Finite Group Databasebeta

← #22595269

Subgroups — #22595269

Order 9088.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556113C212yesmaximal
2#17985932C212yesmaximal, complemented
3#17985926C212yesmaximal, complemented
4#17985925C212yesmaximal, complemented
5#17985901C211yesmaximal, characteristic
6#17985897C211yesmaximal, characteristic, complemented
7#17985873C212yesmaximal, complemented
8#17985870C212yesmaximal, complemented
9#389×C71C211yesmaximal, characteristic, complemented
10C22×D284C2211yescharacteristic
11C22×C4×D71C2212yes—
12#14556113—28no—
13C2×C4⋊Dic71C2211yescharacteristic
14C2×C4⋊Dic71C2211yescharacteristic
15C2×C4⋊Dic71C2211yescharacteristic
16C2×Dic71⋊C4C2212yes—
17C2×Dic71⋊C4C2212yes—
18C2×(C2×D71)⋊C4C2212yes—
19C2×(C2×D71)⋊C4C2212yes—
20C2×(C2×D71)⋊C4C2212yes—
21C2×(C2×D71)⋊C4C2212yes—
22C2×(C2×D71)⋊C4C2212yes—
23C71⋊#95C2212yes—
24C71⋊#95C2212yes—
25C71⋊#95C2212yes—
26C71⋊#95C2212yes—
27C2×C4⋊C4×C71C2211yescharacteristic
28C2×C4⋊C4×C71C2212yes—
29C2×C4⋊C4×C71C2211yescharacteristic
30C2×C42×C71C2211yescharacteristic
31#95×C71C2212yes—
32C23×D71C2312yes—
33C2×D284—41no—
34C2×D284—41no—
35C2×D284D414yes—
36C22×Dic71C2312yes—
37C22×Dic71C2312yes—
38C22×Dic71C2312yes—
39C2×C4×D71—24no—
40C2×C4×D71—42no—
41C2×C4×D71—42no—
42C4⋊Dic71—22no—
43C4⋊Dic71—41no—
44C4⋊Dic71—41no—
45Dic71⋊C4—24no—
46Dic71⋊C4—42no—
47(C2×D71)⋊C4—24no—
48(C2×D71)⋊C4—24no—
49(C2×D71)⋊C4—24no—
50(C2×D71)⋊C4—24no—
51(C2×D71)⋊C4—24no—
52C22×C4×C71C2312yes—
53C22×C4×C71C2312yes—
54C22×C4×C71C2311yescharacteristic
55C22×C4×C71C2311yescharacteristic
56C22×C4×C71C2311yescharacteristic
57C4⋊C4×C71—24no—
58C4⋊C4×C71—22no—
59C4⋊C4×C71—41no—
60C42×C71—41no—
61C23×C71C2411yescharacteristic
62C22×D71—22no—
63C22×D71—22no—
64C22×D71—22no—
65C22×D71—22no—
66C22×D71—22no—
67C22×D71—22no—
68C22×D71C2×D414yes—
69C2×C4×C71—21no—
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—22no—
77C2×C4×C71—22no—
78C2×C4×C71—22no—
79C2×C4×C71—22no—
80C2×C4×C71—22no—
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—
94C4×D71—48no—
95C22×C71C22×D411yescharacteristic
96C22×C71C2×#4111yescharacteristic
97C22×C71C2×#4111yescharacteristic
98C22×C71H(5,𝔽2)11yescharacteristic
99C22×C71H(5,𝔽2)11yescharacteristic
100C22×C712−1+411yescharacteristic
101C22×C712−1+411yescharacteristic
102C2×D71—24no—
103C2×D71—24no—
104C2×D71—24no—
105C2×D71—42no—
106C2×D71—42no—
107C2×D71—42no—
108C2×D71—42no—
109C4×C71—22no—
110C4×C71—22no—
111C4×C71—22no—
112C4×C71—42no—
113C4×C71—42no—
114Dic71—42no—
115Dic71—42no—
116Dic71—42no—
117C2×C71#53411yescharacteristic
118C2×C71#53911yescharacteristic
119C2×C71#53911yescharacteristic
120C2×C71#54711yescharacteristic
121C2×C71#54711yescharacteristic
122C2×C71#55911yescharacteristic
123C2×C71#56311yescharacteristic
124D71—44no—
125#2724—711nomaximal, Sylow
126C71#272411yescharacteristic, complemented, Sylow
127C2×#123—712no—
128#398—712no—
129#397—712no—
130#397—712no—
131#390—711no—
132#389—711no—
133#389D7111yescharacteristic, complemented
134#385—712no—
135#385—712no—
136C22×D4—711no—
137C23×C4—712no—
138#123—1428no—
139C2×C4⋊C4—711no—
140C2×C4⋊C4—712no—
141C2×C4⋊C4—711no—
142C2×C4⋊C4—712no—
143C2×C4⋊C4—711no—
144C2×C4⋊C4C2×D7112yes—
145C2×C4⋊C4C2×D7111yescharacteristic
146C2×C4⋊C4C2×D7111yescharacteristic
147C2×C22⋊C4—712no—
148C2×C22⋊C4—712no—
149C2×C22⋊C4—712no—
150C2×C22⋊C4—712no—
151C2×C22⋊C4—712no—
152C2×C42C2×D7111yescharacteristic
153#95—712no—
154#95—712no—
155#95—712no—
156#95—712no—
157#95C2×D7112yes—
158C24—712no—
159C2×D4—2841no—
160C2×D4—2841no—
161C2×D4—714no—
162C22×C4—2842no—
163C22×C4—2842no—
164C22×C4—712no—
165C22×C4—712no—
166C22×C4—712no—
167C22×C4—1424no—
168C22×C4C22×D7112yes—
169C22×C4C22×D7112yes—
170C22×C4C22×D7111yescharacteristic
171C22×C4C22×D7111yescharacteristic
172C22×C4C22×D7111yescharacteristic
173C4⋊C4—24no—
174C4⋊C4—22no—
175C4⋊C4—41no—
176C4⋊C4—2842no—
177C4⋊C4—2841no—
178C4⋊C4—2841no—
179C4⋊C4—1424no—
180C4⋊C4—1422no—
181C22⋊C4—1424no—
182C22⋊C4—1424no—
183C22⋊C4—1424no—
184C22⋊C4—1424no—
185C22⋊C4—1424no—
186C42—41no—
187C23—714no—
188C23—1422no—
189C23—1422no—
190C23—1422no—
191C23—1422no—
192C23—1422no—
193C23—1422no—
194C23C23×D7111yescharacteristic
195D4—2844no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—2848no—
209C2×C4—1422no—
210C2×C4—1422no—
211C2×C4—1422no—
212C2×C4—1422no—
213C2×C4—1422no—
214C2×C4—1422no—
215C2×C4—1422no—
216C2×C4—1422no—
217C2×C4—1422no—
218C2×C4D4×D7112yes—
219C2×C4#1176586512yes—
220C2×C4#1176586612yes—
221C22—2842no—
222C22—2842no—
223C22—2842no—
224C22—2842no—
225C22—1424no—
226C22—1424no—
227C22—1424no—
228C22C2×D4×D7111yescharacteristic
229C22C2×#1176586511yescharacteristic
230C22C2×#1176586611yescharacteristic
231C22#1455617311yescharacteristic
232C22#1455617411yescharacteristic
233C22#1455617511yescharacteristic
234C22#1455617611yescharacteristic
235C4—22no—
236C4—22no—
237C4—22no—
238C4—42no—
239C4—42no—
240C4—2842no—
241C4—2842no—
242C4—2842no—
243C2—2844no—
244C2#1798655711yescharacteristic
245C2#1798659611yescharacteristic
246C2#1798659811yescharacteristic
247C2#1798665211yescharacteristic
248C2#1798665411yescharacteristic
249C2#1798673411yescharacteristic
250C2#1798675311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#389×C71C2
hypercenter#389D71
hypocenterC71#2724
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. #17985932C2semidirect
3. #17985926C2semidirect
4. #17985925C2semidirect
6. #17985897C2semidirect
7. #17985873C2semidirect
8. #17985870C2semidirect
9. #389×C71C2semidirect
126. C71#2724semidirect
133. #389D71semidirect