Finite Group Databasebeta

← #22599303

Subgroups — #22599303

Order 9088.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986531C211yesmaximal, characteristic, complemented
2#124×D71C211yesmaximal, characteristic, complemented
3#17986382C211yesmaximal, characteristic, complemented
4#17986380C211yesmaximal, characteristic, complemented
5#17986355C211yesmaximal, characteristic, complemented
6#17986352C211yesmaximal, characteristic, complemented
7#17986222C211yesmaximal, characteristic, complemented
8#17986218C211yesmaximal, characteristic, complemented
9#17986214C211yesmaximal, characteristic, complemented
10#17986156C211yesmaximal, characteristic, complemented
11#17986151C211yesmaximal, characteristic, complemented
12#17986136C211yesmaximal, characteristic, complemented
13#17986131C211yesmaximal, characteristic
14#17986051C211yesmaximal, characteristic, complemented
15#463×C71C211yesmaximal, characteristic, complemented
16C2×Q8×D71C2211yescharacteristic
17C2×D4×D71C2211yescharacteristic
18C2×Dic284C2211yescharacteristic, complemented
19C2×#11765855C2211yescharacteristic, complemented
20C2×#11765854C2211yescharacteristic
21C2×#11765853C2211yescharacteristic
22C2×#11765853C2211yescharacteristic, complemented
23C2×#11765850C2211yescharacteristic
24#14556121—21no—
25#14556119C2211yescharacteristic, complemented
26#14556117C2211yescharacteristic
27#14556116C2211yescharacteristic
28#14556115C2211yescharacteristic
29#14556115C2211yescharacteristic, complemented
30#14556114—21no—
31#14556114—21no—
32#14556110—21no—
33#14556108C2211yescharacteristic
34#14556099C2211yescharacteristic
35C4×Dic142C2211yescharacteristic, complemented
36C4×C22⋊D71—21no—
37#14556087—21no—
38C22⋊C4×D71—21no—
39C22⋊C4×D71—21no—
40C42×D71C2211yescharacteristic
41C4⋊(C71⋊C8)C2211yescharacteristic, complemented
42#14556053C2211yescharacteristic, complemented
43#14556052C2211yescharacteristic, complemented
44#14556051C2211yescharacteristic, complemented
45#14556050C2211yescharacteristic
46#14556049C2211yescharacteristic
47#14556048C2211yescharacteristic
48(C2×D71)⋊C8C2211yescharacteristic
49(C2×D71)⋊C8C2211yescharacteristic
50C8×Dic71C2211yescharacteristic, complemented
51C8×Dic71C2211yescharacteristic, complemented
52C2×SD16×C71C2211yescharacteristic, complemented
53C2×D8×C71C2211yescharacteristic
54#124×C71C2211yescharacteristic
55C4×D4×C71C2211yescharacteristic, complemented
56C4⋊C8×C71C2211yescharacteristic, complemented
57#103×C71C2211yescharacteristic, complemented
58#102×C71C2211yescharacteristic
59C23×D71—21no—
60C2×Dic142—21no—
61C2×Dic142C2311yescharacteristic
62C2×Dic142C2311yescharacteristic
63Q8×D71—41no—
64Q8×D71—41no—
65C2×D284C2311yescharacteristic
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68D4×D71—41no—
69D4×D71—41no—
70C2×C4×D71—21no—
71C2×C4×D71D411yescharacteristic
72C2×C4×D71D411yescharacteristic
73C2×C4×D71C2311yescharacteristic
74Dic284—41no—
75#11765855—41no—
76#11765854—41no—
77#11765853—41no—
78#11765853—41no—
79#11765850—41no—
80C2×C71⋊C8C2311yescharacteristic
81C2×C71⋊C8C2311yescharacteristic
82C4⋊Dic71—21no—
83C4⋊Dic71—21no—
84C4⋊Dic71C2311yescharacteristic
85Dic71⋊C4—21no—
86Dic71⋊C4—21no—
87C22⋊Dic71—21no—
88C22⋊Dic71—21no—
89C22⋊Dic71—21no—
90C22⋊Dic71—21no—
91C22⋊Dic71—21no—
92(C2×D71)⋊C4—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97C4×Dic71—21no—
98C4×Dic71D411yescharacteristic
99C4×Dic71D411yescharacteristic
100C4×Dic71C2311yescharacteristic
101C2×Q8×C71C2311yescharacteristic
102C2×D4×C71C2311yescharacteristic
103C2×D4×C71C2311yescharacteristic
104C22×C4×C71—21no—
105SD16×C71—41no—
106D8×C71—41no—
107C2×C8×C71C2311yescharacteristic
108C2×C8×C71C2311yescharacteristic
109C4⋊C4×C71C2311yescharacteristic
110C22⋊C4×C71—21no—
111C22⋊C4×C71—21no—
112C22⋊C4×C71—21no—
113C42×C71C2311yescharacteristic
114C23×C71—21no—
115C23×C71—21no—
116C22×D71—21no—
117C22×D71—42no—
118C22×D71—42no—
119C22×D71—42no—
120C22×D71C2×D411yescharacteristic
121Q8×C71—21no—
122Q8×C71—21no—
123D4×C71—21no—
124D4×C71—21no—
125D4×C71—21no—
126D4×C71—21no—
127C2×C4×C71—21no—
128C2×C4×C71—21no—
129C2×C4×C71—42no—
130C2×C4×C71C2×D411yescharacteristic
131C2×C4×C71C2×D411yescharacteristic
132C2×C4×C71C2411yescharacteristic
133C22⋊D71—42no—
134C22⋊D71—42no—
135C2×Dic71—21no—
136C2×Dic71—21no—
137C2×Dic71—21no—
138C2×Dic71C2×D411yescharacteristic
139C2×Dic71C2×D411yescharacteristic
140C2×Dic71C2×D411yescharacteristic
141D284—21no—
142D284—21no—
143C4×D71—22no—
144C4×D71—21no—
145C4×D71—21no—
146C4×D71—41no—
147C4×D71—42no—
148Dic142—21no—
149Dic142—21no—
150Dic142—21no—
151Dic142—21no—
152Dic142—42no—
153C8×C71—21no—
154C8×C71—21no—
155C71⋊C8—21no—
156C71⋊C8—21no—
157C22×C71—41no—
158C22×C71—41no—
159C22×C71—41no—
160C22×C71—41no—
161C22×C71—41no—
162C22×C71—41no—
163C22×C71C22×D411yescharacteristic
164C2×D71—21no—
165C2×D71—21no—
166C2×D71—41no—
167C2×D71—41no—
168C2×D71—41no—
169C2×D71—84no—
170C2×D71#13512yes—
171C4×C71—21no—
172C4×C71—21no—
173C4×C71—41no—
174C4×C71—41no—
175C4×C71H(5,𝔽2)11yescharacteristic
176C4×C71H(5,𝔽2)11yescharacteristic
177Dic71—21no—
178Dic71—21no—
179Dic71—21no—
180Dic71—41no—
181Dic71—41no—
182Dic71—41no—
183C2×C71—81no—
184C2×C71—81no—
185C2×C71#53511yescharacteristic
186C2×C71C2×#13511yescharacteristic
187C2×C71#57511yescharacteristic
188D71—22no—
189D71—81no—
190#3211—711nomaximal, Sylow
191C71#321111yescharacteristic, complemented, Sylow
192#529—711no—
193C2×#124—711no—
194#495—711no—
195#495—711no—
196#488—711no—
197#488—711no—
198#464—711no—
199#464—711no—
200#463—711no—
201#463D7111yescharacteristic, complemented
202#451—711no—
203#450—711no—
204#448—711no—
205#447—711no—
206#431—711no—
207C22×Q8—711no—
208C22×D4—711no—
209C2×Q16—711no—
210C2×Q16—711no—
211C2×SD16—711no—
212C2×SD16—711no—
213C2×SD16—711no—
214C2×SD16C2×D7111yescharacteristic, complemented
215C2×D8—711no—
216C2×D8C2×D7111yescharacteristic
217#126—1421no—
218#125—711no—
219#124—711no—
220#124—711no—
221#124—711no—
222#124—711no—
223#124—1421no—
224#124—1421no—
225#124C2×D7111yescharacteristic
226#123—1421no—
227C22⋊Q8—711no—
228#121—711no—
229C4×Q8—711no—
230C4×D4—1421no—
231C4×D4C2×D7111yescharacteristic, complemented
232#117—1421no—
233C2×C22⋊C4—1421no—
234C2×C22⋊C4—1421no—
235C2×C42—711no—
236C4⋊C8—711no—
237C4⋊C8C2×D7111yescharacteristic, complemented
238#103—711no—
239#103—711no—
240#103—711no—
241#103C2×D7111yescharacteristic, complemented
242#102—711no—
243#102—711no—
244#102—711no—
245#102C2×D7111yescharacteristic
246C22⋊C8—711no—
247C22⋊C8—711no—
248C4×C8—711no—
249C4×C8—711no—
250C24—1421no—
251C2×Q8—2841no—
252C2×Q8—2841no—
253C2×Q8—711no—
254C2×Q8—711no—
255C2×Q8—1421no—
256C2×Q8C22×D7111yescharacteristic
257C2×D4—2841no—
258C2×D4—2841no—
259C2×D4—711no—
260C2×D4—1421no—
261C2×D4—1421no—
262C2×D4C22×D7111yescharacteristic
263C2×D4C22×D7111yescharacteristic
264C22×C4—21no—
265C22×C4—711no—
266C22×C4—711no—
267C22×C4—711no—
268C22×C4—1421no—
269Q16—2841no—
270Q16—2841no—
271SD16—41no—
272SD16—2841no—
273SD16—2841no—
274SD16—2841no—
275D8—41no—
276D8—2841no—
277C2×C8—711no—
278C2×C8—711no—
279C2×C8C22×D7111yescharacteristic
280C2×C8C22×D7111yescharacteristic
281C4⋊C4—711no—
282C4⋊C4—1421no—
283C4⋊C4—1421no—
284C4⋊C4—1421no—
285C4⋊C4—1421no—
286C4⋊C4C22×D7111yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—1421no—
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—711no—
301C42—711no—
302C42—711no—
303C42—1421no—
304C42C22×D7111yescharacteristic
305C23—21no—
306C23—21no—
307C23—2842no—
308C23—2842no—
309C23—2842no—
310C23—711no—
311C23—1421no—
312Q8—21no—
313Q8—21no—
314Q8—2842no—
315Q8—1421no—
316Q8—1421no—
317Q8—1421no—
318Q8—1421no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—2842no—
324D4—2842no—
325D4—1421no—
326D4—1421no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—2841no—
331C2×C4—2842no—
332C2×C4—711no—
333C2×C4—711no—
334C2×C4—711no—
335C2×C4—1422no—
336C2×C4—1421no—
337C2×C4—1421no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4D4×D7111yescharacteristic
342C2×C4D4×D7111yescharacteristic
343C2×C4C23×D7111yescharacteristic
344C8—21no—
345C8—21no—
346C8—1421no—
347C8—1421no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—2841no—
355C22—2841no—
356C22—2841no—
357C22—5684no—
358C22—712no—
359C22—1421no—
360C22—1421no—
361C22C2×D4×D7111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—2841no—
367C4—2841no—
368C4—2841no—
369C4—1421no—
370C4—1421no—
371C4—1421no—
372C4#1455617311yescharacteristic
373C4#1455617411yescharacteristic
374C2—81no—
375C2—81no—
376C2—5681no—
377C2—1422no—
378C2#1798656511yescharacteristic
379C2#135×D7111yescharacteristic
380C2#1798679511yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#463×C71C2
socleC22×C71C22×D4
hypercenter#463D71
hypocenterC71#3211
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #17986531C2semidirect
2. #124×D71C2semidirect
3. #17986382C2semidirect
4. #17986380C2semidirect
5. #17986355C2semidirect
6. #17986352C2semidirect
7. #17986222C2semidirect
8. #17986218C2semidirect
9. #17986214C2semidirect
10. #17986156C2semidirect
11. #17986151C2semidirect
12. #17986136C2semidirect
14. #17986051C2semidirect
15. #463×C71C2semidirect
18. C2×Dic284C22semidirect
19. C2×#11765855C22semidirect
22. C2×#11765853C22semidirect
25. #14556119C22semidirect
29. #14556115C22semidirect
35. C4×Dic142C22semidirect
41. C4⋊(C71⋊C8)C22semidirect
42. #14556053C22semidirect
43. #14556052C22semidirect
44. #14556051C22semidirect
50. C8×Dic71C22semidirect
51. C8×Dic71C22semidirect
52. C2×SD16×C71C22semidirect
55. C4×D4×C71C22semidirect
56. C4⋊C8×C71C22semidirect
57. #103×C71C22semidirect
191. C71#3211semidirect
201. #463D71semidirect
214. C2×SD16C2×D71semidirect
231. C4×D4C2×D71semidirect
237. C4⋊C8C2×D71semidirect
241. #103C2×D71semidirect