Finite Group Databasebeta

← #20252693

Subgroups — #20252693

Order 6016.

764 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13094069C211yesmaximal, characteristic, complemented
2C2×#13094051C211yesmaximal, characteristic, complemented
3C2×#13094045C211yesmaximal, characteristic, complemented
4#15689703C211yesmaximal, characteristic, complemented
5#15689283C211yesmaximal, characteristic, complemented
6#15689282C211yesmaximal, characteristic, complemented
7#15689272C211yesmaximal, characteristic, complemented
8#15689270C211yesmaximal, characteristic, complemented
9#15689269C211yesmaximal, characteristic, complemented
10#15689258C211yesmaximal, characteristic, complemented
11#15689257C211yesmaximal, characteristic, complemented
12#15689121C211yesmaximal, characteristic, complemented
13#102×D47C211yesmaximal, characteristic, complemented
14#15689088C211yesmaximal, characteristic, complemented
15C47×#450C211yesmaximal, characteristic, complemented
16#13094069—24no—
17#13094069—24no—
18C2×#10625354C2211yescharacteristic, complemented
19C2×#10625350C2211yescharacteristic
20C2×#10625350C2211yescharacteristic
21C2×#10625352—21no—
22C2×#10625352C2211yescharacteristic
23C2×#10625352C2211yescharacteristic
24C22×C22⋊D47—21no—
25C22×C22⋊D47—21no—
26C2×D4×D47—21no—
27C2×D4×D47C2211yescharacteristic
28C2×D4×D47C2211yescharacteristic
29#13094051—24no—
30#13094045—24no—
31C2×#10625337C2211yescharacteristic, complemented
32C2×#10625325C2211yescharacteristic, complemented
33C2×#10625336C2211yescharacteristic, complemented
34C2×D376C2211yescharacteristic, complemented
35C2×#10625334C2211yescharacteristic, complemented
36C2×#10625334C2211yescharacteristic, complemented
37C2×#10625324C2211yescharacteristic, complemented
38C2×C8×D47C2211yescharacteristic, complemented
39#13094002—21no—
40#13094000C2211yescharacteristic, complemented
41#13093999—21no—
42#13093999C2211yescharacteristic, complemented
43#13093998C2211yescharacteristic, complemented
44#13093997—21no—
45#13093997—21no—
46C4⋊C4×D47C2211yescharacteristic, complemented
47#13093949C2211yescharacteristic, complemented
48#13093947C2211yescharacteristic, complemented
49#13093946C2211yescharacteristic, complemented
50#13093945C2211yescharacteristic, complemented
51#13093945C2211yescharacteristic, complemented
52#13093944C2211yescharacteristic, complemented
53C22⋊(C47⋊C8)C2211yescharacteristic, complemented
54(C2×D47)⋊C8C2211yescharacteristic, complemented
55(C2×D47)⋊C8C2211yescharacteristic, complemented
56C22×D4×C47C2211yescharacteristic
57C2×SD16×C47C2211yescharacteristic, complemented
58C2×SD16×C47C2211yescharacteristic, complemented
59C22⋊Q8×C47C2211yescharacteristic, complemented
60#102×C47C2211yescharacteristic, complemented
61#102×C47C2211yescharacteristic, complemented
62C22⋊C8×C47C2211yescharacteristic, complemented
63C24×C47—21no—
64C23×D47—21no—
65C23×D47—21no—
66C2×Q8×C47C2311yescharacteristic
67C2×D4×C47—22no—
68C2×D4×C47—22no—
69C2×D4×C47—21no—
70C2×D4×C47C2311yescharacteristic
71C2×D4×C47C2311yescharacteristic
72C22×C4×C47C2311yescharacteristic
73C2×C22⋊D47—28no—
74C2×C22⋊D47—28no—
75C2×C22⋊D47—21no—
76C2×C22⋊D47—21no—
77C2×C22⋊D47—21no—
78C2×C22⋊D47—21no—
79C2×C22⋊D47—21no—
80C2×C22⋊D47—21no—
81C2×C22⋊D47D411yescharacteristic
82C2×C22⋊D47D411yescharacteristic
83C22×Dic47—21no—
84C22×Dic47—21no—
85#10625354—22no—
86#10625354—22no—
87#10625352—28no—
88#10625352—22no—
89#10625352—22no—
90#10625352—22no—
91#10625352D414yescomplemented
92D4×D47—28no—
93D4×D47—22no—
94D4×D47—22no—
95D4×D47—22no—
96D4×D47D414yescomplemented
97#10625350—22no—
98#10625350—22no—
99#10625350—22no—
100#10625350—22no—
101C2×D188—21no—
102C2×D188—21no—
103C2×D188D411yescharacteristic
104C2×D188C2311yescharacteristic
105C2×D188C2311yescharacteristic
106C2×C4×D47—21no—
107C2×C4×D47—21no—
108C2×C4×D47—21no—
109C2×C4×D47C2311yescharacteristic
110C2×C4×D47C2311yescharacteristic
111C2×Dic94D411yescharacteristic
112C2×Dic94C2311yescharacteristic
113SD16×C47—22no—
114SD16×C47—22no—
115C2×C8×C47C2311yescharacteristic
116C2×C8×C47C2311yescharacteristic
117C4⋊C4×C47—21no—
118C4⋊C4×C47C2311yescharacteristic
119C22⋊C4×C47—21no—
120#10625337—22no—
121#10625336—22no—
122#10625334—22no—
123#10625334—22no—
124(C2×D47)⋊C4—21no—
125(C2×D47)⋊C4—21no—
126(C2×D47)⋊C4—21no—
127C4⋊Dic47C2311yescharacteristic
128Dic47⋊C4—21no—
129Dic47⋊C4—21no—
130C2×C47⋊C8C2311yescharacteristic
131C2×C47⋊C8C2311yescharacteristic
132D376—22no—
133#10625325—22no—
134#10625324—22no—
135C8×D47—22no—
136C23×C47—24no—
137C23×C47—21no—
138C23×C47—21no—
139C23×C47—81no—
140C23×C47—81no—
141C23×C47C2×D411yescharacteristic
142C22×D47—21no—
143C22×D47—24no—
144C22×D47—24no—
145C22×D47—21no—
146C22×D47—81no—
147C22×D47—81no—
148C22×D47—81no—
149C22×D47—81no—
150C22×D47C2×D411yescharacteristic
151C22×D47C2×D411yescharacteristic
152Q8×C47—21no—
153Q8×C47—21no—
154D4×C47—24no—
155D4×C47—21no—
156D4×C47—21no—
157D4×C47C2×D412yes—
158D4×C47C2×D412yes—
159C2×C4×C47—21no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47C2×D411yescharacteristic
164C2×C4×C47C2411yescharacteristic
165C22⋊D47—24no—
166C22⋊D47—24no—
167C22⋊D47—24no—
168C22⋊D47—22no—
169C22⋊D47—24no—
170C22⋊D47—22no—
171C22⋊D47—24no—
172C22⋊D47—81no—
173C2×Dic47—24no—
174C2×Dic47—21no—
175C2×Dic47—24no—
176C2×Dic47—21no—
177C2×Dic47C2×D411yescharacteristic
178C2×Dic47C2×D411yescharacteristic
179D188—22no—
180D188—21no—
181D188—21no—
182D188—21no—
183D188—42no—
184D188—81no—
185D188C2×D412yes—
186C4×D47—24no—
187C4×D47—21no—
188C4×D47—21no—
189C4×D47—42no—
190C4×D47—81no—
191C4×D47C2×D412yes—
192C4×D47C2×D412yes—
193Dic94—21no—
194Dic94—22no—
195Dic94C2×D412yes—
196C8×C47—21no—
197C8×C47—21no—
198C47⋊C8—21no—
199C47⋊C8—21no—
200C22×C47—22no—
201C22×C47—22no—
202C22×C47—21no—
203C22×C47—21no—
204C22×C47—21no—
205C22×C47—41no—
206C22×C47—41no—
207C22×C47—41no—
208C22×C47—41no—
209C22×C47—84no—
210C22×C47C22×D411yescharacteristic
211C2×D47—21no—
212C2×D47—21no—
213C2×D47—21no—
214C2×D47—22no—
215C2×D47—21no—
216C2×D47—21no—
217C2×D47—41no—
218C2×D47—41no—
219C2×D47—41no—
220C2×D47—41no—
221C2×D47—41no—
222C2×D47—84no—
223C2×D47—84no—
224C2×D47#12012yes—
225C4×C47—21no—
226C4×C47—41no—
227C4×C47—41no—
228C4×C47C22×D411yescharacteristic
229C4×C47C22×D411yescharacteristic
230Dic47—21no—
231Dic47—22no—
232Dic47—41no—
233Dic47#12012yes—
234#3012—471nomaximal, Sylow
235C2×C47—42no—
236C2×C47—42no—
237C2×C47—41no—
238C2×C47C2×#12011yescharacteristic
239C2×C47#57611yescharacteristic
240C2×C47#57711yescharacteristic
241D47—22no—
242D47—41no—
243D47—42no—
244D47—81no—
245C2×H(5,𝔽2)—471no—
246C2×AGL(1,ℤ/8)—471no—
247C2×#135—471no—
248#537—471no—
249#452—471no—
250#452—471no—
251#450—471no—
252#450D4711yescharacteristic, complemented
253#449—471no—
254#449—471no—
255#447—471no—
256#447—471no—
257#417—471no—
258C2×#102—471no—
259#408—471no—
260C47#301211yescharacteristic, complemented, Sylow
261H(5,𝔽2)—944no—
262H(5,𝔽2)—944no—
263C2×#41—471no—
264C2×#41—471no—
265C2×#41—471no—
266C2×#41—471no—
267C2×#41—471no—
268C2×#41—941no—
269C22×D4—471no—
270C22×D4—471no—
271C22×D4—941no—
272C22×D4—941no—
273C22×D4—941no—
274C22×D4C2×D4711yescharacteristic
275AGL(1,ℤ/8)—944no—
276#135—944no—
277C2×Q16—471no—
278C2×SD16—471no—
279C2×SD16—471no—
280C2×SD16C2×D4711yescharacteristic, complemented
281C2×SD16C2×D4711yescharacteristic, complemented
282C2×D8—471no—
283C2×D8—471no—
284C2×D8—471no—
285C2×M16—471no—
286C22×C8—471no—
287C22⋊Q8—471no—
288C22⋊Q8—941no—
289C22⋊Q8C2×D4711yescharacteristic, complemented
290#121—471no—
291#121—471no—
292#121—941no—
293#121—941no—
294#121—941no—
295C2×C4⋊C4—471no—
296#103—471no—
297#103—471no—
298#102—471no—
299#102—471no—
300#102—471no—
301#102—471no—
302#102C2×D4711yescharacteristic, complemented
303#102C2×D4711yescharacteristic, complemented
304C22⋊C8—471no—
305C22⋊C8—471no—
306C22⋊C8—471no—
307C22⋊C8C2×D4711yescharacteristic, complemented
308C24—21no—
309C24—941no—
310C24—941no—
311#41—474no—
312#41—942no—
313#41—942no—
314#41—942no—
315#41—942no—
316#41—942no—
317#41—942no—
318#41—942no—
319#41—942no—
320#41—948no—
321#41—942no—
322C2×Q8—471no—
323C2×Q8—471no—
324C2×Q8C22×D4711yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—474no—
329C2×D4—471no—
330C2×D4—471no—
331C2×D4—471no—
332C2×D4—471no—
333C2×D4—471no—
334C2×D4—941no—
335C2×D4—941no—
336C2×D4—942no—
337C2×D4—941no—
338C2×D4—941no—
339C2×D4—942no—
340C2×D4—948no—
341C2×D4—941no—
342C2×D4—941no—
343C2×D4—948no—
344C2×D4—948no—
345C2×D4—941no—
346C2×D4—942no—
347C2×D4—941no—
348C2×D4C22×D4711yescharacteristic
349C2×D4C22×D4711yescharacteristic
350C22×C4—471no—
351C22×C4—471no—
352C22×C4—941no—
353C22×C4—941no—
354C22×C4—941no—
355C22×C4—941no—
356C22×C4—941no—
357C22×C4C22×D4711yescharacteristic
358Q16—942no—
359SD16—22no—
360SD16—22no—
361SD16—942no—
362SD16—942no—
363D8—942no—
364D8—942no—
365D8—942no—
366M16—942no—
367C2×C8—471no—
368C2×C8—471no—
369C2×C8—942no—
370C2×C8C22×D4711yescharacteristic
371C2×C8C22×D4711yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—471no—
374C4⋊C4—941no—
375C4⋊C4—941no—
376C4⋊C4C22×D4711yescharacteristic
377C22⋊C4—21no—
378C22⋊C4—941no—
379C22⋊C4—941no—
380C22⋊C4—941no—
381C23—24no—
382C23—21no—
383C23—21no—
384C23—81no—
385C23—81no—
386C23—471no—
387C23—471no—
388C23—944no—
389C23—944no—
390C23—941no—
391C23—941no—
392C23—3761no—
393C23—3761no—
394C23—3761no—
395C23—3761no—
396C23D4×D4711yescharacteristic
397Q8—21no—
398Q8—21no—
399Q8—472no—
400Q8—942no—
401Q8—941no—
402D4—24no—
403D4—21no—
404D4—21no—
405D4—472no—
406D4—942no—
407D4—942no—
408D4—944no—
409D4—942no—
410D4—944no—
411D4—944no—
412D4—944no—
413D4—944no—
414D4—941no—
415D4—941no—
416D4—941no—
417D4—3761no—
418D4—3761no—
419D4—1882no—
420D4D4×D4712yes—
421D4D4×D4712yes—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—471no—
427C2×C4—472no—
428C2×C4—472no—
429C2×C4—471no—
430C2×C4—944no—
431C2×C4—944no—
432C2×C4—944no—
433C2×C4—941no—
434C2×C4—941no—
435C2×C4—941no—
436C2×C4—941no—
437C2×C4—3761no—
438C2×C4—1882no—
439C2×C4D4×D4711yescharacteristic
440C2×C4C23×D4711yescharacteristic
441C8—21no—
442C8—21no—
443C8—941no—
444C8—941no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—84no—
455C22—472no—
456C22—941no—
457C22—941no—
458C22—942no—
459C22—941no—
460C22—941no—
461C22—941no—
462C22—3764no—
463C22—3764no—
464C22—1881no—
465C22—1881no—
466C22—1881no—
467C22—1881no—
468C22—1881no—
469C22C2×D4×D4711yescharacteristic
470C4—21no—
471C4—41no—
472C4—41no—
473C4—472no—
474C4—941no—
475C4—942no—
476C4—1881no—
477C4C2×D4×D4711yescharacteristic
478C4C2×D4×D4711yescharacteristic
479C2—41no—
480C2—42no—
481C2—42no—
482C2—942no—
483C2—3761no—
484C2—1881no—
485C2—1882no—
486C2#120×D4711yescharacteristic
487C2#1568992711yescharacteristic
488C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#450C2
socleC22×C47C22×D4
hypercenter#450D47
hypocenterC47#3012
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#13094069C2semidirect
2. C2×#13094051C2semidirect
3. C2×#13094045C2semidirect
4. #15689703C2semidirect
5. #15689283C2semidirect
6. #15689282C2semidirect
7. #15689272C2semidirect
8. #15689270C2semidirect
9. #15689269C2semidirect
10. #15689258C2semidirect
11. #15689257C2semidirect
12. #15689121C2semidirect
13. #102×D47C2semidirect
14. #15689088C2semidirect
15. C47×#450C2semidirect
18. C2×#10625354C22semidirect
31. C2×#10625337C22semidirect
32. C2×#10625325C22semidirect
33. C2×#10625336C22semidirect
34. C2×D376C22semidirect
35. C2×#10625334C22semidirect
36. C2×#10625334C22semidirect
37. C2×#10625324C22semidirect
38. C2×C8×D47C22semidirect
40. #13094000C22semidirect
42. #13093999C22semidirect
43. #13093998C22semidirect
46. C4⋊C4×D47C22semidirect
47. #13093949C22semidirect
48. #13093947C22semidirect
49. #13093946C22semidirect
50. #13093945C22semidirect
51. #13093945C22semidirect
52. #13093944C22semidirect
53. C22⋊(C47⋊C8)C22semidirect
54. (C2×D47)⋊C8C22semidirect
55. (C2×D47)⋊C8C22semidirect
57. C2×SD16×C47C22semidirect
58. C2×SD16×C47C22semidirect
59. C22⋊Q8×C47C22semidirect
60. #102×C47C22semidirect
61. #102×C47C22semidirect
62. C22⋊C8×C47C22semidirect
91. #10625352D4semidirect
96. D4×D47D4semidirect
252. #450D47semidirect
260. C47#3012semidirect
280. C2×SD16C2×D47semidirect
281. C2×SD16C2×D47semidirect
289. C22⋊Q8C2×D47semidirect
302. #102C2×D47semidirect
303. #102C2×D47semidirect
307. C22⋊C8C2×D47semidirect