Group #36463766 — subgroups

Subgroups — #36463766

Order 22784.

330 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 97 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×#19151722	C₂	1	1	yes	maximal, characteristic
2	#26022052	C₂	1	2	yes	maximal
3	#26018192	C₂	1	1	yes	maximal, characteristic
4	#26018191	C₂	1	2	yes	maximal
5	C₈₉×#1322	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₇₈	C₄	1	1	yes	characteristic
7	#19151722	—	2	2	no	—
8	#19151722	—	2	2	no	—
9	C₂×#15667941	C₄	1	1	yes	characteristic
10	C₂×#15667941	C₂²	1	1	yes	characteristic
11	C₂×C₄×#10623494	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₈₉	C₄	1	1	yes	characteristic
13	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
14	#19151416	—	2	2	no	—
15	C₂²⋊#13083549	C₂²	1	2	yes	—
16	#19151373	—	2	2	no	—
17	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
19	C₂²×Dic₁₇₈	C₈	1	1	yes	characteristic
20	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
21	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₇₈	—	2	2	no	—
23	C₄×Dic₁₇₈	—	2	2	no	—
24	C₂×C₄⋊Dic₈₉	C₈	1	1	yes	characteristic
25	C₂×#13083553	C₈	1	1	yes	characteristic
26	C₂×#13083553	C₈	1	1	yes	characteristic
27	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
29	C₂×#13083549	—	2	2	no	—
30	#15667941	—	2	2	no	—
31	#15667941	—	2	2	no	—
32	C₄×#10623494	—	2	1	no	—
33	C₄×#10623494	—	2	1	no	—
34	C₈×Dic₈₉	—	2	1	no	—
35	C₈×Dic₈₉	—	2	1	no	—
36	C₈×Dic₈₉	D₄	1	2	yes	—
37	C₈×Dic₈₉	D₄	1	2	yes	—
38	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₆×C₈₉	—	2	2	no	—
42	C₄⋊C₈×C₈₉	—	2	2	no	—
43	C₂×Dic₁₇₈	—	2	2	no	—
44	C₂×Dic₁₇₈	—	2	2	no	—
45	C₂×Dic₁₇₈	—	2	2	no	—
46	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
47	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
48	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
49	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
50	C₂×#10623494	—	2	2	no	—
51	C₂×#10623494	—	2	1	no	—
52	C₂×#10623494	—	4	1	no	—
53	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×#10623494	C₂²⋊C₄	1	1	yes	characteristic
55	C₄⋊Dic₈₉	—	2	2	no	—
56	#13083553	—	2	2	no	—
57	#13083553	—	2	2	no	—
58	C₄×Dic₈₉	—	2	1	no	—
59	C₄×Dic₈₉	—	2	1	no	—
60	C₄×Dic₈₉	C₂²⋊C₄	1	2	yes	—
61	C₄×Dic₈₉	M₁₆	1	2	yes	—
62	#13083549	—	4	2	no	—
63	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
64	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
65	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₈₉	—	2	1	no	—
67	C₂×C₈×C₈₉	—	4	1	no	—
68	C₂×C₈×C₈₉	—	4	1	no	—
69	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
70	C₄²×C₈₉	—	2	1	no	—
71	C₄²×C₈₉	—	2	1	no	—
72	C₁₆×C₈₉	—	4	2	no	—
73	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
74	C₂×C₄×C₈₉	—	2	1	no	—
75	C₂×C₄×C₈₉	—	2	1	no	—
76	C₂×C₄×C₈₉	—	2	1	no	—
77	C₂×C₄×C₈₉	—	2	1	no	—
78	C₂×C₄×C₈₉	—	2	1	no	—
79	C₂×C₄×C₈₉	—	4	1	no	—
80	C₂×C₄×C₈₉	M₃₂	1	2	yes	—
81	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₈₉	—	2	1	no	—
84	C₂×Dic₈₉	—	2	1	no	—
85	C₂×Dic₈₉	—	2	1	no	—
86	C₂×Dic₈₉	—	2	1	no	—
87	C₂×Dic₈₉	—	2	1	no	—
88	C₂×Dic₈₉	—	4	1	no	—
89	C₂×Dic₈₉	—	4	1	no	—
90	C₂×Dic₈₉	C₂²⋊C₈	1	2	yes	—
91	C₂×Dic₈₉	C₂²⋊C₈	1	2	yes	—
92	C₂×Dic₈₉	M₃₂	1	2	yes	—
93	Dic₁₇₈	—	2	8	no	—
94	C₈×C₈₉	—	2	2	no	—
95	C₈×C₈₉	—	4	1	no	—
96	#10623494	—	2	1	no	—
97	#10623494	—	4	1	no	—
98	#10623494	#101	1	2	yes	—
99	C₂²×C₈₉	—	2	1	no	—
100	C₂²×C₈₉	—	2	1	no	—
101	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
102	C₂²×C₈₉	C₂×M₃₂	1	1	yes	characteristic
103	C₂²×C₈₉	C₂×M₃₂	1	1	yes	characteristic
104	C₄×C₈₉	—	2	2	no	—
105	C₄×C₈₉	—	2	1	no	—
106	C₄×C₈₉	—	4	1	no	—
107	C₄×C₈₉	#410	1	1	yes	characteristic
108	C₄×C₈₉	C₂×#101	1	1	yes	characteristic
109	Dic₈₉	—	2	2	no	—
110	Dic₈₉	—	2	2	no	—
111	Dic₈₉	—	2	2	no	—
112	Dic₈₉	—	4	1	no	—
113	#11494	—	89	1	no	maximal, Sylow
114	C₂×C₈₉	—	2	1	no	—
115	C₂×C₈₉	—	2	1	no	—
116	C₂×C₈₉	#1461	1	1	yes	characteristic
117	C₂×C₈₉	#2112	1	1	yes	characteristic
118	C₂×C₈₉	#2115	1	1	yes	characteristic
119	C₂×C₈×Q₈	—	89	1	no	—
120	#2163	—	89	2	no	—
121	#1322	—	89	1	no	—
122	#1322	—	89	2	no	—
123	#1322	D₈₉	1	1	yes	characteristic
124	C₈₉	#11494	1	1	yes	characteristic, complemented, Sylow
125	C₂×C₄×Q₈	—	89	1	no	—
126	C₈×Q₈	—	178	2	no	—
127	C₈×Q₈	—	178	2	no	—
128	C₂×C₄⋊C₈	—	89	1	no	—
129	C₂×C₄⋊C₈	—	89	1	no	—
130	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
131	C₂×C₄×C₈	—	89	1	no	—
132	C₂×C₄×C₈	—	89	1	no	—
133	C₂×C₄×C₈	—	89	1	no	—
134	C₄⋊C₁₆	—	178	2	no	—
135	C₂²⋊C₁₆	—	89	2	no	—
136	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	—
137	#346	—	178	2	no	—
138	C₂²×Q₈	—	89	1	no	—
139	C₂²×C₈	—	89	1	no	—
140	C₂²×C₈	—	89	1	no	—
141	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
143	C₄×Q₈	—	178	2	no	—
144	C₄×Q₈	—	178	2	no	—
145	C₂×C₄⋊C₄	—	89	1	no	—
146	C₂×C₄⋊C₄	—	89	1	no	—
147	C₂×C₄⋊C₄	—	89	1	no	—
148	C₂×C₄²	—	89	1	no	—
149	C₂×C₄²	—	89	1	no	—
150	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
151	C₂×C₁₆	—	2	2	no	—
152	C₂×C₁₆	—	178	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	178	2	no	—
155	C₄⋊C₈	—	178	2	no	—
156	C₄×C₈	—	89	2	no	—
157	C₄×C₈	—	89	2	no	—
158	C₄×C₈	—	178	1	no	—
159	C₄×C₈	—	178	1	no	—
160	C₄×C₈	—	178	1	no	—
161	C₄×C₈	—	178	1	no	—
162	C₂×Q₈	—	178	2	no	—
163	C₂×Q₈	—	178	2	no	—
164	C₂×Q₈	—	178	2	no	—
165	C₂²×C₄	—	89	1	no	—
166	C₂²×C₄	—	89	1	no	—
167	C₂²×C₄	—	89	1	no	—
168	C₂²×C₄	—	89	1	no	—
169	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
170	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	—	89	1	no	—
176	C₂×C₈	—	89	1	no	—
177	C₂×C₈	—	356	1	no	—
178	C₂×C₈	—	178	2	no	—
179	C₂×C₈	—	178	1	no	—
180	C₂×C₈	D₄×D₈₉	1	2	yes	—
181	C₄⋊C₄	—	178	2	no	—
182	C₄⋊C₄	—	178	2	no	—
183	C₄⋊C₄	—	178	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	2	1	no	—
186	C₄²	—	89	2	no	—
187	C₄²	—	89	2	no	—
188	C₄²	—	178	1	no	—
189	C₄²	—	178	1	no	—
190	C₁₆	—	4	2	no	—
191	C₁₆	—	356	2	no	—
192	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
193	Q₈	—	178	8	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	4	1	no	—
200	C₂×C₄	—	89	2	no	—
201	C₂×C₄	—	89	2	no	—
202	C₂×C₄	—	89	2	no	—
203	C₂×C₄	—	356	1	no	—
204	C₂×C₄	—	356	1	no	—
205	C₂×C₄	—	178	1	no	—
206	C₂×C₄	—	178	1	no	—
207	C₂×C₄	—	178	1	no	—
208	C₂×C₄	—	178	1	no	—
209	C₂×C₄	—	178	1	no	—
210	C₂×C₄	#15667951	1	2	yes	—
211	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
212	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	4	1	no	—
215	C₈	—	89	2	no	—
216	C₈	—	356	1	no	—
217	C₈	—	178	1	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	C₂²⋊C₈×D₈₉	1	1	yes	characteristic
221	C₂²	M₃₂×D₈₉	1	1	yes	characteristic
222	C₂²	C₂×#15667951	1	1	yes	characteristic
223	C₄	—	2	1	no	—
224	C₄	—	2	2	no	—
225	C₄	—	4	1	no	—
226	C₄	—	356	1	no	—
227	C₄	—	178	2	no	—
228	C₄	—	178	2	no	—
229	C₄	—	178	2	no	—
230	C₄	#19151570	1	1	yes	characteristic
231	C₄	#101×D₈₉	1	1	yes	characteristic
232	C₂	—	2	1	no	—
233	C₂	—	2	1	no	—
234	C₂	#26018574	1	1	yes	characteristic
235	C₂	#26021861	1	1	yes	characteristic
236	C₂	#26021871	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19151722

C₂

yes

maximal, characteristic

#26022052

C₂

yes

maximal

#26018192

C₂

yes

maximal, characteristic

#26018191

C₂

yes

maximal

C₈₉×#1322

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₇₈

C₄

yes

—

—

C₄

yes

characteristic

C₂×#15667941

C₂²

yes

characteristic

C₂×C₄×#10623494

C₄

yes

characteristic

C₂×C₈×Dic₈₉

C₄

yes

characteristic

C₂×C₈×Dic₈₉

C₂²

yes

characteristic

#19151416

—

C₂²⋊#13083549

C₂²

yes

—

#19151373

—

C₂×C₄⋊C₈×C₈₉

C₂²

yes

characteristic

C₂²⋊C₁₆×C₈₉

C₂²

yes

—

C₂²×Dic₁₇₈

C₈

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

characteristic

C₂²×#10623494

C₂×C₄

yes

characteristic

C₄×Dic₁₇₈

—

C₄×Dic₁₇₈

—

C₂×C₄⋊Dic₈₉

C₈

yes

characteristic

C₂×#13083553

C₈

yes

characteristic

C₂×#13083553

C₈

yes

characteristic

C₂×C₄×Dic₈₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

—

—

—

—

C₈×Dic₈₉

—

C₈×Dic₈₉

—

C₈×Dic₈₉

D₄

yes

—

C₈×Dic₈₉

D₄

yes

—

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₄²×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

—

C₄⋊C₈×C₈₉

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂×Dic₁₇₈

—

C₂²×Dic₈₉

C₂×C₈

yes

characteristic

C₂²×Dic₈₉

C₂×C₈

yes

characteristic

C₂²×Dic₈₉

C₂×C₈

yes

characteristic

C₂²×Dic₈₉

C₂×C₈

yes

—

—

—

C₂²⋊C₄

yes

characteristic

C₂×#10623494

C₂²⋊C₄

yes

characteristic

C₄⋊Dic₈₉

—

#13083553

—

#13083553

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

C₂²⋊C₄

yes

—

C₄×Dic₈₉

M₁₆

yes

—

#13083549

—

C₂²×C₄×C₈₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₈₉

C₂×C₈

yes

characteristic

C₂²×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

—

C₄²×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

C₂²×C₈

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

M₃₂

yes

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×M₁₆

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

C₂²⋊C₈

yes

—

C₂×Dic₈₉

C₂²⋊C₈

yes

—

C₂×Dic₈₉

M₃₂

yes

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

—

—

yes

—

C₂²×C₈₉

—

100

C₂²×C₈₉

—

101

C₂²×C₈₉

C₂×C₂²⋊C₈

yes

characteristic

102

C₂²×C₈₉

C₂×M₃₂

yes

characteristic

103

C₂²×C₈₉

C₂×M₃₂

yes

characteristic

104

C₄×C₈₉

—

105

C₄×C₈₉

—

106

C₄×C₈₉

—

107

C₄×C₈₉

#410

yes

characteristic

108

C₄×C₈₉

C₂×#101

yes

characteristic

109

Dic₈₉

—

110

Dic₈₉

—

111

Dic₈₉

—

112

Dic₈₉

—

113

#11494

—

maximal, Sylow

114

C₂×C₈₉

—

115

C₂×C₈₉

—

116

C₂×C₈₉

#1461

yes

characteristic

117

C₂×C₈₉

#2112

yes

characteristic

118

C₂×C₈₉

#2115

yes

characteristic

119

C₂×C₈×Q₈

—

120

#2163

—

121

#1322

—

122

#1322

—

123

#1322

D₈₉

yes

characteristic

124

C₈₉

#11494

yes

characteristic, complemented, Sylow

125

C₂×C₄×Q₈

—

126

C₈×Q₈

—

178

—

127

C₈×Q₈

—

178

—

128

C₂×C₄⋊C₈

—

129

C₂×C₄⋊C₈

—

130

C₂×C₄⋊C₈

C₂×D₈₉

yes

characteristic

131

C₂×C₄×C₈

—

132

C₂×C₄×C₈

—

133

C₂×C₄×C₈

—

134

C₄⋊C₁₆

—

178

—

135

C₂²⋊C₁₆

—

136

C₂²⋊C₁₆

C₂×D₈₉

yes

—

137

#346

—

178

—

138

C₂²×Q₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₂²×C₈

C₄×D₈₉

yes

characteristic

142

C₂²×C₈

C₂²×D₈₉

yes

characteristic

143

C₄×Q₈

—

178

—

144

C₄×Q₈

—

178

—

145

C₂×C₄⋊C₄

—

146

C₂×C₄⋊C₄

—

147

C₂×C₄⋊C₄

—

148

C₂×C₄²

—

149

C₂×C₄²

—

150

C₂×C₄²

C₄×D₈₉

yes

characteristic

151

C₂×C₁₆

—

152

C₂×C₁₆

—

178

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

178

—

155

C₄⋊C₈

—

178

—

156

C₄×C₈

—

157

C₄×C₈

—

158

C₄×C₈

—

178

—

159

C₄×C₈

—

178

—

160

C₄×C₈

—

178

—

161

C₄×C₈

—

178

—

162

C₂×Q₈

—

178

—

163

C₂×Q₈

—

178

—

164

C₂×Q₈

—

178

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₈×D₈₉

yes

characteristic

170

C₂²×C₄

C₈×D₈₉

yes

characteristic

171

C₂²×C₄

C₂×C₄×D₈₉

yes

characteristic

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

356

—

178

C₂×C₈

—

178

—

179

C₂×C₈

—

178

—

180

C₂×C₈

D₄×D₈₉

yes

—

181

C₄⋊C₄

—

178

—

182

C₄⋊C₄

—

178

—

183

C₄⋊C₄

—

178

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

187

C₄²

—

188

C₄²

—

178

—

189

C₄²

—

178

—

190

C₁₆

—

191

C₁₆

—

356

—

192

C₂³

C₂×C₈×D₈₉

yes

characteristic

193

Q₈

—

178

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

356

—

204

C₂×C₄

—

356

—

205

C₂×C₄

—

178

—

206

C₂×C₄

—

178

—

207

C₂×C₄

—

178

—

208

C₂×C₄

—

178

—

209

C₂×C₄

—

178

—

210

C₂×C₄

#15667951

yes

—

211

C₂×C₄

C₂²⋊C₄×D₈₉

yes

characteristic

212

C₂×C₄

M₁₆×D₈₉

yes

characteristic

213

C₈

—

214

C₈

—

215

C₈

—

216

C₈

—

356

—

217

C₈

—

178

—

218

C₂²

—

219

C₂²

—

220

C₂²

C₂²⋊C₈×D₈₉

yes

characteristic

221

C₂²

M₃₂×D₈₉

yes

characteristic

222

C₂²

C₂×#15667951

yes

characteristic

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

356

—

227

C₄

—

178

—

228

C₄

—

178

—

229

C₄

—

178

—

230

C₄

#19151570

yes

characteristic

231

C₄

#101×D₈₉

yes

characteristic

232

C₂

—

233

C₂

—

234

C₂

#26018574

yes

characteristic

235

C₂

#26021861

yes

characteristic

236

C₂

#26021871

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₈₉
commutator, prime radical	C₂³×C₈₉	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₈₉×#1322	C₂
socle	C₂²×C₈₉	C₂×C₂²⋊C₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#1322	D₈₉
hypocenter	C₈₉	#11494
LCS	G ▷ C₂³×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1322

subgroup

G/H

center

C₂×C₄

C₂²⋊C₄×D₈₉

commutator, prime radical

C₂³×C₈₉

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₈₉×#1322

C₂

socle

C₂²×C₈₉

C₂×C₂²⋊C₈

cosocle

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1322

N	H ≅ G/N	type
124. C₈₉	#11494	semidirect

H ≅ G/N

type

124. C₈₉

#11494

semidirect

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

subgroup	index
C₂×#19151722	2
#26022052	2
#26018192	2
#26018191	2
C₈₉×#1322	2
#11494	89

subgroup

index

C₈₉×#1322

Subgroups — #36463766

Conjugacy classes of subgroups

Complements

Maximal subgroups