Finite Group Databasebeta

← #20253524

Subgroups — #20253524

Order 6016.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689655C211yesmaximal, characteristic, complemented
2C4×D4×D47C211yesmaximal, characteristic, complemented
3#15689455C211yesmaximal, characteristic, complemented
4#15689435C211yesmaximal, characteristic, complemented
5#15689422C211yesmaximal, characteristic, complemented
6#15689421C211yesmaximal, characteristic, complemented
7#15689337C211yesmaximal, characteristic, complemented
8#15689336C211yesmaximal, characteristic, complemented
9#15689275C211yesmaximal, characteristic, complemented
10#15689255C211yesmaximal, characteristic
11#15689233C211yesmaximal, characteristic, complemented
12#15689225C211yesmaximal, characteristic, complemented
13#15689223C211yesmaximal, characteristic, complemented
14#15689178C211yesmaximal, characteristic, complemented
15C47×#442C211yesmaximal, characteristic, complemented
16C2×D4×D47C2211yescharacteristic
17C22×C4×D47—21no—
18C2×#10625325C2211yescharacteristic
19C2×#10625335C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21#13094017—21no—
22#13094015C2211yescharacteristic, complemented
23#13094011C2211yescharacteristic, complemented
24#13094006—21no—
25#13094004C2211yescharacteristic
26#13093995C2211yescharacteristic
27C4×Dic94C2211yescharacteristic, complemented
28C4×D188C2211yescharacteristic
29D4×Dic47C2211yescharacteristic
30#13093986C2211yescharacteristic
31C4×C22⋊D47—21no—
32C4×C22⋊D47—21no—
33(C22⋊D47)⋊C4—21no—
34#13093983—21no—
35C4⋊C4×D47C2211yescharacteristic
36C22⋊C4×D47—21no—
37C42×D47C2211yescharacteristic
38#13093958C2211yescharacteristic, complemented
39#13093957C2211yescharacteristic, complemented
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42Dic47⋊C8C2211yescharacteristic, complemented
43#13093949C2211yescharacteristic, complemented
44#13093947C2211yescharacteristic, complemented
45#13093946C2211yescharacteristic
46#13093945C2211yescharacteristic
47#13093945C2211yescharacteristic, complemented
48#13093944C2211yescharacteristic
49(C2×D47)⋊C8C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic
51#13093935C2211yescharacteristic, 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—
66C22×Dic47—21no—
67D4×D47—22no—
68D4×D47—22no—
69C2×D188C2311yescharacteristic
70C2×C4×D47—21no—
71C2×C4×D47—21no—
72C2×C4×D47—21no—
73C2×C4×D47—44no—
74C2×C4×D47D411yescharacteristic
75C2×C4×D47D411yescharacteristic
76C2×C4×D47C2311yescharacteristic
77C2×Dic94C2311yescharacteristic
78D8×C47—22no—
79C2×C8×C47C2311yescharacteristic
80C2×C8×C47C2311yescharacteristic
81C4⋊C4×C47C2311yescharacteristic
82C4⋊C4×C47C2311yescharacteristic
83C22⋊C4×C47—21no—
84C22⋊C4×C47—21no—
85C42×C47C2311yescharacteristic
86C22⋊Dic47—21no—
87C22⋊Dic47—21no—
88C22⋊Dic47—21no—
89C22⋊Dic47—21no—
90#10625335—22no—
91#10625334—22no—
92(C2×D47)⋊C4—21no—
93(C2×D47)⋊C4—21no—
94(C2×D47)⋊C4—21no—
95C4⋊Dic47—21no—
96C4⋊Dic47—21no—
97C4⋊Dic47C2311yescharacteristic
98C4⋊Dic47C2311yescharacteristic
99Dic47⋊C4—21no—
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47D411yescharacteristic
104C4×Dic47D411yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108#10625325—22no—
109C23×C47—21no—
110C23×C47—21no—
111C22×D47—24no—
112C22×D47—21no—
113C22×D47—42no—
114C22×D47—42no—
115C22×D47C2×D411yescharacteristic
116D4×C47—21no—
117D4×C47—21no—
118D4×C47—21no—
119D4×C47#4112yes—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—42no—
123C2×C4×C47—42no—
124C2×C4×C47C2×D411yescharacteristic
125C2×C4×C47C2×D411yescharacteristic
126C2×C4×C47C2411yescharacteristic
127C22⋊D47—24no—
128C22⋊D47—42no—
129C2×Dic47—21no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—42no—
133C2×Dic47C2×D411yescharacteristic
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136D188—21no—
137D188#4112yes—
138C4×D47—22no—
139C4×D47—21no—
140C4×D47—21no—
141C4×D47—41no—
142C4×D47—42no—
143C4×D47—42no—
144C4×D47—42no—
145Dic94—21no—
146Dic94—21no—
147C8×C47—21no—
148C8×C47—21no—
149C47⋊C8—21no—
150C47⋊C8—21no—
151C22×C47—22no—
152C22×C47—41no—
153C22×C47—41no—
154C22×C47—41no—
155C22×C47—41no—
156C22×C47—41no—
157C22×C47C22×D411yescharacteristic
158C2×D47—21no—
159C2×D47—21no—
160C2×D47—22no—
161C2×D47—48no—
162C2×D47—41no—
163C2×D47—41no—
164C2×D47AGL(1,ℤ/8)12yes—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—41no—
168C4×C47—41no—
169C4×C47C2×#4111yescharacteristic
170C4×C47C2×#4111yescharacteristic
171Dic47—21no—
172Dic47—21no—
173Dic47—21no—
174Dic47—41no—
175Dic47—41no—
176Dic47—41no—
177#3114—471nomaximal, Sylow
178C2×C47—42no—
179C2×C47—81no—
180C2×C47#52511yescharacteristic
181C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
182C2×C47#57511yescharacteristic
183D47—22no—
184D47—42no—
185#529—471no—
186C2×C4×D4—471no—
187#483—471no—
188#480—471no—
189#478—471no—
190#478—471no—
191#463—471no—
192#463—471no—
193#450—471no—
194#447—471no—
195#442—471no—
196#442D4711yescharacteristic, complemented
197#440—471no—
198#440—471no—
199#432—471no—
200C47#311411yescharacteristic, complemented, Sylow
201C22×D4—471no—
202C23×C4—941no—
203C2×SD16—471no—
204C2×SD16—471no—
205C2×D8—471no—
206C2×D8C2×D4711yescharacteristic
207#126—941no—
208#125—471no—
209#124—471no—
210#123—941no—
211C22⋊Q8—471no—
212#121—471no—
213C4×Q8—471no—
214C4×D4—471no—
215C4×D4—471no—
216C4×D4—471no—
217C4×D4—941no—
218C4×D4—941no—
219C4×D4—941no—
220C4×D4C2×D4711yescharacteristic
221C4×D4C2×D4711yescharacteristic, complemented
222#117—941no—
223C2×C4⋊C4—471no—
224C2×C22⋊C4—941no—
225C2×C42—471no—
226#107—471no—
227#107—471no—
228#106—471no—
229#106C2×D4711yescharacteristic, complemented
230C4⋊C8—471no—
231C4⋊C8—471no—
232#103—471no—
233#103—471no—
234#102—471no—
235#102—471no—
236#102—471no—
237#102—471no—
238#102C2×D4711yescharacteristic
239#102C2×D4711yescharacteristic, complemented
240C22⋊C8—471no—
241C22⋊C8—471no—
242#97—471no—
243#97C2×D4711yescharacteristic, complemented
244C24—941no—
245C2×Q8—471no—
246C2×D4—471no—
247C2×D4—941no—
248C2×D4—942no—
249C2×D4—942no—
250C2×D4—941no—
251C2×D4C22×D4711yescharacteristic
252C2×D4C22×D4711yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—471no—
258C22×C4—941no—
259C22×C4—941no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—1884no—
263SD16—942no—
264SD16—942no—
265D8—22no—
266D8—942no—
267C2×C8—471no—
268C2×C8—471no—
269C2×C8C22×D4711yescharacteristic
270C2×C8C22×D4711yescharacteristic
271C4⋊C4—471no—
272C4⋊C4—471no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—941no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4C22×D4711yescharacteristic
279C4⋊C4C22×D4711yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C22⋊C4—941no—
286C22⋊C4—941no—
287C22⋊C4—941no—
288C22⋊C4—941no—
289C42—471no—
290C42—471no—
291C42—471no—
292C42—941no—
293C42C22×D4711yescharacteristic
294C23—21no—
295C23—21no—
296C23—471no—
297C23—944no—
298C23—941no—
299C23—1882no—
300C23—1882no—
301Q8—941no—
302Q8—941no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—472no—
307D4—944no—
308D4—941no—
309D4—1882no—
310D4#1062535012yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—471no—
316C2×C4—471no—
317C2×C4—471no—
318C2×C4—942no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—941no—
323C2×C4—941no—
324C2×C4—1881no—
325C2×C4—1882no—
326C2×C4—1882no—
327C2×C4—1882no—
328C2×C4—1882no—
329C2×C4D4×D4711yescharacteristic
330C2×C4D4×D4711yescharacteristic
331C2×C4C23×D4711yescharacteristic
332C8—21no—
333C8—21no—
334C8—941no—
335C8—941no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—472no—
343C22—941no—
344C22—941no—
345C22—942no—
346C22—1888no—
347C22—1881no—
348C22—1881no—
349C22C2×D4×D4711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—941no—
355C4—941no—
356C4—941no—
357C4—1881no—
358C4—1881no—
359C4—1881no—
360C4#41×D4711yescharacteristic
361C4C2×#1062535011yescharacteristic
362C2—42no—
363C2—81no—
364C2—942no—
365C2—1882no—
366C2#1568963211yescharacteristic
367C2AGL(1,ℤ/8)×D4711yescharacteristic
368C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3114
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. #15689655C2semidirect
2. C4×D4×D47C2semidirect
3. #15689455C2semidirect
4. #15689435C2semidirect
5. #15689422C2semidirect
6. #15689421C2semidirect
7. #15689337C2semidirect
8. #15689336C2semidirect
9. #15689275C2semidirect
11. #15689233C2semidirect
12. #15689225C2semidirect
13. #15689223C2semidirect
14. #15689178C2semidirect
15. C47×#442C2semidirect
22. #13094015C22semidirect
23. #13094011C22semidirect
27. C4×Dic94C22semidirect
38. #13093958C22semidirect
39. #13093957C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. Dic47⋊C8C22semidirect
43. #13093949C22semidirect
44. #13093947C22semidirect
47. #13093945C22semidirect
51. #13093935C22semidirect
54. C4×D4×C47C22semidirect
55. #106×C47C22semidirect
57. #102×C47C22semidirect
58. #97×C47C22semidirect
196. #442D47semidirect
200. C47#3114semidirect
221. C4×D4C2×D47semidirect
229. #106C2×D47semidirect
239. #102C2×D47semidirect
243. #97C2×D47semidirect