Finite Group Databasebeta

← #20255347

Subgroups — #20255347

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#15689774C211yesmaximal, characteristic, complemented
2#15689764C211yesmaximal, characteristic, complemented
3#15689484C211yesmaximal, characteristic, complemented
4#15689443C211yesmaximal, characteristic, complemented
5#15689412C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689354C211yesmaximal, characteristic, complemented
8#15689341C211yesmaximal, characteristic, complemented
9#15689271C211yesmaximal, characteristic, complemented
10#15689259C211yesmaximal, characteristic, complemented
11#15689234C211yesmaximal, characteristic, complemented
12#15689191C211yesmaximal, characteristic, complemented
13#15689123C211yesmaximal, characteristic, complemented
14C2×#13093944C211yesmaximal, characteristic, complemented
15C47×#483C211yesmaximal, characteristic, complemented
16C2×#10625354C2211yescharacteristic
17C2×#10625350—21no—
18C22×D188C2211yescharacteristic
19C2×#10625336C2211yescharacteristic, complemented
20C2×D376C2211yescharacteristic
21C2×D376C2211yescharacteristic
22C2×#10625324C2211yescharacteristic, complemented
23C22×C47⋊C8C2211yescharacteristic
24#13094023C2211yescharacteristic, complemented
25#13094013C2211yescharacteristic
26#13094009—21no—
27#13094009—21no—
28#13094007—21no—
29#13094002—21no—
30#13093999—21no—
31#13093999C2211yescharacteristic
32#13093999C2211yescharacteristic, complemented
33#13093998C2211yescharacteristic
34#13093994—21no—
35#13093986C2211yescharacteristic
36#13093986C2211yescharacteristic, complemented
37C4×C22⋊D47C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic, complemented
39C22⋊C4×D47—21no—
40#13093955C2211yescharacteristic, complemented
41Dic47⋊C8C2211yescharacteristic, complemented
42#13093948C2211yescharacteristic, complemented
43#13093946C2211yescharacteristic
44#13093946C2211yescharacteristic
45#13093944C2211yescharacteristic
46#13093944C2211yescharacteristic
47#13093944C2211yescharacteristic
48#13093944C2211yescharacteristic
49#13093944C2211yescharacteristic, complemented
50(C2×D47)⋊C8C2211yescharacteristic, complemented
51#13093934C2211yescharacteristic, complemented
52C22⋊Q8×C47C2211yescharacteristic
53C2×C4⋊C4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56#103×C47C2211yescharacteristic, complemented
57#103×C47C2211yescharacteristic, complemented
58C22⋊C8×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47C2311yescharacteristic
61C22×C4×C47—21no—
62C22×C4×C47C2311yescharacteristic
63C2×C22⋊D47—21no—
64C2×C22⋊D47D411yescharacteristic
65#10625354—22no—
66#10625354—41no—
67#10625350—44no—
68C2×D188—22no—
69C2×D188—21no—
70C2×D188—21no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—41no—
74C2×D188C2311yescharacteristic
75C2×D188C2311yescharacteristic
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47C2311yescharacteristic
82C2×Dic94—21no—
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47—21no—
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C4⋊C4×C47C2311yescharacteristic
90C22⋊C4×C47—21no—
91C22⋊Dic47D411yescharacteristic
92#10625336—41no—
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)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4D411yescharacteristic
101C4⋊Dic47C2311yescharacteristic
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4D411yescharacteristic
105C4×Dic47C2311yescharacteristic
106C2×C47⋊C8—41no—
107C2×C47⋊C8C2311yescharacteristic
108C2×C47⋊C8C2311yescharacteristic
109D376—22no—
110D376—41no—
111#10625324—41no—
112C23×C47C2×D411yescharacteristic
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—21no—
116C22×D47—42no—
117C22×D47—42no—
118C22×D47—81no—
119C22×D47C2×D411yescharacteristic
120Q8×C47—21no—
121Q8×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—42no—
129C2×C4×C47C2×D411yescharacteristic
130C2×C4×C47C2411yescharacteristic
131C22⋊D47—22no—
132C22⋊D47—42no—
133C2×Dic47—21no—
134C2×Dic47C2×D411yescharacteristic
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—21no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—42no—
143D188—42no—
144D188—42no—
145D188—81no—
146D188#4112yescomplemented
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—42no—
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×C47AGL(1,ℤ/8)12yes—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—22no—
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
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×C47—41no—
180C4×C47C2×#4111yescharacteristic
181C4×C47H(5,𝔽2)11yescharacteristic
182Dic47—21no—
183Dic47—21no—
184Dic47—21no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—22no—
188C2×C47#54611yescharacteristic
189C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C47#57711yescharacteristic
191D47—41no—
192D47—42no—
193D47—81no—
194D47—81no—
195#547—471no—
196#546—471no—
197#489—471no—
198#483D4711yescharacteristic, complemented
199#481—471no—
200#476—471no—
201#469—471no—
202#465—471no—
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×SD16—471no—
215C2×D8—471no—
216C2×D8—471no—
217C2×M16—471no—
218C22×C8—471no—
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—471no—
229#121—941no—
230#120—941no—
231C4×D4—471no—
232C4×D4—471no—
233C4×D4—471no—
234C2×C4⋊C4—471no—
235C2×C4⋊C4C2×D4711yescharacteristic
236C2×C22⋊C4—941no—
237#106—471no—
238#106C2×D4711yescharacteristic, complemented
239#106C2×D4711yescharacteristic, complemented
240C4⋊C8—471no—
241#103—471no—
242#103C2×D4711yescharacteristic, complemented
243#103C2×D4711yescharacteristic, complemented
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102—471no—
250#102—471no—
251C22⋊C8—471no—
252C22⋊C8C2×D4711yescharacteristic
253#97—471no—
254C24—941no—
255#41—942no—
256#41—1884no—
257#41—1881no—
258C2×Q8—941no—
259C2×Q8C22×D4711yescharacteristic
260C2×D4—471no—
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—941no—
270C2×D4—1881no—
271C22×C4—21no—
272C22×C4—471no—
273C22×C4—941no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4C22×D4711yescharacteristic
278SD16—1881no—
279D8—942no—
280D8—1881no—
281M16—1881no—
282C2×C8—471no—
283C2×C8—471no—
284C2×C8—1881no—
285C2×C8C22×D4711yescharacteristic
286C2×C8C22×D4711yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—471no—
290C4⋊C4—471no—
291C4⋊C4—941no—
292C4⋊C4—941no—
293C4⋊C4C22×D4711yescharacteristic
294C4⋊C4C22×D4711yescharacteristic
295C4⋊C4C22×D4711yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—471no—
298C22⋊C4—471no—
299C22⋊C4—941no—
300C22⋊C4—941no—
301C22⋊C4—941no—
302C22⋊C4—941no—
303C22⋊C4—941no—
304C22⋊C4—941no—
305C22⋊C4—941no—
306C42—471no—
307C23—471no—
308C23—941no—
309C23—941no—
310C23—941no—
311C23—3761no—
312C23—1882no—
313C23—1882no—
314C23D4×D4711yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1882no—
318D4—472no—
319D4—942no—
320D4—941no—
321D4—941no—
322D4—941no—
323D4—941no—
324D4—941no—
325D4—3761no—
326D4—1882no—
327D4—1882no—
328D4—1882no—
329D4—1882no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—471no—
338C2×C4—471no—
339C2×C4—471no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—941no—
343C2×C4—3761no—
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—941no—
356C22—942no—
357C22—941no—
358C22—941no—
359C22—3764no—
360C22—1881no—
361C22—1881no—
362C22—1881no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22#1309405112yes—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—941no—
376C4—941no—
377C4—941no—
378C4—1881no—
379C4#41×D4711yescharacteristic
380C4#1309407011yescharacteristic
381C2—22no—
382C2—3761no—
383C2—3761no—
384C2—1881no—
385C2—1882no—
386C2#1568976511yescharacteristic
387C2C2×#1309405111yescharacteristic
388C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #15689774C2semidirect
2. #15689764C2semidirect
3. #15689484C2semidirect
4. #15689443C2semidirect
5. #15689412C2semidirect
6. #15689377C2semidirect
7. #15689354C2semidirect
8. #15689341C2semidirect
9. #15689271C2semidirect
10. #15689259C2semidirect
11. #15689234C2semidirect
12. #15689191C2semidirect
13. #15689123C2semidirect
14. C2×#13093944C2semidirect
15. C47×#483C2semidirect
19. C2×#10625336C22semidirect
22. C2×#10625324C22semidirect
24. #13094023C22semidirect
32. #13093999C22semidirect
36. #13093986C22semidirect
38. C4⋊C4×D47C22semidirect
40. #13093955C22semidirect
41. Dic47⋊C8C22semidirect
42. #13093948C22semidirect
49. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093934C22semidirect
54. #106×C47C22semidirect
55. #106×C47C22semidirect
56. #103×C47C22semidirect
57. #103×C47C22semidirect
146. D188#41semidirect
198. #483D47semidirect
210. C47#3306semidirect
238. #106C2×D47semidirect
239. #106C2×D47semidirect
242. #103C2×D47semidirect
243. #103C2×D47semidirect