Finite Group Databasebeta

← #20255235

Subgroups — #20255235

Order 6016.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689826C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic, complemented
3#15689480C211yesmaximal, characteristic, complemented
4#15689460C211yesmaximal, characteristic, complemented
5#15689449C211yesmaximal, characteristic, complemented
6#15689360C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689269C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11C4×#10625334C211yesmaximal, characteristic, complemented
12#15689188C211yesmaximal, characteristic, complemented
13#15689116C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#478C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×D4×D47C2211yescharacteristic
18C2×#10625325C2211yescharacteristic, complemented
19C2×D376C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×C8×D47C2211yescharacteristic
22C2×C8×D47C2211yescharacteristic, complemented
23#13094019—21no—
24#13094012C2211yescharacteristic
25#13094009—21no—
26#13094008—21no—
27#13094004C2211yescharacteristic
28#13093999—21no—
29#13093999C2211yescharacteristic
30#13093999C2211yescharacteristic
31#13093999C2211yescharacteristic, complemented
32#13093998—21no—
33#13093994—21no—
34C4×D188C2211yescharacteristic
35C4×D188C2211yescharacteristic, complemented
36#13093986—21no—
37#13093982C2211yescharacteristic, complemented
38C4⋊C4×D47C2211yescharacteristic
39C2×(C2×D47)⋊C4—21no—
40#13093957C2211yescharacteristic, complemented
41#13093949C2211yescharacteristic, complemented
42#13093947C2211yescharacteristic, complemented
43#13093947C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic
45#13093945C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic, complemented
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51C4×C47⋊C8C2211yescharacteristic, complemented
52#125×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#107×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×D4×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C2×C22⋊D47—21no—
63C2×C22⋊D47—21no—
64C22×Dic47—21no—
65#10625352—22no—
66#10625352—41no—
67D4×D47—22no—
68D4×D47—41no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188D411yescharacteristic
73C2×D188C2311yescharacteristic
74C2×D188C2311yescharacteristic
75C2×C4×D47—21no—
76C2×C4×D47—21no—
77C2×C4×D47C2311yescharacteristic
78C2×C4×D47C2311yescharacteristic
79C2×Dic94C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C2×C8×C47C2311yescharacteristic
82C4⋊C4×C47—21no—
83C4⋊C4×C47—21no—
84C4⋊C4×C47C2311yescharacteristic
85C4⋊C4×C47C2311yescharacteristic
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C42×C47C2311yescharacteristic
89#10625334—22no—
90(C2×D47)⋊C4—21no—
91(C2×D47)⋊C4—21no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96(C2×D47)⋊C4—21no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4D411yescharacteristic
99(C2×D47)⋊C4D411yescharacteristic
100C4⋊Dic47—21no—
101C4⋊Dic47D411yescharacteristic
102C4⋊Dic47C2311yescharacteristic
103Dic47⋊C4—21no—
104C4×Dic47—21no—
105C2×C47⋊C8C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107D376—41no—
108#10625325—41no—
109C8×D47—41no—
110C8×D47—41no—
111C23×C47—21no—
112C22×D47—21no—
113C22×D47—21no—
114C22×D47—42no—
115C22×D47—42no—
116C22×D47—81no—
117C22×D47C2×D411yescharacteristic
118C22×D47C2×D411yescharacteristic
119D4×C47—21no—
120D4×C47#4112yes—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—81no—
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2×D411yescharacteristic
127C2×C4×C47C2411yescharacteristic
128C22⋊D47—42no—
129C22⋊D47—42no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—42no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135D188—22no—
136D188—21no—
137D188—21no—
138D188—21no—
139D188—21no—
140D188—42no—
141D188—81no—
142D188—81no—
143C4×D47—21no—
144C4×D47—21no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—81no—
148C4×D47—81no—
149Dic94—21no—
150Dic94—21no—
151C8×C47—21no—
152C8×C47—21no—
153C47⋊C8—21no—
154C47⋊C8—21no—
155C22×C47—22no—
156C22×C47—41no—
157C22×C47—41no—
158C22×C47C22×D411yescharacteristic
159C2×D47—21no—
160C2×D47—21no—
161C2×D47—21no—
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—41no—
165C2×D47—41no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—84no—
171C2×D47#13512yes—
172C4×C47—21no—
173C4×C47—21no—
174C4×C47—41no—
175C4×C47—41no—
176C4×C47—41no—
177C4×C47C2×#4111yescharacteristic
178C4×C47H(5,𝔽2)11yescharacteristic
179Dic47—21no—
180Dic47—21no—
181Dic47—41no—
182Dic47—41no—
183#3297—471nomaximal, Sylow
184C2×C47—42no—
185C2×C47#54611yescharacteristic
186C2×C47C2×#13511yescharacteristic
187C2×C47#57611yescharacteristic
188D47—22no—
189D47—41no—
190D47—81no—
191D47—81no—
192#553—471no—
193#546—471no—
194#488—471no—
195#484—471no—
196#482—471no—
197#478D4711yescharacteristic, complemented
198#466—471no—
199#465—471no—
200#463—471no—
201#449—471no—
202#447—471no—
203C4×D8—471no—
204C8×D4—471no—
205#416—471no—
206C2×#102—471no—
207C47#329711yescharacteristic, complemented, Sylow
208C2×#41—471no—
209C22×D4—471no—
210C2×SD16—471no—
211C2×D8—471no—
212C2×D8—471no—
213C22×C8—471no—
214C22×C8—471no—
215#126—941no—
216#125C2×D4711yescharacteristic, complemented
217#124—471no—
218#123—941no—
219#123—941no—
220C22⋊Q8—471no—
221#121—471no—
222#121—471no—
223#121—471no—
224#121—941no—
225#121—941no—
226#120—941no—
227C4×D4—471no—
228C4×D4—471no—
229C4×D4—941no—
230C4×D4C2×D4711yescharacteristic
231#117—471no—
232C2×C4⋊C4—471no—
233C2×C22⋊C4—941no—
234#107—471no—
235#107C2×D4711yescharacteristic, complemented
236#106C2×D4711yescharacteristic, complemented
237C4⋊C8C2×D4711yescharacteristic, complemented
238#103—471no—
239#103—471no—
240#103—471no—
241#102—471no—
242#102—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102C2×D4711yescharacteristic
247#102C2×D4711yescharacteristic
248C22⋊C8—471no—
249C22⋊C8—471no—
250C4×C8—471no—
251C24—941no—
252#41—942no—
253#41—1881no—
254C2×Q8—471no—
255C2×D4—471no—
256C2×D4—471no—
257C2×D4—471no—
258C2×D4—941no—
259C2×D4—941no—
260C2×D4—941no—
261C2×D4—941no—
262C2×D4—942no—
263C2×D4—941no—
264C2×D4—1881no—
265C2×D4C22×D4711yescharacteristic
266C22×C4—21no—
267C22×C4—471no—
268C22×C4—471no—
269C22×C4—941no—
270C22×C4—941no—
271C22×C4—941no—
272SD16—1881no—
273D8—942no—
274D8—1881no—
275C2×C8—471no—
276C2×C8—471no—
277C2×C8—1881no—
278C2×C8—1881no—
279C2×C8C22×D4711yescharacteristic
280C2×C8C22×D4711yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—471no—
284C4⋊C4—471no—
285C4⋊C4—941no—
286C4⋊C4—941no—
287C4⋊C4C22×D4711yescharacteristic
288C4⋊C4C22×D4711yescharacteristic
289C4⋊C4C22×D4711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—471no—
292C22⋊C4—471no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C22⋊C4—941no—
296C22⋊C4—941no—
297C22⋊C4—941no—
298C22⋊C4—941no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C42—941no—
302C42C22×D4711yescharacteristic
303C23—21no—
304C23—471no—
305C23—471no—
306C23—941no—
307C23—941no—
308C23—3761no—
309C23—1882no—
310C23—1882no—
311Q8—941no—
312Q8—941no—
313D4—21no—
314D4—942no—
315D4—941no—
316D4—941no—
317D4—941no—
318D4—941no—
319D4—3761no—
320D4—3761no—
321D4—1882no—
322D4—1882no—
323D4—1882no—
324D4#1062535412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—471no—
330C2×C4—471no—
331C2×C4—941no—
332C2×C4—941no—
333C2×C4—941no—
334C2×C4—941no—
335C2×C4—941no—
336C2×C4—941no—
337C2×C4—3761no—
338C2×C4—3761no—
339C2×C4—1882no—
340C2×C4D4×D4711yescharacteristic
341C2×C4D4×D4711yescharacteristic
342C2×C4C23×D4711yescharacteristic
343C8—21no—
344C8—21no—
345C8—941no—
346C8—941no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—472no—
351C22—941no—
352C22—941no—
353C22—941no—
354C22—941no—
355C22—941no—
356C22—3764no—
357C22—1881no—
358C22—1881no—
359C22—1881no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22C2×D4×D4711yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—941no—
370C4—941no—
371C4—1881no—
372C4—1881no—
373C4C2×#1062535411yescharacteristic
374C4#1309407011yescharacteristic
375C2—42no—
376C2—942no—
377C2—3761no—
378C2—3761no—
379C2—1881no—
380C2#1568976411yescharacteristic
381C2#135×D4711yescharacteristic
382C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#478C2
socleC22×C47C22×D4
hypercenter#478D47
hypocenterC47#3297
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #15689826C2semidirect
2. #15689768C2semidirect
3. #15689480C2semidirect
4. #15689460C2semidirect
5. #15689449C2semidirect
6. #15689360C2semidirect
7. #15689353C2semidirect
8. #15689339C2semidirect
9. #15689269C2semidirect
10. #15689258C2semidirect
11. C4×#10625334C2semidirect
12. #15689188C2semidirect
13. #15689116C2semidirect
14. #102×D47C2semidirect
15. C47×#478C2semidirect
18. C2×#10625325C22semidirect
22. C2×C8×D47C22semidirect
31. #13093999C22semidirect
35. C4×D188C22semidirect
37. #13093982C22semidirect
40. #13093957C22semidirect
41. #13093949C22semidirect
42. #13093947C22semidirect
43. #13093947C22semidirect
48. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. C4×C47⋊C8C22semidirect
52. #125×C47C22semidirect
54. #107×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
197. #478D47semidirect
207. C47#3297semidirect
216. #125C2×D47semidirect
235. #107C2×D47semidirect
236. #106C2×D47semidirect
237. C4⋊C8C2×D47semidirect