Finite Group Databasebeta

← D47×#2383 #26378935

Subgroups — D47×#2383 #26378935

Order 12032.

2502 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D47C211yesmaximal, characteristic
2#20246581C211yesmaximal, characteristic, complemented
3#20246580C211yesmaximal, characteristic, complemented
4#20246579C213yesmaximal, complemented
5#20246578C213yesmaximal, complemented
6#20246577C211yesmaximal, characteristic, complemented
7#20246576C213yesmaximal, complemented
8#20246575C213yesmaximal, complemented
9#389×D47C213yesmaximal, complemented
10#388×D47C213yesmaximal
11#387×D47C213yesmaximal, complemented
12#385×D47C213yesmaximal
13#384×D47C211yesmaximal, characteristic, complemented
14#383×D47C211yesmaximal, characteristic, complemented
15C47×#2383C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C2×#13094019C2213yes—
18C2×#13094018C2211yescharacteristic
19C2×#13094017C2213yes—
20#126×D47C4116yescomplemented
21C2×C4⋊C4×D47C2213yes—
22C2×C4⋊C4×D47C2213yes—
23C2×C4⋊C4×D47C2213yes—
24C2×C4⋊C4×D47C2213yes—
25C2×C22⋊C4×D47C2213yes—
26C2×C22⋊C4×D47C2213yes—
27C2×C42×D47C2213yes—
28C2×C42×D47C2211yescharacteristic
29#15689022C2213yescomplemented
30#15689021C2213yescomplemented
31#15689020C2213yescomplemented
32#15689020C2213yescomplemented
33#15689019C2213yescomplemented
34#15689018C2213yescomplemented
35#15689018C2213yescomplemented
36#15689017C2213yes—
37#15689016C2213yes—
38#15689015C2213yes—
39#15689014C2213yes—
40#15689013C2213yes—
41#15689012C2213yes—
42#15689011C2213yes—
43#15689010C2213yescomplemented
44#15689009C2213yescomplemented
45#15689008C2213yescomplemented
46#15689007C2213yescomplemented
47#15689006C2213yescomplemented
48#15689005C2213yescomplemented
49#15689004C2213yescomplemented
50#15688998C2213yes—
51#15688997C2213yes—
52#15688997C2213yes—
53#15688996C2213yes—
54#15688995C2213yes—
55#15688994C2213yes—
56#15688994C2213yes—
57#15688993C2211yescharacteristic, complemented
58#15688992C2213yescomplemented
59#15688992C2213yescomplemented
60#15688991C2211yescharacteristic, complemented
61#15688990C2213yescomplemented
62#15688990C2213yescomplemented
63#95×D47C2213yes—
64#95×D47C2213yes—
65#95×D47C2213yes—
66#95×D47C2213yes—
67C2×#126×C47C2211yescharacteristic
68C47×#389C2213yescomplemented
69C47×#388C2213yes—
70C47×#387C2213yescomplemented
71C47×#385C2213yes—
72C47×#384C2211yescharacteristic, complemented
73C47×#383C2211yescharacteristic, complemented
74C24×D47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C22×C4×D47—46no—
77C22×C4×D47C2313yes—
78C22×C4×D47C2311yescharacteristic
79C22×C4×D47C2311yescharacteristic
80C22×C4×D47C2313yes—
81C22×C4×D47C2313yes—
82C22×C4×D47C2313yes—
83C22×C4×D47C2311yescharacteristic
84C22×C4×D47C2311yescharacteristic
85#13094019C2×C4124yescomplemented
86#13094018C2×C418yescomplemented
87#13094017C2×C4124yescomplemented
88C2×C4⋊Dic47C2313yes—
89C2×C4⋊Dic47C2313yes—
90C2×C4⋊Dic47C2313yes—
91C2×C4⋊Dic47C2313yes—
92C2×Dic47⋊C4C2313yes—
93C2×Dic47⋊C4C2313yes—
94C2×Dic47⋊C4C2313yes—
95C2×Dic47⋊C4C2313yes—
96C2×Dic47⋊C4C2313yes—
97C2×Dic47⋊C4C2313yes—
98C2×Dic47⋊C4C2313yes—
99C2×Dic47⋊C4C2313yes—
100C4⋊C4×D47—46no—
101C4⋊C4×D47—46no—
102C4⋊C4×D47—46no—
103C4⋊C4×D47C2×C4124yescomplemented
104C2×C22⋊Dic47C2313yes—
105C2×C22⋊Dic47C2313yes—
106C2×(C2×D47)⋊C4C2313yes—
107C2×(C2×D47)⋊C4C2313yes—
108C2×(C2×D47)⋊C4C2313yes—
109C2×(C2×D47)⋊C4C2313yes—
110C22⋊C4×D47—46no—
111C22⋊C4×D47C2×C4124yes—
112C2×C4×Dic47C2313yes—
113C2×C4×Dic47C2313yes—
114C2×C4×Dic47C2313yes—
115C2×C4×Dic47C2313yes—
116C42×D47—46no—
117C42×D47C2×C418yescomplemented
118C47⋊#95C2313yes—
119C47⋊#95C2313yes—
120C47⋊#95C2313yes—
121C47⋊#95C2313yes—
122C47⋊#95C2313yes—
123C47⋊#95C2313yes—
124C47⋊#95C2313yes—
125C47⋊#95C2313yes—
126C47⋊#95C2313yes—
127C47⋊#95C2313yes—
128C47⋊#95C2313yes—
129C47⋊#95C2313yes—
130C23×C4×C47C2311yescharacteristic
131#126×C47C2×C418yescomplemented
132C2×C4⋊C4×C47C2313yes—
133C2×C4⋊C4×C47C2313yes—
134C2×C4⋊C4×C47C2313yes—
135C2×C4⋊C4×C47C2313yes—
136C2×C22⋊C4×C47C2313yes—
137C2×C22⋊C4×C47C2313yes—
138C2×C42×C47C2313yes—
139C2×C42×C47C2311yescharacteristic
140#95×C47C2313yes—
141#95×C47C2313yes—
142#95×C47C2313yes—
143#95×C47C2313yes—
144C24×C47C2411yescharacteristic
145C23×D47—26no—
146C23×D47—26no—
147C23×D47C22×C414yes—
148C23×D47C2411yescharacteristic
149C23×D47C2411yescharacteristic
150C22×C4×C47—43no—
151C22×C4×C47C2413yes—
152C22×C4×C47C2413yes—
153C22×C4×C47C2411yescharacteristic
154C22×C4×C47C2411yescharacteristic
155C22×C4×C47C2413yes—
156C22×C4×C47C2413yes—
157C22×Dic47—43no—
158C22×Dic47C2413yes—
159C22×Dic47C2411yescharacteristic
160C22×Dic47C2411yescharacteristic
161C22×Dic47C2413yes—
162C22×Dic47C2413yes—
163C22×Dic47C2413yes—
164C2×C4×D47—26no—
165C2×C4×D47—26no—
166C2×C4×D47—26no—
167C2×C4×D47—26no—
168C2×C4×D47—26no—
169C2×C4×D47—26no—
170C2×C4×D47—26no—
171C2×C4×D47—26no—
172C2×C4×D47—26no—
173C2×C4×D47—26no—
174C2×C4×D47—212no—
175C2×C4×D47—43no—
176C2×C4×D47—43no—
177C2×C4×D47—416no—
178C2×C4×D47C22×C4112yes—
179C2×C4×D47C22×C4112yes—
180C4⋊C4×C47—43no—
181C4⋊C4×C47—43no—
182C4⋊C4×C47—43no—
183C4⋊C4×C47C22×C4112yescomplemented
184C22⋊C4×C47—43no—
185C22⋊C4×C47C22×C4112yes—
186C42×C47—43no—
187C42×C47C22×C414yescomplemented
188C22⋊Dic47—43no—
189C22⋊Dic47C22×C4112yes—
190(C2×D47)⋊C4—43no—
191(C2×D47)⋊C4—43no—
192(C2×D47)⋊C4C22×C4112yes—
193(C2×D47)⋊C4C22×C4112yes—
194C4⋊Dic47—43no—
195C4⋊Dic47—43no—
196C4⋊Dic47—43no—
197C4⋊Dic47C22×C4112yescomplemented
198Dic47⋊C4—43no—
199Dic47⋊C4—43no—
200Dic47⋊C4—43no—
201Dic47⋊C4—43no—
202Dic47⋊C4—43no—
203Dic47⋊C4—43no—
204Dic47⋊C4C22×C4112yescomplemented
205Dic47⋊C4C22×C4112yescomplemented
206C4×Dic47—43no—
207C4×Dic47—43no—
208C4×Dic47—43no—
209C4×Dic47C22×C4112yescomplemented
210C23×C47—23no—
211C23×C47—23no—
212C23×C47C23×C412yes—
213C23×C47C2511yescharacteristic
214C22×D47—23no—
215C22×D47—23no—
216C22×D47—224no—
217C22×D47—44no—
218C22×D47—412no—
219C22×D47C23×C412yes—
220C22×D47C23×C412yes—
221C22×D47H(5,𝔽2)16yes—
222C22×D472−1+416yes—
223C2×C4×C47—23no—
224C2×C4×C47—23no—
225C2×C4×C47—23no—
226C2×C4×C47—23no—
227C2×C4×C47—23no—
228C2×C4×C47—23no—
229C2×C4×C47—23no—
230C2×C4×C47—23no—
231C2×C4×C47—23no—
232C2×C4×C47—23no—
233C2×C4×C47—26no—
234C2×C4×C47—44no—
235C2×C4×C47C23×C416yes—
236C2×C4×C47C23×C416yes—
237C2×Dic47—23no—
238C2×Dic47—23no—
239C2×Dic47—23no—
240C2×Dic47—23no—
241C2×Dic47—23no—
242C2×Dic47—23no—
243C2×Dic47—23no—
244C2×Dic47—23no—
245C2×Dic47—23no—
246C2×Dic47—23no—
247C2×Dic47—26no—
248C2×Dic47—44no—
249C2×Dic47C23×C416yes—
250C2×Dic47C23×C416yes—
251C4×D47—224no—
252C4×D47—224no—
253C4×D47—44no—
254C4×D47—44no—
255C4×D47—412no—
256C4×D47—44no—
257C4×D47—44no—
258C4×D47—412no—
259C2×#2383—471nomaximal, Sylow
260C22×C47—26no—
261C22×C47—41no—
262C22×C47—43no—
263C22×C47C24×C411yescharacteristic
264C22×C47C2×H(5,𝔽2)13yes—
265C22×C47C2×2−1+413yes—
266C2×D47—26no—
267C2×D47—41no—
268C2×D47—43no—
269C2×D47—416no—
270C2×D47#520112yes—
271C2×D47#56014yes—
272C2×D47#563112yes—
273C4×C47—26no—
274C4×C47—26no—
275C4×C47—41no—
276C4×C47—41no—
277C4×C47—43no—
278C4×C47—43no—
279Dic47—26no—
280Dic47—26no—
281Dic47—41no—
282Dic47—41no—
283Dic47—43no—
284Dic47—43no—
285C22×#126—471no—
286#2383—473no—
287#2383—473no—
288#2383—473no—
289#2383—473no—
290#2383—471no—
291#2383—471no—
292#2383—471no—
293#2383D4711yescharacteristic, direct product factor
294C2×#389—473no—
295C2×#388—473no—
296C2×#387—473no—
297C2×#385—473no—
298C2×#384—471no—
299C2×#383—471no—
300C2×C47—42no—
301C2×C47C2×#52013yes—
302C2×C47C2×#56011yescharacteristic
303C2×C47C2×#56313yes—
304D47—42no—
305D47#238318yesdirect product factor
306C24×C4—471no—
307C2×#126—4716no—
308C2×#126—473no—
309C2×#126—473no—
310C2×#126—471no—
311C2×#126C2×D4711yescharacteristic
312C22×C4⋊C4—473no—
313C22×C4⋊C4—473no—
314C22×C4⋊C4—473no—
315C22×C4⋊C4—473no—
316C22×C22⋊C4—473no—
317C22×C22⋊C4—473no—
318C22×C42—471no—
319C22×C42—473no—
320#389—473no—
321#389—473no—
322#389—473no—
323#389—473no—
324#389—473no—
325#389—473no—
326#389—473no—
327#389C2×D4713yescomplemented
328#388—473no—
329#388—473no—
330#388—473no—
331#388—473no—
332#388—473no—
333#388—473no—
334#388—473no—
335#388C2×D4713yes—
336#387—473no—
337#387—473no—
338#387—473no—
339#387—473no—
340#387—473no—
341#387—473no—
342#387—473no—
343#387C2×D4713yescomplemented
344#385—473no—
345#385—473no—
346#385—473no—
347#385—473no—
348#385—473no—
349#385—473no—
350#385—473no—
351#385C2×D4713yes—
352#384—473no—
353#384—473no—
354#384—471no—
355#384C2×D4711yescharacteristic, complemented
356#383—471no—
357#383—473no—
358#383—473no—
359#383C2×D4711yescharacteristic, complemented
360C2×#95—473no—
361C2×#95—473no—
362C2×#95—473no—
363C2×#95—473no—
364C47C2×#238311yescharacteristic, complemented, Sylow
365C25—471no—
366C23×C4—473no—
367C23×C4—473no—
368C23×C4—471no—
369C23×C4—473no—
370C23×C4—473no—
371C23×C4—471no—
372C23×C4—471no—
373C23×C4—471no—
374C23×C4—471no—
375C23×C4—1886no—
376C23×C4C22×D4711yescharacteristic
377#126—4724no—
378#126—4724no—
379#126—478no—
380#126C4×D4718yescomplemented
381C2×C4⋊C4—473no—
382C2×C4⋊C4—473no—
383C2×C4⋊C4—473no—
384C2×C4⋊C4—4724no—
385C2×C4⋊C4—473no—
386C2×C4⋊C4—473no—
387C2×C4⋊C4—473no—
388C2×C4⋊C4—473no—
389C2×C4⋊C4—473no—
390C2×C4⋊C4—473no—
391C2×C4⋊C4—473no—
392C2×C4⋊C4—473no—
393C2×C4⋊C4—473no—
394C2×C4⋊C4—1886no—
395C2×C4⋊C4—1886no—
396C2×C4⋊C4—1886no—
397C2×C4⋊C4C22×D4713yes—
398C2×C4⋊C4C22×D4713yes—
399C2×C4⋊C4C22×D4713yes—
400C2×C4⋊C4C22×D4713yes—
401C2×C22⋊C4—473no—
402C2×C22⋊C4—473no—
403C2×C22⋊C4—473no—
404C2×C22⋊C4—4724no—
405C2×C22⋊C4—473no—
406C2×C22⋊C4—473no—
407C2×C22⋊C4—473no—
408C2×C22⋊C4—1886no—
409C2×C22⋊C4C22×D4713yes—
410C2×C22⋊C4C22×D4713yes—
411C2×C42—473no—
412C2×C42—478no—
413C2×C42—473no—
414C2×C42—473no—
415C2×C42—473no—
416C2×C42—1886no—
417C2×C42C22×D4713yes—
418C2×C42C22×D4711yescharacteristic
419#95—473no—
420#95—473no—
421#95—473no—
422#95—473no—
423#95—473no—
424#95—473no—
425#95—473no—
426#95—473no—
427#95—473no—
428#95—473no—
429#95—473no—
430#95—473no—
431#95C22×D4713yes—
432#95C22×D4713yes—
433#95C22×D4713yes—
434#95C22×D4713yes—
435C24—471no—
436C24—474no—
437C24—471no—
438C24—946no—
439C24—946no—
440C24C23×D4711yescharacteristic
441C22×C4—43no—
442C22×C4—473no—
443C22×C4—473no—
444C22×C4—4712no—
445C22×C4—4712no—
446C22×C4—473no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—473no—
450C22×C4—946no—
451C22×C4—946no—
452C22×C4—946no—
453C22×C4—946no—
454C22×C4—946no—
455C22×C4—946no—
456C22×C4—946no—
457C22×C4—946no—
458C22×C4—946no—
459C22×C4—946no—
460C22×C4—9412no—
461C22×C4—1883no—
462C22×C4—1883no—
463C22×C4—18816no—
464C22×C4—1883no—
465C22×C4C23×D4713yes—
466C22×C4C23×D4711yescharacteristic
467C22×C4C23×D4711yescharacteristic
468C22×C4C23×D4713yes—
469C22×C4C23×D4713yes—
470C22×C4C23×D4713yes—
471C4⋊C4—43no—
472C4⋊C4—43no—
473C4⋊C4—43no—
474C4⋊C4—4712no—
475C4⋊C4—4712no—
476C4⋊C4—4712no—
477C4⋊C4—1883no—
478C4⋊C4—1883no—
479C4⋊C4—1883no—
480C4⋊C4—1883no—
481C4⋊C4—1883no—
482C4⋊C4—1883no—
483C4⋊C4—1883no—
484C4⋊C4—1883no—
485C4⋊C4—1883no—
486C4⋊C4C2×C4×D47112yescomplemented
487C22⋊C4—43no—
488C22⋊C4—4712no—
489C22⋊C4—4712no—
490C22⋊C4—4712no—
491C22⋊C4—1883no—
492C22⋊C4—1883no—
493C22⋊C4—1883no—
494C22⋊C4C2×C4×D47112yes—
495C42—43no—
496C42—4712no—
497C42—1883no—
498C42—1883no—
499C42—1883no—
500C42C2×C4×D4714yescomplemented
501C23—23no—
502C23—23no—
503C23—472no—
504C23—476no—
505C23—476no—
506C23—472no—
507C23—9424no—
508C23—943no—
509C23—943no—
510C23—1884no—
511C23—18812no—
512C23C22×C4×D4712yes—
513C23C24×D4711yescharacteristic
514C2×C4—23no—
515C2×C4—23no—
516C2×C4—23no—
517C2×C4—23no—
518C2×C4—23no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—26no—
525C2×C4—44no—
526C2×C4—476no—
527C2×C4—476no—
528C2×C4—9424no—
529C2×C4—9424no—
530C2×C4—943no—
531C2×C4—943no—
532C2×C4—943no—
533C2×C4—943no—
534C2×C4—943no—
535C2×C4—943no—
536C2×C4—943no—
537C2×C4—943no—
538C2×C4—943no—
539C2×C4—943no—
540C2×C4—946no—
541C2×C4—18812no—
542C2×C4—18812no—
543C2×C4—1884no—
544C2×C4—1884no—
545C2×C4—1884no—
546C2×C4—1884no—
547C2×C4—1884no—
548C2×C4C22×C4×D4716yes—
549C2×C4C22×C4×D4716yes—
550C22—26no—
551C22—41no—
552C22—43no—
553C22—4712no—
554C22—474no—
555C22—4712no—
556C22—946no—
557C22—18816no—
558C22—1881no—
559C22—1883no—
560C22C23×C4×D4711yescharacteristic
561C22H(5,𝔽2)×D4713yes—
562C222−1+4×D4713yes—
563C4—26no—
564C4—26no—
565C4—41no—
566C4—41no—
567C4—43no—
568C4—43no—
569C4—946no—
570C4—946no—
571C4—1881no—
572C4—1881no—
573C4—1883no—
574C4—1883no—
575C2—42no—
576C2—478no—
577C2—1882no—
578C2#520×D4713yes—
579C2#560×D4711yescharacteristic
580C2#563×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2383C2
socle, cosocleC23×C47C25
prime radicalC24×D47C23
hypercenter#2383D47
hypocenterC47C2×#2383
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2383

Complements

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

NH ≅ G/Ntype
2. #20246581C2semidirect
3. #20246580C2semidirect
4. #20246579C2semidirect
5. #20246578C2semidirect
6. #20246577C2semidirect
7. #20246576C2semidirect
8. #20246575C2semidirect
9. #389×D47C2semidirect
11. #387×D47C2semidirect
13. #384×D47C2semidirect
14. #383×D47C2semidirect
15. C47×#2383C2semidirect
20. #126×D47C4semidirect
29. #15689022C22semidirect
30. #15689021C22semidirect
31. #15689020C22semidirect
32. #15689020C22semidirect
33. #15689019C22semidirect
34. #15689018C22semidirect
35. #15689018C22semidirect
43. #15689010C22semidirect
44. #15689009C22semidirect
45. #15689008C22semidirect
46. #15689007C22semidirect
47. #15689006C22semidirect
48. #15689005C22semidirect
49. #15689004C22semidirect
57. #15688993C22semidirect
58. #15688992C22semidirect
59. #15688992C22semidirect
60. #15688991C22semidirect
61. #15688990C22semidirect
62. #15688990C22semidirect
68. C47×#389C22semidirect
70. C47×#387C22semidirect
72. C47×#384C22semidirect
73. C47×#383C22semidirect
85. #13094019C2×C4semidirect
86. #13094018C2×C4semidirect
87. #13094017C2×C4semidirect
103. C4⋊C4×D47C2×C4semidirect
117. C42×D47C2×C4semidirect
131. #126×C47C2×C4semidirect
183. C4⋊C4×C47C22×C4semidirect
187. C42×C47C22×C4semidirect
197. C4⋊Dic47C22×C4semidirect
204. Dic47⋊C4C22×C4semidirect
205. Dic47⋊C4C22×C4semidirect
209. C4×Dic47C22×C4semidirect
293. #2383D47direct (N × H)
305. D47#2383direct (N × H)
327. #389C2×D47semidirect
343. #387C2×D47semidirect
355. #384C2×D47semidirect
359. #383C2×D47semidirect
364. C47C2×#2383semidirect
380. #126C4×D47semidirect
486. C4⋊C4C2×C4×D47semidirect
500. C42C2×C4×D47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#126×D472
#202465812
#202465802
#202465792
#202465782
#202465772
#202465762
#202465752
#389×D472
#388×D472
#387×D472
#385×D472
#384×D472
#383×D472
C47×#23832
C2×#238347