Finite Group Databasebeta

← #22591817

Subgroups — #22591817

Order 9088.

560 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556111C211yesmaximal, characteristic
2C2×C4×C22⋊D71C211yesmaximal, characteristic
3#17985940C211yesmaximal, characteristic, complemented
4#17985933C211yesmaximal, characteristic, complemented
5#17985928C211yesmaximal, characteristic, complemented
6#17985926C211yesmaximal, characteristic, complemented
7#17985882C211yesmaximal, characteristic, complemented
8#17985881C211yesmaximal, characteristic, complemented
9#17985878C211yesmaximal, characteristic
10#17985873C211yesmaximal, characteristic, complemented
11#17985872C211yesmaximal, characteristic, complemented
12#17985862C211yesmaximal, characteristic, complemented
13#17985861C211yesmaximal, characteristic, complemented
14#17985859C211yesmaximal, characteristic, complemented
15C2×#95×C71C211yesmaximal, characteristic, complemented
16C22×C22⋊D71C2211yescharacteristic
17C22×C4×D71C2211yescharacteristic
18#14556111—24no—
19C4×C22⋊D71—24no—
20C2×C4⋊Dic71C2211yescharacteristic
21C2×C4⋊Dic71C2211yescharacteristic
22C2×Dic71⋊C4C2211yescharacteristic
23C2×Dic71⋊C4C2211yescharacteristic
24C2×Dic71⋊C4C2211yescharacteristic
25C2×Dic71⋊C4C2211yescharacteristic
26C2×Dic71⋊C4C2211yescharacteristic
27C2×C22⋊Dic71C2211yescharacteristic
28C2×C22⋊Dic71C2211yescharacteristic
29C2×C22⋊Dic71C2211yescharacteristic
30C2×(C2×D71)⋊C4C2211yescharacteristic
31C2×(C2×D71)⋊C4C2211yescharacteristic
32C2×(C2×D71)⋊C4C2211yescharacteristic
33C2×(C2×D71)⋊C4C2211yescharacteristic
34C2×(C2×D71)⋊C4C2211yescharacteristic
35C2×C4×Dic71C2211yescharacteristic
36C71⋊#95C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C71⋊#95C2211yescharacteristic
45C71⋊#95C2211yescharacteristic
46C23×C4×C71C2211yescharacteristic
47C23×C4×C71C2211yescharacteristic
48C23×C4×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51#95×C71C2211yescharacteristic
52#95×C71C2211yescharacteristic
53C23×D71C2311yescharacteristic
54C2×C22⋊D71—22no—
55C2×C22⋊D71—22no—
56C2×C22⋊D71D414yes—
57C22×Dic71C2311yescharacteristic
58C22×Dic71C2311yescharacteristic
59C22×Dic71C2311yescharacteristic
60C22×Dic71C2311yescharacteristic
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C22×Dic71C2311yescharacteristic
64C2×C4×D71—22no—
65C2×C4×D71—22no—
66C2×C4×D71—41no—
67C4⋊Dic71—22no—
68C4⋊Dic71—41no—
69Dic71⋊C4—22no—
70Dic71⋊C4—22no—
71Dic71⋊C4—22no—
72Dic71⋊C4—22no—
73Dic71⋊C4—41no—
74C22⋊Dic71—22no—
75C22⋊Dic71—22no—
76C22⋊Dic71—22no—
77(C2×D71)⋊C4—22no—
78(C2×D71)⋊C4—22no—
79(C2×D71)⋊C4—22no—
80(C2×D71)⋊C4—22no—
81(C2×D71)⋊C4—41no—
82C4×Dic71—22no—
83C24×C71C2311yescharacteristic
84C22×C4×C71—22no—
85C22×C4×C71—22no—
86C22×C4×C71—22no—
87C22×C4×C71—22no—
88C22×C4×C71—22no—
89C22×C4×C71—22no—
90C22×C4×C71—22no—
91C22×C4×C71—41no—
92C22×C4×C71—41no—
93C22×C4×C71C2311yescharacteristic
94C22×C4×C71C2311yescharacteristic
95C22×C4×C71C2311yescharacteristic
96C22×C4×C71C2311yescharacteristic
97C22×C4×C71C2311yescharacteristic
98C22×C4×C71C2311yescharacteristic
99C23×C71—21no—
100C23×C71—21no—
101C23×C71—21no—
102C23×C71—21no—
103C23×C71C2×D412yes—
104C23×C71#4112yes—
105C23×C71#4112yes—
106C23×C71C2411yescharacteristic
107C22×D71—21no—
108C22×D71—21no—
109C22×D71—21no—
110C22×D71—21no—
111C22×D71—21no—
112C22×D71—21no—
113C22×D71C2×D412yes—
114C2×C4×C71—21no—
115C2×C4×C71—21no—
116C2×C4×C71—21no—
117C2×C4×C71—21no—
118C2×C4×C71—21no—
119C2×C4×C71—21no—
120C2×C4×C71—21no—
121C2×C4×C71—21no—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—21no—
126C2×C4×C71—21no—
127C2×C4×C71—21no—
128C2×C4×C71—21no—
129C2×C4×C71—21no—
130C2×C4×C71—44no—
131C2×C4×C71—44no—
132C2×C4×C71—44no—
133C2×C4×C71#4112yes—
134C2×C4×C71#4112yes—
135C22⋊D71—28no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71—21no—
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71—21no—
142C2×Dic71—21no—
143C2×Dic71—21no—
144C2×Dic71—21no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—21no—
149C2×Dic71—21no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152C2×Dic71—21no—
153C2×Dic71—21no—
154C2×Dic71—21no—
155C2×Dic71—21no—
156C2×Dic71C2×D412yes—
157C4×D71—44no—
158C22×C71—22no—
159C22×C71—22no—
160C22×C71—22no—
161C22×C71—22no—
162C22×C71—22no—
163C22×C71—22no—
164C22×C71#12314yes—
165C22×C71C22×D411yescharacteristic
166C22×C71C2×#4111yescharacteristic
167C22×C71C2×#4111yescharacteristic
168C22×C71C2×#4111yescharacteristic
169C22×C71C2×#4111yescharacteristic
170C22×C71H(5,𝔽2)11yescharacteristic
171C22×C712−1+411yescharacteristic
172C2×D71—22no—
173C2×D71—22no—
174C2×D71—22no—
175C2×D71—41no—
176C2×D71—41no—
177C2×D71—41no—
178C2×D71—41no—
179C4×C71—22no—
180C4×C71—22no—
181C4×C71—41no—
182C4×C71—41no—
183C4×C71—41no—
184C4×C71—41no—
185Dic71—22no—
186Dic71—41no—
187Dic71—41no—
188Dic71—41no—
189Dic71—41no—
190Dic71—41no—
191Dic71—41no—
192C2×C71—24no—
193C2×C71C2×#12311yescharacteristic
194C2×C71#52911yescharacteristic
195C2×C71#53911yescharacteristic
196C2×C71#54611yescharacteristic
197C2×C71#54711yescharacteristic
198C2×C71#55111yescharacteristic
199C2×C71#55211yescharacteristic
200D71—42no—
201#2419—711nomaximal, Sylow
202C71#241911yescharacteristic, complemented, Sylow
203C2×#123—711no—
204C2×C4×D4—711no—
205#400—711no—
206#398—711no—
207#397—711no—
208#397—711no—
209#387—711no—
210#387—711no—
211#386—711no—
212#385—711no—
213#385—711no—
214#381—711no—
215#381—711no—
216#380—711no—
217C2×#95D7111yescharacteristic, complemented
218C22×D4—711no—
219C23×C4—711no—
220C23×C4C2×D7111yescharacteristic
221C23×C4C2×D7111yescharacteristic
222C23×C4C2×D7111yescharacteristic
223#123—1424no—
224C4×D4—1424no—
225C2×C4⋊C4—711no—
226C2×C4⋊C4—711no—
227C2×C4⋊C4—711no—
228C2×C4⋊C4—711no—
229C2×C4⋊C4—711no—
230C2×C4⋊C4—711no—
231C2×C4⋊C4—711no—
232C2×C22⋊C4—711no—
233C2×C22⋊C4—711no—
234C2×C22⋊C4—711no—
235C2×C22⋊C4—711no—
236C2×C22⋊C4—711no—
237C2×C22⋊C4—711no—
238C2×C22⋊C4—711no—
239C2×C22⋊C4—711no—
240C2×C42—711no—
241#95—711no—
242#95—711no—
243#95—711no—
244#95—711no—
245#95—711no—
246#95—711no—
247#95—711no—
248#95—711no—
249#95—711no—
250#95—711no—
251#95C2×D7111yescharacteristic
252#95C2×D7111yescharacteristic
253#95C2×D7111yescharacteristic
254#95C2×D7111yescharacteristic
255C24—711no—
256C24C22×D7111yescharacteristic
257C2×D4—714no—
258C2×D4—1422no—
259C2×D4—1422no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—2841no—
270C22×C4—711no—
271C22×C4—711no—
272C22×C4—711no—
273C22×C4—711no—
274C22×C4—711no—
275C22×C4—711no—
276C22×C4—711no—
277C22×C4—1422no—
278C22×C4—1422no—
279C22×C4C22×D7111yescharacteristic
280C22×C4C22×D7111yescharacteristic
281C22×C4C22×D7111yescharacteristic
282C22×C4C22×D7111yescharacteristic
283C22×C4C22×D7111yescharacteristic
284C22×C4C22×D7111yescharacteristic
285C4⋊C4—2841no—
286C4⋊C4—2841no—
287C4⋊C4—1422no—
288C4⋊C4—1422no—
289C4⋊C4—1422no—
290C4⋊C4—1422no—
291C4⋊C4—1422no—
292C22⋊C4—2841no—
293C22⋊C4—1422no—
294C22⋊C4—1422no—
295C22⋊C4—1422no—
296C22⋊C4—1422no—
297C22⋊C4—1422no—
298C22⋊C4—1422no—
299C22⋊C4—1422no—
300C42—1422no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—712no—
306C23—1421no—
307C23—1421no—
308C23—1421no—
309C23—1421no—
310C23—1421no—
311C23—1421no—
312C23D4×D7112yes—
313C23#1176586412yes—
314C23#1176586512yes—
315C23C23×D7111yescharacteristic
316D4—1428no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—2844no—
337C2×C4—712no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4—1421no—
345C2×C4—1421no—
346C2×C4—1421no—
347C2×C4—1421no—
348C2×C4—1421no—
349C2×C4—1421no—
350C2×C4—1421no—
351C2×C4—1421no—
352C2×C4—1421no—
353C2×C4—1421no—
354C2×C4—1421no—
355C2×C4—1421no—
356C2×C4—1421no—
357C2×C4—1421no—
358C2×C4#1176586512yes—
359C2×C4#1176586512yes—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—2841no—
367C22—2841no—
368C22—2841no—
369C22—2841no—
370C22—1422no—
371C22—1422no—
372C22—1422no—
373C22#1455611014yes—
374C22C2×D4×D7111yescharacteristic
375C22C2×#1176586411yescharacteristic
376C22C2×#1176586511yescharacteristic
377C22C2×#1176586511yescharacteristic
378C22C2×#1176586511yescharacteristic
379C22#1455617311yescharacteristic
380C22#1455617611yescharacteristic
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—2841no—
388C4—2841no—
389C4—2841no—
390C4—2841no—
391C4—2841no—
392C4—2841no—
393C4—1422no—
394C2—24no—
395C2—2842no—
396C2C2×#1455611011yescharacteristic
397C2#1798653311yescharacteristic
398C2#1798659611yescharacteristic
399C2#1798663911yescharacteristic
400C2#1798665011yescharacteristic
401C2#1798667511yescharacteristic
402C2#1798668411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
FittingC2×#95×C71C2
hypercenterC2×#95D71
hypocenterC71#2419
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #17985940C2semidirect
4. #17985933C2semidirect
5. #17985928C2semidirect
6. #17985926C2semidirect
7. #17985882C2semidirect
8. #17985881C2semidirect
10. #17985873C2semidirect
11. #17985872C2semidirect
12. #17985862C2semidirect
13. #17985861C2semidirect
14. #17985859C2semidirect
15. C2×#95×C71C2semidirect
202. C71#2419semidirect
217. C2×#95D71semidirect