Finite Group Databasebeta

← #22599177

Subgroups — #22599177

Order 9088.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986510C211yesmaximal, characteristic, complemented
2#17986340C211yesmaximal, characteristic, complemented
3#17986337C211yesmaximal, characteristic, complemented
4#17986323C211yesmaximal, characteristic, complemented
5#17986320C211yesmaximal, characteristic, complemented
6#17986255C211yesmaximal, characteristic, complemented
7#17986250C211yesmaximal, characteristic, complemented
8#17986247C211yesmaximal, characteristic, complemented
9#17986243C211yesmaximal, characteristic, complemented
10#17986161C211yesmaximal, characteristic, complemented
11#17986159C211yesmaximal, characteristic, complemented
12#17986144C211yesmaximal, characteristic, complemented
13#17986142C211yesmaximal, characteristic, complemented
14#17985963C211yesmaximal, characteristic, complemented
15#525×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C2×#11765855C2211yescharacteristic, complemented
18C2×#11765853C2211yescharacteristic, complemented
19C2×#11765852C2211yescharacteristic, complemented
20C2×#11765850C2211yescharacteristic, complemented
21C2×#11765849C2211yescharacteristic
22C2×#11765849C2211yescharacteristic
23#14556111—21no—
24#14556107C2211yescharacteristic
25#14556107C2211yescharacteristic
26#14556102C2211yescharacteristic
27#14556102C2211yescharacteristic
28#14556097—21no—
29C4×C22⋊D71—21no—
30C4×C22⋊D71—21no—
31#14556087C2211yescharacteristic
32#14556061C2211yescharacteristic, complemented
33#14556061C2211yescharacteristic, complemented
34#14556059C2211yescharacteristic, complemented
35#14556059C2211yescharacteristic, complemented
36#14556052C2211yescharacteristic, complemented
37#14556052C2211yescharacteristic, complemented
38#14556051C2211yescharacteristic, complemented
39#14556051C2211yescharacteristic, complemented
40#14556049C2211yescharacteristic, complemented
41#14556049C2211yescharacteristic, complemented
42#14556048C2211yescharacteristic, complemented
43#14556048C2211yescharacteristic, complemented
44C22⋊(C71⋊C8)C2211yescharacteristic
45C22⋊(C71⋊C8)C2211yescharacteristic
46C22⋊(C71⋊C8)C2211yescharacteristic
47C22⋊(C71⋊C8)C2211yescharacteristic
48C2×#41×C71C2211yescharacteristic
49C23×C4×C71C2211yescharacteristic
50#123×C71—21no—
51C22⋊Q8×C71C2211yescharacteristic
52C22⋊Q8×C71C2211yescharacteristic
53#121×C71C2211yescharacteristic
54#121×C71C2211yescharacteristic
55#120×C71—21no—
56C4×D4×C71—21no—
57C4×D4×C71—21no—
58#117×C71C2211yescharacteristic
59#11765865—41no—
60#11765865—41no—
61C2×Dic142C2311yescharacteristic
62C2×D284C2311yescharacteristic
63C2×C22⋊D71—21no—
64C2×C22⋊D71—21no—
65C2×C22⋊D71—21no—
66C2×C4×D71—21no—
67#11765855—41no—
68#11765853—41no—
69#11765852—41no—
70#11765850—41no—
71#11765849—41no—
72#11765849—41no—
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C2×C71⋊C8C2311yescharacteristic
77C4⋊Dic71C2311yescharacteristic
78C4⋊Dic71C2311yescharacteristic
79Dic71⋊C4—21no—
80Dic71⋊C4—21no—
81C22⋊Dic71—21no—
82C22⋊Dic71—21no—
83C22⋊Dic71—21no—
84(C2×D71)⋊C4—21no—
85(C2×D71)⋊C4—21no—
86C4×Dic71—21no—
87C24×C71D411yescharacteristic
88#41×C71—41no—
89#41×C71—41no—
90C2×Q8×C71C2311yescharacteristic
91C2×D4×C71—21no—
92C2×D4×C71—21no—
93C2×D4×C71—21no—
94C2×D4×C71C2311yescharacteristic
95C22×C4×C71—21no—
96C22×C4×C71—41no—
97C22×C4×C71—41no—
98C22×C4×C71D411yescharacteristic
99C22×C4×C71D411yescharacteristic
100C22×C4×C71D411yescharacteristic
101C22×C4×C71C2311yescharacteristic
102C22×C4×C71C2311yescharacteristic
103C22×C4×C71C2311yescharacteristic
104C4⋊C4×C71—21no—
105C4⋊C4×C71—21no—
106C4⋊C4×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C22⋊C4×C71—21no—
109C22⋊C4×C71—21no—
110C22⋊C4×C71—21no—
111C22⋊C4×C71—21no—
112C22⋊C4×C71—21no—
113C42×C71—21no—
114C23×C71—21no—
115C23×C71—41no—
116C23×C71—41no—
117C23×C71—41no—
118C23×C71C2×D411yescharacteristic
119C23×C71C2×D411yescharacteristic
120C23×C71C2×D411yescharacteristic
121C22×D71—21no—
122Q8×C71—21no—
123Q8×C71—21no—
124D4×C71—21no—
125D4×C71—21no—
126D4×C71—42no—
127D4×C71—42no—
128D4×C71—42no—
129C2×C4×C71—21no—
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71—21no—
133C2×C4×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71—21no—
136C2×C4×C71—21no—
137C2×C4×C71—21no—
138C2×C4×C71—41no—
139C2×C4×C71—41no—
140C2×C4×C71—41no—
141C2×C4×C71—42no—
142C2×C4×C71C2×D411yescharacteristic
143C2×C4×C71C2×D411yescharacteristic
144C2×C4×C71C2×D411yescharacteristic
145C2×C4×C71C2411yescharacteristic
146C22⋊D71—42no—
147C22⋊D71—42no—
148C22⋊D71—42no—
149C2×Dic71—21no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152D284—21no—
153D284—21no—
154C4×D71—42no—
155Dic142—21no—
156Dic142—21no—
157C71⋊C8—21no—
158C71⋊C8—21no—
159C71⋊C8—21no—
160C71⋊C8—21no—
161C22×C71—21no—
162C22×C71—21no—
163C22×C71—21no—
164C22×C71—21no—
165C22×C71—21no—
166C22×C71—21no—
167C22×C71—21no—
168C22×C71—21no—
169C22×C71—21no—
170C22×C71—44no—
171C22×C71—41no—
172C22×C71—41no—
173C22×C71—41no—
174C22×C71C22×D411yescharacteristic
175C2×D71—41no—
176C2×D71—41no—
177C2×D71—41no—
178C4×C71—21no—
179C4×C71—21no—
180C4×C71—21no—
181C4×C71—41no—
182C4×C71—41no—
183C4×C71—41no—
184C4×C71H(5,𝔽2)11yescharacteristic
185C4×C71H(5,𝔽2)11yescharacteristic
186Dic71—41no—
187Dic71—41no—
188Dic71—41no—
189C2×C71—41no—
190C2×C71—41no—
191C2×C71—41no—
192C2×C71—81no—
193C2×C71#53411yescharacteristic
194C2×C71#57511yescharacteristic
195C2×C71#57511yescharacteristic
196D71—81no—
197#3197—711nomaximal, Sylow
198C71#319711yescharacteristic, complemented, Sylow
199#525—711no—
200#525D7111yescharacteristic, complemented
201#485—711no—
202#485—711no—
203#482—711no—
204#482—711no—
205#470—711no—
206#469—711no—
207#468—711no—
208#468—711no—
209#452—711no—
210#452—711no—
211#449—711no—
212#449—711no—
213#407—711no—
214C2×#41—711no—
215C2×#41C2×D7111yescharacteristic
216C23×C4C2×D7111yescharacteristic
217C2×Q16—711no—
218C2×SD16—711no—
219C2×SD16—711no—
220C2×D8—711no—
221C2×M16—711no—
222C2×M16—711no—
223#123—21no—
224#123—1421no—
225C22⋊Q8—711no—
226C22⋊Q8—711no—
227C22⋊Q8C2×D7111yescharacteristic
228C22⋊Q8C2×D7111yescharacteristic
229#121—711no—
230#121—711no—
231#121C2×D7111yescharacteristic
232#121C2×D7111yescharacteristic
233#120—21no—
234#120—1421no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1421no—
238C4×D4—1421no—
239#117—711no—
240#117C2×D7111yescharacteristic
241#107—711no—
242#107—711no—
243#106—711no—
244#106—711no—
245#103—711no—
246#103—711no—
247#103—711no—
248#103—711no—
249#102—711no—
250#102—711no—
251#102—711no—
252#102—711no—
253C22⋊C8—711no—
254C22⋊C8—711no—
255C22⋊C8—711no—
256C22⋊C8—711no—
257C24C22⋊D7111yescharacteristic
258#41—41no—
259#41—41no—
260#41—2841no—
261#41—2841no—
262C2×Q8—711no—
263C2×Q8C22×D7111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—711no—
268C2×D4—1421no—
269C2×D4—1421no—
270C2×D4—1421no—
271C2×D4C22×D7111yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1421no—
276C22×C4C22⋊D7111yescharacteristic
277C22×C4C22⋊D7111yescharacteristic
278C22×C4C22⋊D7111yescharacteristic
279C22×C4C22×D7111yescharacteristic
280C22×C4C22×D7111yescharacteristic
281C22×C4C22×D7111yescharacteristic
282Q16—2841no—
283SD16—2841no—
284SD16—2841no—
285D8—2841no—
286M16—2841no—
287M16—2841no—
288C2×C8—711no—
289C2×C8—711no—
290C2×C8—711no—
291C2×C8—711no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—711no—
295C4⋊C4—711no—
296C4⋊C4—1421no—
297C4⋊C4—1421no—
298C4⋊C4C22×D7111yescharacteristic
299C4⋊C4C22×D7111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1421no—
306C22⋊C4—1421no—
307C22⋊C4—1421no—
308C22⋊C4—1421no—
309C22⋊C4—1421no—
310C42—21no—
311C42—1421no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—1421no—
317C23C2×C22⋊D7111yescharacteristic
318C23C2×C22⋊D7111yescharacteristic
319C23C2×C22⋊D7111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1421no—
323Q8—1421no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—2842no—
330D4—2842no—
331D4—2842no—
332D4—1421no—
333D4—1421no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—2842no—
348C2×C4—1421no—
349C2×C4—1421no—
350C2×C4—1421no—
351C2×C4C2×C22⋊D7111yescharacteristic
352C2×C4C2×C22⋊D7111yescharacteristic
353C2×C4C2×C22⋊D7111yescharacteristic
354C2×C4C23×D7111yescharacteristic
355C8—1421no—
356C8—1421no—
357C8—1421no—
358C8—1421no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—2841no—
373C22—2841no—
374C22—2841no—
375C22C22×C22⋊D7111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—2841no—
383C4—2841no—
384C4—2841no—
385C4#1455617311yescharacteristic
386C4#1455617311yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—5681no—
392C2#1798655811yescharacteristic
393C2#1798679711yescharacteristic
394C2#1798679711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#525×C71C2
socleC22×C71C22×D4
hypercenter#525D71
hypocenterC71#3197
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #17986510C2semidirect
2. #17986340C2semidirect
3. #17986337C2semidirect
4. #17986323C2semidirect
5. #17986320C2semidirect
6. #17986255C2semidirect
7. #17986250C2semidirect
8. #17986247C2semidirect
9. #17986243C2semidirect
10. #17986161C2semidirect
11. #17986159C2semidirect
12. #17986144C2semidirect
13. #17986142C2semidirect
14. #17985963C2semidirect
15. #525×C71C2semidirect
17. C2×#11765855C22semidirect
18. C2×#11765853C22semidirect
19. C2×#11765852C22semidirect
20. C2×#11765850C22semidirect
32. #14556061C22semidirect
33. #14556061C22semidirect
34. #14556059C22semidirect
35. #14556059C22semidirect
36. #14556052C22semidirect
37. #14556052C22semidirect
38. #14556051C22semidirect
39. #14556051C22semidirect
40. #14556049C22semidirect
41. #14556049C22semidirect
42. #14556048C22semidirect
43. #14556048C22semidirect
198. C71#3197semidirect
200. #525D71semidirect