Finite Group Databasebeta

← #22594847

Subgroups — #22594847

Order 9088.

568 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556110C212yesmaximal, complemented
2#17985939C212yesmaximal, complemented
3#17985924C211yesmaximal, characteristic, complemented
4#17985921C212yesmaximal, complemented
5#17985908C211yesmaximal, characteristic
6#17985878C212yesmaximal, complemented
7#17985877C212yesmaximal, complemented
8#17985856C212yesmaximal, complemented
9#385×C71C211yesmaximal, characteristic, complemented
10C22×D284C2211yescharacteristic
11C22×C22⋊D71C2212yes—
12C22×C4×D71C2212yes—
13#14556110—28no—
14C2×C4⋊Dic71C2212yes—
15C2×C4⋊Dic71C2211yescharacteristic
16C2×Dic71⋊C4C2212yes—
17C2×C22⋊Dic71C2212yes—
18C2×(C2×D71)⋊C4C2212yes—
19C2×(C2×D71)⋊C4C2212yes—
20C2×(C2×D71)⋊C4C2212yes—
21C2×(C2×D71)⋊C4C2212yes—
22C71⋊#95C2211yescharacteristic
23C71⋊#95C2212yes—
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2211yescharacteristic
27C23×C4×C71C2211yescharacteristic
28C2×C4⋊C4×C71C2212yes—
29C2×C22⋊C4×C71C2211yescharacteristic
30C2×C22⋊C4×C71C2211yescharacteristic
31#95×C71C2212yes—
32C23×D71C2312yes—
33C2×D284—24no—
34C2×D284—41no—
35C2×C22⋊D71—24no—
36C2×C22⋊D71—24no—
37C2×C22⋊D71—42no—
38C22×Dic71C2312yes—
39C22×Dic71C2312yes—
40C22×Dic71C2312yes—
41C2×C4×D71—24no—
42C2×C4×D71—24no—
43C2×C4×D71—42no—
44C4⋊Dic71—24no—
45C4⋊Dic71—41no—
46Dic71⋊C4—24no—
47C22⋊Dic71—24no—
48(C2×D71)⋊C4—24no—
49(C2×D71)⋊C4—42no—
50(C2×D71)⋊C4—42no—
51(C2×D71)⋊C4—42no—
52C24×C71C2311yescharacteristic
53C22×C4×C71—42no—
54C22×C4×C71—41no—
55C22×C4×C71C2311yescharacteristic
56C22×C4×C71C2312yes—
57C22×C4×C71C2311yescharacteristic
58C22×C4×C71C2312yes—
59C4⋊C4×C71—42no—
60C22⋊C4×C71—41no—
61C22⋊C4×C71D414yescomplemented
62C23×C71—22no—
63C23×C71—21no—
64C23×C71—22no—
65C23×C71—21no—
66C23×C71C2×D412yes—
67C23×C71C2411yescharacteristic
68C22×D71—22no—
69C22×D71—22no—
70C22×D71—22no—
71C22×D71—22no—
72C22×D71—22no—
73C22×D71—22no—
74C22×D71#4114yes—
75C2×C4×C71—22no—
76C2×C4×C71—22no—
77C2×C4×C71—22no—
78C2×C4×C71—21no—
79C2×C4×C71—21no—
80C2×C4×C71—22no—
81C2×C4×C71—22no—
82C2×C4×C71—22no—
83C2×C4×C71—22no—
84C2×C4×C71—44no—
85C2×C4×C71C2×D414yes—
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×Dic71—22no—
96D284—44no—
97C4×D71—48no—
98C22×C71—22no—
99C22×C71—24no—
100C22×C71—42no—
101C22×C71—41no—
102C22×C71—41no—
103C22×C71C22×D411yescharacteristic
104C22×C71C2×#4112yes—
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—24no—
116C4×C71—41no—
117C4×C71—41no—
118C4×C71—42no—
119Dic71—42no—
120Dic71—42no—
121Dic71—42no—
122C2×C71—42no—
123C2×C71#53711yescharacteristic
124C2×C71#53912yes—
125C2×C71#54612yes—
126C2×C71#55111yescharacteristic
127C2×C71#56011yescharacteristic
128D71—44no—
129#2693—711nomaximal, Sylow
130C71#269311yescharacteristic, complemented, Sylow
131C2×#123—712no—
132#400—712no—
133#397—711no—
134#396—712no—
135#392—711no—
136#386—712no—
137#386—712no—
138#385D7111yescharacteristic, complemented
139#380—712no—
140C22×D4—712no—
141C22×D4—711no—
142C23×C4—712no—
143C23×C4C2×D7111yescharacteristic
144#123—1428no—
145C2×C4⋊C4—711no—
146C2×C4⋊C4—712no—
147C2×C4⋊C4—712no—
148C2×C4⋊C4C2×D7112yes—
149C2×C22⋊C4—712no—
150C2×C22⋊C4—712no—
151C2×C22⋊C4—712no—
152C2×C22⋊C4—712no—
153C2×C22⋊C4—712no—
154C2×C22⋊C4C2×D7111yescharacteristic
155C2×C22⋊C4C2×D7111yescharacteristic
156#95—711no—
157#95—712no—
158#95—712no—
159#95—712no—
160#95—711no—
161#95C2×D7112yes—
162C24—712no—
163C24C22×D7111yescharacteristic
164C2×D4—2841no—
165C2×D4—2842no—
166C2×D4—1424no—
167C2×D4—1424no—
168C2×D4—1424no—
169C22×C4—41no—
170C22×C4—42no—
171C22×C4—2842no—
172C22×C4—712no—
173C22×C4—712no—
174C22×C4—712no—
175C22×C4—1424no—
176C22×C4—1424no—
177C22×C4C22×D7111yescharacteristic
178C22×C4C22×D7112yes—
179C22×C4C22×D7111yescharacteristic
180C22×C4C22×D7112yes—
181C4⋊C4—42no—
182C4⋊C4—2841no—
183C4⋊C4—1424no—
184C4⋊C4—1424no—
185C22⋊C4—41no—
186C22⋊C4—2842no—
187C22⋊C4—2842no—
188C22⋊C4—2842no—
189C22⋊C4—1424no—
190C22⋊C4—1424no—
191C22⋊C4D28414yescomplemented
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—714no—
197C23—1422no—
198C23—1422no—
199C23—1422no—
200C23—1422no—
201C23—1422no—
202C23—1422no—
203C23C2×D28412yes—
204C23C23×D7111yescharacteristic
205D4—2844no—
206D4—2848no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—44no—
217C2×C4—2848no—
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×C4—1422no—
227C2×C4C2×D28414yes—
228C22—22no—
229C22—24no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—2842no—
234C22—2842no—
235C22—2842no—
236C22—2842no—
237C22—1424no—
238C22—1424no—
239C22—1424no—
240C22C22×D28411yescharacteristic
241C22#41×D7112yes—
242C22#1455617311yescharacteristic
243C22#1455617312yes—
244C22#1455617611yescharacteristic
245C4—24no—
246C4—41no—
247C4—42no—
248C4—41no—
249C4—2842no—
250C4—2842no—
251C4—2842no—
252C2—42no—
253C2—2844no—
254C2#1798658011yescharacteristic
255C2#1798659512yes—
256C2#1798664412yes—
257C2#1798667711yescharacteristic
258C2#1798673811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#385×C71C2
hypercenter#385D71
hypocenterC71#2693
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14556110C2semidirect
2. #17985939C2semidirect
3. #17985924C2semidirect
4. #17985921C2semidirect
6. #17985878C2semidirect
7. #17985877C2semidirect
8. #17985856C2semidirect
9. #385×C71C2semidirect
61. C22⋊C4×C71D4semidirect
130. C71#2693semidirect
138. #385D71semidirect
191. C22⋊C4D284semidirect