Finite Group Databasebeta

← #20255413

Subgroups — #20255413

Order 6016.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689815C211yesmaximal, characteristic, complemented
2D4×C22⋊D47C211yesmaximal, characteristic
3#15689486C211yesmaximal, characteristic, complemented
4#15689445C211yesmaximal, characteristic, complemented
5#15689437C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689366C211yesmaximal, characteristic, complemented
8#15689354C211yesmaximal, characteristic, complemented
9#15689321C211yesmaximal, characteristic, complemented
10#15689272C211yesmaximal, characteristic, complemented
11#15689224C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic, complemented
13#15689126C211yesmaximal, characteristic, complemented
14C2×#13093945C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16C22×C22⋊D47—21no—
17C2×D4×D47C2211yescharacteristic
18C2×#10625336C2211yescharacteristic, complemented
19C2×#10625324C2211yescharacteristic, complemented
20C22×C47⋊C8C2211yescharacteristic, complemented
21#13094020C2211yescharacteristic
22#13094019—21no—
23#13094015—21no—
24#13094015C2211yescharacteristic, complemented
25#13094008—21no—
26#13094000C2211yescharacteristic, complemented
27#13093998C2211yescharacteristic
28#13093996—21no—
29#13093995C2211yescharacteristic
30#13093993—21no—
31#13093992—21no—
32Q8×Dic47C2211yescharacteristic, complemented
33D4×Dic47C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35#13093982C2211yescharacteristic, complemented
36#13093980—21no—
37C2×C4⋊Dic47C2211yescharacteristic, complemented
38#13093958C2211yescharacteristic, complemented
39#13093958C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic, complemented
44#13093946C2211yescharacteristic, complemented
45#13093945C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic, complemented
48#13093945C2211yescharacteristic, complemented
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C22×D4×C47C2211yescharacteristic
53C2×SD16×C47C2211yescharacteristic
54C2×SD16×C47C2211yescharacteristic, complemented
55C22⋊Q8×C47C2211yescharacteristic, complemented
56#102×C47C2211yescharacteristic
57#102×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic, complemented
59C24×C47—21no—
60C23×D47—21no—
61C2×Q8×C47C2311yescharacteristic
62C2×D4×C47—22no—
63C2×D4×C47—21no—
64C2×D4×C47—41no—
65C2×D4×C47C2311yescharacteristic
66C2×D4×C47C2311yescharacteristic
67C22×C4×C47C2311yescharacteristic
68C2×C22⋊D47—21no—
69C2×C22⋊D47—21no—
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47—44no—
74C2×C22⋊D47D411yescharacteristic
75C22×Dic47—21no—
76C22×Dic47—21no—
77D4×D47—22no—
78D4×D47—41no—
79C2×D188C2311yescharacteristic
80C2×C4×D47C2311yescharacteristic
81SD16×C47—22no—
82SD16×C47—41no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2311yescharacteristic
87C22⋊C4×C47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90C22⋊Dic47D411yescharacteristic
91#10625336—41no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4D411yescharacteristic
96C4⋊Dic47—21no—
97C4⋊Dic47—21no—
98C4⋊Dic47—21no—
99C4⋊Dic47C2311yescharacteristic
100C4⋊Dic47C2311yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47—21no—
106C4×Dic47—21no—
107C4×Dic47C2311yescharacteristic
108C2×C47⋊C8—41no—
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112C23×C47—21no—
113C23×C47—21no—
114C23×C47—42no—
115C23×C47—42no—
116C23×C47—81no—
117C23×C47C2×D411yescharacteristic
118C22×D47—21no—
119C22×D47—42no—
120C22×D47—42no—
121C22×D47—81no—
122C22×D47C2×D411yescharacteristic
123Q8×C47—21no—
124Q8×C47—21no—
125D4×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—42no—
129D4×C47#4112yes—
130C2×C4×C47—21no—
131C2×C4×C47—21no—
132C2×C4×C47—21no—
133C2×C4×C47—21no—
134C2×C4×C47C2×D411yescharacteristic
135C2×C4×C47C2411yescharacteristic
136C22⋊D47—22no—
137C22⋊D47—42no—
138C22⋊D47—42no—
139C22⋊D47—42no—
140C22⋊D47—42no—
141C22⋊D47—81no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C2×Dic47—42no—
146C2×Dic47—42no—
147C2×Dic47C2×D411yescharacteristic
148C2×Dic47C2×D411yescharacteristic
149C2×Dic47C2×D411yescharacteristic
150D188—21no—
151D188—21no—
152C4×D47—21no—
153C4×D47—21no—
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—84no—
167C22×C47AGL(1,ℤ/8)12yes—
168C22×C47C22×D411yescharacteristic
169C2×D47—21no—
170C2×D47—21no—
171C2×D47—21no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—41no—
175C2×D47—84no—
176C4×C47—21no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C2×#4111yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—21no—
182Dic47—21no—
183Dic47—21no—
184Dic47—41no—
185Dic47—41no—
186Dic47—41no—
187#3310—471nomaximal, Sylow
188C2×C47—22no—
189C2×C47—42no—
190C2×C47—81no—
191C2×C47#54611yescharacteristic
192C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
193C2×C47#57711yescharacteristic
194D47—41no—
195D47—81no—
196#552—471no—
197D42—471no—
198#490—471no—
199#482—471no—
200#480—471no—
201#478—471no—
202#468—471no—
203#465—471no—
204#460—471no—
205#450—471no—
206#450D4711yescharacteristic, complemented
207#440—471no—
208#435—471no—
209#418—471no—
210C2×#102—471no—
211C47#331011yescharacteristic, complemented, Sylow
212C22×D4—471no—
213C22×D4—941no—
214C22×D4C2×D4711yescharacteristic
215C2×SD16—471no—
216C2×SD16C2×D4711yescharacteristic
217C2×SD16C2×D4711yescharacteristic, complemented
218C2×M16—471no—
219C22×C8—471no—
220#127—471no—
221#126—941no—
222#125—471no—
223#125—941no—
224#123—941no—
225C22⋊Q8—471no—
226C22⋊Q8C2×D4711yescharacteristic, complemented
227#121—471no—
228#121—471no—
229#121—941no—
230#120—941no—
231#120—941no—
232C4×Q8—471no—
233C4×D4—471no—
234C4×D4—471no—
235#117—471no—
236#117—941no—
237C2×C4⋊C4—471no—
238#107—471no—
239#107—471no—
240#106—471no—
241C4⋊C8—471no—
242#103—471no—
243#102—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102C2×D4711yescharacteristic
251#102C2×D4711yescharacteristic, complemented
252C22⋊C8—471no—
253C22⋊C8C2×D4711yescharacteristic, complemented
254#97—471no—
255C24—21no—
256C24—941no—
257C2×Q8C22×D4711yescharacteristic
258C2×D4—22no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—942no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1881no—
270C2×D4—1884no—
271C2×D4C22×D4711yescharacteristic
272C2×D4C22×D4711yescharacteristic
273C22×C4—471no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4C22×D4711yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—1881no—
280M16—1881no—
281C2×C8—471no—
282C2×C8—471no—
283C2×C8—1881no—
284C2×C8C22×D4711yescharacteristic
285C2×C8C22×D4711yescharacteristic
286C4⋊C4—21no—
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⋊C4—941no—
296C4⋊C4C22×D4711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—471no—
299C22⋊C4—471no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C42—471no—
306C42—941no—
307C42—941no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—471no—
314C23—941no—
315C23—3761no—
316C23—1882no—
317C23—1882no—
318C23D4×D4711yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—942no—
326D4—941no—
327D4—941no—
328D4—3761no—
329D4—1882no—
330D4—1882no—
331D4—1882no—
332D4—1882no—
333D4#1062535212yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—471no—
339C2×C4—471no—
340C2×C4—471no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—941no—
344C2×C4—941no—
345C2×C4—941no—
346C2×C4—1882no—
347C2×C4—1882no—
348C2×C4D4×D4711yescharacteristic
349C2×C4C23×D4711yescharacteristic
350C8—21no—
351C8—21no—
352C8—941no—
353C8—941no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—84no—
363C22—941no—
364C22—941no—
365C22—941no—
366C22—3764no—
367C22—1881no—
368C22—1881no—
369C22—1881no—
370C22#1309405112yes—
371C22C2×D4×D4711yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—941no—
376C4—941no—
377C4—941no—
378C4—1881no—
379C4—1881no—
380C4—1881no—
381C4C2×#1062535211yescharacteristic
382C4#1309406911yescharacteristic
383C2—22no—
384C2—42no—
385C2—81no—
386C2—3761no—
387C2—1881no—
388C2#1568976011yescharacteristic
389C2C2×#1309405111yescharacteristic
390C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3310
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #15689815C2semidirect
3. #15689486C2semidirect
4. #15689445C2semidirect
5. #15689437C2semidirect
6. #15689421C2semidirect
7. #15689366C2semidirect
8. #15689354C2semidirect
9. #15689321C2semidirect
10. #15689272C2semidirect
11. #15689224C2semidirect
12. #15689191C2semidirect
13. #15689126C2semidirect
14. C2×#13093945C2semidirect
15. C47×#450C2semidirect
18. C2×#10625336C22semidirect
19. C2×#10625324C22semidirect
20. C22×C47⋊C8C22semidirect
24. #13094015C22semidirect
26. #13094000C22semidirect
32. Q8×Dic47C22semidirect
35. #13093982C22semidirect
37. C2×C4⋊Dic47C22semidirect
38. #13093958C22semidirect
39. #13093958C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093948C22semidirect
43. #13093946C22semidirect
44. #13093946C22semidirect
47. #13093945C22semidirect
48. #13093945C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
54. C2×SD16×C47C22semidirect
55. C22⋊Q8×C47C22semidirect
57. #102×C47C22semidirect
58. C22⋊C8×C47C22semidirect
206. #450D47semidirect
211. C47#3310semidirect
217. C2×SD16C2×D47semidirect
226. C22⋊Q8C2×D47semidirect
251. #102C2×D47semidirect
253. C22⋊C8C2×D47semidirect