Finite Group Databasebeta

← #20255099

Subgroups — #20255099

Order 6016.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094043C211yesmaximal, characteristic, complemented
2C22×#10625335C211yesmaximal, characteristic, complemented
3#15689779C211yesmaximal, characteristic, complemented
4#15689767C211yesmaximal, characteristic, complemented
5#15689506C211yesmaximal, characteristic, complemented
6#15689351C211yesmaximal, characteristic, complemented
7#15689350C211yesmaximal, characteristic, complemented
8#15689344C211yesmaximal, characteristic, complemented
9#15689336C211yesmaximal, characteristic, complemented
10#15689286C211yesmaximal, characteristic, complemented
11#15689281C211yesmaximal, characteristic, complemented
12#15689265C211yesmaximal, characteristic, complemented
13#15689214C211yesmaximal, characteristic, complemented
14(C22⋊D47)⋊C8C211yesmaximal, characteristic, complemented
15C47×#447C211yesmaximal, characteristic, complemented
16C2×#10625352C2211yescharacteristic
17C2×#10625352C2211yescharacteristic, complemented
18C22×Dic94C2211yescharacteristic
19#13094043—24no—
20C2×Dic188C2211yescharacteristic, complemented
21C2×Dic188C2211yescharacteristic, complemented
22C2×#10625335—24no—
23C2×#10625335C2211yescharacteristic
24C2×#10625335C2211yescharacteristic
25C2×#10625335C2211yescharacteristic
26C2×#10625335C2211yescharacteristic
27C2×#10625335C2211yescharacteristic, complemented
28C22×C47⋊C8C2211yescharacteristic
29C2×C8×D47C2211yescharacteristic, complemented
30#13094011C2211yescharacteristic
31#13094011C2211yescharacteristic, complemented
32#13094010—21no—
33#13094005—21no—
34#13094004C2211yescharacteristic, complemented
35#13094003C2211yescharacteristic
36#13094001—21no—
37#13093996—21no—
38#13093996—21no—
39#13093995C2211yescharacteristic
40#13093993—21no—
41#13093989C2211yescharacteristic, complemented
42D4×Dic47—21no—
43D4×Dic47C2211yescharacteristic
44C4×C22⋊D47C2211yescharacteristic
45C2×C22⋊Dic47—21no—
46#13093955C2211yescharacteristic, complemented
47Dic47⋊C8C2211yescharacteristic, complemented
48#13093949C2211yescharacteristic, complemented
49#13093949C2211yescharacteristic, complemented
50#13093947C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52(C2×D47)⋊C8C2211yescharacteristic, complemented
53C8×Dic47C2211yescharacteristic, complemented
54C22×D4×C47C2211yescharacteristic
55C2×D8×C47C2211yescharacteristic
56C2×D8×C47C2211yescharacteristic
57#121×C47C2211yescharacteristic
58#102×C47C2211yescharacteristic
59#102×C47C2211yescharacteristic
60C22⋊C8×C47C2211yescharacteristic
61C24×C47—21no—
62C2×D4×C47—22no—
63C2×D4×C47—21no—
64C2×D4×C47—21no—
65C2×D4×C47—41no—
66C2×D4×C47C2311yescharacteristic
67C2×D4×C47C2311yescharacteristic
68C2×D4×C47C2311yescharacteristic
69C22×C4×C47C2311yescharacteristic
70C2×C22⋊D47—21no—
71C2×C22⋊D47—21no—
72C2×C22⋊D47—21no—
73C2×C22⋊D47D411yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78#10625352—22no—
79#10625352—22no—
80#10625352—41no—
81#10625352—41no—
82C2×C4×D47C2311yescharacteristic
83C2×Dic94—22no—
84C2×Dic94—21no—
85C2×Dic94—41no—
86C2×Dic94C2311yescharacteristic
87C2×Dic94C2311yescharacteristic
88C2×Dic94C2311yescharacteristic
89D8×C47—22no—
90D8×C47—41no—
91C2×C8×C47C2311yescharacteristic
92C2×C8×C47C2311yescharacteristic
93C4⋊C4×C47C2311yescharacteristic
94C22⋊C4×C47—21no—
95C22⋊Dic47—21no—
96C22⋊Dic47—21no—
97C22⋊Dic47—21no—
98C22⋊Dic47—21no—
99C22⋊Dic47—21no—
100C22⋊Dic47—21no—
101C22⋊Dic47—21no—
102C22⋊Dic47D411yescharacteristic
103#10625335—22no—
104#10625335—22no—
105#10625335—22no—
106#10625335—22no—
107#10625335D414yescomplemented
108(C2×D47)⋊C4—21no—
109(C2×D47)⋊C4D411yescharacteristic
110C4⋊Dic47—21no—
111C4⋊Dic47C2311yescharacteristic
112Dic47⋊C4—21no—
113Dic47⋊C4—21no—
114Dic47⋊C4D411yescharacteristic
115C4×Dic47—21no—
116C4×Dic47C2311yescharacteristic
117C2×C47⋊C8—22no—
118C2×C47⋊C8C2311yescharacteristic
119C2×C47⋊C8C2311yescharacteristic
120Dic188—22no—
121Dic188—41no—
122C8×D47—22no—
123C23×C47—21no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—42no—
127C23×C47—42no—
128C23×C47—81no—
129C23×C47C2×D411yescharacteristic
130C22×D47C2×D411yescharacteristic
131D4×C47—21no—
132D4×C47—21no—
133D4×C47—21no—
134D4×C47—21no—
135D4×C47—21no—
136D4×C47—42no—
137D4×C47—42no—
138D4×C47C2×D412yes—
139C2×C4×C47—21no—
140C2×C4×C47—21no—
141C2×C4×C47—21no—
142C2×C4×C47C2×D411yescharacteristic
143C2×C4×C47C2411yescharacteristic
144C22⋊D47—22no—
145C22⋊D47—42no—
146C22⋊D47—42no—
147C22⋊D47—81no—
148C2×Dic47—21no—
149C2×Dic47—21no—
150C2×Dic47—21no—
151C2×Dic47—21no—
152C2×Dic47—42no—
153C2×Dic47—42no—
154C2×Dic47—42no—
155C2×Dic47—81no—
156C2×Dic47C2×D411yescharacteristic
157C2×Dic47C2×D411yescharacteristic
158C2×Dic47C2×D411yescharacteristic
159C4×D47—21no—
160C4×D47—21no—
161Dic94—21no—
162Dic94—21no—
163Dic94—21no—
164Dic94—21no—
165Dic94—21no—
166Dic94—42no—
167Dic94C2×D412yes—
168C8×C47—21no—
169C8×C47—21no—
170C47⋊C8—21no—
171C47⋊C8C2×D412yes—
172C22×C47—21no—
173C22×C47—21no—
174C22×C47—22no—
175C22×C47—41no—
176C22×C47—41no—
177C22×C47—41no—
178C22×C47—41no—
179C22×C47—41no—
180C22×C47—41no—
181C22×C47—41no—
182C22×C47—41no—
183C22×C47—84no—
184C22×C47#13512yescomplemented
185C22×C47C22×D411yescharacteristic
186C2×D47—21no—
187C2×D47—21no—
188C2×D47—21no—
189C4×C47—21no—
190C4×C47—41no—
191C4×C47C22×D411yescharacteristic
192C4×C47H(5,𝔽2)11yescharacteristic
193Dic47—22no—
194Dic47—21no—
195Dic47—21no—
196Dic47—21no—
197Dic47—41no—
198Dic47—41no—
199Dic47—41no—
200#3282—471nomaximal, Sylow
201C2×C47—22no—
202C2×C47—42no—
203C2×C47—81no—
204C2×C47—81no—
205C2×C47D4211yescharacteristic
206C2×C47C2×#13511yescharacteristic
207C2×C47#57711yescharacteristic
208D47—41no—
209C2×#135—471no—
210C22×SD16—471no—
211#548—471no—
212#546—471no—
213#495—471no—
214#465—471no—
215#465—471no—
216#464—471no—
217#463—471no—
218#452—471no—
219#451—471no—
220#449—471no—
221#447D4711yescharacteristic, complemented
222C4×SD16—471no—
223C8×D4—471no—
224C47#328211yescharacteristic, complemented, Sylow
225C2×#41—471no—
226C2×#41—471no—
227C22×Q8—471no—
228C22×D4C2×D4711yescharacteristic
229#135—944no—
230C2×Q16—471no—
231C2×Q16—471no—
232C2×SD16—471no—
233C2×SD16—471no—
234C2×SD16—471no—
235C2×SD16—471no—
236C2×SD16—471no—
237C2×SD16—944no—
238C2×D8C2×D4711yescharacteristic
239C2×D8C2×D4711yescharacteristic
240C22×C8—471no—
241C22×C8—471no—
242#124—471no—
243#124—471no—
244#124—941no—
245#123—941no—
246C22⋊Q8—471no—
247C22⋊Q8—471no—
248C22⋊Q8—941no—
249#121—471no—
250#121—941no—
251#121—941no—
252#121C2×D4711yescharacteristic
253#120—941no—
254C4×Q8—471no—
255C4×D4—471no—
256C4×D4—471no—
257C4×D4—941no—
258C2×C22⋊C4—941no—
259#106—471no—
260C4⋊C8—471no—
261#103—471no—
262#103—471no—
263#103—471no—
264#102—471no—
265#102C2×D4711yescharacteristic
266#102C2×D4711yescharacteristic
267C22⋊C8—471no—
268C22⋊C8C2×D4711yescharacteristic
269C4×C8—471no—
270C24—21no—
271#41—942no—
272#41—942no—
273#41—1881no—
274#41—1881no—
275C2×Q8—471no—
276C2×Q8—471no—
277C2×Q8—471no—
278C2×Q8—942no—
279C2×Q8—941no—
280C2×Q8—1881no—
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—471no—
286C2×D4—941no—
287C2×D4—941no—
288C2×D4—941no—
289C2×D4C22×D4711yescharacteristic
290C2×D4C22×D4711yescharacteristic
291C2×D4C22×D4711yescharacteristic
292C22×C4—471no—
293C22×C4—941no—
294C22×C4—941no—
295C22×C4—941no—
296C22×C4—941no—
297C22×C4C22×D4711yescharacteristic
298Q16—942no—
299Q16—1881no—
300SD16—474no—
301SD16—942no—
302SD16—942no—
303SD16—942no—
304SD16—942no—
305D8—22no—
306D8—41no—
307C2×C8—471no—
308C2×C8—471no—
309C2×C8—942no—
310C2×C8—942no—
311C2×C8C22×D4711yescharacteristic
312C2×C8C22×D4711yescharacteristic
313C4⋊C4—471no—
314C4⋊C4—471no—
315C4⋊C4—941no—
316C4⋊C4—941no—
317C4⋊C4—941no—
318C4⋊C4C22×D4711yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—471no—
321C22⋊C4—471no—
322C22⋊C4—941no—
323C22⋊C4—941no—
324C22⋊C4—941no—
325C22⋊C4—941no—
326C22⋊C4—941no—
327C22⋊C4—941no—
328C22⋊C4—941no—
329C22⋊C4—941no—
330C42—471no—
331C42—941no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—471no—
339C23D4×D4711yescharacteristic
340Q8—472no—
341Q8—941no—
342Q8—941no—
343Q8—941no—
344Q8—941no—
345Q8—941no—
346Q8—1882no—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—942no—
355D4—3761no—
356D4—1882no—
357D4—1882no—
358D4D4×D4712yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—471no—
363C2×C4—471no—
364C2×C4—471no—
365C2×C4—941no—
366C2×C4—941no—
367C2×C4—941no—
368C2×C4—941no—
369C2×C4—941no—
370C2×C4—941no—
371C2×C4—3761no—
372C2×C4—1882no—
373C2×C4—1882no—
374C2×C4—1882no—
375C2×C4D4×D4711yescharacteristic
376C2×C4C23×D4711yescharacteristic
377C8—21no—
378C8—21no—
379C8—472no—
380C8—941no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—84no—
393C22—941no—
394C22—941no—
395C22—941no—
396C22#1309404312yescomplemented
397C22C2×D4×D4711yescharacteristic
398C4—21no—
399C4—41no—
400C4—941no—
401C4—942no—
402C4—941no—
403C4—941no—
404C4—1881no—
405C4—1881no—
406C4—1881no—
407C4C2×D4×D4711yescharacteristic
408C4#1309406911yescharacteristic
409C2—22no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—1881no—
414C2#1568975511yescharacteristic
415C2C2×#1309404311yescharacteristic
416C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#447C2
socleC22×C47C22×D4
hypercenter#447D47
hypocenterC47#3282
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#13094043C2semidirect
2. C22×#10625335C2semidirect
3. #15689779C2semidirect
4. #15689767C2semidirect
5. #15689506C2semidirect
6. #15689351C2semidirect
7. #15689350C2semidirect
8. #15689344C2semidirect
9. #15689336C2semidirect
10. #15689286C2semidirect
11. #15689281C2semidirect
12. #15689265C2semidirect
13. #15689214C2semidirect
14. (C22⋊D47)⋊C8C2semidirect
15. C47×#447C2semidirect
17. C2×#10625352C22semidirect
20. C2×Dic188C22semidirect
21. C2×Dic188C22semidirect
27. C2×#10625335C22semidirect
29. C2×C8×D47C22semidirect
31. #13094011C22semidirect
34. #13094004C22semidirect
41. #13093989C22semidirect
46. #13093955C22semidirect
47. Dic47⋊C8C22semidirect
48. #13093949C22semidirect
49. #13093949C22semidirect
50. #13093947C22semidirect
51. #13093945C22semidirect
52. (C2×D47)⋊C8C22semidirect
53. C8×Dic47C22semidirect
107. #10625335D4semidirect
184. C22×C47#135semidirect
221. #447D47semidirect
224. C47#3282semidirect
396. C22#13094043semidirect