Finite Group Databasebeta

← #22591494

Subgroups — #22591494

Order 9088.

576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556102C211yesmaximal, characteristic
2#17985899C212yesmaximal, complemented
3#17985889C212yesmaximal, complemented
4#17985884C212yesmaximal, complemented
5#17985877C212yesmaximal, complemented
6#17985875C212yesmaximal, complemented
7#17985870C212yesmaximal, complemented
8#17985862C211yesmaximal, characteristic, complemented
9#380×C71C211yesmaximal, characteristic, complemented
10C22×D284C2211yescharacteristic
11C22×C22⋊D71C2212yes—
12C22×C4×D71C2212yes—
13#14556102C418yescomplemented
14C2×C4⋊Dic71C2211yescharacteristic
15C2×Dic71⋊C4C2212yes—
16C2×C22⋊Dic71C2212yes—
17C2×(C2×D71)⋊C4C2212yes—
18C2×(C2×D71)⋊C4C2212yes—
19C2×(C2×D71)⋊C4C2212yes—
20C2×(C2×D71)⋊C4C2212yes—
21C2×C4×Dic71C2212yes—
22C71⋊#95C2211yescharacteristic
23C71⋊#95C2212yes—
24C71⋊#95C2211yescharacteristic
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C23×C4×C71C2211yescharacteristic
28C2×C4⋊C4×C71C2212yes—
29C2×C22⋊C4×C71C2211yescharacteristic
30C2×C22⋊C4×C71C2211yescharacteristic
31#95×C71C2212yes—
32C23×D71C2312yes—
33C2×D284—42no—
34C2×D284C2×C414yes—
35C2×C22⋊D71—42no—
36C2×C22⋊D71—42no—
37C2×C22⋊D71C2×C418yescomplemented
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C22×Dic71C2312yes—
41C2×C4×D71—42no—
42C2×C4×D71—42no—
43C2×C4×D71—42no—
44C4⋊Dic71C2×C414yescomplemented
45Dic71⋊C4—42no—
46C22⋊Dic71—42no—
47(C2×D71)⋊C4—42no—
48(C2×D71)⋊C4—42no—
49(C2×D71)⋊C4—42no—
50(C2×D71)⋊C4C2×C418yescomplemented
51C4×Dic71—42no—
52C24×C71C2311yescharacteristic
53C22×C4×C71—42no—
54C22×C4×C71C2×C414yescomplemented
55C22×C4×C71C2312yes—
56C22×C4×C71C2312yes—
57C22×C4×C71C2311yescharacteristic
58C22×C4×C71C2311yescharacteristic
59C4⋊C4×C71—42no—
60C22⋊C4×C71—41no—
61C22⋊C4×C71—41no—
62C23×C71—21no—
63C23×C71—22no—
64C23×C71—22no—
65C23×C71—21no—
66C23×C71C22×C412yes—
67C23×C71C2411yescharacteristic
68C22×D71—22no—
69C22×D71—22no—
70C22×D71—22no—
71C22×D71—22no—
72C22×D71—22no—
73C22×D71—22no—
74C22×D71C22×C414yes—
75C2×C4×C71—22no—
76C2×C4×C71—22no—
77C2×C4×C71—22no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—22no—
83C2×C4×C71—44no—
84C2×C4×C71C22×C412yes—
85C2×C4×C71C22×C412yes—
86C22⋊D71—48no—
87C2×Dic71—22no—
88C2×Dic71—22no—
89C2×Dic71—22no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93C2×Dic71—22no—
94C2×Dic71—22no—
95C2×Dic71C22×C414yes—
96D284—44no—
97C4×D71—48no—
98C22×C71—22no—
99C22×C71—22no—
100C22×C71—22no—
101C22×C71—42no—
102C22×C71—42no—
103C22×C71C23×C411yescharacteristic
104C22×C71H(5,𝔽2)12yes—
105C22×C71H(5,𝔽2)11yescharacteristic
106C22×C71H(5,𝔽2)12yes—
107C22×C712−1+411yescharacteristic
108C2×D71—24no—
109C2×D71—24no—
110C2×D71—24no—
111C2×D71—42no—
112C2×D71—42no—
113C2×D71—42no—
114C2×D71—42no—
115C4×C71—22no—
116C4×C71—22no—
117C4×C71—42no—
118C4×C71—42no—
119Dic71—24no—
120Dic71—42no—
121Dic71—42no—
122C2×C71—42no—
123C2×C71#51811yescharacteristic
124C2×C71#51811yescharacteristic
125C2×C71#52011yescharacteristic
126C2×C71#56012yes—
127C2×C71#56212yes—
128D71—44no—
129#2377—711nomaximal, Sylow
130C71#237711yescharacteristic, complemented, Sylow
131C2×#121—711no—
132#390—712no—
133#388—712no—
134#387—712no—
135#386—712no—
136#386—712no—
137#385—712no—
138#381—711no—
139#380D7111yescharacteristic, complemented
140C22×D4—712no—
141C22×D4—711no—
142C23×C4—712no—
143C23×C4C2×D7111yescharacteristic
144#121—718no—
145C2×C4⋊C4—712no—
146C2×C4⋊C4—711no—
147C2×C4⋊C4C2×D7112yes—
148C2×C22⋊C4—712no—
149C2×C22⋊C4—712no—
150C2×C22⋊C4—712no—
151C2×C22⋊C4—712no—
152C2×C22⋊C4—712no—
153C2×C22⋊C4C2×D7111yescharacteristic
154C2×C22⋊C4C2×D7111yescharacteristic
155C2×C42—712no—
156#95—711no—
157#95—712no—
158#95—711no—
159#95—712no—
160#95—712no—
161#95C2×D7112yes—
162C24—712no—
163C24C22×D7111yescharacteristic
164C2×D4—2842no—
165C2×D4—2842no—
166C2×D4—2842no—
167C2×D4—718no—
168C2×D4—714no—
169C22×C4—42no—
170C22×C4—2842no—
171C22×C4—2842no—
172C22×C4—2842no—
173C22×C4—712no—
174C22×C4—712no—
175C22×C4—712no—
176C22×C4C4×D7114yescomplemented
177C22×C4C22×D7112yes—
178C22×C4C22×D7112yes—
179C22×C4C22×D7111yescharacteristic
180C22×C4C22×D7111yescharacteristic
181C4⋊C4—42no—
182C4⋊C4—2842no—
183C4⋊C4—714no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—2842no—
187C22⋊C4—2842no—
188C22⋊C4—2842no—
189C22⋊C4—2842no—
190C22⋊C4—718no—
191C42—2842no—
192C23—21no—
193C23—22no—
194C23—22no—
195C23—21no—
196C23—714no—
197C23—1422no—
198C23—1422no—
199C23—1422no—
200C23—1422no—
201C23—1422no—
202C23—1422no—
203C23C2×C4×D7112yes—
204C23C23×D7111yescharacteristic
205D4—2844no—
206D4—2848no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—44no—
216C2×C4—2848no—
217C2×C4—714no—
218C2×C4—1422no—
219C2×C4—1422no—
220C2×C4—1422no—
221C2×C4—1422no—
222C2×C4—1422no—
223C2×C4—1422no—
224C2×C4—1422no—
225C2×C4—1422no—
226C2×C4C2×C4×D7112yes—
227C2×C4C2×C4×D7112yes—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—42no—
232C22—42no—
233C22—2842no—
234C22—2842no—
235C22—2842no—
236C22—2842no—
237C22—1424no—
238C22—1424no—
239C22—1424no—
240C22C22×C4×D7111yescharacteristic
241C22#1455617312yes—
242C22#1455617311yescharacteristic
243C22#1455617412yes—
244C22#1455617611yescharacteristic
245C4—22no—
246C4—22no—
247C4—42no—
248C4—42no—
249C4—2842no—
250C4—2842no—
251C4—1424no—
252C2—42no—
253C2—2844no—
254C2#1798647211yescharacteristic
255C2#1798647311yescharacteristic
256C2#1798648011yescharacteristic
257C2#1798673712yes—
258C2#1798674512yes—
subgroupG/H
center, FrattiniC23C23×D71
commutatorC22×C71C23×C4
Fitting#380×C71C2
socleC23×C71C24
hypercenter#380D71
hypocenterC71#2377
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ #380

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #17985899C2semidirect
3. #17985889C2semidirect
4. #17985884C2semidirect
5. #17985877C2semidirect
6. #17985875C2semidirect
7. #17985870C2semidirect
8. #17985862C2semidirect
9. #380×C71C2semidirect
13. #14556102C4semidirect
37. C2×C22⋊D71C2×C4semidirect
44. C4⋊Dic71C2×C4semidirect
50. (C2×D71)⋊C4C2×C4semidirect
54. C22×C4×C71C2×C4semidirect
130. C71#2377semidirect
139. #380D71semidirect
176. C22×C4C4×D71semidirect