Finite Group Databasebeta

← #22600499

Subgroups — #22600499

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#17986712C211yesmaximal, characteristic, complemented
2#17986640C211yesmaximal, characteristic, complemented
3#17986360C211yesmaximal, characteristic, complemented
4#17986325C211yesmaximal, characteristic, complemented
5#17986278C211yesmaximal, characteristic, complemented
6#17986247C211yesmaximal, characteristic, complemented
7#17986236C211yesmaximal, characteristic, complemented
8#17986217C211yesmaximal, characteristic, complemented
9#17986147C211yesmaximal, characteristic, complemented
10#17986135C211yesmaximal, characteristic, complemented
11#17986110C211yesmaximal, characteristic, complemented
12#17986073C211yesmaximal, characteristic, complemented
13#17986003C211yesmaximal, characteristic, complemented
14#17985994C211yesmaximal, characteristic, complemented
15#485×C71C211yesmaximal, characteristic, complemented
16C2×#11765866C2211yescharacteristic
17C22×D284C2211yescharacteristic
18C2×#11765852C2211yescharacteristic, complemented
19C2×D568C2211yescharacteristic
20C2×D568C2211yescharacteristic
21C2×#11765849C2211yescharacteristic
22C2×C8×D71C2211yescharacteristic, complemented
23#14556127C2211yescharacteristic, complemented
24#14556117C2211yescharacteristic
25#14556116—21no—
26#14556114—21no—
27#14556113—21no—
28#14556103—21no—
29#14556103C2211yescharacteristic
30#14556103C2211yescharacteristic, complemented
31#14556102C2211yescharacteristic
32#14556101—21no—
33#14556098—21no—
34#14556090C2211yescharacteristic
35#14556090C2211yescharacteristic, complemented
36C4×C22⋊D71C2211yescharacteristic
37#14556086C2211yescharacteristic, complemented
38#14556085—21no—
39C22⋊C4×D71—21no—
40#14556061C2211yescharacteristic, complemented
41Dic71⋊C8C2211yescharacteristic, complemented
42#14556052C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic
44#14556050C2211yescharacteristic
45#14556048C2211yescharacteristic
46#14556048C2211yescharacteristic
47#14556048C2211yescharacteristic
48#14556048C2211yescharacteristic
49#14556048C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51#14556038C2211yescharacteristic, complemented
52C22⋊Q8×C71C2211yescharacteristic
53#117×C71C2211yescharacteristic
54#107×C71C2211yescharacteristic, complemented
55#106×C71C2211yescharacteristic, complemented
56#103×C71C2211yescharacteristic, complemented
57#103×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic
59C23×D71—21no—
60#11765866—22no—
61#11765866—41no—
62C2×Dic142—21no—
63C2×D284—22no—
64C2×D284—21no—
65C2×D284—21no—
66C2×D284—21no—
67C2×D284—21no—
68C2×D284—41no—
69C2×D284C2311yescharacteristic
70C2×D284C2311yescharacteristic
71C2×D284C2311yescharacteristic
72C2×C22⋊D71—21no—
73C2×C22⋊D71D411yescharacteristic
74C2×C4×D71—21no—
75C2×C4×D71—21no—
76C2×C4×D71—21no—
77C2×C4×D71C2311yescharacteristic
78#11765852—41no—
79D568—22no—
80D568—41no—
81#11765849—41no—
82C2×C71⋊C8C2311yescharacteristic
83C2×C71⋊C8C2311yescharacteristic
84C8×D71—41no—
85C4⋊Dic71C2311yescharacteristic
86Dic71⋊C4—21no—
87Dic71⋊C4D411yescharacteristic
88C22⋊Dic71D411yescharacteristic
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)⋊C4—21no—
97(C2×D71)⋊C4D411yescharacteristic
98C4×Dic71—21no—
99C4×Dic71C2311yescharacteristic
100C2×Q8×C71C2311yescharacteristic
101C22×C4×C71C2311yescharacteristic
102C2×C8×C71C2311yescharacteristic
103C2×C8×C71C2311yescharacteristic
104C4⋊C4×C71—21no—
105C4⋊C4×C71C2311yescharacteristic
106C4⋊C4×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C22⋊C4×C71—21no—
109C22⋊C4×C71—21no—
110C42×C71—21no—
111C23×C71C2×D411yescharacteristic
112C22×D71—21no—
113C22×D71—21no—
114C22×D71—21no—
115C22×D71—42no—
116C22×D71—42no—
117C22×D71—81no—
118C22×D71C2×D411yescharacteristic
119Q8×C71—21no—
120Q8×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×C71C2×D411yescharacteristic
128C2×C4×C71C2411yescharacteristic
129C22⋊D71—41no—
130C22⋊D71—81no—
131C2×Dic71—21no—
132C2×Dic71C2×D411yescharacteristic
133C2×Dic71C2×D411yescharacteristic
134C2×Dic71C2×D411yescharacteristic
135D284—21no—
136D284—21no—
137D284—21no—
138D284—21no—
139D284—21no—
140D284—42no—
141D284—42no—
142D284—81no—
143D284—81no—
144D284#4112yes—
145C4×D71—21no—
146C4×D71—21no—
147C4×D71—42no—
148C4×D71—42no—
149C4×D71—81no—
150Dic142—81no—
151C8×C71—21no—
152C8×C71—21no—
153C71⋊C8—21no—
154C71⋊C8—21no—
155C22×C71—21no—
156C22×C71—21no—
157C22×C71—21no—
158C22×C71C22×D411yescharacteristic
159C2×D71—21no—
160C2×D71—22no—
161C2×D71—21no—
162C2×D71—21no—
163C2×D71—41no—
164C2×D71—41no—
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—41no—
174C4×C71—41no—
175C4×C71—41no—
176C4×C71—41no—
177C4×C71C2×#4111yescharacteristic
178C4×C71H(5,𝔽2)11yescharacteristic
179Dic71—21no—
180Dic71—21no—
181Dic71—21no—
182Dic71—41no—
183C2×C71—41no—
184C2×C71#54611yescharacteristic
185C2×C71#57511yescharacteristic
186C2×C71#57611yescharacteristic
187D71—41no—
188D71—42no—
189D71—81no—
190D71—81no—
191#3319—711nomaximal, Sylow
192C71#331911yescharacteristic, complemented, Sylow
193#555—711no—
194#546—711no—
195#489—711no—
196#485D7111yescharacteristic, complemented
197#482—711no—
198#474—711no—
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⋊Q8—711no—
216#124—711no—
217#124—1421no—
218#124—1421no—
219#123—1421no—
220C22⋊Q8C2×D7111yescharacteristic
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×D4—711no—
230#117—711no—
231#117—1421no—
232#117C2×D7111yescharacteristic
233C2×C22⋊C4—1421no—
234#107—711no—
235#107C2×D7111yescharacteristic, complemented
236#106C2×D7111yescharacteristic, complemented
237C4⋊C8—711no—
238#103—711no—
239#103C2×D7111yescharacteristic, complemented
240#103C2×D7111yescharacteristic, complemented
241#102—711no—
242#102—711no—
243#102—711no—
244#102—711no—
245#102—711no—
246#102—711no—
247#102—711no—
248C22⋊C8—711no—
249C22⋊C8C2×D7111yescharacteristic
250#97—711no—
251C24—1421no—
252#41—2841no—
253#41—1422no—
254C2×Q8—1421no—
255C2×Q8C22×D7111yescharacteristic
256C2×D4—2841no—
257C2×D4—711no—
258C2×D4—711no—
259C2×D4—711no—
260C2×D4—711no—
261C2×D4—1421no—
262C2×D4—1422no—
263C2×D4—1421no—
264C2×D4—1421no—
265C2×D4—1421no—
266C2×D4—1421no—
267C22×C4—711no—
268C22×C4—1421no—
269C22×C4—1421no—
270C22×C4—1421no—
271C22×C4C22×D7111yescharacteristic
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—21no—
290C22⋊C4—711no—
291C22⋊C4—711no—
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—21no—
301C42—711no—
302C42—1421no—
303C23—2842no—
304C23—2842no—
305C23—5681no—
306C23—711no—
307C23—1421no—
308C23—1421no—
309C23—1421no—
310C23D4×D7111yescharacteristic
311Q8—21no—
312Q8—21no—
313Q8—5681no—
314D4—2842no—
315D4—2842no—
316D4—2841no—
317D4—5681no—
318D4—5681no—
319D4—5681no—
320D4—712no—
321D4—1421no—
322D4—1421no—
323D4—1421no—
324D4—1421no—
325D4—1421no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2842no—
333C2×C4—2842no—
334C2×C4—5681no—
335C2×C4—711no—
336C2×C4—711no—
337C2×C4—711no—
338C2×C4—1421no—
339C2×C4—1421no—
340C2×C4—1421no—
341C2×C4D4×D7111yescharacteristic
342C2×C4C23×D7111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1421no—
346C8—1421no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—2841no—
351C22—2841no—
352C22—2841no—
353C22—2841no—
354C22—2841no—
355C22—2841no—
356C22—2841no—
357C22—2841no—
358C22—5684no—
359C22—1422no—
360C22—1421no—
361C22—1421no—
362C22—1421no—
363C22C2×D4×D7111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—2841no—
370C4—1421no—
371C4—1421no—
372C4—1421no—
373C4#41×D7111yescharacteristic
374C4#1455617411yescharacteristic
375C2—41no—
376C2—2842no—
377C2—2841no—
378C2—5681no—
379C2—5681no—
380C2#1798664111yescharacteristic
381C2#1798679811yescharacteristic
382C2#1798680111yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#485×C71C2
socleC22×C71C22×D4
hypercenter#485D71
hypocenterC71#3319
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #17986712C2semidirect
2. #17986640C2semidirect
3. #17986360C2semidirect
4. #17986325C2semidirect
5. #17986278C2semidirect
6. #17986247C2semidirect
7. #17986236C2semidirect
8. #17986217C2semidirect
9. #17986147C2semidirect
10. #17986135C2semidirect
11. #17986110C2semidirect
12. #17986073C2semidirect
13. #17986003C2semidirect
14. #17985994C2semidirect
15. #485×C71C2semidirect
18. C2×#11765852C22semidirect
22. C2×C8×D71C22semidirect
23. #14556127C22semidirect
30. #14556103C22semidirect
35. #14556090C22semidirect
37. #14556086C22semidirect
40. #14556061C22semidirect
41. Dic71⋊C8C22semidirect
42. #14556052C22semidirect
49. #14556048C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. #14556038C22semidirect
54. #107×C71C22semidirect
55. #106×C71C22semidirect
56. #103×C71C22semidirect
57. #103×C71C22semidirect
192. C71#3319semidirect
196. #485D71semidirect
235. #107C2×D71semidirect
236. #106C2×D71semidirect
239. #103C2×D71semidirect
240. #103C2×D71semidirect