Finite Group Databasebeta

← #22600493

Subgroups — #22600493

Order 9088.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986715C211yesmaximal, characteristic, complemented
2#17986644C211yesmaximal, characteristic, complemented
3#17986361C211yesmaximal, characteristic, complemented
4#17986342C211yesmaximal, characteristic, complemented
5#17986326C211yesmaximal, characteristic, complemented
6#17986246C211yesmaximal, characteristic, complemented
7#17986236C211yesmaximal, characteristic, complemented
8#17986215C211yesmaximal, characteristic, complemented
9#17986145C211yesmaximal, characteristic, complemented
10#17986134C211yesmaximal, characteristic, complemented
11#17986109C211yesmaximal, characteristic, complemented
12#17986069C211yesmaximal, characteristic, complemented
13#17986002C211yesmaximal, characteristic, complemented
14#17985992C211yesmaximal, characteristic, complemented
15#474×C71C211yesmaximal, characteristic, complemented
16C2×#11765864C2211yescharacteristic
17C2×D4×D71C2211yescharacteristic
18C2×#11765854C2211yescharacteristic, complemented
19C2×D568C2211yescharacteristic
20C2×#11765850C2211yescharacteristic
21C2×#11765848C2211yescharacteristic
22C2×C8×D71C2211yescharacteristic, complemented
23#14556117—21no—
24#14556117—21no—
25#14556116C2211yescharacteristic
26#14556112—21no—
27#14556108C2211yescharacteristic
28#14556103—21no—
29#14556103C2211yescharacteristic
30#14556103C2211yescharacteristic
31#14556103C2211yescharacteristic, complemented
32#14556102—21no—
33#14556098—21no—
34C4×D284C2211yescharacteristic
35C4×D284C2211yescharacteristic, complemented
36#14556086—21no—
37#14556086C2211yescharacteristic
38#14556086C2211yescharacteristic, complemented
39C2×(C2×D71)⋊C4—21no—
40#14556059C2211yescharacteristic, complemented
41#14556053C2211yescharacteristic, complemented
42#14556051C2211yescharacteristic, complemented
43#14556051C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic
45#14556049C2211yescharacteristic
46#14556048C2211yescharacteristic
47#14556048C2211yescharacteristic
48#14556048C2211yescharacteristic, complemented
49(C2×D71)⋊C8C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51#14556039C2211yescharacteristic, complemented
52C4⋊Q8×C71C2211yescharacteristic, complemented
53C4×D4×C71C2211yescharacteristic
54#107×C71C2211yescharacteristic, complemented
55#107×C71C2211yescharacteristic, complemented
56C4⋊C8×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic
58#102×C71C2211yescharacteristic
59C23×D71—21no—
60#11765864—22no—
61#11765864—41no—
62C2×Dic142C2311yescharacteristic
63C2×D284—21no—
64C2×D284—21no—
65C2×D284—21no—
66C2×D284D411yescharacteristic
67C2×D284C2311yescharacteristic
68C2×D284C2311yescharacteristic
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71D4×D71—22no—
72D4×D71—41no—
73C22×Dic71—21no—
74C2×C4×D71—21no—
75C2×C4×D71C2311yescharacteristic
76C2×C4×D71C2311yescharacteristic
77#11765854—41no—
78D568—41no—
79#11765850—22no—
80#11765848—41no—
81C2×C71⋊C8C2311yescharacteristic
82C2×C71⋊C8C2311yescharacteristic
83C8×D71—41no—
84C4⋊Dic71—21no—
85C4⋊Dic71D411yescharacteristic
86C4⋊Dic71C2311yescharacteristic
87(C2×D71)⋊C4—21no—
88(C2×D71)⋊C4—21no—
89(C2×D71)⋊C4—21no—
90(C2×D71)⋊C4—21no—
91(C2×D71)⋊C4—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4D411yescharacteristic
97(C2×D71)⋊C4D411yescharacteristic
98C4×Dic71—21no—
99C4×Dic71—21no—
100C2×Q8×C71—21no—
101C2×D4×C71C2311yescharacteristic
102C22×C4×C71—21no—
103C2×C8×C71C2311yescharacteristic
104C2×C8×C71C2311yescharacteristic
105C4⋊C4×C71—21no—
106C4⋊C4×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C4⋊C4×C71C2311yescharacteristic
109C22⋊C4×C71—21no—
110C42×C71C2311yescharacteristic
111C23×C71—21no—
112C22×D71—21no—
113C22×D71—21no—
114C22×D71—42no—
115C22×D71—42no—
116C22×D71—81no—
117C22×D71C2×D411yescharacteristic
118C22×D71C2×D411yescharacteristic
119Q8×C71—81no—
120D4×C71—21no—
121D4×C71#4112yes—
122C2×C4×C71—21no—
123C2×C4×C71—21no—
124C2×C4×C71—21no—
125C2×C4×C71—81no—
126C2×C4×C71C2×D411yescharacteristic
127C2×C4×C71C2×D411yescharacteristic
128C2×C4×C71C2411yescharacteristic
129C22⋊D71—42no—
130C22⋊D71—42no—
131C2×Dic71—21no—
132C2×Dic71—21no—
133C2×Dic71—42no—
134C2×Dic71C2×D411yescharacteristic
135C2×Dic71C2×D411yescharacteristic
136D284—21no—
137D284—21no—
138D284—21no—
139D284—21no—
140D284—41no—
141D284—81no—
142D284—81no—
143D284—81no—
144C4×D71—21no—
145C4×D71—21no—
146C4×D71—21no—
147C4×D71—21no—
148C4×D71—42no—
149Dic142—21no—
150Dic142—21no—
151C8×C71—21no—
152C8×C71—21no—
153C71⋊C8—21no—
154C71⋊C8—21no—
155C22×C71—22no—
156C22×C71—41no—
157C22×C71—41no—
158C22×C71C22×D411yescharacteristic
159C2×D71—21no—
160C2×D71—21no—
161C2×D71—21no—
162C2×D71—21no—
163C2×D71—21no—
164C2×D71—21no—
165C2×D71—41no—
166C2×D71—41no—
167C2×D71—41no—
168C2×D71—41no—
169C2×D71—41no—
170C2×D71—41no—
171C2×D71—84no—
172C4×C71—21no—
173C4×C71—21no—
174C4×C71—41no—
175C4×C71—41no—
176C4×C71—41no—
177C4×C71C2×#4111yescharacteristic
178C4×C71H(5,𝔽2)11yescharacteristic
179Dic71—21no—
180Dic71—21no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—42no—
184C2×C71#54611yescharacteristic
185C2×C71#57511yescharacteristic
186C2×C71#57611yescharacteristic
187D71—41no—
188D71—41no—
189D71—81no—
190D71—81no—
191#3319—711nomaximal, Sylow
192C71#331911yescharacteristic, complemented, Sylow
193#555—711no—
194#546—711no—
195#489—711no—
196#485—711no—
197#482—711no—
198#474D7111yescharacteristic, complemented
199#468—711no—
200#466—711no—
201#463—711no—
202#449—711no—
203#447—711no—
204#442—711no—
205#435—711no—
206#418—711no—
207#416—711no—
208C2×#41—711no—
209C22×D4—711no—
210C2×SD16—711no—
211C2×D8—711no—
212C2×D8—711no—
213C2×M16—711no—
214C22×C8—711no—
215C4⋊Q8C2×D7111yescharacteristic, complemented
216#124—711no—
217#124—1421no—
218#124—1421no—
219#123—1421no—
220C22⋊Q8—711no—
221#121—711no—
222#121—711no—
223#121—711no—
224#121—1421no—
225#121—1421no—
226#120—1421no—
227C4×D4—711no—
228C4×D4—711no—
229C4×D4C2×D7111yescharacteristic
230#117—711no—
231#117—711no—
232#117—1421no—
233C2×C22⋊C4—1421no—
234#107C2×D7111yescharacteristic, complemented
235#107C2×D7111yescharacteristic, complemented
236#106—711no—
237C4⋊C8C2×D7111yescharacteristic, complemented
238#103—711no—
239#103—711no—
240#103—711no—
241#102—711no—
242#102—711no—
243#102—711no—
244#102—711no—
245#102—711no—
246#102C2×D7111yescharacteristic
247#102C2×D7111yescharacteristic
248C22⋊C8—711no—
249C22⋊C8—711no—
250#97—711no—
251C24—1421no—
252#41—2841no—
253#41—1422no—
254C2×Q8—21no—
255C2×Q8—711no—
256C2×D4—2841no—
257C2×D4—711no—
258C2×D4—711no—
259C2×D4—711no—
260C2×D4—1421no—
261C2×D4—1421no—
262C2×D4—1421no—
263C2×D4—1421no—
264C2×D4—1421no—
265C2×D4—1422no—
266C2×D4C22×D7111yescharacteristic
267C22×C4—21no—
268C22×C4—711no—
269C22×C4—711no—
270C22×C4—1421no—
271C22×C4—1421no—
272SD16—2841no—
273D8—2841no—
274D8—1422no—
275M16—2841no—
276C2×C8—2841no—
277C2×C8—711no—
278C2×C8—711no—
279C2×C8C22×D7111yescharacteristic
280C2×C8C22×D7111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—711no—
283C4⋊C4—711no—
284C4⋊C4—1421no—
285C4⋊C4C22×D7111yescharacteristic
286C4⋊C4C22×D7111yescharacteristic
287C4⋊C4C22×D7111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—711no—
290C22⋊C4—711no—
291C22⋊C4—1421no—
292C22⋊C4—1421no—
293C22⋊C4—1421no—
294C22⋊C4—1421no—
295C22⋊C4—1421no—
296C22⋊C4—1421no—
297C22⋊C4—1421no—
298C22⋊C4—1421no—
299C22⋊C4—1421no—
300C42—1421no—
301C42—1421no—
302C42C22×D7111yescharacteristic
303C23—21no—
304C23—2842no—
305C23—2842no—
306C23—5681no—
307C23—711no—
308C23—711no—
309C23—1421no—
310C23—1421no—
311Q8—81no—
312Q8—1421no—
313Q8—1421no—
314D4—21no—
315D4—2841no—
316D4—2842no—
317D4—2842no—
318D4—5681no—
319D4—5681no—
320D4—5681no—
321D4—1421no—
322D4—1421no—
323D4—1421no—
324D4—1421no—
325D4#1176586612yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—81no—
330C2×C4—2842no—
331C2×C4—2842no—
332C2×C4—711no—
333C2×C4—711no—
334C2×C4—1421no—
335C2×C4—1421no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4D4×D7111yescharacteristic
341C2×C4D4×D7111yescharacteristic
342C2×C4C23×D7111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1421no—
346C8—1421no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—2841no—
351C22—2841no—
352C22—2841no—
353C22—2841no—
354C22—2841no—
355C22—2841no—
356C22—5684no—
357C22—1421no—
358C22—1421no—
359C22—1421no—
360C22—1421no—
361C22—1421no—
362C22—1421no—
363C22C2×D4×D7111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2841no—
370C4—2841no—
371C4—1421no—
372C4—1421no—
373C4C2×#1176586611yescharacteristic
374C4#1455617411yescharacteristic
375C2—42no—
376C2—2841no—
377C2—2841no—
378C2—5681no—
379C2—5681no—
380C2#1798664011yescharacteristic
381C2#1798679811yescharacteristic
382C2#1798680011yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#474×C71C2
socleC22×C71C22×D4
hypercenter#474D71
hypocenterC71#3319
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #17986715C2semidirect
2. #17986644C2semidirect
3. #17986361C2semidirect
4. #17986342C2semidirect
5. #17986326C2semidirect
6. #17986246C2semidirect
7. #17986236C2semidirect
8. #17986215C2semidirect
9. #17986145C2semidirect
10. #17986134C2semidirect
11. #17986109C2semidirect
12. #17986069C2semidirect
13. #17986002C2semidirect
14. #17985992C2semidirect
15. #474×C71C2semidirect
18. C2×#11765854C22semidirect
22. C2×C8×D71C22semidirect
31. #14556103C22semidirect
35. C4×D284C22semidirect
38. #14556086C22semidirect
40. #14556059C22semidirect
41. #14556053C22semidirect
42. #14556051C22semidirect
43. #14556051C22semidirect
48. #14556048C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. #14556039C22semidirect
52. C4⋊Q8×C71C22semidirect
54. #107×C71C22semidirect
55. #107×C71C22semidirect
56. C4⋊C8×C71C22semidirect
192. C71#3319semidirect
198. #474D71semidirect
215. C4⋊Q8C2×D71semidirect
234. #107C2×D71semidirect
235. #107C2×D71semidirect
237. C4⋊C8C2×D71semidirect