Finite Group Databasebeta

← #20255355

Subgroups — #20255355

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#15689764C211yesmaximal, characteristic, complemented
3#15689484C211yesmaximal, characteristic, complemented
4#15689451C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689412C211yesmaximal, characteristic, complemented
7#15689375C211yesmaximal, characteristic, complemented
8#15689340C211yesmaximal, characteristic, complemented
9#15689267C211yesmaximal, characteristic, complemented
10#15689256C211yesmaximal, characteristic, complemented
11#15689232C211yesmaximal, characteristic, complemented
12#15689194C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14C2×#13093946C211yesmaximal, characteristic, complemented
15C47×#465C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625352—21no—
18C22×D188C2211yescharacteristic
19C2×#10625334C2211yescharacteristic
20C2×#10625334C2211yescharacteristic
21C2×#10625324C2211yescharacteristic, complemented
22#13094023C2211yescharacteristic, complemented
23#13094013C2211yescharacteristic
24#13094009—21no—
25#13094006—21no—
26#13094005—21no—
27#13094001—21no—
28#13093999—21no—
29#13093999C2211yescharacteristic
30#13093995C2211yescharacteristic, complemented
31#13093994—21no—
32D4×Dic47C2211yescharacteristic, complemented
33#13093986C2211yescharacteristic
34C4×C22⋊D47C2211yescharacteristic
35C2×C4⋊Dic47C2211yescharacteristic
36C4⋊C4×D47C2211yescharacteristic, complemented
37C22⋊C4×D47—21no—
38#13093955C2211yescharacteristic, complemented
39#13093955C2211yescharacteristic, complemented
40Dic47⋊C8C2211yescharacteristic, complemented
41#13093948C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093946C2211yescharacteristic
46#13093946C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49C22⋊(C47⋊C8)C2211yescharacteristic
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C2×SD16×C47C2211yescharacteristic, complemented
53C22×C8×C47C2211yescharacteristic
54C22⋊Q8×C47C2211yescharacteristic
55#121×C47C2211yescharacteristic
56#106×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58#102×C47C2211yescharacteristic, complemented
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C2×D4×C47—21no—
62C2×D4×C47C2311yescharacteristic
63C22×C4×C47C2311yescharacteristic
64C2×C22⋊D47—21no—
65C2×C22⋊D47D411yescharacteristic
66C22×Dic47—21no—
67C22×Dic47—21no—
68#10625354—22no—
69#10625354—41no—
70#10625352—44no—
71C2×D188—22no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188—21no—
75C2×D188—41no—
76C2×D188C2311yescharacteristic
77C2×D188C2311yescharacteristic
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47C2311yescharacteristic
82C2×Dic94—21no—
83SD16×C47—41no—
84C2×C8×C47—41no—
85C2×C8×C47C2311yescharacteristic
86C2×C8×C47C2311yescharacteristic
87C4⋊C4×C47—21no—
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47—21no—
91C22⋊C4×C47—21no—
92C22⋊Dic47—21no—
93C22⋊Dic47—21no—
94C22⋊Dic47D411yescharacteristic
95#10625334—22no—
96#10625334—41no—
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101(C2×D47)⋊C4D411yescharacteristic
102C4⋊Dic47—21no—
103C4⋊Dic47C2311yescharacteristic
104C4⋊Dic47C2311yescharacteristic
105Dic47⋊C4—21no—
106Dic47⋊C4—21no—
107Dic47⋊C4D411yescharacteristic
108C4×Dic47C2311yescharacteristic
109C2×C47⋊C8C2311yescharacteristic
110C2×C47⋊C8C2311yescharacteristic
111#10625324—41no—
112C23×C47—21no—
113C23×C47C2×D411yescharacteristic
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47C2×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47—21no—
122D4×C47—21no—
123D4×C47—21no—
124D4×C47—42no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47C2×D411yescharacteristic
131C2×C4×C47C2411yescharacteristic
132C22⋊D47—22no—
133C22⋊D47—42no—
134C2×Dic47—21no—
135C2×Dic47—21no—
136C2×Dic47—42no—
137C2×Dic47—42no—
138C2×Dic47C2×D411yescharacteristic
139C2×Dic47C2×D411yescharacteristic
140C2×Dic47C2×D411yescharacteristic
141D188—21no—
142D188—21no—
143D188—21no—
144D188—42no—
145D188—42no—
146D188—81no—
147D188#4112yescomplemented
148C4×D47—21no—
149C4×D47—21no—
150C4×D47—42no—
151C4×D47—42no—
152C4×D47—81no—
153Dic94—42no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47AGL(1,ℤ/8)12yes—
164C22×C47C22×D411yescharacteristic
165C2×D47—21no—
166C2×D47—22no—
167C2×D47—21no—
168C2×D47—21no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—41no—
174C2×D47—84no—
175C4×C47—21no—
176C4×C47—41no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47C2×#4111yescharacteristic
180C4×C47H(5,𝔽2)11yescharacteristic
181Dic47—21no—
182Dic47—21no—
183Dic47—21no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—22no—
188C2×C47—81no—
189C2×C47#54611yescharacteristic
190C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C47#57711yescharacteristic
192D47—41no—
193D47—42no—
194D47—81no—
195#547—471no—
196#546—471no—
197#489—471no—
198#483—471no—
199#481—471no—
200#476—471no—
201#469—471no—
202#465D4711yescharacteristic, complemented
203#463—471no—
204#449—471no—
205#447—471no—
206#442—471no—
207#435—471no—
208#417—471no—
209C2×#102—471no—
210C47#330611yescharacteristic, complemented, Sylow
211C2×#41—471no—
212C2×#41—941no—
213C22×D4—471no—
214C2×SD16C2×D4711yescharacteristic, complemented
215C2×D8—471no—
216C2×D8—471no—
217C2×M16—471no—
218C22×C8C2×D4711yescharacteristic
219C4⋊Q8—471no—
220#124—471no—
221#123—941no—
222#123—941no—
223#123—941no—
224C22⋊Q8—941no—
225C22⋊Q8C2×D4711yescharacteristic
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#106C2×D4711yescharacteristic, complemented
240C4⋊C8—471no—
241#103—471no—
242#103—471no—
243#103C2×D4711yescharacteristic, complemented
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102C2×D4711yescharacteristic, complemented
251C22⋊C8—471no—
252C22⋊C8—471no—
253#97—471no—
254C24—941no—
255#41—942no—
256#41—1881no—
257#41—1884no—
258C2×Q8—941no—
259C2×Q8C22×D4711yescharacteristic
260C2×D4—21no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—471no—
264C2×D4—942no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—941no—
268C2×D4—941no—
269C2×D4—1881no—
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—41no—
279D8—942no—
280D8—1881no—
281M16—1881no—
282C2×C8—41no—
283C2×C8—471no—
284C2×C8—471no—
285C2×C8C22×D4711yescharacteristic
286C2×C8C22×D4711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—471no—
289C4⋊C4—471no—
290C4⋊C4—471no—
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—
306C42—471no—
307C23—21no—
308C23—471no—
309C23—941no—
310C23—941no—
311C23—3761no—
312C23—1882no—
313C23—1882no—
314C23D4×D4711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1882no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—472no—
322D4—942no—
323D4—941no—
324D4—941no—
325D4—941no—
326D4—3761no—
327D4—1882no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—471no—
336C2×C4—471no—
337C2×C4—471no—
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—41no—
356C22—41no—
357C22—41no—
358C22—941no—
359C22—942no—
360C22—941no—
361C22—941no—
362C22—3764no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22#1309405112yes—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—941no—
375C4—941no—
376C4—941no—
377C4—1881no—
378C4—1881no—
379C4#41×D4711yescharacteristic
380C4#1309406911yescharacteristic
381C2—22no—
382C2—81no—
383C2—3761no—
384C2—1881no—
385C2—1882no—
386C2#1568976211yescharacteristic
387C2C2×#1309405111yescharacteristic
388C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#465C2
socleC22×C47C22×D4
hypercenter#465D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #15689773C2semidirect
2. #15689764C2semidirect
3. #15689484C2semidirect
4. #15689451C2semidirect
5. #15689443C2semidirect
6. #15689412C2semidirect
7. #15689375C2semidirect
8. #15689340C2semidirect
9. #15689267C2semidirect
10. #15689256C2semidirect
11. #15689232C2semidirect
12. #15689194C2semidirect
13. #15689123C2semidirect
14. C2×#13093946C2semidirect
15. C47×#465C2semidirect
21. C2×#10625324C22semidirect
22. #13094023C22semidirect
30. #13093995C22semidirect
32. D4×Dic47C22semidirect
36. C4⋊C4×D47C22semidirect
38. #13093955C22semidirect
39. #13093955C22semidirect
40. Dic47⋊C8C22semidirect
41. #13093948C22semidirect
42. #13093948C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
52. C2×SD16×C47C22semidirect
56. #106×C47C22semidirect
57. #103×C47C22semidirect
58. #102×C47C22semidirect
147. D188#41semidirect
202. #465D47semidirect
210. C47#3306semidirect
214. C2×SD16C2×D47semidirect
239. #106C2×D47semidirect
243. #103C2×D47semidirect
250. #102C2×D47semidirect