Finite Group Databasebeta

← #22600301

Subgroups — #22600301

Order 9088.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17986653C211yesmaximal, characteristic, complemented
2#17986358C211yesmaximal, characteristic, complemented
3#17986327C211yesmaximal, characteristic, complemented
4#17986315C211yesmaximal, characteristic, complemented
5#17986289C211yesmaximal, characteristic, complemented
6#17986250C211yesmaximal, characteristic, complemented
7#17986230C211yesmaximal, characteristic, complemented
8#17986211C211yesmaximal, characteristic, complemented
9#17986144C211yesmaximal, characteristic, complemented
10#17986133C211yesmaximal, characteristic, complemented
11#17986109C211yesmaximal, characteristic, complemented
12#17986071C211yesmaximal, characteristic, complemented
13#17986000C211yesmaximal, characteristic, complemented
14C2×#14556049C211yesmaximal, characteristic, complemented
15#546×C71C211yesmaximal, characteristic, complemented
16C2×#11765864—21no—
17C2×#11765852C2211yescharacteristic, complemented
18C2×#11765850C2211yescharacteristic
19C2×#11765850C2211yescharacteristic
20C2×#11765849C2211yescharacteristic, complemented
21C22×C71⋊C8C2211yescharacteristic
22#14556128C2211yescharacteristic, complemented
23#14556112—21no—
24#14556112—21no—
25#14556108—21no—
26#14556102C2211yescharacteristic
27#14556102C2211yescharacteristic, complemented
28C4×D284C2211yescharacteristic, complemented
29C2×C4⋊Dic71C2211yescharacteristic
30C2×C4⋊Dic71C2211yescharacteristic, complemented
31#14556059C2211yescharacteristic, complemented
32#14556059C2211yescharacteristic, complemented
33#14556059C2211yescharacteristic, complemented
34C4⋊(C71⋊C8)C2211yescharacteristic, complemented
35#14556052C2211yescharacteristic, complemented
36#14556052C2211yescharacteristic, complemented
37#14556052C2211yescharacteristic, complemented
38#14556049C2211yescharacteristic
39#14556049C2211yescharacteristic
40#14556049C2211yescharacteristic
41#14556049C2211yescharacteristic
42#14556049C2211yescharacteristic
43#14556049C2211yescharacteristic
44#14556048C2211yescharacteristic, complemented
45C22⋊(C71⋊C8)C2211yescharacteristic
46C22⋊(C71⋊C8)C2211yescharacteristic, complemented
47#14556039C2211yescharacteristic, complemented
48C2×#41×C71C2211yescharacteristic
49C22×D4×C71C2211yescharacteristic
50#124×C71C2211yescharacteristic
51#123×C71—21no—
52C22⋊Q8×C71C2211yescharacteristic
53#121×C71—21no—
54#121×C71C2211yescharacteristic
55#120×C71—21no—
56C4×D4×C71C2211yescharacteristic
57C4×D4×C71C2211yescharacteristic
58C2×C22⋊C4×C71—21no—
59#11765864—44no—
60C2×Dic142—21no—
61C2×D284C2311yescharacteristic
62C2×C22⋊D71—21no—
63C2×C22⋊D71—21no—
64C22×Dic71—21no—
65C22×Dic71—21no—
66C2×C4×D71—21no—
67#11765852—41no—
68#11765850—22no—
69#11765850—41no—
70#11765849—41no—
71C2×C71⋊C8—41no—
72C2×C71⋊C8C2311yescharacteristic
73C2×C71⋊C8C2311yescharacteristic
74C2×C71⋊C8C2311yescharacteristic
75C2×C71⋊C8C2311yescharacteristic
76C4⋊Dic71—21no—
77C4⋊Dic71—21no—
78C4⋊Dic71—21no—
79C4⋊Dic71C2311yescharacteristic
80C4⋊Dic71C2311yescharacteristic
81C4⋊Dic71C2311yescharacteristic
82(C2×D71)⋊C4—21no—
83(C2×D71)⋊C4—21no—
84(C2×D71)⋊C4—21no—
85C24×C71—21no—
86#41×C71—22no—
87#41×C71—41no—
88C2×Q8×C71C2311yescharacteristic
89C2×D4×C71—22no—
90C2×D4×C71—21no—
91C2×D4×C71—21no—
92C2×D4×C71—21no—
93C2×D4×C71—41no—
94C2×D4×C71D411yescharacteristic
95C2×D4×C71C2311yescharacteristic
96C2×D4×C71C2311yescharacteristic
97C22×C4×C71—21no—
98C22×C4×C71—21no—
99C22×C4×C71C2311yescharacteristic
100C22×C4×C71C2311yescharacteristic
101C4⋊C4×C71—21no—
102C4⋊C4×C71D411yescharacteristic
103C4⋊C4×C71C2311yescharacteristic
104C22⋊C4×C71—21no—
105C22⋊C4×C71—21no—
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—42no—
115C23×C71—42no—
116C23×C71—81no—
117C23×C71C2×D411yescharacteristic
118C23×C71C2×D411yescharacteristic
119C22×D71—21no—
120Q8×C71—21no—
121Q8×C71—21no—
122D4×C71—22no—
123D4×C71—21no—
124D4×C71—21no—
125D4×C71—21no—
126D4×C71—42no—
127D4×C71—42no—
128D4×C71—81no—
129D4×C71#4112yescomplemented
130C2×C4×C71—21no—
131C2×C4×C71—21no—
132C2×C4×C71—21no—
133C2×C4×C71—21no—
134C2×C4×C71—21no—
135C2×C4×C71—21no—
136C2×C4×C71—42no—
137C2×C4×C71—81no—
138C2×C4×C71C2×D411yescharacteristic
139C2×C4×C71C2×D411yescharacteristic
140C2×C4×C71C2×D411yescharacteristic
141C2×C4×C71C2×D411yescharacteristic
142C2×C4×C71C2411yescharacteristic
143C22⋊D71—42no—
144C22⋊D71—42no—
145C2×Dic71—21no—
146C2×Dic71—21no—
147C2×Dic71—21no—
148C2×Dic71—42no—
149C2×Dic71—42no—
150D284—21no—
151D284—21no—
152C4×D71—42no—
153Dic142—42no—
154C71⋊C8—21no—
155C71⋊C8—21no—
156C71⋊C8—21no—
157C71⋊C8—21no—
158C22×C71—21no—
159C22×C71—21no—
160C22×C71—21no—
161C22×C71—22no—
162C22×C71—21no—
163C22×C71—21no—
164C22×C71—41no—
165C22×C71—41no—
166C22×C71—41no—
167C22×C71—41no—
168C22×C71—41no—
169C22×C71—84no—
170C22×C71AGL(1,ℤ/8)12yes—
171C22×C71C22×D411yescharacteristic
172C2×D71—41no—
173C2×D71—41no—
174C2×D71—41no—
175C4×C71—21no—
176C4×C71—21no—
177C4×C71—21no—
178C4×C71—21no—
179C4×C71—41no—
180C4×C71—41no—
181C4×C71C2×#4111yescharacteristic
182C4×C71H(5,𝔽2)11yescharacteristic
183Dic71—41no—
184Dic71—41no—
185Dic71—41no—
186C2×C71—22no—
187C2×C71—41no—
188C2×C71—42no—
189C2×C71—81no—
190C2×C71#54611yescharacteristic
191C2×C71C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C71#57711yescharacteristic
193D71—81no—
194#3306—711nomaximal, Sylow
195C71#330611yescharacteristic, complemented, Sylow
196#547—711no—
197#546D7111yescharacteristic, complemented
198#489—711no—
199#483—711no—
200#481—711no—
201#476—711no—
202#469—711no—
203#465—711no—
204#463—711no—
205#449—711no—
206#447—711no—
207#442—711no—
208#435—711no—
209#417—711no—
210C2×#102—711no—
211C2×#41—1421no—
212C2×#41C2×D7111yescharacteristic
213C22×D4C2×D7111yescharacteristic
214C2×SD16—711no—
215C2×D8—711no—
216C2×D8—711no—
217C2×M16—711no—
218C22×C8—711no—
219C4⋊Q8—711no—
220#124C2×D7111yescharacteristic
221#123—21no—
222#123—1421no—
223#123—1421no—
224C22⋊Q8—1421no—
225C22⋊Q8C2×D7111yescharacteristic
226#121—21no—
227#121—711no—
228#121—711no—
229#121C2×D7111yescharacteristic
230#120—21no—
231C4×D4—711no—
232C4×D4C2×D7111yescharacteristic
233C4×D4C2×D7111yescharacteristic
234C2×C4⋊C4—711no—
235C2×C4⋊C4—711no—
236C2×C22⋊C4—21no—
237#106—711no—
238#106—711no—
239#106—711no—
240C4⋊C8—711no—
241#103—711no—
242#103—711no—
243#103—711no—
244#102—711no—
245#102—711no—
246#102—711no—
247#102—711no—
248#102—711no—
249#102—711no—
250#102—711no—
251C22⋊C8—711no—
252C22⋊C8—711no—
253#97—711no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—2844no—
258C2×Q8—1421no—
259C2×Q8C22×D7111yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—711no—
266C2×D4—1421no—
267C2×D4—1421no—
268C2×D4C22⋊D7111yescharacteristic
269C2×D4C22×D7111yescharacteristic
270C2×D4C22×D7111yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1421no—
274C22×C4—1421no—
275C22×C4—1421no—
276C22×C4C22×D7111yescharacteristic
277C22×C4C22×D7111yescharacteristic
278SD16—2841no—
279D8—2841no—
280D8—1422no—
281M16—2841no—
282C2×C8—2841no—
283C2×C8—711no—
284C2×C8—711no—
285C2×C8—711no—
286C2×C8—711no—
287C4⋊C4—21no—
288C4⋊C4—711no—
289C4⋊C4—711no—
290C4⋊C4—711no—
291C4⋊C4—1421no—
292C4⋊C4—1421no—
293C4⋊C4—1421no—
294C4⋊C4C22⋊D7111yescharacteristic
295C4⋊C4C22×D7111yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1421no—
302C22⋊C4—1421no—
303C22⋊C4—1421no—
304C22⋊C4C22⋊D7111yescharacteristic
305C22⋊C4C22⋊D7111yescharacteristic
306C42C22×D7111yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—1421no—
313C23C2×C22⋊D7111yescharacteristic
314C23C2×C22⋊D7111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—2842no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—2842no—
326D4—2842no—
327D4—1421no—
328D4—1421no—
329D4#1176586412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—2842no—
339C2×C4—2842no—
340C2×C4—2842no—
341C2×C4—1421no—
342C2×C4—1421no—
343C2×C4—1421no—
344C2×C4C2×C22⋊D7111yescharacteristic
345C2×C4C2×C22⋊D7111yescharacteristic
346C2×C4C2×C22⋊D7111yescharacteristic
347C2×C4C2×C22⋊D7111yescharacteristic
348C2×C4C23×D7111yescharacteristic
349C8—1421no—
350C8—1421no—
351C8—1421no—
352C8—1421no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—2841no—
366C22—2841no—
367C22—2841no—
368C22#1455615312yes—
369C22C22×C22⋊D7111yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—2841no—
377C4—2841no—
378C4—2841no—
379C4C2×#1176586411yescharacteristic
380C4#1455617311yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—5681no—
386C2#1798664311yescharacteristic
387C2C2×#1455615311yescharacteristic
388C2#1798681011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D71
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
Fitting#546×C71C2
socleC22×C71C22×D4
hypercenter#546D71
hypocenterC71#3306
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #17986653C2semidirect
2. #17986358C2semidirect
3. #17986327C2semidirect
4. #17986315C2semidirect
5. #17986289C2semidirect
6. #17986250C2semidirect
7. #17986230C2semidirect
8. #17986211C2semidirect
9. #17986144C2semidirect
10. #17986133C2semidirect
11. #17986109C2semidirect
12. #17986071C2semidirect
13. #17986000C2semidirect
14. C2×#14556049C2semidirect
15. #546×C71C2semidirect
17. C2×#11765852C22semidirect
20. C2×#11765849C22semidirect
22. #14556128C22semidirect
27. #14556102C22semidirect
28. C4×D284C22semidirect
30. C2×C4⋊Dic71C22semidirect
31. #14556059C22semidirect
32. #14556059C22semidirect
33. #14556059C22semidirect
34. C4⋊(C71⋊C8)C22semidirect
35. #14556052C22semidirect
36. #14556052C22semidirect
37. #14556052C22semidirect
44. #14556048C22semidirect
46. C22⋊(C71⋊C8)C22semidirect
47. #14556039C22semidirect
129. D4×C71#41semidirect
195. C71#3306semidirect
197. #546D71semidirect
329. D4#11765864semidirect