Finite Group Databasebeta

← #22599204

Subgroups — #22599204

Order 9088.

442 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986568C211yesmaximal, characteristic, complemented
2#17986565C211yesmaximal, characteristic, complemented
3#17986326C211yesmaximal, characteristic, complemented
4#17986325C211yesmaximal, characteristic, complemented
5#17986323C211yesmaximal, characteristic, complemented
6#17986253C211yesmaximal, characteristic, complemented
7#17986251C211yesmaximal, characteristic, complemented
8#17986236C211yesmaximal, characteristic, complemented
9#17986234C211yesmaximal, characteristic, complemented
10#17986135C211yesmaximal, characteristic, complemented
11#17986134C211yesmaximal, characteristic, complemented
12#17986134C211yesmaximal, characteristic, complemented
13#17986132C211yesmaximal, characteristic, complemented
14#17985964C211yesmaximal, characteristic, complemented
15#482×C71C211yesmaximal, characteristic, complemented
16C2×#11765865C2211yescharacteristic
17C22×D284C2211yescharacteristic, complemented
18C2×D4×D71C2211yescharacteristic, complemented
19C2×D568C2211yescharacteristic
20C2×D568C2211yescharacteristic
21C2×#11765850C2211yescharacteristic
22C2×#11765850C2211yescharacteristic
23C2×#11765848C2211yescharacteristic, complemented
24C2×C8×D71C2211yescharacteristic, complemented
25#14556125—21no—
26#14556124—21no—
27#14556116—21no—
28#14556114—21no—
29#14556103C2211yescharacteristic
30#14556103C2211yescharacteristic
31#14556103C2211yescharacteristic, complemented
32#14556103C2211yescharacteristic, complemented
33#14556103C2211yescharacteristic, complemented
34#14556102C2211yescharacteristic
35#14556099C2211yescharacteristic, complemented
36#14556098—21no—
37#14556098—21no—
38#14556098—21no—
39#14556096—21no—
40#14556086C2211yescharacteristic, complemented
41#14556061C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556048C2211yescharacteristic, complemented
46#14556048C2211yescharacteristic, complemented
47#14556048C2211yescharacteristic, complemented
48#14556048C2211yescharacteristic, complemented
49C22⋊(C71⋊C8)C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52#121×C71C2211yescharacteristic
53#117×C71C2211yescharacteristic, complemented
54#107×C71C2211yescharacteristic, complemented
55#106×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58C22⋊C8×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71—21no—
61#11765865—41no—
62#11765865—41no—
63C2×Dic142D411yescharacteristic
64C2×D284—21no—
65C2×D284—21no—
66C2×D284—21no—
67C2×D284—21no—
68C2×D284—21no—
69C2×D284—21no—
70C2×D284—41no—
71C2×D284—41no—
72C2×D284D411yescharacteristic
73C2×D284C2311yescharacteristic
74C2×D284C2311yescharacteristic
75C2×D284C2311yescharacteristic
76C2×C22⋊D71—21no—
77C2×C22⋊D71—21no—
78C2×C22⋊D71—21no—
79C2×C22⋊D71D411yescharacteristic
80C2×C22⋊D71D411yescharacteristic
81D4×D71—41no—
82D4×D71—41no—
83C2×C4×D71C2311yescharacteristic
84C2×C4×D71C2311yescharacteristic
85D568—41no—
86D568—41no—
87#11765850—41no—
88#11765850—41no—
89#11765848—41no—
90C2×C71⋊C8C2311yescharacteristic
91C2×C71⋊C8C2311yescharacteristic
92C8×D71—41no—
93C4⋊Dic71C2311yescharacteristic
94C22⋊Dic71—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97(C2×D71)⋊C4—21no—
98(C2×D71)⋊C4—21no—
99(C2×D71)⋊C4—21no—
100(C2×D71)⋊C4—21no—
101(C2×D71)⋊C4—21no—
102C4×Dic71—21no—
103C2×D4×C71—21no—
104C2×D4×C71C2311yescharacteristic
105C22×C4×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C2×C8×C71C2311yescharacteristic
108C4⋊C4×C71C2311yescharacteristic
109C4⋊C4×C71C2311yescharacteristic
110C4⋊C4×C71C2311yescharacteristic
111C22⋊C4×C71—21no—
112C22⋊C4×C71—21no—
113C42×C71—21no—
114C23×C71—21no—
115C23×C71C2×D411yescharacteristic
116C22×D71—21no—
117C22×D71—21no—
118C22×D71—21no—
119C22×D71—42no—
120C22×D71—42no—
121C22×D71—81no—
122C22×D71—81no—
123C22×D71—81no—
124C22×D71—81no—
125C22×D71C2×D411yescharacteristic
126C22×D71C2×D411yescharacteristic
127D4×C71—21no—
128D4×C71—21no—
129D4×C71—81no—
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71—21no—
133C2×C4×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71C2×D411yescharacteristic
136C2×C4×C71C2411yescharacteristic
137C22⋊D71—41no—
138C22⋊D71—41no—
139C22⋊D71—42no—
140C22⋊D71—81no—
141C22⋊D71—81no—
142C2×Dic71—21no—
143C2×Dic71C2×D411yescharacteristic
144C2×Dic71C2×D411yescharacteristic
145D284—21no—
146D284—21no—
147D284—21no—
148D284—21no—
149D284—21no—
150D284—21no—
151D284—41no—
152D284—42no—
153D284—81no—
154D284—81no—
155D284—81no—
156D284—81no—
157D284—81no—
158C4×D71—21no—
159C4×D71—21no—
160C4×D71—21no—
161C4×D71—21no—
162Dic142—41no—
163C8×C71—21no—
164C8×C71—21no—
165C71⋊C8—21no—
166C71⋊C8—21no—
167C22×C71—21no—
168C22×C71—21no—
169C22×C71—21no—
170C22×C71—41no—
171C22×C71—41no—
172C22×C71—41no—
173C22×C71C22×D411yescharacteristic
174C2×D71—21no—
175C2×D71—21no—
176C2×D71—21no—
177C2×D71—21no—
178C2×D71—21no—
179C2×D71—21no—
180C2×D71—41no—
181C2×D71—41no—
182C2×D71—41no—
183C2×D71—41no—
184C2×D71—41no—
185C2×D71—41no—
186C2×D71—41no—
187C2×D71—41no—
188C2×D71—41no—
189C2×D71—84no—
190C2×D71—84no—
191C4×C71—21no—
192C4×C71—41no—
193C4×C71—41no—
194C4×C71—41no—
195C4×C71H(5,𝔽2)11yescharacteristic
196C4×C71H(5,𝔽2)11yescharacteristic
197Dic71—21no—
198Dic71—21no—
199Dic71—41no—
200C2×C71—41no—
201C2×C71—81no—
202C2×C71#53411yescharacteristic
203C2×C71#57611yescharacteristic
204C2×C71#57611yescharacteristic
205D71—41no—
206D71—41no—
207D71—81no—
208D71—81no—
209D71—81no—
210#3199—711nomaximal, Sylow
211C71#319911yescharacteristic, complemented, Sylow
212#535—711no—
213#535—711no—
214#482—711no—
215#482—711no—
216#482—711no—
217#482D7111yescharacteristic, complemented
218#469—711no—
219#469—711no—
220#466—711no—
221#466—711no—
222#447—711no—
223#447—711no—
224#447—711no—
225#447—711no—
226#408—711no—
227C2×#41—711no—
228C22×D4—711no—
229C22×D4—711no—
230C2×D8—711no—
231C2×D8—711no—
232C2×D8—711no—
233C2×D8—711no—
234C2×M16—711no—
235C22×C8—711no—
236#127—1421no—
237#127—1421no—
238#124—1421no—
239#124—1421no—
240#121—711no—
241#121—711no—
242#121—711no—
243#121—711no—
244#121—711no—
245#121—711no—
246#121—711no—
247#121C2×D7111yescharacteristic
248#120—1421no—
249#120—1421no—
250#120—1421no—
251#120—1421no—
252#117—711no—
253#117C2×D7111yescharacteristic, complemented
254#107—711no—
255#107C2×D7111yescharacteristic, complemented
256#106—711no—
257#106C2×D7111yescharacteristic, complemented
258#102—711no—
259#102—711no—
260#102—711no—
261#102—711no—
262#102—711no—
263#102—711no—
264#102C2×D7111yescharacteristic, complemented
265#102C2×D7111yescharacteristic, complemented
266C22⋊C8—711no—
267C22⋊C8—711no—
268C22⋊C8—711no—
269C22⋊C8C2×D7111yescharacteristic, complemented
270C24—1421no—
271C24—1421no—
272#41—2841no—
273#41—2841no—
274C2×Q8—711no—
275C2×D4—21no—
276C2×D4—2841no—
277C2×D4—2841no—
278C2×D4—2841no—
279C2×D4—2841no—
280C2×D4—711no—
281C2×D4—711no—
282C2×D4—711no—
283C2×D4—711no—
284C2×D4—711no—
285C2×D4—711no—
286C2×D4—1421no—
287C2×D4—1421no—
288C2×D4—1421no—
289C2×D4—1421no—
290C2×D4—1421no—
291C2×D4—1421no—
292C2×D4—1421no—
293C2×D4—1421no—
294C2×D4—1421no—
295C2×D4C22×D7111yescharacteristic
296C22×C4—711no—
297C22×C4—711no—
298C22×C4C22×D7111yescharacteristic
299D8—2841no—
300D8—2841no—
301D8—2841no—
302D8—2841no—
303M16—2841no—
304C2×C8—2841no—
305C2×C8—711no—
306C2×C8—711no—
307C2×C8C22×D7111yescharacteristic
308C2×C8C22×D7111yescharacteristic
309C4⋊C4—711no—
310C4⋊C4C22×D7111yescharacteristic
311C4⋊C4C22×D7111yescharacteristic
312C4⋊C4C22×D7111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1421no—
316C22⋊C4—1421no—
317C22⋊C4—1421no—
318C22⋊C4—1421no—
319C22⋊C4—1421no—
320C22⋊C4—1421no—
321C22⋊C4—1421no—
322C22⋊C4—1421no—
323C42—21no—
324C42—1421no—
325C23—21no—
326C23—2842no—
327C23—2842no—
328C23—5681no—
329C23—5681no—
330C23—5681no—
331C23—5681no—
332C23—711no—
333C23—711no—
334C23—1421no—
335C23—1421no—
336C23—1421no—
337C23D4×D7111yescharacteristic
338Q8—2841no—
339D4—21no—
340D4—21no—
341D4—81no—
342D4—2842no—
343D4—2841no—
344D4—2841no—
345D4—2841no—
346D4—2842no—
347D4—5681no—
348D4—5681no—
349D4—5681no—
350D4—5681no—
351D4—5681no—
352D4—5681no—
353D4—5681no—
354D4—1421no—
355D4—1421no—
356D4—1421no—
357D4—1421no—
358D4—1421no—
359D4—1421no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—711no—
366C2×C4—711no—
367C2×C4—1421no—
368C2×C4—1421no—
369C2×C4—1421no—
370C2×C4—1421no—
371C2×C4—1421no—
372C2×C4D4×D7111yescharacteristic
373C2×C4C23×D7111yescharacteristic
374C8—21no—
375C8—21no—
376C8—1421no—
377C8—1421no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—2841no—
385C22—2841no—
386C22—2841no—
387C22—2841no—
388C22—2841no—
389C22—2841no—
390C22—2841no—
391C22—2841no—
392C22—2841no—
393C22—5684no—
394C22—5684no—
395C22—1421no—
396C22—1421no—
397C22—1421no—
398C22—1421no—
399C22—1421no—
400C22—1421no—
401C22C2×D4×D7111yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—2841no—
407C4—1421no—
408C4—1421no—
409C4#1455617411yescharacteristic
410C4#1455617411yescharacteristic
411C2—41no—
412C2—81no—
413C2—2841no—
414C2—2841no—
415C2—5681no—
416C2—5681no—
417C2—5681no—
418C2#1798656011yescharacteristic
419C2#1798680111yescharacteristic
420C2#1798680311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#482×C71C2
socleC22×C71C22×D4
hypercenter#482D71
hypocenterC71#3199
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #17986568C2semidirect
2. #17986565C2semidirect
3. #17986326C2semidirect
4. #17986325C2semidirect
5. #17986323C2semidirect
6. #17986253C2semidirect
7. #17986251C2semidirect
8. #17986236C2semidirect
9. #17986234C2semidirect
10. #17986135C2semidirect
11. #17986134C2semidirect
12. #17986134C2semidirect
13. #17986132C2semidirect
14. #17985964C2semidirect
15. #482×C71C2semidirect
17. C22×D284C22semidirect
18. C2×D4×D71C22semidirect
23. C2×#11765848C22semidirect
24. C2×C8×D71C22semidirect
31. #14556103C22semidirect
32. #14556103C22semidirect
33. #14556103C22semidirect
35. #14556099C22semidirect
40. #14556086C22semidirect
41. #14556061C22semidirect
42. #14556059C22semidirect
43. #14556050C22semidirect
44. #14556050C22semidirect
45. #14556048C22semidirect
46. #14556048C22semidirect
47. #14556048C22semidirect
48. #14556048C22semidirect
49. C22⋊(C71⋊C8)C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. (C2×D71)⋊C8C22semidirect
53. #117×C71C22semidirect
54. #107×C71C22semidirect
55. #106×C71C22semidirect
56. #102×C71C22semidirect
57. #102×C71C22semidirect
58. C22⋊C8×C71C22semidirect
211. C71#3199semidirect
217. #482D71semidirect
253. #117C2×D71semidirect
255. #107C2×D71semidirect
257. #106C2×D71semidirect
264. #102C2×D71semidirect
265. #102C2×D71semidirect
269. C22⋊C8C2×D71semidirect