Finite Group Databasebeta

← #22600486

Subgroups — #22600486

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#17986699C211yesmaximal, characteristic, complemented
2D4×D284C211yesmaximal, characteristic, complemented
3#17986364C211yesmaximal, characteristic, complemented
4#17986325C211yesmaximal, characteristic, complemented
5#17986319C211yesmaximal, characteristic, complemented
6#17986299C211yesmaximal, characteristic, complemented
7#17986251C211yesmaximal, characteristic, complemented
8#17986234C211yesmaximal, characteristic, complemented
9#17986194C211yesmaximal, characteristic, complemented
10#17986131C211yesmaximal, characteristic, complemented
11#17986131C211yesmaximal, characteristic, complemented
12#17986072C211yesmaximal, characteristic, complemented
13#17986002C211yesmaximal, characteristic, complemented
14#102×D71C211yesmaximal, characteristic, complemented
15#442×C71C211yesmaximal, characteristic, complemented
16C22×D284—21no—
17C2×D4×D71C2211yescharacteristic
18C2×D4×D71C2211yescharacteristic
19C2×#11765850C2211yescharacteristic, complemented
20C2×#11765850C2211yescharacteristic, complemented
21C2×#11765848C2211yescharacteristic, complemented
22C2×C8×D71C2211yescharacteristic, complemented
23#14556125C2211yescharacteristic
24#14556121—21no—
25#14556120C2211yescharacteristic, complemented
26#14556111—21no—
27#14556103C2211yescharacteristic
28#14556103C2211yescharacteristic
29#14556102—21no—
30#14556101—21no—
31#14556099C2211yescharacteristic, complemented
32#14556099C2211yescharacteristic, complemented
33#14556098—21no—
34#14556098—21no—
35C4×D284C2211yescharacteristic
36C4×C22⋊D71—21no—
37#14556086C2211yescharacteristic, complemented
38C4⋊C4×D71C2211yescharacteristic, complemented
39#14556061C2211yescharacteristic, complemented
40#14556059C2211yescharacteristic, complemented
41C4⋊(C71⋊C8)C2211yescharacteristic, complemented
42#14556050C2211yescharacteristic, complemented
43#14556050C2211yescharacteristic, complemented
44#14556050C2211yescharacteristic, complemented
45#14556050C2211yescharacteristic, complemented
46#14556049C2211yescharacteristic
47#14556049C2211yescharacteristic
48#14556048C2211yescharacteristic, complemented
49#14556048C2211yescharacteristic, complemented
50(C2×D71)⋊C8C2211yescharacteristic, complemented
51(C2×D71)⋊C8C2211yescharacteristic, complemented
52C2×D8×C71C2211yescharacteristic
53C4×D4×C71C2211yescharacteristic
54C4×D4×C71C2211yescharacteristic, complemented
55#106×C71C2211yescharacteristic, complemented
56#102×C71C2211yescharacteristic
57#102×C71C2211yescharacteristic, complemented
58#97×C71C2211yescharacteristic, complemented
59C23×D71—21no—
60C23×D71—21no—
61C2×D284—21no—
62C2×D284—21no—
63C2×D284—21no—
64C2×D284—21no—
65C2×D284—44no—
66C2×D284D411yescharacteristic
67C2×D284C2311yescharacteristic
68C2×D284C2311yescharacteristic
69C2×C22⋊D71—21no—
70C2×C22⋊D71—21no—
71C2×C22⋊D71—21no—
72C2×C22⋊D71—21no—
73D4×D71—22no—
74D4×D71—22no—
75D4×D71—41no—
76D4×D71—41no—
77C2×C4×D71—21no—
78C2×C4×D71C2311yescharacteristic
79C2×C4×D71C2311yescharacteristic
80#11765850—41no—
81#11765850—41no—
82#11765848—41no—
83C2×C71⋊C8C2311yescharacteristic
84C2×C71⋊C8C2311yescharacteristic
85C8×D71—41no—
86C4⋊Dic71D411yescharacteristic
87C4⋊Dic71C2311yescharacteristic
88C4⋊Dic71C2311yescharacteristic
89Dic71⋊C4—21no—
90Dic71⋊C4—21no—
91Dic71⋊C4—21no—
92C22⋊Dic71—21no—
93C22⋊Dic71—21no—
94(C2×D71)⋊C4—21no—
95(C2×D71)⋊C4—21no—
96(C2×D71)⋊C4—21no—
97(C2×D71)⋊C4D411yescharacteristic
98(C2×D71)⋊C4D411yescharacteristic
99C4×Dic71—21no—
100C2×D4×C71C2311yescharacteristic
101C2×D4×C71C2311yescharacteristic
102C22×C4×C71—21no—
103C22×C4×C71—21no—
104D8×C71—22no—
105C2×C8×C71C2311yescharacteristic
106C2×C8×C71C2311yescharacteristic
107C4⋊C4×C71C2311yescharacteristic
108C4⋊C4×C71C2311yescharacteristic
109C22⋊C4×C71—21no—
110C22⋊C4×C71—21no—
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#4112yes—
128C2×C4×C71—21no—
129C2×C4×C71—21no—
130C2×C4×C71—42no—
131C2×C4×C71—81no—
132C2×C4×C71C2×D411yescharacteristic
133C2×C4×C71C2×D411yescharacteristic
134C2×C4×C71C2411yescharacteristic
135C22⋊D71—42no—
136C22⋊D71—42no—
137C22⋊D71—42no—
138C22⋊D71—81no—
139C2×Dic71—21no—
140C2×Dic71—21no—
141C2×Dic71C2×D411yescharacteristic
142C2×Dic71C2×D411yescharacteristic
143D284—22no—
144D284—21no—
145D284—21no—
146D284—21no—
147D284—21no—
148D284—42no—
149D284—42no—
150D284—42no—
151D284—81no—
152C4×D71—21no—
153C4×D71—21no—
154C4×D71—21no—
155C4×D71—21no—
156C4×D71—81no—
157C8×C71—21no—
158C8×C71—21no—
159C71⋊C8—21no—
160C71⋊C8—21no—
161C22×C71—22no—
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—21no—
172C2×D71—21no—
173C2×D71—41no—
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—42no—
193C2×C71—81no—
194C2×C71#54611yescharacteristic
195C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C71#57611yescharacteristic
197D71—22no—
198D71—41no—
199D71—81no—
200D71—81no—
201#3318—711nomaximal, Sylow
202C71#331811yescharacteristic, complemented, Sylow
203#553—711no—
204D42—711no—
205#490—711no—
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#442D7111yescharacteristic, complemented
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×D8C2×D7111yescharacteristic
224C2×M16—711no—
225C22×C8—711no—
226#127—711no—
227#126—1421no—
228#125—711no—
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—1421no—
240C4×D4C2×D7111yescharacteristic
241C4×D4C2×D7111yescharacteristic, complemented
242#117—711no—
243C2×C4⋊C4—711no—
244#107—711no—
245#106—711no—
246#106C2×D7111yescharacteristic, complemented
247C4⋊C8—711no—
248#102—711no—
249#102—711no—
250#102—711no—
251#102—711no—
252#102—711no—
253#102—711no—
254#102—711no—
255#102—711no—
256#102C2×D7111yescharacteristic
257#102C2×D7111yescharacteristic, complemented
258C22⋊C8—711no—
259C22⋊C8—711no—
260#97C2×D7111yescharacteristic, complemented
261C24—1421no—
262C24—1421no—
263C2×D4—2844no—
264C2×D4—2841no—
265C2×D4—2841no—
266C2×D4—711no—
267C2×D4—711no—
268C2×D4—711no—
269C2×D4—1421no—
270C2×D4—1421no—
271C2×D4—1421no—
272C2×D4—1421no—
273C2×D4—1421no—
274C2×D4—1422no—
275C2×D4—1422no—
276C2×D4—1421no—
277C2×D4—1421no—
278C2×D4—1421no—
279C2×D4C22×D7111yescharacteristic
280C2×D4C22×D7111yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—711no—
284C22×C4—711no—
285C22×C4—1421no—
286D8—22no—
287D8—2841no—
288D8—2841no—
289M16—2841no—
290C2×C8—2841no—
291C2×C8—711no—
292C2×C8—711no—
293C2×C8C22×D7111yescharacteristic
294C2×C8C22×D7111yescharacteristic
295C4⋊C4—711no—
296C4⋊C4—711no—
297C4⋊C4—711no—
298C4⋊C4—1421no—
299C4⋊C4—1421no—
300C4⋊C4—1421no—
301C4⋊C4C22×D7111yescharacteristic
302C4⋊C4C22×D7111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—711no—
306C22⋊C4—711no—
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—2842no—
330D4—2842no—
331D4—2842no—
332D4—2842no—
333D4—2842no—
334D4—2842no—
335D4—5681no—
336D4—5681no—
337D4—1422no—
338D4—1421no—
339D4—1421no—
340D4—1421no—
341D4—1421no—
342D4#1176586512yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
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—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—2841no—
370C22—2841no—
371C22—2841no—
372C22—2841no—
373C22—2841no—
374C22—2841no—
375C22—5684no—
376C22—5684no—
377C22—712no—
378C22—1421no—
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—
392C4C2×#1176586511yescharacteristic
393C4#1455617411yescharacteristic
394C2—42no—
395C2—81no—
396C2—2841no—
397C2—5681no—
398C2—5681no—
399C2—1422no—
400C2#1798664511yescharacteristic
401C2AGL(1,ℤ/8)×D7111yescharacteristic
402C2#1798680311yescharacteristic
subgroupG/H
centerC22C2×D4×D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#442×C71C2
socleC22×C71C22×D4
hypercenter#442D71
hypocenterC71#3318
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #17986699C2semidirect
2. D4×D284C2semidirect
3. #17986364C2semidirect
4. #17986325C2semidirect
5. #17986319C2semidirect
6. #17986299C2semidirect
7. #17986251C2semidirect
8. #17986234C2semidirect
9. #17986194C2semidirect
10. #17986131C2semidirect
11. #17986131C2semidirect
12. #17986072C2semidirect
13. #17986002C2semidirect
14. #102×D71C2semidirect
15. #442×C71C2semidirect
19. C2×#11765850C22semidirect
20. C2×#11765850C22semidirect
21. C2×#11765848C22semidirect
22. C2×C8×D71C22semidirect
25. #14556120C22semidirect
31. #14556099C22semidirect
32. #14556099C22semidirect
37. #14556086C22semidirect
38. C4⋊C4×D71C22semidirect
39. #14556061C22semidirect
40. #14556059C22semidirect
41. C4⋊(C71⋊C8)C22semidirect
42. #14556050C22semidirect
43. #14556050C22semidirect
44. #14556050C22semidirect
45. #14556050C22semidirect
48. #14556048C22semidirect
49. #14556048C22semidirect
50. (C2×D71)⋊C8C22semidirect
51. (C2×D71)⋊C8C22semidirect
54. C4×D4×C71C22semidirect
55. #106×C71C22semidirect
57. #102×C71C22semidirect
58. #97×C71C22semidirect
202. C71#3318semidirect
214. #442D71semidirect
241. C4×D4C2×D71semidirect
246. #106C2×D71semidirect
257. #102C2×D71semidirect
260. #97C2×D71semidirect