Finite Group Databasebeta

← #22595301

Subgroups — #22595301

Order 9088.

476 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556123C212yesmaximal, complemented
2#17985936C212yesmaximal, complemented
3#17985921C212yesmaximal, complemented
4#17985916C212yesmaximal
5#17985901C211yesmaximal, characteristic
6#17985898C212yesmaximal, complemented
7#17985897C211yesmaximal, characteristic, complemented
8#17985891C212yesmaximal, complemented
9#389×C71C211yesmaximal, characteristic, complemented
10C22×D284C2211yescharacteristic
11#14556123—28no—
12C2×C4⋊Dic71C2211yescharacteristic
13C2×C4⋊Dic71C2212yes—
14C2×C4⋊Dic71C2211yescharacteristic
15C2×C4⋊Dic71C2211yescharacteristic
16C2×C4⋊Dic71C2212yes—
17C2×Dic71⋊C4C2212yes—
18C2×(C2×D71)⋊C4C2212yes—
19C2×(C2×D71)⋊C4C2212yes—
20C2×(C2×D71)⋊C4C2212yes—
21C2×(C2×D71)⋊C4C2212yes—
22C2×(C2×D71)⋊C4C2212yes—
23C2×(C2×D71)⋊C4C2212yes—
24C2×C4×Dic71C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C2×C4⋊C4×C71C2212yes—
28C2×C4⋊C4×C71C2211yescharacteristic
29C2×C4⋊C4×C71C2211yescharacteristic
30C2×C42×C71C2211yescharacteristic
31#95×C71C2212yes—
32C23×D71C2312yes—
33C2×D284—22no—
34C2×D284—41no—
35C2×D284—41no—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C4⋊Dic71—24no—
40C4⋊Dic71—22no—
41C4⋊Dic71—41no—
42C4⋊Dic71—42no—
43C4⋊Dic71—41no—
44Dic71⋊C4—24no—
45(C2×D71)⋊C4—24no—
46(C2×D71)⋊C4—24no—
47(C2×D71)⋊C4—24no—
48(C2×D71)⋊C4—24no—
49(C2×D71)⋊C4—42no—
50(C2×D71)⋊C4—42no—
51C4×Dic71—24no—
52C22×C4×C71C2312yes—
53C22×C4×C71C2312yes—
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2311yescharacteristic
56C22×C4×C71C2311yescharacteristic
57C4⋊C4×C71—24no—
58C4⋊C4×C71—41no—
59C4⋊C4×C71D414yescomplemented
60C42×C71—41no—
61C23×C71C2411yescharacteristic
62C22×D71—22no—
63C22×D71—22no—
64C22×D71—22no—
65C22×D71—22no—
66C22×D71—22no—
67C22×D71—22no—
68C22×D71—22no—
69C2×C4×C71—22no—
70C2×C4×C71—21no—
71C2×C4×C71—21no—
72C2×C4×C71—21no—
73C2×C4×C71—21no—
74C2×C4×C71—21no—
75C2×C4×C71—22no—
76C2×C4×C71—21no—
77C2×C4×C71—22no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71C2×D414yes—
81C2×C4×C71C2×D412yes—
82C2×C4×C71#4112yes—
83C2×C4×C71#4112yes—
84C2×Dic71—22no—
85C2×Dic71—22no—
86C2×Dic71—22no—
87C2×Dic71—22no—
88C2×Dic71—22no—
89C2×Dic71—22no—
90C2×Dic71—22no—
91C2×Dic71—22no—
92C2×Dic71—22no—
93D284—44no—
94C22×C71C22×D411yescharacteristic
95C22×C71C2×#4111yescharacteristic
96C22×C71C2×#4111yescharacteristic
97C22×C71H(5,𝔽2)11yescharacteristic
98C22×C71H(5,𝔽2)11yescharacteristic
99C22×C712−1+411yescharacteristic
100C22×C712−1+411yescharacteristic
101C2×D71—42no—
102C2×D71—42no—
103C2×D71—42no—
104C2×D71—42no—
105C2×D71—42no—
106C2×D71—42no—
107C2×D71—42no—
108C4×C71—22no—
109C4×C71—22no—
110C4×C71—22no—
111C4×C71—24no—
112C4×C71—42no—
113Dic71—42no—
114Dic71—42no—
115Dic71—42no—
116C2×C71#53711yescharacteristic
117C2×C71#53811yescharacteristic
118C2×C71#53911yescharacteristic
119C2×C71#54711yescharacteristic
120C2×C71#55011yescharacteristic
121C2×C71#55611yescharacteristic
122C2×C71#56311yescharacteristic
123D71—82no—
124#2727—711nomaximal, Sylow
125C71#272711yescharacteristic, complemented, Sylow
126C2×#126—712no—
127#399—712no—
128#396—712no—
129#394—712no—
130#390—711no—
131#389—712no—
132#389—711no—
133#389D7111yescharacteristic, complemented
134#388—712no—
135C22×D4—711no—
136#126—1428no—
137C2×C4⋊C4—711no—
138C2×C4⋊C4—711no—
139C2×C4⋊C4—712no—
140C2×C4⋊C4—712no—
141C2×C4⋊C4—712no—
142C2×C4⋊C4—711no—
143C2×C4⋊C4C2×D7112yes—
144C2×C4⋊C4C2×D7111yescharacteristic
145C2×C4⋊C4C2×D7111yescharacteristic
146C2×C22⋊C4—712no—
147C2×C22⋊C4—712no—
148C2×C22⋊C4—712no—
149C2×C22⋊C4—712no—
150C2×C22⋊C4—712no—
151C2×C22⋊C4—712no—
152C2×C42—712no—
153C2×C42C2×D7111yescharacteristic
154#95—712no—
155#95—712no—
156#95C2×D7112yes—
157C24—712no—
158C2×D4—2841no—
159C2×D4—2841no—
160C2×D4—1422no—
161C22×C4—712no—
162C22×C4—712no—
163C22×C4—712no—
164C22×C4C22×D7112yes—
165C22×C4C22×D7112yes—
166C22×C4C22×D7111yescharacteristic
167C22×C4C22×D7111yescharacteristic
168C22×C4C22×D7111yescharacteristic
169C4⋊C4—24no—
170C4⋊C4—41no—
171C4⋊C4—2841no—
172C4⋊C4—2841no—
173C4⋊C4—2842no—
174C4⋊C4—1424no—
175C4⋊C4—1424no—
176C4⋊C4—1422no—
177C4⋊C4D28414yescomplemented
178C22⋊C4—2842no—
179C22⋊C4—2842no—
180C22⋊C4—1424no—
181C22⋊C4—1424no—
182C22⋊C4—1424no—
183C22⋊C4—1424no—
184C42—41no—
185C42—1424no—
186C23—1422no—
187C23—1422no—
188C23—1422no—
189C23—1422no—
190C23—1422no—
191C23—1422no—
192C23—1422no—
193C23C23×D7111yescharacteristic
194D4—2844no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—1422no—
207C2×C4—1422no—
208C2×C4—1422no—
209C2×C4—1422no—
210C2×C4—1422no—
211C2×C4—1422no—
212C2×C4—1422no—
213C2×C4—1422no—
214C2×C4—1422no—
215C2×C4C2×D28414yes—
216C2×C4C2×D28412yes—
217C2×C4#1176586412yes—
218C2×C4#1176586612yes—
219C22—2842no—
220C22—2842no—
221C22—2842no—
222C22—2842no—
223C22—2842no—
224C22—2842no—
225C22—2842no—
226C22C22×D28411yescharacteristic
227C22C2×#1176586411yescharacteristic
228C22C2×#1176586611yescharacteristic
229C22#1455617311yescharacteristic
230C22#1455617411yescharacteristic
231C22#1455617511yescharacteristic
232C22#1455617611yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—24no—
237C4—42no—
238C4—2842no—
239C4—2842no—
240C4—2842no—
241C2—5682no—
242C2#1798658011yescharacteristic
243C2#1798658611yescharacteristic
244C2#1798659811yescharacteristic
245C2#1798665311yescharacteristic
246C2#1798667111yescharacteristic
247C2#1798672311yescharacteristic
248C2#1798675311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#389×C71C2
hypercenter#389D71
hypocenterC71#2727
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14556123C2semidirect
2. #17985936C2semidirect
3. #17985921C2semidirect
6. #17985898C2semidirect
7. #17985897C2semidirect
8. #17985891C2semidirect
9. #389×C71C2semidirect
59. C4⋊C4×C71D4semidirect
125. C71#2727semidirect
133. #389D71semidirect
177. C4⋊C4D284semidirect