Finite Group Databasebeta

← #20255353

Subgroups — #20255353

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#15689767C211yesmaximal, characteristic, complemented
3#15689481C211yesmaximal, characteristic, complemented
4#15689454C211yesmaximal, characteristic, complemented
5#15689440C211yesmaximal, characteristic, complemented
6#15689411C211yesmaximal, characteristic, complemented
7#15689373C211yesmaximal, characteristic, complemented
8#15689350C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11#15689235C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625352—21no—
17C2×#10625352C2211yescharacteristic
18C2×#10625335C2211yescharacteristic, complemented
19C2×#10625324C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic
21#13094023C2211yescharacteristic, complemented
22#13094011C2211yescharacteristic
23#13094006—21no—
24#13094005—21no—
25#13094005—21no—
26#13094003C2211yescharacteristic
27#13094001—21no—
28#13093996—21no—
29#13093995C2211yescharacteristic
30#13093995C2211yescharacteristic, complemented
31#13093993—21no—
32D4×Dic47C2211yescharacteristic
33D4×Dic47C2211yescharacteristic, complemented
34C4×C22⋊D47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37C2×C22⋊Dic47—21no—
38#13093956C2211yescharacteristic, complemented
39#13093956C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093945C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×D8×C47C2211yescharacteristic
54C2×D8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic
58C22⋊C8×C47C2211yescharacteristic
59C24×C47—21no—
60C2×D4×C47—22no—
61C2×D4×C47—21no—
62C2×D4×C47—21no—
63C2×D4×C47—41no—
64C2×D4×C47C2311yescharacteristic
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47D411yescharacteristic
72C22×Dic47—21no—
73C22×Dic47—21no—
74C22×Dic47—21no—
75C22×Dic47—21no—
76#10625352—22no—
77#10625352—41no—
78#10625352—44no—
79C2×C4×D47—21no—
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94C2311yescharacteristic
83D8×C47—22no—
84D8×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47—21no—
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47D411yescharacteristic
97#10625335—41no—
98(C2×D47)⋊C4D411yescharacteristic
99C4⋊Dic47—21no—
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106Dic47⋊C4D411yescharacteristic
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8—41no—
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—21no—
115C23×C47—42no—
116C23×C47—42no—
117C23×C47—81no—
118C23×C47C2×D411yescharacteristic
119C22×D47C2×D411yescharacteristic
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—21no—
125D4×C47—42no—
126D4×C47—42no—
127D4×C47#4112yescomplemented
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—21no—
131C2×C4×C47C2×D411yescharacteristic
132C2×C4×C47C2411yescharacteristic
133C22⋊D47—22no—
134C22⋊D47—42no—
135C22⋊D47—42no—
136C22⋊D47—81no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—21no—
141C2×Dic47—42no—
142C2×Dic47—42no—
143C2×Dic47—42no—
144C2×Dic47—81no—
145C2×Dic47C2×D411yescharacteristic
146C2×Dic47C2×D411yescharacteristic
147C2×Dic47C2×D411yescharacteristic
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—42no—
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—22no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
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—21no—
173C2×D47—21no—
174C2×D47—21no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47C2×#4111yescharacteristic
178C4×C47H(5,𝔽2)11yescharacteristic
179Dic47—21no—
180Dic47—21no—
181Dic47—21no—
182Dic47—41no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—22no—
188C2×C47—42no—
189C2×C47—81no—
190C2×C47—81no—
191C2×C47#54611yescharacteristic
192C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C47#57711yescharacteristic
194D47—41no—
195#547—471no—
196#546—471no—
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#447D4711yescharacteristic, complemented
206#442—471no—
207#435—471no—
208#417—471no—
209C2×#102—471no—
210C47#330611yescharacteristic, complemented, Sylow
211C2×#41—471no—
212C2×#41—941no—
213C22×D4C2×D4711yescharacteristic
214C2×SD16—471no—
215C2×D8C2×D4711yescharacteristic
216C2×D8C2×D4711yescharacteristic
217C2×M16—471no—
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—471no—
228#121—941no—
229#121C2×D4711yescharacteristic
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#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#102C2×D4711yescharacteristic
250#102C2×D4711yescharacteristic
251C22⋊C8—471no—
252C22⋊C8C2×D4711yescharacteristic
253#97—471no—
254C24—21no—
255#41—942no—
256#41—1881no—
257#41—1884no—
258C2×Q8—471no—
259C2×Q8—941no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—471no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4C22×D4711yescharacteristic
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—22no—
280D8—41no—
281M16—1881no—
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—471no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4—941no—
294C4⋊C4—941no—
295C4⋊C4C22×D4711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—471no—
298C22⋊C4—471no—
299C22⋊C4—941no—
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—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—471no—
314C23D4×D4711yescharacteristic
315Q8—941no—
316Q8—941no—
317Q8—1882no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—942no—
326D4—3761no—
327D4—1882no—
328D4—1882no—
329D4#1062535212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—471no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—941no—
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—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—941no—
366C22—941no—
367C22—941no—
368C22#1309404812yes—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—41no—
372C4—941no—
373C4—941no—
374C4—941no—
375C4—1881no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4C2×#1062535211yescharacteristic
380C4#1309406911yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—1881no—
386C2#1568976011yescharacteristic
387C2C2×#1309404811yescharacteristic
388C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #15689773C2semidirect
2. #15689767C2semidirect
3. #15689481C2semidirect
4. #15689454C2semidirect
5. #15689440C2semidirect
6. #15689411C2semidirect
7. #15689373C2semidirect
8. #15689350C2semidirect
9. #15689336C2semidirect
10. #15689265C2semidirect
11. #15689235C2semidirect
12. #15689191C2semidirect
13. #15689121C2semidirect
14. C2×#13093945C2semidirect
15. C47×#447C2semidirect
18. C2×#10625335C22semidirect
19. C2×#10625324C22semidirect
21. #13094023C22semidirect
30. #13093995C22semidirect
33. D4×Dic47C22semidirect
36. C4⋊C4×D47C22semidirect
38. #13093956C22semidirect
39. #13093956C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
49. #13093945C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
127. D4×C47#41semidirect
205. #447D47semidirect
210. C47#3306semidirect
329. D4#10625352semidirect