Finite Group Databasebeta

← #20255344

Subgroups — #20255344

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#15689773C211yesmaximal, characteristic, complemented
2#15689770C211yesmaximal, characteristic, complemented
3#15689481C211yesmaximal, characteristic, complemented
4#15689455C211yesmaximal, characteristic, complemented
5#15689439C211yesmaximal, characteristic, complemented
6#15689412C211yesmaximal, characteristic, complemented
7#15689351C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689266C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic, complemented
11#15689232C211yesmaximal, characteristic, complemented
12#15689192C211yesmaximal, characteristic, complemented
13#15689125C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#469C211yesmaximal, characteristic, complemented
16C2×#10625350C2211yescharacteristic
17C2×#10625352—21no—
18C2×D4×D47C2211yescharacteristic
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625334C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22#13094023C2211yescharacteristic, complemented
23#13094011C2211yescharacteristic
24#13094006—21no—
25#13094006—21no—
26#13094005—21no—
27#13094004C2211yescharacteristic
28#13094001—21no—
29#13093995—21no—
30#13093995C2211yescharacteristic
31#13093992—21no—
32D4×Dic47C2211yescharacteristic, complemented
33#13093986C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic, complemented
36C4⋊C4×D47C2211yescharacteristic
37C22⋊C4×D47—21no—
38#13093955C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093949C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic
51#13093934C2211yescharacteristic, complemented
52C2×D8×C47C2211yescharacteristic
53C2×M16×C47C2211yescharacteristic, complemented
54#121×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic, complemented
56#106×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47—21no—
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C2×D4×C47C2311yescharacteristic
64C22×C4×C47C2311yescharacteristic
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C2×C22⋊D47D411yescharacteristic
69C22×Dic47—21no—
70C22×Dic47—21no—
71#10625352—44no—
72D4×D47—22no—
73D4×D47—41no—
74#10625350—22no—
75#10625350—41no—
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94C2311yescharacteristic
83D8×C47—41no—
84M16×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C22⋊C4×C47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47D411yescharacteristic
96#10625335—41no—
97#10625334—22no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4D411yescharacteristic
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4D411yescharacteristic
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111C8×D47—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47C2×D411yescharacteristic
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47C2×D411yescharacteristic
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—42no—
125D4×C47—81no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—22no—
133C22⋊D47—42no—
134C22⋊D47—42no—
135C22⋊D47—42no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—42no—
140C2×Dic47—42no—
141C2×Dic47C2×D411yescharacteristic
142C2×Dic47C2×D411yescharacteristic
143C2×Dic47C2×D411yescharacteristic
144D188—21no—
145D188#4112yescomplemented
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—42no—
149C4×D47—42no—
150C4×D47—81no—
151Dic94—21no—
152Dic94—21no—
153Dic94—42no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—21no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47—41no—
165C22×C47—41no—
166C22×C47—41no—
167C22×C47C22×D411yescharacteristic
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—22no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—84no—
174C2×D47AGL(1,ℤ/8)12yes—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47C2×#4111yescharacteristic
179C4×C47H(5,𝔽2)11yescharacteristic
180Dic47—21no—
181Dic47—21no—
182Dic47—21no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—41no—
188C2×C47—81no—
189C2×C47—81no—
190C2×C47#54611yescharacteristic
191C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C47#57711yescharacteristic
193D47—22no—
194D47—42no—
195#547—471no—
196#546—471no—
197#489—471no—
198#483—471no—
199#481—471no—
200#476—471no—
201#469D4711yescharacteristic, complemented
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—471no—
212C2×#41—941no—
213C22×D4—471no—
214C2×SD16—471no—
215C2×D8—471no—
216C2×D8C2×D4711yescharacteristic
217C2×M16C2×D4711yescharacteristic, complemented
218C22×C8—471no—
219C4⋊Q8—471no—
220#124—471no—
221#123—941no—
222#123—941no—
223#123—941no—
224C22⋊Q8—471no—
225C22⋊Q8—941no—
226#121—471no—
227#121—941no—
228#121C2×D4711yescharacteristic
229#121C2×D4711yescharacteristic, complemented
230#120—941no—
231C4×D4—471no—
232C4×D4—471no—
233C4×D4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C22⋊C4—941no—
237#106—471no—
238#106—471no—
239#106C2×D4711yescharacteristic, complemented
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#102C2×D4711yescharacteristic
250#102C2×D4711yescharacteristic, complemented
251C22⋊C8—471no—
252C22⋊C8—471no—
253#97—471no—
254C24—941no—
255#41—942no—
256#41—1881no—
257#41—1884no—
258C2×Q8—471no—
259C2×Q8—941no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—941no—
265C2×D4—942no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—1881no—
269C2×D4C22×D4711yescharacteristic
270C2×D4C22×D4711yescharacteristic
271C22×C4—471no—
272C22×C4—941no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278SD16—1881no—
279D8—41no—
280D8—942no—
281M16—41no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—1881no—
285C2×C8C22×D4711yescharacteristic
286C2×C8C22×D4711yescharacteristic
287C4⋊C4—471no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—941no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4C22×D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—471no—
299C22⋊C4—471no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C42—471no—
307C23—21no—
308C23—21no—
309C23—471no—
310C23—941no—
311C23—3761no—
312C23—1882no—
313C23—1882no—
314C23D4×D4711yescharacteristic
315Q8—941no—
316Q8—941no—
317Q8—1882no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—81no—
324D4—472no—
325D4—942no—
326D4—941no—
327D4—1882no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—3761no—
343C2×C4—1882no—
344C2×C4—1882no—
345C2×C4—1882no—
346C2×C4—1882no—
347C2×C4D4×D4711yescharacteristic
348C2×C4C23×D4711yescharacteristic
349C8—21no—
350C8—21no—
351C8—941no—
352C8—941no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—472no—
363C22—941no—
364C22—941no—
365C22—942no—
366C22—3764no—
367C22—1881no—
368C22—1881no—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—941no—
374C4—941no—
375C4—941no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4#41×D4711yescharacteristic
380C4#1309406911yescharacteristic
381C2—41no—
382C2—81no—
383C2—81no—
384C2—942no—
385C2—1882no—
386C2#1568976211yescharacteristic
387C2AGL(1,ℤ/8)×D4711yescharacteristic
388C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#469C2
socleC22×C47C22×D4
hypercenter#469D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #15689773C2semidirect
2. #15689770C2semidirect
3. #15689481C2semidirect
4. #15689455C2semidirect
5. #15689439C2semidirect
6. #15689412C2semidirect
7. #15689351C2semidirect
8. #15689336C2semidirect
9. #15689266C2semidirect
10. #15689255C2semidirect
11. #15689232C2semidirect
12. #15689192C2semidirect
13. #15689125C2semidirect
14. #102×D47C2semidirect
15. C47×#469C2semidirect
19. C2×#10625335C22semidirect
22. #13094023C22semidirect
32. D4×Dic47C22semidirect
35. C2×C4⋊Dic47C22semidirect
38. #13093955C22semidirect
39. #13093955C22semidirect
40. Dic47⋊C8C22semidirect
41. #13093949C22semidirect
42. #13093949C22semidirect
43. #13093947C22semidirect
49. C22⋊(C47⋊C8)C22semidirect
51. #13093934C22semidirect
53. C2×M16×C47C22semidirect
55. #121×C47C22semidirect
56. #106×C47C22semidirect
58. #102×C47C22semidirect
145. D188#41semidirect
201. #469D47semidirect
210. C47#3306semidirect
217. C2×M16C2×D47semidirect
229. #121C2×D47semidirect
239. #106C2×D47semidirect
250. #102C2×D47semidirect