Finite Group Databasebeta

← #22588438

Subgroups — #22588438

Order 9088.

306 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#117×D71C211yesmaximal, characteristic
2#17985962C211yesmaximal, characteristic
3C4×(C2×D71)⋊C4C211yesmaximal, characteristic
4#17985760C211yesmaximal, characteristic, complemented
5#17985759C211yesmaximal, characteristic, complemented
6#17985758C211yesmaximal, characteristic, complemented
7#339×C71C211yesmaximal, characteristic, complemented
8C22×C4×D71C2211yescharacteristic
9C2×#11765849C2211yescharacteristic
10#14556087C2211yescharacteristic
11#14556086C411yescharacteristic, complemented
12#14556086C411yescharacteristic, complemented
13#14556085—21no—
14#14556084—21no—
15C4⋊C4×D71C411yescharacteristic, complemented
16C4⋊C4×D71C411yescharacteristic, complemented
17C2×(C2×D71)⋊C4—21no—
18C22⋊C4×D71—21no—
19C2×C4×Dic71C2211yescharacteristic
20C42×D71—21no—
21(C2×D71)⋊C8—21no—
22(C2×D71)⋊C8—21no—
23C71⋊#95—21no—
24C2×M16×C71C2211yescharacteristic
25#117×C71C2211yescharacteristic
26C2×C42×C71C2211yescharacteristic
27C23×D71D411yescharacteristic
28C22×Dic71—21no—
29C22×Dic71D411yescharacteristic
30C2×C4×D71—21no—
31C2×C4×D71—21no—
32C2×C4×D71—21no—
33C2×C4×D71—21no—
34C2×C4×D71—21no—
35C2×C4×D71—21no—
36C2×C4×D71C2×C411yescharacteristic
37C2×C4×D71C2×C411yescharacteristic
38C2×C4×D71D411yescharacteristic
39C2×C4×D71D411yescharacteristic
40#11765849—21no—
41#11765849—21no—
42C2×C71⋊C8—21no—
43C4⋊Dic71C2×C411yescharacteristic
44C4⋊Dic71C2×C411yescharacteristic
45Dic71⋊C4—21no—
46Dic71⋊C4—21no—
47C22⋊Dic71—21no—
48(C2×D71)⋊C4—24no—
49(C2×D71)⋊C4—21no—
50(C2×D71)⋊C4—21no—
51C4×Dic71—21no—
52C4×Dic71—21no—
53C4×Dic71—21no—
54C4×Dic71—21no—
55C4×Dic71—21no—
56C22×C4×C71—21no—
57C22×C4×C71C2311yescharacteristic
58M16×C71—21no—
59M16×C71—21no—
60C2×C8×C71—21no—
61C4⋊C4×C71C2×C411yescharacteristic
62C4⋊C4×C71C2×C411yescharacteristic
63C22⋊C4×C71—21no—
64C42×C71—21no—
65C42×C71—21no—
66C42×C71—21no—
67C23×C71C2×D411yescharacteristic
68C22×D71—21no—
69C22×D71—21no—
70C22×D71—22no—
71C22×D71—41no—
72C22×D71C22⋊C411yescharacteristic
73C22×D71C22⋊C411yescharacteristic
74C2×C4×C71—22no—
75C2×C4×C71—21no—
76C2×C4×C71—21no—
77C2×C4×C71—41no—
78C2×C4×C71—41no—
79C2×C4×C71C22×C411yescharacteristic
80C2×C4×C71C2×D411yescharacteristic
81C2×C4×C71#4111yescharacteristic
82C2×C4×C71#4111yescharacteristic
83C2×C4×C71#4111yescharacteristic
84C2×C4×C71#4111yescharacteristic
85C2×Dic71—21no—
86C2×Dic71—21no—
87C2×Dic71—22no—
88C2×Dic71—21no—
89C2×Dic71—21no—
90C2×Dic71—41no—
91C2×Dic71—41no—
92C2×Dic71C22⋊C411yescharacteristic
93C2×Dic71C22⋊C411yescharacteristic
94C4×D71—21no—
95C4×D71—21no—
96C4×D71—21no—
97C4×D71—21no—
98C4×D71—21no—
99C4×D71—21no—
100C4×D71—21no—
101C4×D71—21no—
102C4×D71—42no—
103C4×D71—42no—
104C8×C71—41no—
105C71⋊C8—41no—
106C22×C71—21no—
107C22×C71—21no—
108C22×C71C2×C22⋊C411yescharacteristic
109C22×C71#12311yescharacteristic
110C22×C71#12311yescharacteristic
111C2×D71—21no—
112C2×D71—21no—
113C2×D71—21no—
114C2×D71—21no—
115C2×D71—21no—
116C2×D71—42no—
117C2×D71—42no—
118C2×D71#10412yes—
119C4×C71—42no—
120C4×C71—41no—
121C4×C71—41no—
122C4×C71#11711yescharacteristic
123C4×C71#11711yescharacteristic
124C4×C71#12311yescharacteristic
125C4×C71#12311yescharacteristic
126Dic71—21no—
127Dic71—21no—
128Dic71—42no—
129Dic71—41no—
130Dic71—41no—
131C2×C71—21no—
132C2×C71—21no—
133C2×C71#38111yescharacteristic
134C2×C71C2×#10411yescharacteristic
135C2×C71#42111yescharacteristic
136D71—22no—
137D71—41no—
138#1826—711nomaximal, Sylow
139C71#182611yescharacteristic, complemented, Sylow
140C2×#117—711no—
141#407—711no—
142C4×C22⋊C4—711no—
143#339—711no—
144#339—711no—
145#339—711no—
146#339D7111yescharacteristic, complemented
147C23×C4—711no—
148C2×M16—711no—
149C2×M16C2×D7111yescharacteristic
150#117—711no—
151#117—711no—
152#117—711no—
153#117—1421no—
154#117—1421no—
155#117C2×D7111yescharacteristic
156C2×C4⋊C4—711no—
157C2×C4⋊C4—711no—
158C2×C22⋊C4—1421no—
159C2×C22⋊C4—1421no—
160C2×C42—711no—
161C2×C42—1421no—
162C2×C42C2×D7111yescharacteristic
163C22⋊C8—1421no—
164C22⋊C8—1421no—
165#95—1421no—
166C24—711no—
167C22×C4—21no—
168C22×C4—711no—
169C22×C4—711no—
170C22×C4—711no—
171C22×C4—711no—
172C22×C4—711no—
173C22×C4—1421no—
174C22×C4—1421no—
175C22×C4—1421no—
176C22×C4—1421no—
177C22×C4—1421no—
178C22×C4—1421no—
179C22×C4—1421no—
180C22×C4C22×D7111yescharacteristic
181M16—21no—
182M16—21no—
183M16—1421no—
184M16—1421no—
185C2×C8—21no—
186C2×C8—1421no—
187C4⋊C4—711no—
188C4⋊C4—711no—
189C4⋊C4—1421no—
190C4⋊C4—1421no—
191C4⋊C4C4×D7111yescharacteristic
192C4⋊C4C4×D7111yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—1421no—
195C22⋊C4—1421no—
196C22⋊C4—1424no—
197C22⋊C4—1421no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—1421no—
202C42—1421no—
203C42—1421no—
204C42—1421no—
205C42—1421no—
206C23—2841no—
207C23—711no—
208C23—711no—
209C23—1422no—
210C23—1421no—
211C23—1421no—
212C23D4×D7111yescharacteristic
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—2842no—
219C2×C4—2842no—
220C2×C4—2841no—
221C2×C4—2841no—
222C2×C4—711no—
223C2×C4—711no—
224C2×C4—1422no—
225C2×C4—1421no—
226C2×C4—1421no—
227C2×C4—1421no—
228C2×C4—1421no—
229C2×C4—1421no—
230C2×C4—1421no—
231C2×C4—1421no—
232C2×C4—1421no—
233C2×C4—1421no—
234C2×C4—1421no—
235C2×C4—1421no—
236C2×C4—1421no—
237C2×C4C2×C4×D7111yescharacteristic
238C2×C4D4×D7111yescharacteristic
239C2×C4#1176586411yescharacteristic
240C2×C4#1176586511yescharacteristic
241C2×C4#1176586511yescharacteristic
242C2×C4#1176586611yescharacteristic
243C8—41no—
244C8—2841no—
245C22—21no—
246C22—21no—
247C22—2842no—
248C22—2842no—
249C22—712no—
250C22—1421no—
251C22—1421no—
252C22—1421no—
253C22—1421no—
254C22—1421no—
255C22C22⋊C4×D7111yescharacteristic
256C22#1455611011yescharacteristic
257C22#1455611311yescharacteristic
258C4—42no—
259C4—41no—
260C4—41no—
261C4—2842no—
262C4—2841no—
263C4—2841no—
264C4—1421no—
265C4—1421no—
266C4#1455608511yescharacteristic
267C4#1455608611yescharacteristic
268C4#1455611011yescharacteristic
269C4#1455611311yescharacteristic
270C2—21no—
271C2—21no—
272C2—2841no—
273C2—1422no—
274C2#1798586111yescharacteristic
275C2#104×D7111yescharacteristic
276C2#1798601411yescharacteristic
subgroupG/H
centerC2×C4D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#339×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#339D71
hypocenterC71#1826
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
4. #17985760C2semidirect
5. #17985759C2semidirect
6. #17985758C2semidirect
7. #339×C71C2semidirect
11. #14556086C4semidirect
12. #14556086C4semidirect
15. C4⋊C4×D71C4semidirect
16. C4⋊C4×D71C4semidirect
139. C71#1826semidirect
146. #339D71semidirect