Finite Group Databasebeta

← #22593587

Subgroups — #22593587

Order 9088.

476 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17985937C211yesmaximal, characteristic, complemented
2#17985914C211yesmaximal, characteristic
3#17985912C211yesmaximal, characteristic, complemented
4#17985911C211yesmaximal, characteristic, complemented
5#17985903C211yesmaximal, characteristic, complemented
6#17985889C211yesmaximal, characteristic, complemented
7#17985876C211yesmaximal, characteristic
8#17985875C211yesmaximal, characteristic
9#17985867C211yesmaximal, characteristic, complemented
10#17985866C211yesmaximal, characteristic, complemented
11#17985861C211yesmaximal, characteristic, complemented
12#17985860C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
14C4×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
15#388×C71C211yesmaximal, characteristic, complemented
16C22×Dic142C2211yescharacteristic
17C22×C22⋊D71C2211yescharacteristic
18C23×Dic71C2211yescharacteristic
19C22×C4×D71C2211yescharacteristic
20C2×Dic71⋊C4C2211yescharacteristic
21C2×C22⋊Dic71C2211yescharacteristic
22C2×C22⋊Dic71C2211yescharacteristic
23C2×(C2×D71)⋊C4C2211yescharacteristic
24C2×(C2×D71)⋊C4C2211yescharacteristic
25C2×(C2×D71)⋊C4C2211yescharacteristic
26C2×(C2×D71)⋊C4C2211yescharacteristic
27C2×(C2×D71)⋊C4C2211yescharacteristic
28C2×C4×Dic71C2211yescharacteristic
29C2×C4×Dic71C2211yescharacteristic
30C71⋊#95C2211yescharacteristic
31C71⋊#95C2211yescharacteristic
32C71⋊#95C2211yescharacteristic
33C71⋊#95C2211yescharacteristic
34C71⋊#95C2211yescharacteristic
35C71⋊#95C2211yescharacteristic
36C71⋊#95C2211yescharacteristic
37C71⋊#95C2211yescharacteristic
38C71⋊#95C2211yescharacteristic
39C71⋊#95C2211yescharacteristic
40C71⋊#95C2211yescharacteristic
41C71⋊#95C2211yescharacteristic
42C71⋊#95C2211yescharacteristic
43C71⋊#95C2211yescharacteristic
44C2×C4⋊C4×C71C2211yescharacteristic
45C2×C22⋊C4×C71C2211yescharacteristic
46C2×C22⋊C4×C71C2211yescharacteristic
47C2×C22⋊C4×C71C2211yescharacteristic
48C2×C42×C71C2211yescharacteristic
49#95×C71C2211yescharacteristic
50#95×C71C2211yescharacteristic
51C23×D71C2311yescharacteristic
52C2×Dic142—22no—
53C2×Dic142—41no—
54C2×Dic142—41no—
55C2×C22⋊D71—22no—
56C2×C22⋊D71—22no—
57C2×C22⋊D71—41no—
58C22×Dic71—22no—
59C22×Dic71—22no—
60C22×Dic71—41no—
61C22×Dic71C2311yescharacteristic
62C22×Dic71C2311yescharacteristic
63C22×Dic71C2311yescharacteristic
64C22×Dic71C2311yescharacteristic
65C22×Dic71C2311yescharacteristic
66C22×Dic71C2311yescharacteristic
67C22×Dic71C2311yescharacteristic
68C2×C4×D71—22no—
69C2×C4×D71—22no—
70C2×C4×D71—41no—
71Dic71⋊C4—41no—
72C22⋊Dic71—22no—
73C22⋊Dic71—41no—
74(C2×D71)⋊C4—22no—
75(C2×D71)⋊C4—22no—
76(C2×D71)⋊C4—22no—
77(C2×D71)⋊C4—41no—
78(C2×D71)⋊C4—41no—
79C4×Dic71—22no—
80C4×Dic71—41no—
81C24×C71C2311yescharacteristic
82C22×C4×C71C2311yescharacteristic
83C22×C4×C71C2311yescharacteristic
84C22×C4×C71C2311yescharacteristic
85C22×C4×C71C2311yescharacteristic
86C22×C4×C71C2311yescharacteristic
87C22×C4×C71C2311yescharacteristic
88C4⋊C4×C71—41no—
89C22⋊C4×C71—22no—
90C22⋊C4×C71—22no—
91C22⋊C4×C71—41no—
92C42×C71—22no—
93C23×C71—21no—
94C23×C71—21no—
95C23×C71—21no—
96C23×C71—21no—
97C23×C71—21no—
98C23×C71—21no—
99C23×C71#4112yes—
100C23×C71C2411yescharacteristic
101C22×D71—21no—
102C22×D71—21no—
103C22×D71—21no—
104C22×D71—21no—
105C22×D71—21no—
106C22×D71—21no—
107C22×D71#4112yes—
108C2×C4×C71—21no—
109C2×C4×C71—21no—
110C2×C4×C71—21no—
111C2×C4×C71—21no—
112C2×C4×C71—21no—
113C2×C4×C71—21no—
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#4112yes—
126C22⋊D71—44no—
127C2×Dic71—21no—
128C2×Dic71—21no—
129C2×Dic71—21no—
130C2×Dic71—21no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—21no—
134C2×Dic71—21no—
135C2×Dic71—21no—
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—44no—
147C2×Dic71#4112yes—
148C2×Dic71#4112yes—
149C4×D71—44no—
150Dic142—44no—
151C22×C71—22no—
152C22×C71—22no—
153C22×C71—22no—
154C22×C71—41no—
155C22×C71—41no—
156C22×C71—41no—
157C22×C71—41no—
158C22×C71C2×#4111yescharacteristic
159C22×C71C2×#4111yescharacteristic
160C22×C71C2×#4111yescharacteristic
161C22×C71C2×#4111yescharacteristic
162C22×C71C2×#4111yescharacteristic
163C22×C71H(5,𝔽2)11yescharacteristic
164C22×C71H(5,𝔽2)11yescharacteristic
165C2×D71—22no—
166C2×D71—22no—
167C2×D71—22no—
168C2×D71—41no—
169C2×D71—41no—
170C2×D71—41no—
171C2×D71—41no—
172C4×C71—22no—
173C4×C71—41no—
174C4×C71—41no—
175C4×C71—41no—
176C4×C71—41no—
177C4×C71—41no—
178Dic71—22no—
179Dic71—22no—
180Dic71—41no—
181Dic71—41no—
182Dic71—41no—
183Dic71—41no—
184Dic71—41no—
185C2×C71—42no—
186C2×C71#52911yescharacteristic
187C2×C71#52911yescharacteristic
188C2×C71#53811yescharacteristic
189C2×C71#55111yescharacteristic
190C2×C71#55111yescharacteristic
191C2×C71#55111yescharacteristic
192C2×C71#55511yescharacteristic
193D71—42no—
194#2572—711nomaximal, Sylow
195C71#257211yescharacteristic, complemented, Sylow
196#400—711no—
197#394—711no—
198#393—711no—
199#393—711no—
200#391—711no—
201#388—711no—
202#388D7111yescharacteristic, complemented
203#386—711no—
204#386—711no—
205#383—711no—
206#383—711no—
207#381—711no—
208#381—711no—
209C4×C22⋊C4—711no—
210C4×C22⋊C4—711no—
211C22×Q8—711no—
212C22×D4—711no—
213C23×C4—711no—
214C23×C4—711no—
215C2×C4⋊C4—711no—
216C2×C4⋊C4C2×D7111yescharacteristic
217C2×C22⋊C4—711no—
218C2×C22⋊C4—711no—
219C2×C22⋊C4—711no—
220C2×C22⋊C4—711no—
221C2×C22⋊C4—711no—
222C2×C22⋊C4—711no—
223C2×C22⋊C4—711no—
224C2×C22⋊C4C2×D7111yescharacteristic
225C2×C22⋊C4C2×D7111yescharacteristic
226C2×C22⋊C4C2×D7111yescharacteristic
227C2×C42—711no—
228C2×C42—711no—
229C2×C42C2×D7111yescharacteristic
230#95—711no—
231#95—711no—
232#95—711no—
233#95—711no—
234#95—711no—
235#95—711no—
236#95—711no—
237#95—711no—
238#95—711no—
239#95—711no—
240#95—711no—
241#95—711no—
242#95—711no—
243#95—711no—
244#95C2×D7111yescharacteristic
245#95C2×D7111yescharacteristic
246C24—711no—
247C24C22×D7111yescharacteristic
248C2×Q8—2841no—
249C2×Q8—2841no—
250C2×Q8—1422no—
251C2×D4—2841no—
252C2×D4—1422no—
253C2×D4—1422no—
254C22×C4—2841no—
255C22×C4—2841no—
256C22×C4—711no—
257C22×C4—711no—
258C22×C4—711no—
259C22×C4—711no—
260C22×C4—711no—
261C22×C4—711no—
262C22×C4—711no—
263C22×C4—1422no—
264C22×C4—1422no—
265C22×C4—1422no—
266C22×C4—1422no—
267C22×C4C22×D7111yescharacteristic
268C22×C4C22×D7111yescharacteristic
269C22×C4C22×D7111yescharacteristic
270C22×C4C22×D7111yescharacteristic
271C22×C4C22×D7111yescharacteristic
272C22×C4C22×D7111yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—2841no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—41no—
278C22⋊C4—2841no—
279C22⋊C4—2841no—
280C22⋊C4—2841no—
281C22⋊C4—1422no—
282C22⋊C4—1422no—
283C22⋊C4—1422no—
284C22⋊C4—1422no—
285C42—22no—
286C42—2841no—
287C42—1422no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—712no—
295C23—1421no—
296C23—1421no—
297C23—1421no—
298C23—1421no—
299C23—1421no—
300C23—1421no—
301C23#1176586512yes—
302C23C23×D7111yescharacteristic
303Q8—2844no—
304D4—2844no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—2844no—
323C2×C4—2844no—
324C2×C4—712no—
325C2×C4—712no—
326C2×C4—1421no—
327C2×C4—1421no—
328C2×C4—1421no—
329C2×C4—1421no—
330C2×C4—1421no—
331C2×C4—1421no—
332C2×C4—1421no—
333C2×C4—1421no—
334C2×C4—1421no—
335C2×C4—1421no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4—1421no—
345C2×C4#1176586412yes—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—2841no—
354C22—2841no—
355C22—2841no—
356C22—2841no—
357C22—1422no—
358C22—1422no—
359C22—1422no—
360C22#41×D7111yescharacteristic
361C22#41×D7111yescharacteristic
362C22#41×D7111yescharacteristic
363C22C2×#1176586411yescharacteristic
364C22C2×#1176586511yescharacteristic
365C22#1455617311yescharacteristic
366C22#1455617411yescharacteristic
367C4—22no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—2841no—
374C4—2841no—
375C4—2841no—
376C4—2841no—
377C4—2841no—
378C4—1422no—
379C4—1422no—
380C2—42no—
381C2—2842no—
382C2#1798652911yescharacteristic
383C2#1798653211yescharacteristic
384C2#1798658311yescharacteristic
385C2#1798667211yescharacteristic
386C2#1798667311yescharacteristic
387C2#1798667811yescharacteristic
388C2#1798671311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D71
commutator, socleC23×C71C24
Fitting#388×C71C2
hypercenter#388D71
hypocenterC71#2572
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #17985937C2semidirect
3. #17985912C2semidirect
4. #17985911C2semidirect
5. #17985903C2semidirect
6. #17985889C2semidirect
9. #17985867C2semidirect
10. #17985866C2semidirect
11. #17985861C2semidirect
12. #17985860C2semidirect
13. C22⋊C4×Dic71C2semidirect
14. C4×(C2×D71)⋊C4C2semidirect
15. #388×C71C2semidirect
195. C71#2572semidirect
202. #388D71semidirect