Finite Group Databasebeta

← #20255349

Subgroups — #20255349

Order 6016.

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#15689777C211yesmaximal, characteristic, complemented
2#15689482C211yesmaximal, characteristic, complemented
3#15689451C211yesmaximal, characteristic, complemented
4#15689439C211yesmaximal, characteristic, complemented
5#15689413C211yesmaximal, characteristic, complemented
6#15689374C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689335C211yesmaximal, characteristic, complemented
9#15689268C211yesmaximal, characteristic, complemented
10#15689257C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689195C211yesmaximal, characteristic, complemented
13#15689124C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15C47×#546C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625336C2211yescharacteristic, complemented
18C2×#10625334C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625329C2211yescharacteristic, complemented
21C22×C47⋊C8C2211yescharacteristic
22#13094024C2211yescharacteristic, complemented
23#13094008—21no—
24#13094008—21no—
25#13094004—21no—
26#13093998C2211yescharacteristic
27#13093998C2211yescharacteristic, complemented
28C4×D188C2211yescharacteristic, complemented
29C2×C4⋊Dic47C2211yescharacteristic
30C2×C4⋊Dic47C2211yescharacteristic, complemented
31#13093955C2211yescharacteristic, complemented
32#13093955C2211yescharacteristic, complemented
33#13093955C2211yescharacteristic, complemented
34C4⋊(C47⋊C8)C2211yescharacteristic, complemented
35#13093948C2211yescharacteristic, complemented
36#13093948C2211yescharacteristic, complemented
37#13093948C2211yescharacteristic, complemented
38#13093945C2211yescharacteristic
39#13093945C2211yescharacteristic
40#13093945C2211yescharacteristic
41#13093945C2211yescharacteristic
42#13093945C2211yescharacteristic
43#13093945C2211yescharacteristic
44#13093944C2211yescharacteristic, complemented
45C22⋊(C47⋊C8)C2211yescharacteristic
46C22⋊(C47⋊C8)C2211yescharacteristic, complemented
47#13093935C2211yescharacteristic, complemented
48C2×#41×C47C2211yescharacteristic
49C22×D4×C47C2211yescharacteristic
50#124×C47C2211yescharacteristic
51#123×C47—21no—
52C22⋊Q8×C47C2211yescharacteristic
53#121×C47—21no—
54#121×C47C2211yescharacteristic
55#120×C47—21no—
56C4×D4×C47C2211yescharacteristic
57C4×D4×C47C2211yescharacteristic
58C2×C22⋊C4×C47—21no—
59C24×C47—21no—
60#41×C47—22no—
61#41×C47—41no—
62C2×Q8×C47C2311yescharacteristic
63C2×D4×C47—22no—
64C2×D4×C47—21no—
65C2×D4×C47—21no—
66C2×D4×C47—21no—
67C2×D4×C47—41no—
68C2×D4×C47D411yescharacteristic
69C2×D4×C47C2311yescharacteristic
70C2×D4×C47C2311yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47C2311yescharacteristic
74C22×C4×C47C2311yescharacteristic
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C22×Dic47—21no—
78C22×Dic47—21no—
79#10625352—44no—
80C2×D188C2311yescharacteristic
81C2×C4×D47—21no—
82C2×Dic94—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47D411yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C22⋊C4×C47—21no—
87C22⋊C4×C47—21no—
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊C4×C47D411yescharacteristic
92C22⋊C4×C47D411yescharacteristic
93C42×C47C2311yescharacteristic
94#10625336—41no—
95#10625334—22no—
96#10625334—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106#10625329—41no—
107C2×C47⋊C8—41no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C2×C47⋊C8C2311yescharacteristic
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—42no—
115C23×C47—42no—
116C23×C47—81no—
117C23×C47C2×D411yescharacteristic
118C23×C47C2×D411yescharacteristic
119C22×D47—21no—
120Q8×C47—21no—
121Q8×C47—21no—
122D4×C47—22no—
123D4×C47—21no—
124D4×C47—21no—
125D4×C47—21no—
126D4×C47—42no—
127D4×C47—42no—
128D4×C47—81no—
129D4×C47#4112yescomplemented
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—21no—
136C2×C4×C47—42no—
137C2×C4×C47—81no—
138C2×C4×C47C2×D411yescharacteristic
139C2×C4×C47C2×D411yescharacteristic
140C2×C4×C47C2×D411yescharacteristic
141C2×C4×C47C2×D411yescharacteristic
142C2×C4×C47C2411yescharacteristic
143C22⋊D47—42no—
144C22⋊D47—42no—
145C2×Dic47—21no—
146C2×Dic47—21no—
147C2×Dic47—21no—
148C2×Dic47—42no—
149C2×Dic47—42no—
150D188—21no—
151D188—21no—
152C4×D47—42no—
153Dic94—42no—
154C47⋊C8—21no—
155C47⋊C8—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—22no—
162C22×C47—21no—
163C22×C47—21no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47—41no—
168C22×C47—41no—
169C22×C47—84no—
170C22×C47AGL(1,ℤ/8)12yes—
171C22×C47C22×D411yescharacteristic
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—41no—
180C4×C47—41no—
181C4×C47C2×#4111yescharacteristic
182C4×C47H(5,𝔽2)11yescharacteristic
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—22no—
188C2×C47—41no—
189C2×C47—42no—
190C2×C47—81no—
191C2×C47#54611yescharacteristic
192C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C47#57711yescharacteristic
194D47—81no—
195#547—471no—
196#546D4711yescharacteristic, complemented
197#489—471no—
198#483—471no—
199#481—471no—
200#476—471no—
201#469—471no—
202#465—471no—
203#463—471no—
204#449—471no—
205#447—471no—
206#442—471no—
207#435—471no—
208#417—471no—
209C2×#102—471no—
210C47#330611yescharacteristic, complemented, Sylow
211C2×#41—941no—
212C2×#41C2×D4711yescharacteristic
213C22×D4C2×D4711yescharacteristic
214C2×SD16—471no—
215C2×D8—471no—
216C2×D8—471no—
217C2×M16—471no—
218C22×C8—471no—
219C4⋊Q8—471no—
220#124C2×D4711yescharacteristic
221#123—21no—
222#123—941no—
223#123—941no—
224C22⋊Q8—941no—
225C22⋊Q8C2×D4711yescharacteristic
226#121—21no—
227#121—471no—
228#121—471no—
229#121C2×D4711yescharacteristic
230#120—21no—
231C4×D4—471no—
232C4×D4C2×D4711yescharacteristic
233C4×D4C2×D4711yescharacteristic
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C22⋊C4—21no—
237#106—471no—
238#106—471no—
239#106—471no—
240C4⋊C8—471no—
241#103—471no—
242#103—471no—
243#103—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251C22⋊C8—471no—
252C22⋊C8—471no—
253#97—471no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—1884no—
258C2×Q8—941no—
259C2×Q8C22×D4711yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—471no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4C22⋊D4711yescharacteristic
269C2×D4C22×D4711yescharacteristic
270C2×D4C22×D4711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4C22×D4711yescharacteristic
277C22×C4C22×D4711yescharacteristic
278SD16—1881no—
279D8—942no—
280D8—1881no—
281M16—1881no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8—471no—
286C2×C8—1881no—
287C4⋊C4—21no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—471no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4C22⋊D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4C22⋊D4711yescharacteristic
305C22⋊C4C22⋊D4711yescharacteristic
306C42C22×D4711yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—941no—
313C23C2×C22⋊D4711yescharacteristic
314C23C2×C22⋊D4711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1882no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—941no—
326D4—941no—
327D4—1882no—
328D4—1882no—
329D4#1062535212yescomplemented
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—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—1882no—
342C2×C4—1882no—
343C2×C4—1882no—
344C2×C4C2×C22⋊D4711yescharacteristic
345C2×C4C2×C22⋊D4711yescharacteristic
346C2×C4C2×C22⋊D4711yescharacteristic
347C2×C4C2×C22⋊D4711yescharacteristic
348C2×C4C23×D4711yescharacteristic
349C8—941no—
350C8—941no—
351C8—941no—
352C8—941no—
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—1881no—
366C22—1881no—
367C22—1881no—
368C22#1309404912yes—
369C22C22×C22⋊D4711yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4C2×#1062535211yescharacteristic
380C4#1309406911yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—3761no—
386C2#1568976711yescharacteristic
387C2C2×#1309404911yescharacteristic
388C2#1568993411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#546C2
socleC22×C47C22×D4
hypercenter#546D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #15689777C2semidirect
2. #15689482C2semidirect
3. #15689451C2semidirect
4. #15689439C2semidirect
5. #15689413C2semidirect
6. #15689374C2semidirect
7. #15689354C2semidirect
8. #15689335C2semidirect
9. #15689268C2semidirect
10. #15689257C2semidirect
11. #15689233C2semidirect
12. #15689195C2semidirect
13. #15689124C2semidirect
14. C2×#13093945C2semidirect
15. C47×#546C2semidirect
17. C2×#10625336C22semidirect
20. C2×#10625329C22semidirect
22. #13094024C22semidirect
27. #13093998C22semidirect
28. C4×D188C22semidirect
30. C2×C4⋊Dic47C22semidirect
31. #13093955C22semidirect
32. #13093955C22semidirect
33. #13093955C22semidirect
34. C4⋊(C47⋊C8)C22semidirect
35. #13093948C22semidirect
36. #13093948C22semidirect
37. #13093948C22semidirect
44. #13093944C22semidirect
46. C22⋊(C47⋊C8)C22semidirect
47. #13093935C22semidirect
129. D4×C47#41semidirect
196. #546D47semidirect
210. C47#3306semidirect
329. D4#10625352semidirect