Finite Group Databasebeta

← #20255346

Subgroups — #20255346

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#15689776C211yesmaximal, characteristic, complemented
2#15689768C211yesmaximal, characteristic, complemented
3#15689485C211yesmaximal, characteristic, complemented
4#15689455C211yesmaximal, characteristic, complemented
5#15689443C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic, complemented
7#15689353C211yesmaximal, characteristic, complemented
8#15689339C211yesmaximal, characteristic, complemented
9#15689269C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689233C211yesmaximal, characteristic, complemented
12#15689193C211yesmaximal, characteristic, complemented
13#15689121C211yesmaximal, characteristic, complemented
14#102×D47C211yesmaximal, characteristic, complemented
15C47×#476C211yesmaximal, characteristic, complemented
16C2×#10625354—21no—
17C2×#10625352C2211yescharacteristic
18C2×D4×D47C2211yescharacteristic
19C2×#10625325C2211yescharacteristic, complemented
20C2×D376C2211yescharacteristic
21C2×#10625334C2211yescharacteristic
22C2×#10625324C2211yescharacteristic, complemented
23C2×C8×D47C2211yescharacteristic
24#13094012C2211yescharacteristic
25#13094009—21no—
26#13094009—21no—
27#13094008—21no—
28#13094004C2211yescharacteristic
29#13094000—21no—
30#13093999C2211yescharacteristic
31#13093999C2211yescharacteristic
32#13093999C2211yescharacteristic, complemented
33#13093998—21no—
34#13093994—21no—
35C4×D188C2211yescharacteristic
36C4×D188C2211yescharacteristic, complemented
37C4⋊C4×D47C2211yescharacteristic
38C4⋊C4×D47C2211yescharacteristic, complemented
39C2×(C2×D47)⋊C4—21no—
40#13093955C2211yescharacteristic, 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
51#13093935C2211yescharacteristic, complemented
52C4⋊Q8×C47C2211yescharacteristic, complemented
53C4×D4×C47C2211yescharacteristic
54#106×C47C2211yescharacteristic, complemented
55#106×C47C2211yescharacteristic, complemented
56C4⋊C8×C47C2211yescharacteristic, complemented
57#102×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59C23×D47—21no—
60C2×Q8×C47—21no—
61C2×D4×C47C2311yescharacteristic
62C22×C4×C47—21no—
63C2×C22⋊D47—21no—
64C2×C22⋊D47—21no—
65C22×Dic47—21no—
66#10625354—44no—
67#10625352—22no—
68#10625352—41no—
69D4×D47—22no—
70D4×D47—41no—
71C2×D188—21no—
72C2×D188—21no—
73C2×D188—21no—
74C2×D188D411yescharacteristic
75C2×D188C2311yescharacteristic
76C2×D188C2311yescharacteristic
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×C4×D47—21no—
80C2×C4×D47C2311yescharacteristic
81C2×C4×D47C2311yescharacteristic
82C2×Dic94C2311yescharacteristic
83C2×C8×C47C2311yescharacteristic
84C2×C8×C47C2311yescharacteristic
85C4⋊C4×C47—21no—
86C4⋊C4×C47C2311yescharacteristic
87C4⋊C4×C47C2311yescharacteristic
88C4⋊C4×C47C2311yescharacteristic
89C22⋊C4×C47—21no—
90C42×C47C2311yescharacteristic
91#10625334—22no—
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)⋊C4—21no—
99(C2×D47)⋊C4D411yescharacteristic
100(C2×D47)⋊C4D411yescharacteristic
101C4⋊Dic47—21no—
102C4⋊Dic47D411yescharacteristic
103C4⋊Dic47C2311yescharacteristic
104Dic47⋊C4—21no—
105Dic47⋊C4—21no—
106C2×C47⋊C8C2311yescharacteristic
107C2×C47⋊C8C2311yescharacteristic
108D376—41no—
109#10625325—41no—
110#10625324—41no—
111C8×D47—41no—
112C23×C47—21no—
113C22×D47—21no—
114C22×D47—21no—
115C22×D47—42no—
116C22×D47—42no—
117C22×D47—81no—
118C22×D47C2×D411yescharacteristic
119C22×D47C2×D411yescharacteristic
120Q8×C47—42no—
121D4×C47—21no—
122D4×C47#4112yescomplemented
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—81no—
127C2×C4×C47C2×D411yescharacteristic
128C2×C4×C47C2×D411yescharacteristic
129C2×C4×C47C2411yescharacteristic
130C22⋊D47—42no—
131C22⋊D47—42no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47C2×D411yescharacteristic
136C2×Dic47C2×D411yescharacteristic
137D188—22no—
138D188—21no—
139D188—21no—
140D188—21no—
141D188—21no—
142D188—42no—
143D188—42no—
144D188—81no—
145C4×D47—21no—
146C4×D47—21no—
147C4×D47—21no—
148C4×D47—21no—
149C4×D47—42no—
150C4×D47—42no—
151C4×D47—42no—
152Dic94—21no—
153Dic94—21no—
154C8×C47—21no—
155C8×C47—21no—
156C47⋊C8—21no—
157C47⋊C8—21no—
158C22×C47—22no—
159C22×C47—41no—
160C22×C47—41no—
161C22×C47C22×D411yescharacteristic
162C2×D47—21no—
163C2×D47—21no—
164C2×D47—21no—
165C2×D47—21no—
166C2×D47—21no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C2×D47—41no—
171C2×D47—41no—
172C2×D47—41no—
173C2×D47—84no—
174C2×D47AGL(1,ℤ/8)12yes—
175C4×C47—21no—
176C4×C47—21no—
177C4×C47—41no—
178C4×C47—41no—
179C4×C47—41no—
180C4×C47C2×#4111yescharacteristic
181C4×C47H(5,𝔽2)11yescharacteristic
182Dic47—21no—
183Dic47—21no—
184Dic47—41no—
185Dic47—41no—
186#3306—471nomaximal, Sylow
187C2×C47—42no—
188C2×C47#54611yescharacteristic
189C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C47#57711yescharacteristic
191D47—22no—
192D47—41no—
193D47—81no—
194D47—81no—
195#547—471no—
196#546—471no—
197#489—471no—
198#483—471no—
199#481—471no—
200#476D4711yescharacteristic, complemented
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⋊Q8C2×D4711yescharacteristic, complemented
220#124—471no—
221#123—941no—
222#123—941no—
223#123—941no—
224C22⋊Q8—471no—
225C22⋊Q8—941no—
226#121—471no—
227#121—471no—
228#121—471no—
229#121—941no—
230#120—941no—
231C4×D4—471no—
232C4×D4—471no—
233C4×D4C2×D4711yescharacteristic
234C2×C4⋊C4—471no—
235C2×C4⋊C4—471no—
236C2×C22⋊C4—941no—
237#106—471no—
238#106C2×D4711yescharacteristic, complemented
239#106C2×D4711yescharacteristic, complemented
240C4⋊C8C2×D4711yescharacteristic, complemented
241#103—471no—
242#103—471no—
243#103—471no—
244#102—471no—
245#102—471no—
246#102—471no—
247#102—471no—
248#102—471no—
249#102C2×D4711yescharacteristic
250#102C2×D4711yescharacteristic
251C22⋊C8—471no—
252C22⋊C8—471no—
253#97—471no—
254C24—941no—
255#41—942no—
256#41—1881no—
257#41—1884no—
258C2×Q8—21no—
259C2×Q8—471no—
260C2×D4—471no—
261C2×D4—471no—
262C2×D4—471no—
263C2×D4—941no—
264C2×D4—941no—
265C2×D4—941no—
266C2×D4—941no—
267C2×D4—942no—
268C2×D4—941no—
269C2×D4—1881no—
270C2×D4C22×D4711yescharacteristic
271C22×C4—21no—
272C22×C4—471no—
273C22×C4—471no—
274C22×C4—941no—
275C22×C4—941no—
276C22×C4—941no—
277C22×C4—941no—
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—471no—
289C4⋊C4—471no—
290C4⋊C4—941no—
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—
306C42C22×D4711yescharacteristic
307C23—21no—
308C23—471no—
309C23—471no—
310C23—941no—
311C23—941no—
312C23—3761no—
313C23—1882no—
314C23—1882no—
315Q8—42no—
316Q8—941no—
317Q8—941no—
318D4—21no—
319D4—942no—
320D4—941no—
321D4—941no—
322D4—941no—
323D4—941no—
324D4—3761no—
325D4—1882no—
326D4—1882no—
327D4—1882no—
328D4—1882no—
329D4#1062535412yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—81no—
334C2×C4—471no—
335C2×C4—471no—
336C2×C4—941no—
337C2×C4—941no—
338C2×C4—941no—
339C2×C4—941no—
340C2×C4—941no—
341C2×C4—941no—
342C2×C4—1882no—
343C2×C4—1882no—
344C2×C4—1882no—
345C2×C4—1882no—
346C2×C4D4×D4711yescharacteristic
347C2×C4D4×D4711yescharacteristic
348C2×C4C23×D4711yescharacteristic
349C8—21no—
350C8—21no—
351C8—941no—
352C8—941no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—472no—
357C22—941no—
358C22—941no—
359C22—941no—
360C22—941no—
361C22—941no—
362C22—3764no—
363C22—1881no—
364C22—1881no—
365C22—1881no—
366C22—1881no—
367C22—1881no—
368C22—1881no—
369C22C2×D4×D4711yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—941no—
376C4—941no—
377C4—1881no—
378C4—1881no—
379C4C2×#1062535411yescharacteristic
380C4#1309407011yescharacteristic
381C2—42no—
382C2—942no—
383C2—3761no—
384C2—3761no—
385C2—1881no—
386C2#1568976411yescharacteristic
387C2AGL(1,ℤ/8)×D4711yescharacteristic
388C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3306
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #15689776C2semidirect
2. #15689768C2semidirect
3. #15689485C2semidirect
4. #15689455C2semidirect
5. #15689443C2semidirect
6. #15689377C2semidirect
7. #15689353C2semidirect
8. #15689339C2semidirect
9. #15689269C2semidirect
10. #15689258C2semidirect
11. #15689233C2semidirect
12. #15689193C2semidirect
13. #15689121C2semidirect
14. #102×D47C2semidirect
15. C47×#476C2semidirect
19. C2×#10625325C22semidirect
22. C2×#10625324C22semidirect
32. #13093999C22semidirect
36. C4×D188C22semidirect
38. C4⋊C4×D47C22semidirect
40. #13093955C22semidirect
41. #13093949C22semidirect
42. #13093947C22semidirect
43. #13093947C22semidirect
48. #13093944C22semidirect
50. (C2×D47)⋊C8C22semidirect
51. #13093935C22semidirect
52. C4⋊Q8×C47C22semidirect
54. #106×C47C22semidirect
55. #106×C47C22semidirect
56. C4⋊C8×C47C22semidirect
122. D4×C47#41semidirect
200. #476D47semidirect
210. C47#3306semidirect
219. C4⋊Q8C2×D47semidirect
238. #106C2×D47semidirect
239. #106C2×D47semidirect
240. C4⋊C8C2×D47semidirect
329. D4#10625354semidirect