Group #36453225 — subgroups

Subgroups — #36453225

Order 22784.

546 conjugacy classes of subgroups; only the 179 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 179 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	C₄×#15668012	C₂	1	1	yes	maximal, characteristic
2	#26019998	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151328	C₂	1	4	yes	maximal
4	C₈₉×#1842	C₂	1	1	yes	maximal, characteristic
5	C₂×#15668012	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₁₇₈	C₂²	1	2	yes	—
7	C₂×C₄×#10623494	C₂²	1	2	yes	—
8	#19151504	C₄	1	2	yes	—
9	#19151496	—	2	2	no	—
10	#19151468	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₈₉	—	2	2	no	—
12	#19151353	—	2	2	no	—
13	#19151328	—	2	8	no	—
14	C₂×C₄⋊C₈×C₈₉	—	2	2	no	—
15	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
16	C₄³×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₇₈	C₂×C₄	1	2	yes	—
18	C₂²×#10623494	—	2	2	no	—
19	#15668012	—	2	4	no	—
20	C₄×Dic₁₇₈	—	2	4	no	—
21	C₄×Dic₁₇₈	—	2	4	no	—
22	C₂×C₄⋊Dic₈₉	—	2	2	no	—
23	C₂×C₄⋊Dic₈₉	—	2	2	no	—
24	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
25	C₂×#13083553	—	2	2	no	—
26	C₂×C₄×Dic₈₉	—	2	2	no	—
27	C₄×#10623494	—	2	2	no	—
28	C₄×#10623494	D₄	1	4	yes	—
29	#15667919	—	2	4	no	—
30	C₂²×C₈×C₈₉	—	2	2	no	—
31	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₈₉	D₄	1	2	yes	—
34	C₂×C₄²×C₈₉	D₄	1	2	yes	—
35	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₈₉	—	2	4	no	—
37	C₄⋊C₈×C₈₉	—	4	4	no	—
38	C₂×Dic₁₇₈	—	2	4	no	—
39	C₂×Dic₁₇₈	—	2	4	no	—
40	C₂×Dic₁₇₈	—	2	2	no	—
41	C₂×Dic₁₇₈	M₁₆	1	4	yes	—
42	C₂²×Dic₈₉	—	2	2	no	—
43	C₂²×Dic₈₉	—	2	2	no	—
44	C₂×#10623494	—	2	4	no	—
45	C₂×#10623494	—	4	4	no	—
46	C₄⋊Dic₈₉	—	2	8	no	—
47	C₄⋊Dic₈₉	—	2	4	no	—
48	C₄⋊Dic₈₉	—	4	4	no	—
49	#13083553	—	4	4	no	—
50	C₄×Dic₈₉	—	4	2	no	—
51	C₄×Dic₈₉	—	4	2	no	—
52	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
53	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₈₉	—	4	2	no	—
58	C₂×C₈×C₈₉	—	4	4	no	—
59	C₄²×C₈₉	—	2	2	no	—
60	C₄²×C₈₉	—	2	2	no	—
61	C₄²×C₈₉	—	4	2	no	—
62	C₄²×C₈₉	SD₁₆	1	4	yes	—
63	C₄²×C₈₉	Q₁₆	1	4	yes	—
64	C₄²×C₈₉	C₂×D₄	1	2	yes	—
65	C₄²×C₈₉	#41	1	2	yes	—
66	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₈₉	—	2	2	no	—
68	C₂×C₄×C₈₉	—	2	2	no	—
69	C₂×C₄×C₈₉	—	2	2	no	—
70	C₂×C₄×C₈₉	—	2	2	no	—
71	C₂×C₄×C₈₉	—	2	2	no	—
72	C₂×C₄×C₈₉	#103	1	4	yes	—
73	C₂×C₄×C₈₉	#103	1	4	yes	—
74	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
75	C₂×C₄×C₈₉	#121	1	2	yes	—
76	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
77	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
78	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
79	C₂×C₄×C₈₉	#131	1	2	yes	—
80	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
81	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
82	C₂×Dic₈₉	—	2	4	no	—
83	C₂×Dic₈₉	—	4	2	no	—
84	C₂×Dic₈₉	—	4	2	no	—
85	C₂×Dic₈₉	—	4	2	no	—
86	C₂×Dic₈₉	—	4	4	no	—
87	Dic₁₇₈	—	2	8	no	—
88	Dic₁₇₈	—	4	4	no	—
89	C₈×C₈₉	—	8	2	no	—
90	#10623494	—	4	4	no	—
91	C₂²×C₈₉	#390	1	1	yes	characteristic
92	C₂²×C₈₉	#407	1	1	yes	characteristic
93	C₂²×C₈₉	#408	1	1	yes	characteristic
94	C₂²×C₈₉	C₂×#103	1	2	yes	—
95	C₂²×C₈₉	#421	1	2	yes	—
96	C₄×C₈₉	—	2	2	no	—
97	C₄×C₈₉	—	2	4	no	—
98	C₄×C₈₉	—	2	4	no	—
99	C₄×C₈₉	#435	1	4	yes	—
100	C₄×C₈₉	#487	1	2	yes	—
101	C₄×C₈₉	#492	1	1	yes	characteristic
102	C₄×C₈₉	#494	1	1	yes	characteristic
103	Dic₈₉	—	4	4	no	—
104	Dic₈₉	—	8	2	no	—
105	#9643	—	89	1	no	maximal, Sylow
106	C₂×C₈₉	#1481	1	2	yes	—
107	C₂×C₈₉	#1487	1	2	yes	—
108	C₂×C₈₉	#1955	1	1	yes	characteristic
109	C₂×C₈₉	#1956	1	1	yes	characteristic
110	C₂×C₈₉	#1963	1	1	yes	characteristic
111	C₄×C₄⋊Q₈	—	89	1	no	—
112	#1842	D₈₉	1	1	yes	characteristic
113	#1744	—	89	1	no	—
114	C₂×Q₈⋊C₈	—	89	4	no	—
115	C₈₉	#9643	1	1	yes	characteristic, complemented, Sylow
116	C₂×C₄⋊Q₈	—	89	1	no	—
117	C₂×C₄×Q₈	—	89	2	no	—
118	C₂×C₄⋊C₈	—	2	2	no	—
119	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
120	C₂×C₄×C₈	—	89	2	no	—
121	#391	—	89	2	no	—
122	#389	—	178	2	no	—
123	#384	—	89	1	no	—
124	C₄×C₄⋊C₄	—	178	2	no	—
125	C₄³	C₂×D₈₉	1	1	yes	characteristic
126	#336	—	178	2	no	—
127	Q₈⋊C₈	—	178	8	no	—
128	C₂²×Q₈	—	89	2	no	—
129	C₂²×C₈	—	2	2	no	—
130	C₂²×C₈	—	178	2	no	—
131	C₄⋊Q₈	—	178	4	no	—
132	C₄×Q₈	—	178	4	no	—
133	C₄×Q₈	—	178	4	no	—
134	C₂×C₄⋊C₄	—	89	2	no	—
135	C₂×C₄⋊C₄	—	178	2	no	—
136	C₂×C₄⋊C₄	—	178	2	no	—
137	C₂×C₄⋊C₄	—	178	2	no	—
138	C₂×C₄²	—	178	2	no	—
139	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
140	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
141	C₂×C₄²	D₃₅₆	1	2	yes	—
142	C₂×C₄²	C₂²⋊D₈₉	1	2	yes	—
143	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
144	C₄⋊C₈	—	2	4	no	—
145	C₄⋊C₈	—	4	4	no	—
146	C₄×C₈	—	89	4	no	—
147	C₄×C₈	—	178	2	no	—
148	#95	—	178	4	no	—
149	C₂×Q₈	—	89	4	no	—
150	C₂×Q₈	—	178	4	no	—
151	C₂×Q₈	—	178	4	no	—
152	C₂×Q₈	—	178	2	no	—
153	C₂²×C₄	—	178	2	no	—
154	C₂²×C₄	—	178	2	no	—
155	C₂²×C₄	#13083551	1	2	yes	—
156	C₂²×C₄	#13083551	1	2	yes	—
157	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
158	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
159	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
160	C₂×C₈	—	4	2	no	—
161	C₂×C₈	—	4	4	no	—
162	C₂×C₈	—	356	4	no	—
163	C₂×C₈	—	178	4	no	—
164	C₄⋊C₄	—	356	4	no	—
165	C₄⋊C₄	—	356	4	no	—
166	C₄⋊C₄	—	178	8	no	—
167	C₄⋊C₄	—	178	4	no	—
168	C₄²	—	2	2	no	—
169	C₄²	—	2	2	no	—
170	C₄²	—	4	2	no	—
171	C₄²	—	356	2	no	—
172	C₄²	—	356	2	no	—
173	C₄²	#13083562	1	4	yes	—
174	C₄²	#13083564	1	4	yes	—
175	C₄²	D₄×D₈₉	1	2	yes	—
176	C₄²	#13083575	1	2	yes	—
177	C₂³	C₂×#13083551	1	1	yes	characteristic
178	Q₈	—	356	4	no	—
179	Q₈	—	178	8	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	356	2	no	—
186	C₂×C₄	—	356	2	no	—
187	C₂×C₄	—	356	2	no	—
188	C₂×C₄	—	356	4	no	—
189	C₂×C₄	—	178	4	no	—
190	C₂×C₄	#15667935	1	4	yes	—
191	C₂×C₄	#15667935	1	4	yes	—
192	C₂×C₄	#15667974	1	2	yes	—
193	C₂×C₄	#15667987	1	2	yes	—
194	C₂×C₄	#15668001	1	1	yes	characteristic
195	C₂×C₄	#15668008	1	1	yes	characteristic
196	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
197	C₂×C₄	#15668018	1	2	yes	—
198	C₂×C₄	C₂×#13083562	1	2	yes	—
199	C₂×C₄	C₂×#13083564	1	2	yes	—
200	C₈	—	8	2	no	—
201	C₈	—	356	4	no	—
202	C₂²	#19151499	1	1	yes	characteristic
203	C₂²	#19151561	1	1	yes	characteristic
204	C₂²	#19151564	1	1	yes	characteristic
205	C₂²	C₂×#15667935	1	2	yes	—
206	C₂²	#19151614	1	2	yes	—
207	C₄	—	2	4	no	—
208	C₄	—	2	4	no	—
209	C₄	—	2	2	no	—
210	C₄	—	356	4	no	—
211	C₄	—	712	2	no	—
212	C₄	#19151668	1	4	yes	—
213	C₄	#19151950	1	2	yes	—
214	C₄	#19151970	1	1	yes	characteristic
215	C₄	#19151977	1	1	yes	characteristic
216	C₂	#26018654	1	2	yes	—
217	C₂	#26018680	1	2	yes	—
218	C₂	#26021049	1	1	yes	characteristic
219	C₂	#26021053	1	1	yes	characteristic
220	C₂	#26021083	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#15668012

C₂

yes

maximal, characteristic

#26019998

C₂

yes

maximal, characteristic

C₂×#19151328

C₂

yes

maximal

C₈₉×#1842

C₂

yes

maximal, characteristic

C₂×#15668012

C₄

yes

characteristic

C₂×C₄×Dic₁₇₈

C₂²

yes

—

C₂×C₄×#10623494

C₂²

yes

—

#19151504

C₄

yes

—

#19151496

—

#19151468

C₄

yes

characteristic

C₄×C₄⋊Dic₈₉

—

#19151353

—

#19151328

—

C₂×C₄⋊C₈×C₈₉

—

C₂×C₄⋊C₈×C₈₉

C₂²

yes

—

C₄³×C₈₉

C₂²

yes

characteristic

C₂²×Dic₁₇₈

C₂×C₄

yes

—

C₂²×#10623494

—

#15668012

—

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

C₂×C₄

yes

—

C₂×#13083553

—

C₂×C₄×Dic₈₉

—

C₄×#10623494

—

C₄×#10623494

D₄

yes

—

#15667919

—

C₂²×C₈×C₈₉

—

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄⋊C₈×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

M₁₆

yes

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

#13083553

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

SD₁₆

yes

—

C₄²×C₈₉

Q₁₆

yes

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

#103

yes

—

C₂×C₄×C₈₉

#103

yes

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

#121

yes

—

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂×C₄×C₈₉

#131

yes

—

C₂×C₄×C₈₉

C₂×SD₁₆

yes

—

C₂×C₄×C₈₉

C₂×Q₁₆

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

—

C₂²×C₈₉

#421

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#435

yes

—

100

C₄×C₈₉

#487

yes

—

101

C₄×C₈₉

#492

yes

characteristic

102

C₄×C₈₉

#494

yes

characteristic

103

Dic₈₉

—

104

Dic₈₉

—

105

#9643

—

maximal, Sylow

106

C₂×C₈₉

#1481

yes

—

107

C₂×C₈₉

#1487

yes

—

108

C₂×C₈₉

#1955

yes

characteristic

109

C₂×C₈₉

#1956

yes

characteristic

110

C₂×C₈₉

#1963

yes

characteristic

111

C₄×C₄⋊Q₈

—

112

#1842

D₈₉

yes

characteristic

113

#1744

—

114

C₂×Q₈⋊C₈

—

115

C₈₉

#9643

yes

characteristic, complemented, Sylow

116

C₂×C₄⋊Q₈

—

117

C₂×C₄×Q₈

—

118

C₂×C₄⋊C₈

—

119

C₂×C₄⋊C₈

C₂×D₈₉

yes

—

120

C₂×C₄×C₈

—

121

#391

—

122

#389

—

178

—

123

#384

—

124

C₄×C₄⋊C₄

—

178

—

125

C₄³

C₂×D₈₉

yes

characteristic

126

#336

—

178

—

127

Q₈⋊C₈

—

178

—

128

C₂²×Q₈

—

129

C₂²×C₈

—

130

C₂²×C₈

—

178

—

131

C₄⋊Q₈

—

178

—

132

C₄×Q₈

—

178

—

133

C₄×Q₈

—

178

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

178

—

136

C₂×C₄⋊C₄

—

178

—

137

C₂×C₄⋊C₄

—

178

—

138

C₂×C₄²

—

178

—

139

C₂×C₄²

C₄×D₈₉

yes

characteristic

140

C₂×C₄²

C₄×D₈₉

yes

characteristic

141

C₂×C₄²

D₃₅₆

yes

—

142

C₂×C₄²

C₂²⋊D₈₉

yes

—

143

C₂×C₄²

C₂²×D₈₉

yes

characteristic

144

C₄⋊C₈

—

145

C₄⋊C₈

—

146

C₄×C₈

—

147

C₄×C₈

—

178

—

148

#95

—

178

—

149

C₂×Q₈

—

150

C₂×Q₈

—

178

—

151

C₂×Q₈

—

178

—

152

C₂×Q₈

—

178

—

153

C₂²×C₄

—

178

—

154

C₂²×C₄

—

178

—

155

C₂²×C₄

#13083551

yes

—

156

C₂²×C₄

#13083551

yes

—

157

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

158

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

159

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

356

—

163

C₂×C₈

—

178

—

164

C₄⋊C₄

—

356

—

165

C₄⋊C₄

—

356

—

166

C₄⋊C₄

—

178

—

167

C₄⋊C₄

—

178

—

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

356

—

172

C₄²

—

356

—

173

C₄²

#13083562

yes

—

174

C₄²

#13083564

yes

—

175

C₄²

D₄×D₈₉

yes

—

176

C₄²

#13083575

yes

—

177

C₂³

C₂×#13083551

yes

characteristic

178

Q₈

—

356

—

179

Q₈

—

178

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

356

—

186

C₂×C₄

—

356

—

187

C₂×C₄

—

356

—

188

C₂×C₄

—

356

—

189

C₂×C₄

—

178

—

190

C₂×C₄

#15667935

yes

—

191

C₂×C₄

#15667935

yes

—

192

C₂×C₄

#15667974

yes

—

193

C₂×C₄

#15667987

yes

—

194

C₂×C₄

#15668001

yes

characteristic

195

C₂×C₄

#15668008

yes

characteristic

196

C₂×C₄

M₁₆×D₈₉

yes

—

197

C₂×C₄

#15668018

yes

—

198

C₂×C₄

C₂×#13083562

yes

—

199

C₂×C₄

C₂×#13083564

yes

—

200

C₈

—

201

C₈

—

356

—

202

C₂²

#19151499

yes

characteristic

203

C₂²

#19151561

yes

characteristic

204

C₂²

#19151564

yes

characteristic

205

C₂²

C₂×#15667935

yes

—

206

C₂²

#19151614

yes

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

356

—

211

C₄

—

712

—

212

C₄

#19151668

yes

—

213

C₄

#19151950

yes

—

214

C₄

#19151970

yes

characteristic

215

C₄

#19151977

yes

characteristic

216

C₂

#26018654

yes

—

217

C₂

#26018680

yes

—

218

C₂

#26021049

yes

characteristic

219

C₂

#26021053

yes

characteristic

220

C₂

#26021083

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₈₉
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1842	C₂
socle, prime radical	C₂³×C₈₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1842	D₈₉
hypocenter	C₈₉	#9643
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

subgroup

G/H

center

C₂²×C₄

C₂×C₂²⋊D₈₉

commutator

C₂²×C₄×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₈₉×#1842

C₂

socle, prime radical

C₂³×C₈₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1842

N	H ≅ G/N	type
115. C₈₉	#9643	semidirect

H ≅ G/N

type

115. C₈₉

#9643

semidirect

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

subgroup	index
C₄×#15668012	2
#26019998	2
C₂×#19151328	2
C₈₉×#1842	2
#9643	89

subgroup

index

C₈₉×#1842

Subgroups — #36453225

Conjugacy classes of subgroups

Complements

Maximal subgroups