Finite Group Databasebeta

← D47×#2375 #26378852

Subgroups — D47×#2375 #26378852

Order 12032.

4246 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#120×D47C211yesmaximal, characteristic
2#20246529C211yesmaximal, characteristic, complemented
3#20246528C216yesmaximal, complemented
4#20246527C212yesmaximal, complemented
5#20246526C213yesmaximal, complemented
6#20246525C213yesmaximal, complemented
7#390×D47C213yesmaximal, complemented
8#388×D47C216yesmaximal, complemented
9#386×D47C213yesmaximal, complemented
10#379×D47C212yesmaximal, complemented
11C47×#2375C211yesmaximal, characteristic, complemented
12C25×D47C2211yescharacteristic
13C22×D4×D47C2213yes—
14C23×C4×D47C2211yescharacteristic, complemented
15C2×#13093994C2213yes—
16C2×#13093993C2211yescharacteristic
17C2×#13093992C2213yes—
18#120×D47C4116yescomplemented
19C2×C4⋊C4×D47C2213yescomplemented
20C2×C22⋊C4×D47C2216yes—
21C2×C22⋊C4×D47C2216yes—
22C2×C22⋊C4×D47C2213yes—
23C2×C22⋊C4×D47C2213yescomplemented
24C2×C42×D47C2213yescomplemented
25#15689026C2213yescomplemented
26#15689025C2213yescomplemented
27#15689024C2213yescomplemented
28#15689023C2216yescomplemented
29#15689023C2216yescomplemented
30#15689017C2216yescomplemented
31#15689016C2216yescomplemented
32#15689015C2216yescomplemented
33#15689014C2216yescomplemented
34#15689013C2216yescomplemented
35#15689012C2216yescomplemented
36#15689011C2216yescomplemented
37#15689003C2213yescomplemented
38#15689002C2213yescomplemented
39#15689001C2216yescomplemented
40#15689000C2213yescomplemented
41#15688999C2216yescomplemented
42#15688979C2212yescomplemented
43#15688978C2216yescomplemented
44#15688978C2216yescomplemented
45#95×D47C2216yescomplemented
46C2×#120×C47C2211yescharacteristic
47C47×#390C2213yescomplemented
48C47×#388C2216yescomplemented
49C47×#386C2213yescomplemented
50C47×#379C2212yescomplemented
51C24×D47—46no—
52C24×D47—46no—
53C24×D47C2×C418yescomplemented
54C24×D47C2313yes—
55C24×D47C2311yescharacteristic
56C24×D47C2313yes—
57C22×D188C2313yes—
58C22×C22⋊D47C2313yes—
59C22×C22⋊D47C2313yes—
60C2×D4×D47—46no—
61C2×D4×D47—46no—
62C2×D4×D47C2×C4124yes—
63C23×Dic47C2311yescharacteristic, complemented
64C22×C4×D47—46no—
65C22×C4×D47C2312yes—
66C22×C4×D47C2316yes—
67C22×C4×D47C2313yes—
68C22×C4×D47C2312yescomplemented
69#13093994C2×C4124yescomplemented
70#13093993C2×C418yescomplemented
71#13093992C2×C4124yescomplemented
72C2×C4⋊Dic47C2313yescomplemented
73C2×Dic47⋊C4C2316yescomplemented
74C4⋊C4×D47—46no—
75C2×C22⋊Dic47C2316yes—
76C2×C22⋊Dic47C2316yes—
77C2×C22⋊Dic47C2313yes—
78C2×C22⋊Dic47C2313yescomplemented
79C2×(C2×D47)⋊C4C2316yes—
80C2×(C2×D47)⋊C4C2316yes—
81C2×(C2×D47)⋊C4C2316yes—
82C2×(C2×D47)⋊C4C2316yes—
83C2×(C2×D47)⋊C4C2316yes—
84C2×(C2×D47)⋊C4C2316yescomplemented
85C22⋊C4×D47—412no—
86C22⋊C4×D47—412no—
87C22⋊C4×D47—46no—
88C22⋊C4×D47C2×C4124yescomplemented
89C2×C4×Dic47C2316yescomplemented
90C2×C4×Dic47C2313yescomplemented
91C42×D47—46no—
92C47⋊#95C2316yescomplemented
93C47⋊#95C2316yescomplemented
94C47⋊#95C2316yescomplemented
95C25×C47C2311yescharacteristic
96C22×D4×C47C2313yes—
97C23×C4×C47C2311yescharacteristic, complemented
98#120×C47C2×C418yescomplemented
99C2×C4⋊C4×C47C2313yescomplemented
100C2×C22⋊C4×C47C2316yes—
101C2×C22⋊C4×C47C2316yes—
102C2×C22⋊C4×C47C2313yes—
103C2×C22⋊C4×C47C2313yescomplemented
104C2×C42×C47C2313yescomplemented
105#95×C47C2316yescomplemented
106C24×C47—43no—
107C24×C47—43no—
108C24×C47C22×C414yescomplemented
109C24×C47C2413yes—
110C24×C47C2411yescharacteristic
111C23×D47—26no—
112C23×D47—212no—
113C23×D47—212no—
114C23×D47—26no—
115C23×D47—26no—
116C23×D47—26no—
117C23×D47—448no—
118C23×D47—43no—
119C23×D47—43no—
120C23×D47—46no—
121C23×D47—46no—
122C23×D47—448no—
123C23×D47—416no—
124C23×D47C22×C4112yes—
125C23×D47C22×C414yes—
126C23×D47C22×C4112yescomplemented
127C23×D47C2413yes—
128C23×D47C2411yescharacteristic
129C23×D47C2411yescharacteristic
130C2×D4×C47—43no—
131C2×D4×C47—43no—
132C2×D4×C47C22×C4112yes—
133C22×C4×C47—43no—
134C22×C4×C47C2416yes—
135C22×C4×C47C2412yes—
136C22×C4×C47C2413yes—
137C2×C22⋊D47—43no—
138C2×C22⋊D47—43no—
139C2×C22⋊D47—43no—
140C2×C22⋊D47—43no—
141C2×C22⋊D47C22×C4112yes—
142C2×C22⋊D47C22×C4112yes—
143C22×Dic47—43no—
144C22×Dic47C2412yes—
145C22×Dic47C2416yes—
146C22×Dic47C2413yes—
147D4×D47—448no—
148C2×D188—43no—
149C2×D188—43no—
150C2×D188C22×C4112yes—
151C2×C4×D47—26no—
152C2×C4×D47—26no—
153C2×C4×D47—212no—
154C2×C4×D47—212no—
155C2×C4×D47—212no—
156C2×C4×D47—212no—
157C2×C4×D47—46no—
158C2×C4×D47—416no—
159C2×C4×D47C22×C4112yes—
160C4⋊C4×C47—43no—
161C22⋊C4×C47—46no—
162C22⋊C4×C47—46no—
163C22⋊C4×C47—43no—
164C22⋊C4×C47C22×C4112yescomplemented
165C42×C47—43no—
166C22⋊Dic47—46no—
167C22⋊Dic47—46no—
168C22⋊Dic47—43no—
169C22⋊Dic47C22×C4112yescomplemented
170(C2×D47)⋊C4—46no—
171(C2×D47)⋊C4—46no—
172(C2×D47)⋊C4—46no—
173(C2×D47)⋊C4—46no—
174(C2×D47)⋊C4—46no—
175(C2×D47)⋊C4C22×C4124yescomplemented
176C4⋊Dic47—43no—
177Dic47⋊C4—46no—
178C4×Dic47—46no—
179C4×Dic47—43no—
180C23×C47—23no—
181C23×C47—26no—
182C23×C47—26no—
183C23×C47—23no—
184C23×C47—23no—
185C23×C47—23no—
186C23×C47—412no—
187C23×C47—412no—
188C23×C47—44no—
189C23×C47C23×C416yes—
190C23×C47C23×C412yes—
191C23×C47C2511yescharacteristic
192C22×D47—23no—
193C22×D47—26no—
194C22×D47—26no—
195C22×D47—23no—
196C22×D47—23no—
197C22×D47—23no—
198C22×D47—224no—
199C22×D47—224no—
200C22×D47—248no—
201C22×D47—424no—
202C22×D47—412no—
203C22×D47—424no—
204C22×D47—412no—
205C22×D47—412no—
206C22×D47—4128no—
207C22×D47—412no—
208C22×D47—412no—
209C22×D47—424no—
210C22×D47—44no—
211C22×D47—412no—
212C22×D47C23×C416yes—
213C22×D47C23×C412yes—
214C22×D47C23×C412yes—
215C22×D47H(5,𝔽2)16yes—
216C22×D47H(5,𝔽2)16yes—
217D4×C47—412no—
218C2×C4×C47—23no—
219C2×C4×C47—23no—
220C2×C4×C47—26no—
221C2×C4×C47—26no—
222C2×C4×C47—26no—
223C2×C4×C47—26no—
224C2×C4×C47—44no—
225C2×C4×C47C23×C416yes—
226C22⋊D47—412no—
227C22⋊D47—412no—
228C2×Dic47—23no—
229C2×Dic47—23no—
230C2×Dic47—26no—
231C2×Dic47—26no—
232C2×Dic47—26no—
233C2×Dic47—26no—
234C2×Dic47—44no—
235C2×Dic47C23×C416yes—
236D188—412no—
237C4×D47—224no—
238C4×D47—48no—
239C4×D47—424no—
240C4×D47—48no—
241C2×#2375—471nomaximal, Sylow
242C22×C47—26no—
243C22×C47—26no—
244C22×C47—212no—
245C22×C47—416no—
246C22×C47—43no—
247C22×C47—46no—
248C22×C47—43no—
249C22×C47—41no—
250C22×C47—43no—
251C22×C47C24×C411yescharacteristic
252C22×C47C2×H(5,𝔽2)13yes—
253C22×C47C2×H(5,𝔽2)13yes—
254C2×D47—26no—
255C2×D47—26no—
256C2×D47—212no—
257C2×D47—448no—
258C2×D47—43no—
259C2×D47—43no—
260C2×D47—46no—
261C2×D47—41no—
262C2×D47—43no—
263C2×D47—416no—
264C2×D47—448no—
265C2×D47#518112yes—
266C2×D47#560112yes—
267C2×D47H(3,𝔽4)14yes—
268C4×C47—26no—
269C4×C47—46no—
270C4×C47—42no—
271Dic47—26no—
272Dic47—46no—
273Dic47—42no—
274C22×#120—471no—
275#2375—473no—
276#2375—476no—
277#2375—473no—
278#2375—472no—
279#2375—471no—
280#2375D4711yescharacteristic, direct product factor
281C2×#390—473no—
282C2×#388—476no—
283C2×#386—473no—
284C2×#379—472no—
285C2×C47—46no—
286C2×C47—42no—
287C2×C47C2×#51813yes—
288C2×C47C2×#56013yes—
289C2×C47C2×H(3,𝔽4)11yescharacteristic
290D47—42no—
291D47—46no—
292D47#237518yesdirect product factor
293C26—471no—
294C23×D4—473no—
295C24×C4—471no—
296C2×#120—471no—
297C2×#120—473no—
298C2×#120—4716no—
299C2×#120—473no—
300C2×#120C2×D4711yescharacteristic
301C22×C4⋊C4—473no—
302C22×C22⋊C4—473no—
303C22×C22⋊C4—476no—
304C22×C22⋊C4—476no—
305C22×C22⋊C4—473no—
306C22×C42—473no—
307#390—473no—
308#390—473no—
309#390—476no—
310#390—476no—
311#390—473no—
312#390C2×D4713yescomplemented
313#388—476no—
314#388—476no—
315#388—476no—
316#388—476no—
317#388—476no—
318#388—476no—
319#388—476no—
320#388C2×D4716yescomplemented
321#386—473no—
322#386—473no—
323#386—476no—
324#386—473no—
325#386—476no—
326#386C2×D4713yescomplemented
327#379—472no—
328#379—476no—
329#379—476no—
330#379C2×D4712yescomplemented
331C2×#95—476no—
332C47C2×#237511yescharacteristic, complemented, Sylow
333C25—473no—
334C25—471no—
335C25—478no—
336C25—473no—
337C25—1886no—
338C25—1886no—
339C25C22×D4711yescharacteristic
340C22×D4—473no—
341C22×D4—473no—
342C22×D4—4724no—
343C22×D4—473no—
344C22×D4—1886no—
345C22×D4—1886no—
346C22×D4C22×D4713yes—
347C23×C4—473no—
348C23×C4—471no—
349C23×C4—476no—
350C23×C4—472no—
351C23×C4—472no—
352C23×C4—1886no—
353C23×C4C22×D4711yescharacteristic, complemented
354#120—478no—
355#120—4724no—
356#120—4724no—
357#120C4×D4718yescomplemented
358C2×C4⋊C4—476no—
359C2×C4⋊C4—473no—
360C2×C4⋊C4—1886no—
361C2×C4⋊C4C22×D4713yescomplemented
362C2×C22⋊C4—473no—
363C2×C22⋊C4—476no—
364C2×C22⋊C4—4724no—
365C2×C22⋊C4—476no—
366C2×C22⋊C4—476no—
367C2×C22⋊C4—473no—
368C2×C22⋊C4—476no—
369C2×C22⋊C4—476no—
370C2×C22⋊C4—476no—
371C2×C22⋊C4—476no—
372C2×C22⋊C4—476no—
373C2×C22⋊C4—18812no—
374C2×C22⋊C4—18812no—
375C2×C22⋊C4—1886no—
376C2×C22⋊C4C22×D4716yes—
377C2×C22⋊C4C22×D4716yes—
378C2×C22⋊C4C22×D4713yes—
379C2×C22⋊C4C22×D4713yescomplemented
380C2×C42—476no—
381C2×C42—473no—
382C2×C42—1886no—
383C2×C42C22×D4713yescomplemented
384#95—476no—
385#95—476no—
386#95—476no—
387#95C22×D4716yescomplemented
388C24—43no—
389C24—43no—
390C24—471no—
391C24—4712no—
392C24—474no—
393C24—473no—
394C24—471no—
395C24—4712no—
396C24—946no—
397C24—9412no—
398C24—9412no—
399C24—946no—
400C24—946no—
401C24—946no—
402C24—1886no—
403C24—1886no—
404C24—1883no—
405C24—1883no—
406C24—18848no—
407C24—18848no—
408C24—18816no—
409C24C2×C4×D4714yescomplemented
410C24C23×D4713yes—
411C24C23×D4711yescharacteristic
412C2×D4—43no—
413C2×D4—43no—
414C2×D4—4712no—
415C2×D4—4712no—
416C2×D4—4712no—
417C2×D4—1883no—
418C2×D4—1883no—
419C2×D4—18848no—
420C2×D4—1883no—
421C2×D4—1883no—
422C2×D4—1883no—
423C2×D4—1883no—
424C2×D4C2×C4×D47112yes—
425C22×C4—43no—
426C22×C4—473no—
427C22×C4—4712no—
428C22×C4—472no—
429C22×C4—476no—
430C22×C4—946no—
431C22×C4—946no—
432C22×C4—9412no—
433C22×C4—9412no—
434C22×C4—9412no—
435C22×C4—9412no—
436C22×C4—1886no—
437C22×C4—18816no—
438C22×C4—1883no—
439C22×C4C23×D4712yes—
440C22×C4C23×D4716yes—
441C22×C4C23×D4713yes—
442C4⋊C4—43no—
443C4⋊C4—1886no—
444C4⋊C4—1883no—
445C22⋊C4—46no—
446C22⋊C4—46no—
447C22⋊C4—43no—
448C22⋊C4—4712no—
449C22⋊C4—4724no—
450C22⋊C4—1886no—
451C22⋊C4—1886no—
452C22⋊C4—1886no—
453C22⋊C4—1886no—
454C22⋊C4—1886no—
455C22⋊C4—1886no—
456C22⋊C4—1883no—
457C22⋊C4—1886no—
458C22⋊C4C2×C4×D47112yescomplemented
459C42—43no—
460C42—1883no—
461C42—1886no—
462C23—23no—
463C23—26no—
464C23—26no—
465C23—23no—
466C23—23no—
467C23—23no—
468C23—412no—
469C23—412no—
470C23—44no—
471C23—472no—
472C23—476no—
473C23—476no—
474C23—476no—
475C23—472no—
476C23—9424no—
477C23—9424no—
478C23—9448no—
479C23—943no—
480C23—946no—
481C23—946no—
482C23—943no—
483C23—943no—
484C23—943no—
485C23—18812no—
486C23—18824no—
487C23—1884no—
488C23—18812no—
489C23—18812no—
490C23—18824no—
491C23—18812no—
492C23—188128no—
493C23—18812no—
494C23—18824no—
495C23—18812no—
496C23C22×C4×D4716yes—
497C23C22×C4×D4712yes—
498C23C24×D4711yescharacteristic
499D4—412no—
500D4—18812no—
501D4—18812no—
502D4—18812no—
503C2×C4—23no—
504C2×C4—23no—
505C2×C4—26no—
506C2×C4—26no—
507C2×C4—26no—
508C2×C4—26no—
509C2×C4—44no—
510C2×C4—476no—
511C2×C4—9424no—
512C2×C4—943no—
513C2×C4—943no—
514C2×C4—946no—
515C2×C4—946no—
516C2×C4—946no—
517C2×C4—946no—
518C2×C4—18824no—
519C2×C4—1888no—
520C2×C4—1888no—
521C2×C4—1884no—
522C2×C4C22×C4×D4716yes—
523C22—26no—
524C22—26no—
525C22—212no—
526C22—416no—
527C22—43no—
528C22—46no—
529C22—43no—
530C22—41no—
531C22—43no—
532C22—4712no—
533C22—4712no—
534C22—474no—
535C22—946no—
536C22—946no—
537C22—9412no—
538C22—18848no—
539C22—18816no—
540C22—18848no—
541C22—1883no—
542C22—1886no—
543C22—1883no—
544C22—1881no—
545C22—1883no—
546C22C23×C4×D4711yescharacteristic
547C22H(5,𝔽2)×D4713yes—
548C22H(5,𝔽2)×D4713yes—
549C4—26no—
550C4—46no—
551C4—42no—
552C4—946no—
553C4—1886no—
554C4—1882no—
555C2—46no—
556C2—42no—
557C2—478no—
558C2—1886no—
559C2—1882no—
560C2#518×D4713yes—
561C2#560×D4713yes—
562C2H(3,𝔽4)×D4711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC47×#2375C2
socle, cosocleC23×C47C25
prime radicalC2×#120×D47C2
hypercenter#2375D47
hypocenterC47C2×#2375
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2375

Complements

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

NH ≅ G/Ntype
2. #20246529C2semidirect
3. #20246528C2semidirect
4. #20246527C2semidirect
5. #20246526C2semidirect
6. #20246525C2semidirect
7. #390×D47C2semidirect
8. #388×D47C2semidirect
9. #386×D47C2semidirect
10. #379×D47C2semidirect
11. C47×#2375C2semidirect
14. C23×C4×D47C22semidirect
18. #120×D47C4semidirect
19. C2×C4⋊C4×D47C22semidirect
23. C2×C22⋊C4×D47C22semidirect
24. C2×C42×D47C22semidirect
25. #15689026C22semidirect
26. #15689025C22semidirect
27. #15689024C22semidirect
28. #15689023C22semidirect
29. #15689023C22semidirect
30. #15689017C22semidirect
31. #15689016C22semidirect
32. #15689015C22semidirect
33. #15689014C22semidirect
34. #15689013C22semidirect
35. #15689012C22semidirect
36. #15689011C22semidirect
37. #15689003C22semidirect
38. #15689002C22semidirect
39. #15689001C22semidirect
40. #15689000C22semidirect
41. #15688999C22semidirect
42. #15688979C22semidirect
43. #15688978C22semidirect
44. #15688978C22semidirect
45. #95×D47C22semidirect
47. C47×#390C22semidirect
48. C47×#388C22semidirect
49. C47×#386C22semidirect
50. C47×#379C22semidirect
53. C24×D47C2×C4semidirect
63. C23×Dic47C23semidirect
68. C22×C4×D47C23semidirect
69. #13093994C2×C4semidirect
70. #13093993C2×C4semidirect
71. #13093992C2×C4semidirect
72. C2×C4⋊Dic47C23semidirect
73. C2×Dic47⋊C4C23semidirect
78. C2×C22⋊Dic47C23semidirect
84. C2×(C2×D47)⋊C4C23semidirect
88. C22⋊C4×D47C2×C4semidirect
89. C2×C4×Dic47C23semidirect
90. C2×C4×Dic47C23semidirect
92. C47⋊#95C23semidirect
93. C47⋊#95C23semidirect
94. C47⋊#95C23semidirect
97. C23×C4×C47C23semidirect
98. #120×C47C2×C4semidirect
99. C2×C4⋊C4×C47C23semidirect
103. C2×C22⋊C4×C47C23semidirect
104. C2×C42×C47C23semidirect
105. #95×C47C23semidirect
108. C24×C47C22×C4semidirect
126. C23×D47C22×C4semidirect
164. C22⋊C4×C47C22×C4semidirect
169. C22⋊Dic47C22×C4semidirect
175. (C2×D47)⋊C4C22×C4semidirect
280. #2375D47direct (N × H)
292. D47#2375direct (N × H)
312. #390C2×D47semidirect
320. #388C2×D47semidirect
326. #386C2×D47semidirect
330. #379C2×D47semidirect
332. C47C2×#2375semidirect
353. C23×C4C22×D47semidirect
357. #120C4×D47semidirect
361. C2×C4⋊C4C22×D47semidirect
379. C2×C22⋊C4C22×D47semidirect
383. C2×C42C22×D47semidirect
387. #95C22×D47semidirect
409. C24C2×C4×D47semidirect
458. C22⋊C4C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#120×D472
#202465292
#202465282
#202465272
#202465262
#202465252
#390×D472
#388×D472
#386×D472
#379×D472
C47×#23752
C2×#237547