	no	—
171	C₂×Q₈	—	356	2	no	—
172	C₂×Q₈	—	178	4	no	—
173	C₂×Q₈	D₇₁₂	1	1	yes	characteristic
174	C₂×D₄	—	2	1	no	—
175	C₂×D₄	D₇₁₂	1	1	yes	characteristic
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	356	2	no	—
178	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
179	Q₁₆	—	356	8	no	—
180	Q₁₆	—	356	2	no	—
181	Q₁₆	—	356	2	no	—
182	Q₁₆	—	178	4	no	—
183	Q₁₆	—	178	4	no	—
184	SD₁₆	—	356	8	no	—
185	M₁₆	—	2	2	no	—
186	M₁₆	—	4	2	no	—
187	M₁₆	—	356	2	no	—
188	M₁₆	—	178	4	no	—
189	C₂×C₈	—	2	1	no	—
190	C₂×C₈	—	4	1	no	—
191	C₂×C₈	—	4	1	no	—
192	C₂×C₈	—	356	2	no	—
193	C₂×C₈	D₄×D₈₉	1	2	yes	—
194	C₂×C₈	D₄×D₈₉	1	2	yes	—
195	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
196	C₂×C₈	#13083574	1	1	yes	characteristic
197	C₁₆	—	2	2	no	—
198	C₁₆	—	4	1	no	—
199	C₂³	—	2	1	no	—
200	C₂³	#15668034	1	1	yes	characteristic
201	Q₈	—	2	2	no	—
202	Q₈	—	356	4	no	—
203	Q₈	—	356	4	no	—
204	Q₈	—	712	2	no	—
205	Q₈	—	712	2	no	—
206	D₄	—	2	2	no	—
207	D₄	—	4	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	4	1	no	—
210	C₂×C₄	—	4	1	no	—
211	C₂×C₄	—	356	4	no	—
212	C₂×C₄	—	712	2	no	—
213	C₂×C₄	—	712	2	no	—
214	C₂×C₄	#15667982	1	2	yes	—
215	C₂×C₄	#15667986	1	1	yes	characteristic
216	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
217	C₂×C₄	#15668040	1	2	yes	—
218	C₈	—	4	1	no	—
219	C₈	—	356	4	no	—
220	C₈	#15667980	1	1	yes	characteristic
221	C₈	#15667985	1	2	yes	—
222	C₈	#15668008	1	1	yes	characteristic
223	C₂²	—	2	2	no	—
224	C₂²	—	4	1	no	—
225	C₂²	—	4	2	no	—
226	C₂²	#19151745	1	2	yes	—
227	C₂²	#19151834	1	1	yes	characteristic
228	C₄	—	4	1	no	—
229	C₄	—	712	4	no	—
230	C₄	#19151507	1	1	yes	characteristic
231	C₄	#19151734	1	2	yes	—
232	C₄	#19151851	1	1	yes	characteristic
233	C₂	—	2	2	no	—
234	C₂	—	8	1	no	—
235	C₂	#26021250	1	1	yes	characteristic
236	C₂	#26022377	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₇₁₂

C₂

yes

maximal, characteristic, complemented

C₂×#19151873

C₂

yes

maximal

C₂×#19151415

C₂

yes

maximal, complemented

#26018346

C₂

yes

maximal, characteristic, complemented

C₈₉×#2113

C₂

yes

maximal, characteristic

C₂×#15668042

—

C₂²×Dic₃₅₆

C₂²

yes

—

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

—

#19151873

—

#19151873

—

C₂×#15667948

C₂²

yes

—

C₂×#15667930

—

#19151415

—

C₂×#131×C₈₉

C₂²

yes

characteristic

C₂×M₃₂×C₈₉

C₂²

yes

characteristic

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂²⋊C₁₆×C₈₉

—

C₂²×Dic₁₇₈

—

#15668042

—

#15668042

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

D₄

yes

—

C₂×#13083564

—

C₂×#13083562

—

C₂×#13083558

—

Dic₇₁₂

—

#15667948

—

#15667948

D₄

yes

—

#15667930

—

C₂×#41×C₈₉

D₄

yes

characteristic

#131×C₈₉

—

#131×C₈₉

—

C₂×M₁₆×C₈₉

—

C₂×M₁₆×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

D₄

yes

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

Dic₃₅₆

—

—

—

—

—

—

#41×C₈₉

—

#41×C₈₉

—

C₂×Q₈×C₈₉

D₈

yes

characteristic

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

D₈

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₂×C₈×C₈₉

#41

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

#135

yes

characteristic

Q₈×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#120

yes

—

C₂×C₄×C₈₉

#121

yes

characteristic

C₂×C₄×C₈₉

C₂×D₈

yes

characteristic

C₂×C₄×C₈₉

AGL(1,ℤ/8)

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

100

C₈×C₈₉

#120

yes

characteristic

101

C₈×C₈₉

#121

yes

—

102

C₈×C₈₉

#127

yes

characteristic

103

#10623494

—

104

C₂²×C₈₉

—

105

C₂²×C₈₉

—

106

C₂²×C₈₉

—

107

C₂²×C₈₉

#449

yes

—

108

C₂²×C₈₉

#466

yes

characteristic

109

C₄×C₈₉

—

110

C₄×C₈₉

#392

yes

characteristic

111

C₄×C₈₉

#447

yes

—

112

C₄×C₈₉

#469

yes

characteristic

113

Dic₈₉

—

114

#13315

—

maximal, Sylow

115

C₂×C₈₉

—

116

C₂×C₈₉

—

117

C₂×C₈₉

#1999

yes

characteristic

118

C₂×C₈₉

#2222

yes

—

119

C₂²×Q₃₂

—

120

C₂×#473

—

121

C₂×#362

—

122

#2113

D₈₉

yes

characteristic

123

#1381

—

124

C₈₉

#13315

yes

characteristic, complemented, Sylow

125

C₂×#137

—

178

—

126

C₂²×Q₁₆

—

127

C₂×#131

C₂×D₈₉

yes

characteristic

128

C₂×Q₃₂

—

178

—

129

C₂×Q₃₂

—

178

—

130

C₂×M₃₂

C₂×D₈₉

yes

characteristic

131

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

132

#473

—

178

—

133

#473

—

178

—

134

C₂×#108

—

135

C₂×#101

—

178

—

136

#362

—

178

—

137

C₂²⋊C₁₆

—

138

C₂×#41

D₃₅₆

yes

characteristic

139

C₂²×Q₈

—

178

—

140

#137

—

356

—

141

#137

—

178

—

142

C₂×Q₁₆

—

143

C₂×Q₁₆

—

356

—

144

C₂×Q₁₆

—

178

—

145

C₂×Q₁₆

—

178

—

146

C₂×Q₁₆

—

178

—

147

C₂×Q₁₆

—

178

—

148

C₂×Q₁₆

—

178

—

149

C₂×SD₁₆

—

356

—

150

#131

—

151

#131

—

152

C₂×M₁₆

—

153

C₂×M₁₆

—

178

—

154

C₂×M₁₆

D₃₅₆

yes

characteristic

155

C₂²×C₈

—

156

C₂²×C₈

C₂²×D₈₉

yes

characteristic

157

Q₃₂

—

178

—

158

M₃₂

—

159

C₂×C₁₆

—

160

C₂×C₁₆

—

161

C₂×C₁₆

C₂²⋊D₈₉

yes

—

162

#108

—

163

#108

—

178

—

164

#101

—

178

—

165

#41

—

166

#41

—

167

C₂×Q₈

—

356

—

168

C₂×Q₈

—

356

—

169

C₂×Q₈

—

356

—

170

C₂×Q₈

—

356

—

171

C₂×Q₈

—

356

—

172

C₂×Q₈

—

178

—

173

C₂×Q₈

D₇₁₂

yes

characteristic

174

C₂×D₄

—

175

C₂×D₄

D₇₁₂

yes

characteristic

176

C₂²×C₄

—

177

C₂²×C₄

—

356

—

178

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

179

Q₁₆

—

356

—

180

Q₁₆

—

356

—

181

Q₁₆

—

356

—

182

Q₁₆

—

178

—

183

Q₁₆

—

178

—

184

SD₁₆

—

356

—

185

M₁₆

—

186

M₁₆

—

187

M₁₆

—

356

—

188

M₁₆

—

178

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

—

356

—

193

C₂×C₈

D₄×D₈₉

yes

—

194

C₂×C₈

D₄×D₈₉

yes

—

195

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

196

C₂×C₈

#13083574

yes

characteristic

197

C₁₆

—

198

C₁₆

—

199

C₂³

—

200

C₂³

#15668034

yes

characteristic

201

Q₈

—

202

Q₈

—

356

—

203

Q₈

—

356

—

204

Q₈

—

712

—

205

Q₈

—

712

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

356

—

212

C₂×C₄

—

712

—

213

C₂×C₄

—

712

—

214

C₂×C₄

#15667982

yes

—

215

C₂×C₄

#15667986

yes

characteristic

216

C₂×C₄

C₂×D₇₁₂

yes

characteristic

217

C₂×C₄

#15668040

yes

—

218

C₈

—

219

C₈

—

356

—

220

C₈

#15667980

yes

characteristic

221

C₈

#15667985

yes

—

222

C₈

#15668008

yes

characteristic

223

C₂²

—

224

C₂²

—

225

C₂²

—

226

C₂²

#19151745

yes

—

227

C₂²

#19151834

yes

characteristic

228

C₄

—

229

C₄

—

712

—

230

C₄

#19151507

yes

characteristic

231

C₄

#19151734

yes

—

232

C₄

#19151851

yes

characteristic

233

C₂

—

234

C₂

—

235

C₂

#26021250

yes

characteristic

236

C₂

#26022377

yes

—

	subgroup	G/H
center	C₂²	#19151834
commutator, cosocle	C₂²×C₈×C₈₉	C₂³
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#2113	C₂
socle	C₂²×C₈₉	#466
prime radical	C₂×#41×C₈₉	D₄
hypercenter	#2113	D₈₉
hypocenter	C₈₉	#13315
LCS	G ▷ C₂²×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ #2113

subgroup

G/H

center

C₂²

#19151834

commutator, cosocle

C₂²×C₈×C₈₉

C₂³

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₈₉×#2113

C₂

socle

C₂²×C₈₉

#466

prime radical

C₂×#41×C₈₉

D₄

D₈₉

C₈₉

G ▷ C₂²×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ #2113

N	H ≅ G/N	type
1. C₂²×Dic₇₁₂	C₂	semidirect
3. C₂×#19151415	C₂	semidirect
4. #26018346	C₂	semidirect
124. C₈₉	#13315	semidirect

H ≅ G/N

type

1. C₂²×Dic₇₁₂

C₂

semidirect

3. C₂×#19151415

C₂

semidirect

4. #26018346

C₂

semidirect

124. C₈₉

#13315

semidirect

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

subgroup	index
C₂²×Dic₇₁₂	2
C₂×#19151873	2
C₂×#19151415	2
#26018346	2
C₈₉×#2113	2
#13315	89

subgroup

index

C₂²×Dic₇₁₂

C₈₉×#2113

Subgroups — #36473192

Conjugacy classes of subgroups

Complements

Maximal subgroups