Finite Group Databasebeta

← #20255354

Subgroups — #20255354

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#15689778C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic, complemented
3#15689483C211yesmaximal, characteristic, complemented
4#15689455C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689413C211yesmaximal, characteristic, complemented
7#15689375C211yesmaximal, characteristic, complemented
8#15689351C211yesmaximal, characteristic, complemented
9#15689338C211yesmaximal, characteristic, complemented
10#15689265C211yesmaximal, characteristic, complemented
11#15689255C211yesmaximal, characteristic, complemented
12#15689196C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×#10625350—21no—
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×#10625335C2211yescharacteristic, complemented
20C2×#10625334C2211yescharacteristic
21C2×#10625324C2211yescharacteristic, complemented
22C2×C8×D47C2211yescharacteristic
23#13094024C2211yescharacteristic, complemented
24#13094012C2211yescharacteristic
25#13094008—21no—
26#13094006—21no—
27#13094006—21no—
28#13094004C2211yescharacteristic
29#13094003—21no—
30#13093999C2211yescharacteristic
31#13093998—21no—
32#13093995C2211yescharacteristic
33#13093995C2211yescharacteristic, complemented
34#13093994—21no—
35C4×D188C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic
37C4⋊C4×D47C2211yescharacteristic, complemented
38C2×(C2×D47)⋊C4—21no—
39#13093955C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41C4⋊(C47⋊C8)C2211yescharacteristic, complemented
42#13093949C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093945C2211yescharacteristic
48#13093945C2211yescharacteristic
49#13093944C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51(C2×D47)⋊C8C2211yescharacteristic, complemented
52C2×D8×C47C2211yescharacteristic
53C4×D4×C47C2211yescharacteristic
54C4×D4×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58#97×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×D4×C47C2311yescharacteristic
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C22×C4×C47—21no—
64C2×C22⋊D47—21no—
65C2×C22⋊D47—21no—
66C2×C22⋊D47—21no—
67C2×C22⋊D47—21no—
68C22×Dic47—21no—
69#10625352—22no—
70#10625352—41no—
71D4×D47—22no—
72D4×D47—41no—
73#10625350—44no—
74C2×D188—21no—
75C2×D188D411yescharacteristic
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47C2311yescharacteristic
80C2×C4×D47C2311yescharacteristic
81C2×Dic94—21no—
82C2×Dic94C2311yescharacteristic
83D8×C47—22no—
84C2×C8×C47C2311yescharacteristic
85C2×C8×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C22⋊C4×C47—21no—
89C22⋊C4×C47—21no—
90C42×C47C2311yescharacteristic
91C22⋊Dic47—21no—
92C22⋊Dic47—21no—
93#10625335—41no—
94#10625334—41no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4D411yescharacteristic
100(C2×D47)⋊C4D411yescharacteristic
101C4⋊Dic47—21no—
102C4⋊Dic47—21no—
103C4⋊Dic47D411yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105C4⋊Dic47C2311yescharacteristic
106Dic47⋊C4—21no—
107Dic47⋊C4—21no—
108C2×C47⋊C8C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110#10625324—41no—
111C8×D47—41no—
112C23×C47—21no—
113C23×C47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118C22×D47C2×D411yescharacteristic
119C22×D47C2×D411yescharacteristic
120D4×C47—21no—
121D4×C47—21no—
122D4×C47—21no—
123D4×C47#4112yescomplemented
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—42no—
127C2×C4×C47—81no—
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—42no—
132C22⋊D47—42no—
133C22⋊D47—42no—
134C22⋊D47—42no—
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—42no—
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141D188—22no—
142D188—21no—
143D188—21no—
144D188—81no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—42no—
150C4×D47—42no—
151Dic94—21no—
152Dic94—21no—
153Dic94—42no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—22no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—41no—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—21no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—84no—
174C2×D47AGL(1,ℤ/8)12yes—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C2×#4111yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—21no—
182Dic47—21no—
183Dic47—41no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—42no—
188C2×C47—81no—
189C2×C47#54611yescharacteristic
190C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C47#57711yescharacteristic
192D47—22no—
193D47—41no—
194D47—81no—
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#447—471no—
206#442D4711yescharacteristic, complemented
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×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—471no—
229#121—941no—
230#120—941no—
231C4×D4—471no—
232C4×D4C2×D4711yescharacteristic
233C4×D4C2×D4711yescharacteristic, complemented
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#97C2×D4711yescharacteristic, complemented
254C24—941no—
255#41—942no—
256#41—1884no—
257#41—1881no—
258C2×Q8—471no—
259C2×Q8—941no—
260C2×D4—471no—
261C2×D4—471no—
262C2×D4—941no—
263C2×D4—941no—
264C2×D4—942no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—1881no—
269C2×D4C22×D4711yescharacteristic
270C2×D4C22×D4711yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—471no—
274C22×C4—471no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4—941no—
278SD16—1881no—
279D8—22no—
280D8—1881no—
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—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—
306C42C22×D4711yescharacteristic
307C23—21no—
308C23—21no—
309C23—471no—
310C23—471no—
311C23—941no—
312C23—3761no—
313C23—1882no—
314C23—1882no—
315Q8—941no—
316Q8—941no—
317Q8—1882no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—942no—
322D4—941no—
323D4—941no—
324D4—3761no—
325D4—1882no—
326D4—1882no—
327D4—1882no—
328D4—1882no—
329D4#1062535012yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—81no—
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—941no—
343C2×C4—1882no—
344C2×C4—1882no—
345C2×C4—1882no—
346C2×C4D4×D4711yescharacteristic
347C2×C4D4×D4711yescharacteristic
348C2×C4C23×D4711yescharacteristic
349C8—21no—
350C8—21no—
351C8—941no—
352C8—941no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—472no—
360C22—941no—
361C22—941no—
362C22—941no—
363C22—941no—
364C22—941no—
365C22—3764no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—941no—
375C4—941no—
376C4—1881no—
377C4—1881no—
378C4—1881no—
379C4C2×#1062535011yescharacteristic
380C4#1309407011yescharacteristic
381C2—42no—
382C2—81no—
383C2—942no—
384C2—3761no—
385C2—1881no—
386C2#1568976911yescharacteristic
387C2AGL(1,ℤ/8)×D4711yescharacteristic
388C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689778C2semidirect
2. #15689768C2semidirect
3. #15689483C2semidirect
4. #15689455C2semidirect
5. #15689443C2semidirect
6. #15689413C2semidirect
7. #15689375C2semidirect
8. #15689351C2semidirect
9. #15689338C2semidirect
10. #15689265C2semidirect
11. #15689255C2semidirect
12. #15689196C2semidirect
13. #15689121C2semidirect
14. #102×D47C2semidirect
15. C47×#442C2semidirect
19. C2×#10625335C22semidirect
21. C2×#10625324C22semidirect
23. #13094024C22semidirect
33. #13093995C22semidirect
37. C4⋊C4×D47C22semidirect
39. #13093955C22semidirect
40. #13093955C22semidirect
41. C4⋊(C47⋊C8)C22semidirect
42. #13093949C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
51. (C2×D47)⋊C8C22semidirect
54. C4×D4×C47C22semidirect
55. #106×C47C22semidirect
57. #102×C47C22semidirect
58. #97×C47C22semidirect
123. D4×C47#41semidirect
206. #442D47semidirect
210. C47#3306semidirect
233. C4×D4C2×D47semidirect
239. #106C2×D47semidirect
250. #102C2×D47semidirect
253. #97C2×D47semidirect
329. D4#10625350semidirect