Finite Group Databasebeta

← #22600481

Subgroups — #22600481

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#17986695C211yesmaximal, characteristic, complemented
2#17986363C211yesmaximal, characteristic, complemented
3#17986320C211yesmaximal, characteristic, complemented
4#17986315C211yesmaximal, characteristic, complemented
5#17986299C211yesmaximal, characteristic, complemented
6#17986250C211yesmaximal, characteristic, complemented
7#17986233C211yesmaximal, characteristic, complemented
8#17986191C211yesmaximal, characteristic, complemented
9#17986133C211yesmaximal, characteristic, complemented
10#17986133C211yesmaximal, characteristic, complemented
11#17986109C211yesmaximal, characteristic, complemented
12#17986071C211yesmaximal, characteristic, complemented
13#17986004C211yesmaximal, characteristic, complemented
14C2×#14556049C211yesmaximal, characteristic, complemented
15D42×C71C211yesmaximal, characteristic, complemented
16C2×#11765850C2211yescharacteristic
17C2×#11765850C2211yescharacteristic, complemented
18C2×#11765850C2211yescharacteristic, complemented
19C2×#11765849C2211yescharacteristic, complemented
20C22×C71⋊C8C2211yescharacteristic, complemented
21#14556123—21no—
22#14556120C2211yescharacteristic, complemented
23#14556110—21no—
24#14556102C2211yescharacteristic, complemented
25#14556102C2211yescharacteristic, complemented
26#14556100—21no—
27C4×D284C2211yescharacteristic, complemented
28(C22⋊D71)⋊C4—21no—
29#14556087C2211yescharacteristic, complemented
30C2×C4⋊Dic71C2211yescharacteristic, complemented
31#14556061C2211yescharacteristic, complemented
32#14556059C2211yescharacteristic, complemented
33#14556059C2211yescharacteristic, complemented
34C4⋊(C71⋊C8)C2211yescharacteristic, complemented
35#14556049C2211yescharacteristic
36#14556049C2211yescharacteristic
37#14556049C2211yescharacteristic
38#14556049C2211yescharacteristic, complemented
39#14556049C2211yescharacteristic, complemented
40#14556049C2211yescharacteristic, complemented
41#14556049C2211yescharacteristic, complemented
42#14556049C2211yescharacteristic, complemented
43#14556049C2211yescharacteristic, complemented
44#14556048C2211yescharacteristic, complemented
45C22⋊(C71⋊C8)C2211yescharacteristic, complemented
46C22⋊(C71⋊C8)C2211yescharacteristic, complemented
47#14556039C2211yescharacteristic, complemented
48C22×D4×C71—21no—
49C22×D4×C71C2211yescharacteristic
50C22×D4×C71C2211yescharacteristic
51#127×C71C2211yescharacteristic
52#121×C71—21no—
53#121×C71C2211yescharacteristic
54#121×C71C2211yescharacteristic
55#120×C71—21no—
56#120×C71—21no—
57C4×D4×C71C2211yescharacteristic
58C4×D4×C71C2211yescharacteristic
59C2×D284C2311yescharacteristic
60C2×C22⋊D71—21no—
61C2×C22⋊D71—21no—
62C22×Dic71—21no—
63C2×C4×D71—21no—
64#11765850—22no—
65#11765850—41no—
66#11765850—41no—
67#11765849—41no—
68C2×C71⋊C8—41no—
69C2×C71⋊C8C2311yescharacteristic
70C2×C71⋊C8C2311yescharacteristic
71C2×C71⋊C8C2311yescharacteristic
72C2×C71⋊C8C2311yescharacteristic
73C4⋊Dic71—21no—
74C4⋊Dic71C2311yescharacteristic
75C4⋊Dic71C2311yescharacteristic
76C4⋊Dic71C2311yescharacteristic
77Dic71⋊C4—21no—
78Dic71⋊C4—21no—
79C22⋊Dic71—21no—
80(C2×D71)⋊C4—21no—
81(C2×D71)⋊C4—21no—
82(C2×D71)⋊C4—21no—
83C4×Dic71—21no—
84C24×C71—21no—
85C24×C71—21no—
86C2×D4×C71—22no—
87C2×D4×C71—22no—
88C2×D4×C71—21no—
89C2×D4×C71—21no—
90C2×D4×C71—21no—
91C2×D4×C71—21no—
92C2×D4×C71—21no—
93C2×D4×C71—21no—
94C2×D4×C71—41no—
95C2×D4×C71—41no—
96C2×D4×C71—44no—
97C2×D4×C71D411yescharacteristic
98C2×D4×C71C2311yescharacteristic
99C2×D4×C71C2311yescharacteristic
100C2×D4×C71C2311yescharacteristic
101C22×C4×C71—21no—
102C22×C4×C71C2311yescharacteristic
103C22×C4×C71C2311yescharacteristic
104C4⋊C4×C71D411yescharacteristic
105C4⋊C4×C71C2311yescharacteristic
106C22⋊C4×C71—21no—
107C22⋊C4×C71—21no—
108C22⋊C4×C71—21no—
109C22⋊C4×C71D411yescharacteristic
110C22⋊C4×C71D411yescharacteristic
111C42×C71C2311yescharacteristic
112C23×C71—21no—
113C23×C71—21no—
114C23×C71—21no—
115C23×C71—42no—
116C23×C71—42no—
117C23×C71—42no—
118C23×C71—42no—
119C23×C71—81no—
120C23×C71—81no—
121C23×C71C2×D411yescharacteristic
122C23×C71C2×D411yescharacteristic
123C22×D71—21no—
124D4×C71—22no—
125D4×C71—21no—
126D4×C71—21no—
127D4×C71—21no—
128D4×C71—21no—
129D4×C71—21no—
130D4×C71—42no—
131D4×C71—42no—
132D4×C71—42no—
133D4×C71—42no—
134D4×C71—42no—
135D4×C71—81no—
136D4×C71#4112yes—
137C2×C4×C71—21no—
138C2×C4×C71—21no—
139C2×C4×C71—21no—
140C2×C4×C71—21no—
141C2×C4×C71—21no—
142C2×C4×C71—42no—
143C2×C4×C71C2×D411yescharacteristic
144C2×C4×C71C2×D411yescharacteristic
145C2×C4×C71C2×D411yescharacteristic
146C2×C4×C71C2×D411yescharacteristic
147C2×C4×C71C2411yescharacteristic
148C22⋊D71—42no—
149C22⋊D71—81no—
150C2×Dic71—21no—
151C2×Dic71—21no—
152C2×Dic71—21no—
153C2×Dic71—81no—
154D284—21no—
155D284—21no—
156C4×D71—81no—
157C71⋊C8—21no—
158C71⋊C8—21no—
159C71⋊C8—21no—
160C71⋊C8—21no—
161C22×C71—21no—
162C22×C71—21no—
163C22×C71—21no—
164C22×C71—22no—
165C22×C71—21no—
166C22×C71—21no—
167C22×C71—41no—
168C22×C71—41no—
169C22×C71—41no—
170C22×C71—41no—
171C22×C71—41no—
172C22×C71—41no—
173C22×C71—41no—
174C22×C71—41no—
175C22×C71—84no—
176C22×C71—84no—
177C22×C71AGL(1,ℤ/8)12yes—
178C22×C71C22×D411yescharacteristic
179C2×D71—41no—
180C2×D71—41no—
181C2×D71—41no—
182C4×C71—21no—
183C4×C71—21no—
184C4×C71—21no—
185C4×C71—21no—
186C4×C71—41no—
187C4×C71C2×#4111yescharacteristic
188C4×C71H(5,𝔽2)11yescharacteristic
189Dic71—41no—
190Dic71—41no—
191Dic71—41no—
192C2×C71—22no—
193C2×C71—41no—
194C2×C71—42no—
195C2×C71—81no—
196C2×C71—81no—
197C2×C71#54611yescharacteristic
198C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C71#57611yescharacteristic
200D71—81no—
201#3318—711nomaximal, Sylow
202C71#331811yescharacteristic, complemented, Sylow
203#553—711no—
204D42D7111yescharacteristic, complemented
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#442—711no—
215#435—711no—
216#418—711no—
217C2×#102—711no—
218C22×D4—21no—
219C22×D4C2×D7111yescharacteristic
220C22×D4C2×D7111yescharacteristic
221C2×D8—711no—
222C2×D8—711no—
223C2×D8—711no—
224C2×M16—711no—
225C22×C8—711no—
226#127C2×D7111yescharacteristic
227#126—1421no—
228#125—711no—
229#123—1421no—
230#121—21no—
231#121—711no—
232#121—711no—
233#121—1421no—
234#121C2×D7111yescharacteristic
235#121C2×D7111yescharacteristic
236#120—21no—
237#120—21no—
238C4×D4—711no—
239C4×D4—1421no—
240C4×D4C2×D7111yescharacteristic
241C4×D4C2×D7111yescharacteristic
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#102—711no—
255#102—711no—
256#102—711no—
257#102—711no—
258C22⋊C8—711no—
259C22⋊C8—711no—
260#97—711no—
261C24—21no—
262C24—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—44no—
274C2×D4—711no—
275C2×D4—1421no—
276C2×D4—1421no—
277C2×D4C22⋊D7111yescharacteristic
278C2×D4C22×D7111yescharacteristic
279C2×D4C22×D7111yescharacteristic
280C2×D4C22×D7111yescharacteristic
281C22×C4—21no—
282C22×C4—1421no—
283C22×C4—1421no—
284C22×C4C22×D7111yescharacteristic
285C22×C4C22×D7111yescharacteristic
286D8—2841no—
287D8—2841no—
288D8—1422no—
289M16—2841no—
290C2×C8—2841no—
291C2×C8—711no—
292C2×C8—711no—
293C2×C8—711no—
294C2×C8—711no—
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—21no—
306C22⋊C4—1421no—
307C22⋊C4—1421no—
308C22⋊C4—1421no—
309C22⋊C4—1421no—
310C22⋊C4C22⋊D7111yescharacteristic
311C22⋊C4C22⋊D7111yescharacteristic
312C42—1421no—
313C42C22×D7111yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1421no—
324C23C2×C22⋊D7111yescharacteristic
325C23C2×C22⋊D7111yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—81no—
338D4—2842no—
339D4—5681no—
340D4—1421no—
341D4—1421no—
342D4#1176586412yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—5681no—
350C2×C4—5681no—
351C2×C4—1421no—
352C2×C4—1421no—
353C2×C4—1421no—
354C2×C4C2×C22⋊D7111yescharacteristic
355C2×C4C2×C22⋊D7111yescharacteristic
356C2×C4C2×C22⋊D7111yescharacteristic
357C2×C4C2×C22⋊D7111yescharacteristic
358C2×C4C23×D7111yescharacteristic
359C8—1421no—
360C8—1421no—
361C8—1421no—
362C8—1421no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—84no—
379C22—2841no—
380C22—2841no—
381C22—2841no—
382C22#1455615412yes—
383C22C22×C22⋊D7111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—2841no—
390C4—2841no—
391C4—2841no—
392C4C2×#1176586411yescharacteristic
393C4#1455617311yescharacteristic
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—5681no—
400C2#1798664311yescharacteristic
401C2C2×#1455615411yescharacteristic
402C2#1798680211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingD42×C71C2
socleC22×C71C22×D4
hypercenterD42D71
hypocenterC71#3318
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #17986695C2semidirect
2. #17986363C2semidirect
3. #17986320C2semidirect
4. #17986315C2semidirect
5. #17986299C2semidirect
6. #17986250C2semidirect
7. #17986233C2semidirect
8. #17986191C2semidirect
9. #17986133C2semidirect
10. #17986133C2semidirect
11. #17986109C2semidirect
12. #17986071C2semidirect
13. #17986004C2semidirect
14. C2×#14556049C2semidirect
15. D42×C71C2semidirect
17. C2×#11765850C22semidirect
18. C2×#11765850C22semidirect
19. C2×#11765849C22semidirect
20. C22×C71⋊C8C22semidirect
22. #14556120C22semidirect
24. #14556102C22semidirect
25. #14556102C22semidirect
27. C4×D284C22semidirect
29. #14556087C22semidirect
30. C2×C4⋊Dic71C22semidirect
31. #14556061C22semidirect
32. #14556059C22semidirect
33. #14556059C22semidirect
34. C4⋊(C71⋊C8)C22semidirect
38. #14556049C22semidirect
39. #14556049C22semidirect
40. #14556049C22semidirect
41. #14556049C22semidirect
42. #14556049C22semidirect
43. #14556049C22semidirect
44. #14556048C22semidirect
45. C22⋊(C71⋊C8)C22semidirect
46. C22⋊(C71⋊C8)C22semidirect
47. #14556039C22semidirect
202. C71#3318semidirect
204. D42D71semidirect