Finite Group Databasebeta

← #22600480

Subgroups — #22600480

Order 9088.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986702C211yesmaximal, characteristic, complemented
2#17986634C211yesmaximal, characteristic, complemented
3#17986322C211yesmaximal, characteristic, complemented
4#17986316C211yesmaximal, characteristic, complemented
5#17986296C211yesmaximal, characteristic, complemented
6#17986251C211yesmaximal, characteristic, complemented
7#17986234C211yesmaximal, characteristic, complemented
8#17986191C211yesmaximal, characteristic, complemented
9#17986134C211yesmaximal, characteristic, complemented
10#17986134C211yesmaximal, characteristic, complemented
11#17986112C211yesmaximal, characteristic, complemented
12#17986072C211yesmaximal, characteristic, complemented
13#17986002C211yesmaximal, characteristic, complemented
14#102×D71C211yesmaximal, characteristic, complemented
15#490×C71C211yesmaximal, characteristic, complemented
16C2×D4×D71—21no—
17C2×D4×D71C2211yescharacteristic
18C2×D4×D71C2211yescharacteristic
19C2×D568C2211yescharacteristic
20C2×#11765850C2211yescharacteristic, complemented
21C2×#11765850C2211yescharacteristic, complemented
22C2×#11765848C2211yescharacteristic, complemented
23C2×C8×D71C2211yescharacteristic, complemented
24#14556123—21no—
25#14556113—21no—
26#14556103—21no—
27#14556103C2211yescharacteristic, complemented
28#14556103C2211yescharacteristic, complemented
29#14556099—21no—
30#14556099C2211yescharacteristic
31#14556099C2211yescharacteristic
32#14556096—21no—
33#14556096—21no—
34C4×D284C2211yescharacteristic
35C4×D284C2211yescharacteristic
36C4×D284C2211yescharacteristic, complemented
37#14556090—21no—
38#14556086C2211yescharacteristic, complemented
39C4⋊C4×D71C2211yescharacteristic, complemented
40#14556061C2211yescharacteristic, complemented
41#14556060C2211yescharacteristic, complemented
42#14556059C2211yescharacteristic, complemented
43C4⋊(C71⋊C8)C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic
45#14556050C2211yescharacteristic, complemented
46#14556049C2211yescharacteristic, complemented
47#14556049C2211yescharacteristic, complemented
48#14556048C2211yescharacteristic
49#14556048C2211yescharacteristic
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52#127×C71C2211yescharacteristic
53#125×C71C2211yescharacteristic, complemented
54#102×C71C2211yescharacteristic, complemented
55#102×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic, complemented
57#102×C71C2211yescharacteristic, complemented
58#97×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71—21no—
61C2×D284—21no—
62C2×D284—21no—
63C2×D284D411yescharacteristic
64C2×D284C2311yescharacteristic
65C2×D284C2311yescharacteristic
66C2×C22⋊D71—21no—
67C2×C22⋊D71—21no—
68C2×C22⋊D71—21no—
69C2×C22⋊D71—21no—
70D4×D71—22no—
71D4×D71—22no—
72D4×D71—41no—
73D4×D71—41no—
74D4×D71—44no—
75C2×C4×D71—21no—
76C2×C4×D71—21no—
77C2×C4×D71—21no—
78C2×C4×D71C2311yescharacteristic
79C2×C4×D71C2311yescharacteristic
80D568—22no—
81#11765850—41no—
82#11765850—41no—
83#11765848—41no—
84C2×C71⋊C8C2311yescharacteristic
85C2×C71⋊C8C2311yescharacteristic
86C8×D71—41no—
87C4⋊Dic71D411yescharacteristic
88C4⋊Dic71C2311yescharacteristic
89C4⋊Dic71C2311yescharacteristic
90Dic71⋊C4—21no—
91C22⋊Dic71—21no—
92C22⋊Dic71—21no—
93(C2×D71)⋊C4—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97(C2×D71)⋊C4—21no—
98(C2×D71)⋊C4D411yescharacteristic
99(C2×D71)⋊C4D411yescharacteristic
100C4×Dic71—21no—
101C2×D4×C71—21no—
102C2×D4×C71—21no—
103C2×D4×C71C2311yescharacteristic
104C2×D4×C71C2311yescharacteristic
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C4⋊C4×C71—21no—
108C4⋊C4×C71—21no—
109C4⋊C4×C71C2311yescharacteristic
110C4⋊C4×C71C2311yescharacteristic
111C42×C71C2311yescharacteristic
112C23×C71—21no—
113C23×C71—21no—
114C22×D71—21no—
115C22×D71—21no—
116C22×D71—42no—
117C22×D71—42no—
118C22×D71—42no—
119C22×D71—42no—
120C22×D71—81no—
121C22×D71—81no—
122C22×D71C2×D411yescharacteristic
123C22×D71C2×D411yescharacteristic
124D4×C71—21no—
125D4×C71—21no—
126D4×C71—21no—
127D4×C71—21no—
128D4×C71—42no—
129D4×C71—81no—
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71C2×D411yescharacteristic
133C2×C4×C71C2×D411yescharacteristic
134C2×C4×C71C2411yescharacteristic
135C22⋊D71—42no—
136C22⋊D71—42no—
137C22⋊D71—42no—
138C22⋊D71—42no—
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71C2×D411yescharacteristic
142C2×Dic71C2×D411yescharacteristic
143D284—22no—
144D284—21no—
145D284—21no—
146D284—21no—
147D284—42no—
148D284—81no—
149D284#4112yes—
150C4×D71—21no—
151C4×D71—21no—
152C4×D71—21no—
153C4×D71—21no—
154C4×D71—42no—
155C4×D71—81no—
156C4×D71—81no—
157C8×C71—21no—
158C8×C71—21no—
159C71⋊C8—21no—
160C71⋊C8—21no—
161C22×C71—41no—
162C22×C71—41no—
163C22×C71—41no—
164C22×C71—41no—
165C22×C71—41no—
166C22×C71—41no—
167C22×C71C22×D411yescharacteristic
168C2×D71—21no—
169C2×D71—21no—
170C2×D71—21no—
171C2×D71—22no—
172C2×D71—21no—
173C2×D71—21no—
174C2×D71—41no—
175C2×D71—41no—
176C2×D71—41no—
177C2×D71—41no—
178C2×D71—41no—
179C2×D71—84no—
180C2×D71—84no—
181C2×D71AGL(1,ℤ/8)12yes—
182C4×C71—21no—
183C4×C71—21no—
184C4×C71—41no—
185C4×C71—41no—
186C4×C71C2×#4111yescharacteristic
187C4×C71H(5,𝔽2)11yescharacteristic
188Dic71—21no—
189Dic71—21no—
190Dic71—41no—
191Dic71—41no—
192C2×C71—81no—
193C2×C71—81no—
194C2×C71#54611yescharacteristic
195C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C71#57611yescharacteristic
197D71—22no—
198D71—41no—
199D71—42no—
200D71—81no—
201#3318—711nomaximal, Sylow
202C71#331811yescharacteristic, complemented, Sylow
203#553—711no—
204D42—711no—
205#490D7111yescharacteristic, complemented
206#482—711no—
207#481—711no—
208#478—711no—
209#469—711no—
210#466—711no—
211#459—711no—
212#447—711no—
213#447—711no—
214#442—711no—
215#435—711no—
216#418—711no—
217C2×#102—711no—
218C22×D4—711no—
219C22×D4—711no—
220C22×D4—1421no—
221C2×D8—711no—
222C2×D8—711no—
223C2×D8—711no—
224C2×M16—711no—
225C22×C8—711no—
226#127C2×D7111yescharacteristic
227#126—1421no—
228#125C2×D7111yescharacteristic, complemented
229#123—1421no—
230#121—711no—
231#121—711no—
232#121—711no—
233#121—711no—
234#121—1421no—
235#121—1421no—
236#120—1421no—
237#120—1421no—
238C4×D4—711no—
239C4×D4—711no—
240C4×D4—711no—
241C4×D4—1421no—
242#117—711no—
243C2×C4⋊C4—711no—
244#107—711no—
245#106—711no—
246#106—711no—
247C4⋊C8—711no—
248#102—711no—
249#102—711no—
250#102—711no—
251#102—711no—
252#102—711no—
253#102—711no—
254#102C2×D7111yescharacteristic, complemented
255#102C2×D7111yescharacteristic, complemented
256#102C2×D7111yescharacteristic, complemented
257#102C2×D7111yescharacteristic, complemented
258C22⋊C8—711no—
259C22⋊C8—711no—
260#97C2×D7111yescharacteristic, complemented
261C24—1421no—
262C24—1421no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—2844no—
266C2×D4—2841no—
267C2×D4—2841no—
268C2×D4—711no—
269C2×D4—711no—
270C2×D4—711no—
271C2×D4—1421no—
272C2×D4—1421no—
273C2×D4—1421no—
274C2×D4—1421no—
275C2×D4—1422no—
276C2×D4—1422no—
277C2×D4—1421no—
278C2×D4—1421no—
279C2×D4C22×D7111yescharacteristic
280C2×D4C22×D7111yescharacteristic
281C22×C4—711no—
282C22×C4—711no—
283C22×C4—1421no—
284C22×C4—1421no—
285C22×C4—1421no—
286D8—2841no—
287D8—2841no—
288D8—1422no—
289M16—2841no—
290C2×C8—2841no—
291C2×C8—711no—
292C2×C8—711no—
293C2×C8C22×D7111yescharacteristic
294C2×C8C22×D7111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—711no—
298C4⋊C4—711no—
299C4⋊C4—711no—
300C4⋊C4—1421no—
301C4⋊C4C22×D7111yescharacteristic
302C4⋊C4C22×D7111yescharacteristic
303C22⋊C4—711no—
304C22⋊C4—711no—
305C22⋊C4—1421no—
306C22⋊C4—1421no—
307C22⋊C4—1421no—
308C22⋊C4—1421no—
309C22⋊C4—1421no—
310C22⋊C4—1421no—
311C22⋊C4—1421no—
312C42—1421no—
313C42C22×D7111yescharacteristic
314C23—21no—
315C23—21no—
316C23—2842no—
317C23—2842no—
318C23—2842no—
319C23—2842no—
320C23—5681no—
321C23—5681no—
322C23—711no—
323C23—711no—
324C23—1421no—
325C23—1421no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—2842no—
333D4—2842no—
334D4—2842no—
335D4—2842no—
336D4—2842no—
337D4—5681no—
338D4—712no—
339D4—1422no—
340D4—1421no—
341D4—1421no—
342D4—1421no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—2842no—
346C2×C4—5681no—
347C2×C4—5681no—
348C2×C4—711no—
349C2×C4—711no—
350C2×C4—1421no—
351C2×C4—1421no—
352C2×C4—1421no—
353C2×C4—1421no—
354C2×C4—1421no—
355C2×C4—1421no—
356C2×C4D4×D7111yescharacteristic
357C2×C4D4×D7111yescharacteristic
358C2×C4C23×D7111yescharacteristic
359C8—21no—
360C8—21no—
361C8—1421no—
362C8—1421no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—2841no—
370C22—2841no—
371C22—2841no—
372C22—2841no—
373C22—2841no—
374C22—5684no—
375C22—5684no—
376C22—712no—
377C22—1421no—
378C22—1422no—
379C22—1421no—
380C22—1421no—
381C22—1421no—
382C22—1421no—
383C22C2×D4×D7111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—2841no—
389C4—2841no—
390C4—1421no—
391C4—1421no—
392C4#41×D7111yescharacteristic
393C4#1455617411yescharacteristic
394C2—81no—
395C2—81no—
396C2—2842no—
397C2—2841no—
398C2—5681no—
399C2—1422no—
400C2#1798664211yescharacteristic
401C2AGL(1,ℤ/8)×D7111yescharacteristic
402C2#1798680311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#490×C71C2
socleC22×C71C22×D4
hypercenter#490D71
hypocenterC71#3318
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17986702C2semidirect
2. #17986634C2semidirect
3. #17986322C2semidirect
4. #17986316C2semidirect
5. #17986296C2semidirect
6. #17986251C2semidirect
7. #17986234C2semidirect
8. #17986191C2semidirect
9. #17986134C2semidirect
10. #17986134C2semidirect
11. #17986112C2semidirect
12. #17986072C2semidirect
13. #17986002C2semidirect
14. #102×D71C2semidirect
15. #490×C71C2semidirect
20. C2×#11765850C22semidirect
21. C2×#11765850C22semidirect
22. C2×#11765848C22semidirect
23. C2×C8×D71C22semidirect
27. #14556103C22semidirect
28. #14556103C22semidirect
36. C4×D284C22semidirect
38. #14556086C22semidirect
39. C4⋊C4×D71C22semidirect
40. #14556061C22semidirect
41. #14556060C22semidirect
42. #14556059C22semidirect
43. C4⋊(C71⋊C8)C22semidirect
45. #14556050C22semidirect
46. #14556049C22semidirect
47. #14556049C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. (C2×D71)⋊C8C22semidirect
53. #125×C71C22semidirect
54. #102×C71C22semidirect
55. #102×C71C22semidirect
56. #102×C71C22semidirect
57. #102×C71C22semidirect
58. #97×C71C22semidirect
202. C71#3318semidirect
205. #490D71semidirect
228. #125C2×D71semidirect
254. #102C2×D71semidirect
255. #102C2×D71semidirect
256. #102C2×D71semidirect
257. #102C2×D71semidirect
260. #97C2×D71semidirect