Group #36448297 — subgroups

Subgroups — #36448297

Order 22784.

410 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 155 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	#26029333	C₂	1	1	yes	maximal, characteristic
2	#26021189	C₂	1	1	yes	maximal, characteristic
3	#26019004	C₂	1	2	yes	maximal
4	#26018090	C₂	1	2	yes	maximal
5	C₄×#101×C₈₉	C₂	1	1	yes	maximal, characteristic
6	Q₈×#10623494	—	2	2	no	—
7	Q₈×#10623494	—	2	2	no	—
8	#19151651	—	2	2	no	—
9	#19151651	C₂²	1	2	yes	—
10	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
11	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
12	#19151353	—	2	2	no	—
13	#19151351	—	2	2	no	—
14	#19151349	—	2	2	no	—
15	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#101×C₈₉	C₄	1	1	yes	characteristic
17	C₂×#101×C₈₉	C₄	1	1	yes	characteristic
18	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
19	#343×C₈₉	C₄	1	2	yes	—
20	C₂²×#10623494	—	2	1	no	—
21	C₂²×#10623494	—	2	1	no	—
22	C₄⋊#10623494	—	2	2	no	—
23	C₄⋊#10623494	—	2	2	no	—
24	C₄⋊#10623494	—	2	2	no	—
25	C₄⋊#10623494	D₄	1	2	yes	—
26	C₄⋊#10623494	D₄	1	2	yes	—
27	C₂²⋊#10623494	—	2	2	no	—
28	C₄×#10623494	—	2	4	no	—
29	C₄×#10623494	—	2	2	no	—
30	C₄×#10623494	—	2	2	no	—
31	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
33	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
34	C₄×Q₈×C₈₉	—	2	2	no	—
35	C₄×Q₈×C₈₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₈₉	Q₈	1	2	yes	—
38	C₂×C₄²×C₈₉	D₄	1	2	yes	—
39	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
40	#101×C₈₉	—	2	2	no	—
41	#101×C₈₉	C₈	1	4	yes	complemented
42	#97×C₈₉	—	2	2	no	—
43	C₄×C₈×C₈₉	—	2	2	no	—
44	C₂×#10623494	—	2	2	no	—
45	C₂×#10623494	—	2	2	no	—
46	C₂×#10623494	—	2	2	no	—
47	C₂×#10623494	—	4	1	no	—
48	C₂×#10623494	—	4	1	no	—
49	C₂×#10623494	—	4	2	no	—
50	C₂×#10623494	—	4	1	no	—
51	C₂×Q₈×C₈₉	—	2	2	no	—
52	C₂×Q₈×C₈₉	—	2	2	no	—
53	C₂×Q₈×C₈₉	C₂×C₈	1	2	yes	—
54	C₂×Q₈×C₈₉	M₁₆	1	2	yes	—
55	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
57	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
60	M₁₆×C₈₉	—	2	2	no	—
61	M₁₆×C₈₉	—	2	2	no	—
62	M₁₆×C₈₉	—	2	2	no	—
63	M₁₆×C₈₉	C₂×C₈	1	4	yes	—
64	C₂×C₈×C₈₉	—	2	2	no	—
65	C₂×C₈×C₈₉	—	2	2	no	—
66	C₄⋊C₄×C₈₉	—	2	2	no	—
67	C₄⋊C₄×C₈₉	—	2	4	no	—
68	C₄²×C₈₉	—	2	2	no	—
69	C₄²×C₈₉	—	2	2	no	—
70	C₄²×C₈₉	C₂×D₄	1	2	yes	—
71	C₄²×C₈₉	#41	1	2	yes	—
72	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
73	Q₈×C₈₉	—	2	4	no	—
74	Q₈×C₈₉	—	2	4	no	—
75	C₂×C₄×C₈₉	—	2	2	no	—
76	C₂×C₄×C₈₉	—	2	2	no	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	2	1	no	—
79	C₂×C₄×C₈₉	—	2	2	no	—
80	C₂×C₄×C₈₉	—	4	1	no	—
81	C₂×C₄×C₈₉	—	4	2	no	—
82	C₂×C₄×C₈₉	C₄⋊C₈	1	4	yes	—
83	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
85	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
87	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
88	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
89	C₂×C₄×C₈₉	#131	1	2	yes	—
90	C₈×C₈₉	—	2	4	no	—
91	C₈×C₈₉	—	4	2	no	—
92	#10623494	—	4	2	no	—
93	#10623494	—	4	2	no	—
94	#10623494	—	4	2	no	—
95	#10623494	—	8	1	no	—
96	C₂²×C₈₉	—	2	1	no	—
97	C₂²×C₈₉	—	2	1	no	—
98	C₂²×C₈₉	#385	1	1	yes	characteristic
99	C₂²×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
100	C₂²×C₈₉	#424	1	1	yes	characteristic
101	C₄×C₈₉	—	2	4	no	—
102	C₄×C₈₉	—	2	1	no	—
103	C₄×C₈₉	—	2	2	no	—
104	C₄×C₈₉	—	4	2	no	—
105	C₄×C₈₉	C₈×D₄	1	2	yes	—
106	C₄×C₈₉	#435	1	2	yes	—
107	C₄×C₈₉	#454	1	1	yes	characteristic
108	C₄×C₈₉	#456	1	1	yes	characteristic
109	#8836	—	89	1	no	maximal, Sylow
110	C₂×C₈₉	—	2	1	no	—
111	C₂×C₈₉	—	2	1	no	—
112	C₂×C₈₉	#1850	1	1	yes	characteristic
113	C₂×C₈₉	#1857	1	1	yes	characteristic
114	C₂×C₈₉	#1858	1	1	yes	characteristic
115	#2982	—	89	1	no	—
116	#1984	—	89	1	no	—
117	C₄×#101	D₈₉	1	1	yes	characteristic
118	#1565	—	89	2	no	—
119	#1278	—	89	2	no	—
120	C₈₉	#8836	1	1	yes	characteristic, complemented, Sylow
121	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
122	C₈×Q₈	—	178	2	no	—
123	C₈×Q₈	—	178	2	no	—
124	#431	—	89	2	no	—
125	#431	—	178	2	no	—
126	C₂×C₄⋊C₈	—	89	1	no	—
127	C₂×#101	Dic₈₉	1	1	yes	characteristic
128	C₂×#101	Dic₈₉	1	1	yes	characteristic
129	C₄×M₁₆	C₂×D₈₉	1	2	yes	—
130	C₂×C₄×C₈	—	89	1	no	—
131	#343	Dic₈₉	1	2	yes	—
132	#336	—	178	2	no	—
133	#335	—	178	2	no	—
134	#334	—	178	2	no	—
135	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
136	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
137	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
138	C₂²×C₈	—	178	1	no	—
139	C₂²×C₈	—	178	1	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₂×C₄⋊C₄	Dic₁₇₈	1	2	yes	—
143	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
144	C₂×C₄²	D₃₅₆	1	2	yes	—
145	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
146	C₄⋊C₈	—	89	2	no	—
147	C₄⋊C₈	—	89	2	no	—
148	C₄⋊C₈	—	178	2	no	—
149	C₄⋊C₈	—	178	2	no	—
150	C₄⋊C₈	—	178	2	no	—
151	#101	—	2	2	no	—
152	#101	#10623494	1	4	yes	complemented
153	C₂²⋊C₈	—	178	2	no	—
154	#97	—	2	2	no	—
155	C₄×C₈	—	2	2	no	—
156	C₄×C₈	—	178	4	no	—
157	C₄×C₈	—	178	2	no	—
158	C₄×C₈	—	178	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	C₂×#10623494	1	2	yes	—
162	C₂×Q₈	#13083558	1	2	yes	—
163	C₂²×C₄	C₄⋊Dic₈₉	1	2	yes	—
164	C₂²×C₄	C₄⋊Dic₈₉	1	2	yes	—
165	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
167	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
168	M₁₆	—	2	2	no	—
169	M₁₆	—	2	2	no	—
170	M₁₆	—	2	2	no	—
171	M₁₆	C₂×#10623494	1	4	yes	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	356	1	no	—
175	C₂×C₈	—	356	1	no	—
176	C₂×C₈	—	356	2	no	—
177	C₂×C₈	—	356	1	no	—
178	C₂×C₈	—	178	2	no	—
179	C₂×C₈	—	178	2	no	—
180	C₂×C₈	—	178	2	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	D₄×D₈₉	1	2	yes	—
186	C₄²	#13083573	1	2	yes	—
187	C₂³	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
188	Q₈	—	2	4	no	—
189	Q₈	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	C₄⋊#10623494	1	4	yes	—
198	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
199	C₂×C₄	#15667982	1	1	yes	characteristic
200	C₂×C₄	#15667989	1	2	yes	—
201	C₂×C₄	#15667996	1	1	yes	characteristic
202	C₂×C₄	C₂²×#10623494	1	1	yes	characteristic
203	C₂×C₄	C₂×#13083558	1	1	yes	characteristic
204	C₂×C₄	#15668019	1	2	yes	—
205	C₈	—	2	4	no	—
206	C₈	—	4	2	no	—
207	C₈	—	356	2	no	—
208	C₈	—	356	2	no	—
209	C₈	—	356	2	no	—
210	C₈	—	712	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	#19151473	1	1	yes	characteristic
214	C₂²	C₂×C₄⋊#10623494	1	1	yes	characteristic
215	C₂²	#19151625	1	1	yes	characteristic
216	C₄	—	2	4	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	2	no	—
220	C₄	D₄×#10623494	1	2	yes	—
221	C₄	#19151670	1	2	yes	—
222	C₄	#19151773	1	1	yes	characteristic
223	C₄	#19151783	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	#26020432	1	1	yes	characteristic
227	C₂	#26020469	1	1	yes	characteristic
228	C₂	#26020474	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26029333

C₂

yes

maximal, characteristic

#26021189

C₂

yes

maximal, characteristic

#26019004

C₂

yes

maximal

#26018090

C₂

yes

maximal

C₄×#101×C₈₉

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

C₂×C₄⋊#10623494

C₂²

yes

characteristic

C₂×C₄×#10623494

C₂²

yes

—

—

—

C₂×C₄×Q₈×C₈₉

C₂²

yes

characteristic

C₂×#101×C₈₉

C₄

yes

characteristic

C₂×#101×C₈₉

C₄

yes

characteristic

C₄×M₁₆×C₈₉

C₂²

yes

—

#343×C₈₉

C₄

yes

—

—

—

—

—

—

D₄

yes

—

C₄⋊#10623494

D₄

yes

—

—

—

—

—

C₂²×Q₈×C₈₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₈₉

C₂×C₄

yes

—

C₂×M₁₆×C₈₉

C₂×C₄

yes

—

C₄×Q₈×C₈₉

—

C₄×Q₈×C₈₉

—

C₂×C₄⋊C₄×C₈₉

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₈₉

Q₈

yes

—

C₂×C₄²×C₈₉

D₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

#101×C₈₉

—

#101×C₈₉

C₈

yes

complemented

#97×C₈₉

—

C₄×C₈×C₈₉

—

—

—

—

—

—

—

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

C₂×C₈

yes

—

C₂×Q₈×C₈₉

M₁₆

yes

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×Q₈

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

M₁₆×C₈₉

—

M₁₆×C₈₉

C₂×C₈

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₄²×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₄⋊C₈

yes

—

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

#120

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₈₉

#123

yes

characteristic

C₂×C₄×C₈₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

C₂×C₄×C₈₉

#131

yes

—

C₈×C₈₉

—

C₈×C₈₉

—

—

—

—

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#385

yes

characteristic

C₂²×C₈₉

C₂×C₄⋊C₈

yes

characteristic

100

C₂²×C₈₉

#424

yes

characteristic

101

C₄×C₈₉

—

102

C₄×C₈₉

—

103

C₄×C₈₉

—

104

C₄×C₈₉

—

105

C₄×C₈₉

C₈×D₄

yes

—

106

C₄×C₈₉

#435

yes

—

107

C₄×C₈₉

#454

yes

characteristic

108

C₄×C₈₉

yes

109

—

110

C₂×C₈₉

—

111

C₂×C₈₉

—

112

C₂×C₈₉

#1850

yes

characteristic

113

C₂×C₈₉

#1857

yes

characteristic

114

C₂×C₈₉

#1858

yes

characteristic

115

#2982

—

116

#1984

—

117

C₄×#101

D₈₉

yes

characteristic

118

#1565

—

119

#1278

—

120

C₈₉

#8836

yes

characteristic, complemented, Sylow

121

C₂×C₄×Q₈

C₂×D₈₉

yes

characteristic

122

C₈×Q₈

—

178

—

123

C₈×Q₈

—

178

—

124

#431

—

125

#431

—

178

—

126

C₂×C₄⋊C₈

—

127

C₂×#101

Dic₈₉

yes

characteristic

128

C₂×#101

Dic₈₉

yes

characteristic

129

C₄×M₁₆

C₂×D₈₉

yes

—

130

C₂×C₄×C₈

—

131

#343

Dic₈₉

yes

—

132

#336

—

178

—

133

#335

—

178

—

134

#334

—

178

—

135

C₂²×Q₈

C₂×Dic₈₉

yes

characteristic

136

C₂×M₁₆

C₂×Dic₈₉

yes

—

137

C₂×M₁₆

C₂×Dic₈₉

yes

—

138

C₂²×C₈

—

178

—

139

C₂²×C₈

—

178

—

140

C₄×Q₈

—

141

C₄×Q₈

—

142

C₂×C₄⋊C₄

Dic₁₇₈

yes

—

143

C₂×C₄⋊C₄

C₂×Dic₈₉

yes

characteristic

144

C₂×C₄²

D₃₅₆

yes

—

145

C₂×C₄²

C₂²×D₈₉

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

178

—

149

C₄⋊C₈

—

178

—

150

C₄⋊C₈

—

178

—

151

#101

—

152

#101

#10623494

yes

complemented

153

C₂²⋊C₈

—

178

—

154

#97

—

155

C₄×C₈

—

156

C₄×C₈

—

178

—

157

C₄×C₈

—

178

—

158

C₄×C₈

—

178

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₂×#10623494

yes

—

162

C₂×Q₈

#13083558

yes

—

163

C₂²×C₄

C₄⋊Dic₈₉

yes

—

164

C₂²×C₄

C₄⋊Dic₈₉

yes

—

165

C₂²×C₄

C₂²×Dic₈₉

yes

characteristic

166

C₂²×C₄

C₂×D₃₅₆

yes

characteristic

167

C₂²×C₄

C₂×Dic₁₇₈

yes

characteristic

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

M₁₆

C₂×#10623494

yes

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

356

—

175

C₂×C₈

—

356

—

176

C₂×C₈

—

356

—

177

C₂×C₈

—

356

—

178

C₂×C₈

—

178

—

179

C₂×C₈

—

178

—

180

C₂×C₈

—

178

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

D₄×D₈₉

yes

—

186

C₄²

#13083573

yes

—

187

C₂³

C₂×C₄⋊Dic₈₉

yes

characteristic

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

C₄⋊#10623494

yes

—

198

C₂×C₄

D₄×Dic₈₉

yes

—

199

C₂×C₄

#15667982

yes

characteristic

200

C₂×C₄

#15667989

yes

—

201

C₂×C₄

#15667996

yes

characteristic

202

C₂×C₄

C₂²×#10623494

yes

characteristic

203

C₂×C₄

C₂×#13083558

yes

characteristic

204

C₂×C₄

#15668019

yes

—

205

C₈

—

206

C₈

—

207

C₈

—

356

—

208

C₈

—

356

—

209

C₈

—

356

—

210

C₈

—

712

—

211

C₂²

—

212

C₂²

—

213

C₂²

#19151473

yes

characteristic

214

C₂²

C₂×C₄⋊#10623494

yes

characteristic

215

C₂²

#19151625

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

D₄×#10623494

yes

—

221

C₄

#19151670

yes

—

222

C₄

#19151773

yes

characteristic

223

C₄

#19151783

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#26020432

yes

characteristic

227

C₂

#26020469

yes

characteristic

228

C₂

#26020474

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#15667982
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₄×#101×C₈₉	C₂
socle	C₂²×C₈₉	#385
prime radical	C₂³×C₈₉	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄×#101	D₈₉
hypocenter	C₈₉	#8836
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

subgroup

G/H

center

C₂×C₄

#15667982

commutator

C₂×C₄×C₈₉

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₄×#101×C₈₉

C₂

socle

C₂²×C₈₉

#385

prime radical

C₂³×C₈₉

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#101

N	H ≅ G/N	type
41. #101×C₈₉	C₈	semidirect
120. C₈₉	#8836	semidirect
152. #101	#10623494	semidirect

H ≅ G/N

type

41. #101×C₈₉

C₈

semidirect

120. C₈₉

#8836

semidirect

152. #101

#10623494

semidirect

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

subgroup	index
#26029333	2
#26021189	2
#26019004	2
#26018090	2
C₄×#101×C₈₉	2
#8836	89

subgroup

index

C₄×#101×C₈₉

Subgroups — #36448297

Conjugacy classes of subgroups

Complements

Maximal subgroups