Finite Group Databasebeta

← D47×#2401 #26382573

Subgroups — D47×#2401 #26382573

Order 12032.

2294 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246691C211yesmaximal, characteristic, complemented
2#20246690C211yesmaximal, characteristic, complemented
3#20246689C213yesmaximal, complemented
4#20246688C213yesmaximal, complemented
5#20246687C213yesmaximal, complemented
6#20246686C211yesmaximal, characteristic, complemented
7#20246685C213yesmaximal, complemented
8#401×D47C211yesmaximal, characteristic, complemented
9#400×D47C213yesmaximal, complemented
10#397×D47C213yesmaximal
11#396×D47C211yesmaximal, characteristic
12C4×C4⋊C4×D47C213yesmaximal, complemented
13C4×C22⋊C4×D47C213yesmaximal
14#376×D47C211yesmaximal, characteristic, complemented
15C47×#2401C211yesmaximal, characteristic, complemented
16C23×C4×D47C2211yescharacteristic
17C2×C4⋊C4×D47C2213yes—
18C2×C4⋊C4×D47C2213yes—
19C2×C22⋊C4×D47C2213yes—
20C2×C22⋊C4×D47C2213yes—
21C2×C42×D47C2213yes—
22C2×C42×D47C2213yes—
23C47⋊#401C2213yescomplemented
24C47⋊#401C2211yescharacteristic, complemented
25C47⋊#401C2213yescomplemented
26#15689065C2213yescomplemented
27#15689065C2213yescomplemented
28#15689064C2213yescomplemented
29#15689064C2213yescomplemented
30#15689063C2213yescomplemented
31#15689062C2213yescomplemented
32#15689061C2213yescomplemented
33#15689052C2213yes—
34#15689052C2213yes—
35#15689051C2213yes—
36#15689051C2213yes—
37#15689050C2213yes—
38#15689049C2213yes—
39#15689048C2213yes—
40#15689047C2211yescharacteristic
41#15689046C2213yes—
42#15689045C2213yes—
43C4⋊C4×Dic47C2213yescomplemented
44C4⋊C4×Dic47C2213yescomplemented
45C4×Dic47⋊C4C2213yescomplemented
46C4×Dic47⋊C4C2213yescomplemented
47C4×C4⋊Dic47C2213yescomplemented
48#15688974C2213yescomplemented
49#15688974C2213yescomplemented
50C22⋊C4×Dic47C2213yes—
51C22⋊C4×Dic47C2213yes—
52C4×(C2×D47)⋊C4C2213yes—
53C4×(C2×D47)⋊C4C2213yes—
54C4×C22⋊Dic47C2213yes—
55#15688970C2213yes—
56#15688970C2213yes—
57#15688969C2213yescomplemented
58#15688968C2213yescomplemented
59#15688968C2211yescharacteristic, complemented
60#95×D47C2211yescharacteristic
61#95×D47C2213yes—
62#95×D47C2213yes—
63#95×D47C2213yes—
64#95×D47C2213yes—
65#95×D47C2213yes—
66C47×#401C2211yescharacteristic, complemented
67C47×#400C2213yescomplemented
68C47×#397C2213yes—
69C47×#396C2211yescharacteristic
70C4×C4⋊C4×C47C2213yescomplemented
71C4×C22⋊C4×C47C2213yes—
72C47×#376C2211yescharacteristic, complemented
73C24×D47C2311yescharacteristic
74C23×Dic47C2311yescharacteristic
75C22×C4×D47—212no—
76C22×C4×D47C2311yescharacteristic
77C22×C4×D47C2313yes—
78C22×C4×D47C2313yes—
79C22×C4×D47C2313yes—
80C22×C4×D47C2311yescharacteristic
81C22×C4×D47C2311yescharacteristic
82C22×C4×D47C2313yes—
83C22×C4×D47C2311yescharacteristic
84C2×C4⋊Dic47C2313yes—
85C2×C4⋊Dic47C2313yes—
86C2×Dic47⋊C4C2313yes—
87C2×Dic47⋊C4C2313yes—
88C2×Dic47⋊C4C2313yes—
89C2×Dic47⋊C4C2313yes—
90C4⋊C4×D47—212no—
91C4⋊C4×D47—212no—
92C2×C22⋊Dic47C2313yes—
93C2×C22⋊Dic47C2313yes—
94C2×(C2×D47)⋊C4C2313yes—
95C2×(C2×D47)⋊C4C2313yes—
96C2×(C2×D47)⋊C4C2313yes—
97C2×(C2×D47)⋊C4C2313yes—
98C22⋊C4×D47—212no—
99C22⋊C4×D47—212no—
100C2×C4×Dic47C2313yes—
101C2×C4×Dic47C2313yes—
102C2×C4×Dic47C2313yes—
103C2×C4×Dic47C2313yes—
104C2×C4×Dic47C2313yes—
105C2×C4×Dic47C2313yes—
106C42×D47—212no—
107C42×D47—212no—
108C47⋊#95C2313yes—
109C47⋊#95C2313yes—
110C47⋊#95C2313yes—
111C47⋊#95C2313yes—
112C47⋊#95C2313yes—
113C47⋊#95C2313yes—
114C47⋊#95C2313yes—
115C47⋊#95C2313yes—
116C47⋊#95C2313yes—
117C47⋊#95C2313yes—
118C47⋊#95C2313yes—
119C47⋊#95C2313yes—
120C47⋊#95C2313yes—
121C47⋊#95C2313yes—
122C47⋊#95C2313yes—
123C47⋊#95C2313yes—
124C23×C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2313yes—
126C2×C4⋊C4×C47C2313yes—
127C2×C22⋊C4×C47C2313yes—
128C2×C22⋊C4×C47C2313yes—
129C2×C42×C47C2313yes—
130C2×C42×C47C2313yes—
131#95×C47C2311yescharacteristic
132#95×C47C2313yes—
133#95×C47C2313yes—
134#95×C47C2313yes—
135#95×C47C2313yes—
136#95×C47C2313yes—
137C24×C47C2411yescharacteristic
138C23×D47—26no—
139C23×D47—26no—
140C23×D47#4114yes—
141C23×D47C2411yescharacteristic
142C23×D47C2411yescharacteristic
143C22×C4×C47—26no—
144C22×C4×C47C2413yes—
145C22×C4×C47C2413yes—
146C22×C4×C47C2413yes—
147C22×C4×C47C2411yescharacteristic
148C22×C4×C47C2413yes—
149C22×C4×C47C2411yescharacteristic
150C22×Dic47—26no—
151C22×Dic47C2411yescharacteristic
152C22×Dic47C2413yes—
153C22×Dic47C2413yes—
154C22×Dic47C2413yes—
155C22×Dic47C2413yes—
156C22×Dic47C2411yescharacteristic
157C2×C4×D47—26no—
158C2×C4×D47—26no—
159C2×C4×D47—26no—
160C2×C4×D47—26no—
161C2×C4×D47—26no—
162C2×C4×D47—26no—
163C2×C4×D47—26no—
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—416no—
172C2×C4×D47#41112yes—
173C2×C4×D47#41112yes—
174C4⋊C4×C47—26no—
175C4⋊C4×C47—26no—
176C22⋊C4×C47—26no—
177C22⋊C4×C47—26no—
178C42×C47—26no—
179C42×C47—26no—
180C22⋊Dic47—26no—
181C22⋊Dic47—26no—
182(C2×D47)⋊C4—26no—
183(C2×D47)⋊C4—26no—
184(C2×D47)⋊C4—26no—
185(C2×D47)⋊C4—26no—
186C4⋊Dic47—26no—
187C4⋊Dic47—26no—
188Dic47⋊C4—26no—
189Dic47⋊C4—26no—
190Dic47⋊C4—26no—
191Dic47⋊C4—26no—
192C4×Dic47—26no—
193C4×Dic47—26no—
194C4×Dic47—26no—
195C4×Dic47—26no—
196C4×Dic47—26no—
197C4×Dic47—26no—
198C23×C47—23no—
199C23×C47—23no—
200C23×C47C2×#4112yes—
201C23×C47C2511yescharacteristic
202C22×D47—23no—
203C22×D47—23no—
204C22×D47—224no—
205C22×D47—44no—
206C22×D47—412no—
207C22×D47C2×#4112yes—
208C22×D47C2×#4116yes—
209C22×D47C2×#4112yes—
210C22×D47C2×#4116yes—
211C2×C4×C47—23no—
212C2×C4×C47—23no—
213C2×C4×C47—23no—
214C2×C4×C47—23no—
215C2×C4×C47—23no—
216C2×C4×C47—23no—
217C2×C4×C47—23no—
218C2×C4×C47—23no—
219C2×C4×C47—23no—
220C2×C4×C47—23no—
221C2×C4×C47—23no—
222C2×C4×C47—23no—
223C2×C4×C47—44no—
224C2×C4×C47C2×#4116yes—
225C2×C4×C47C2×#4116yes—
226C2×Dic47—23no—
227C2×Dic47—23no—
228C2×Dic47—23no—
229C2×Dic47—23no—
230C2×Dic47—23no—
231C2×Dic47—23no—
232C2×Dic47—23no—
233C2×Dic47—23no—
234C2×Dic47—23no—
235C2×Dic47—23no—
236C2×Dic47—23no—
237C2×Dic47—23no—
238C2×Dic47—44no—
239C2×Dic47C2×#4116yes—
240C2×Dic47C2×#4116yes—
241C4×D47—224no—
242C4×D47—44no—
243C4×D47—412no—
244C4×D47—412no—
245C4×D47—412no—
246C4×D47—44no—
247C4×D47—44no—
248C4×D47#126116yes—
249C2×#2401—471nomaximal, Sylow
250C22×C47—26no—
251C22×C47—41no—
252C22×C47—43no—
253C22×C47C22×#4113yes—
254C22×C47C22×#4111yescharacteristic
255C22×C47C22×#4113yes—
256C2×D47—26no—
257C2×D47—41no—
258C2×D47—43no—
259C2×D47—416no—
260C2×D47C2×#12614yes—
261C2×D47#529112yes—
262C2×D47#529112yes—
263C4×C47—26no—
264C4×C47—41no—
265C4×C47—43no—
266C4×C47—43no—
267C4×C47—43no—
268C4×C47C2×#12614yes—
269Dic47—26no—
270Dic47—41no—
271Dic47—43no—
272Dic47—43no—
273Dic47—43no—
274Dic47C2×#12614yes—
275#2401—471no—
276#2401—473no—
277#2401—473no—
278#2401—471no—
279#2401—473no—
280#2401—473no—
281#2401—471no—
282#2401D4711yescharacteristic, direct product factor
283C2×#401—471no—
284C2×#400—473no—
285C2×#397—473no—
286C2×#396—471no—
287C2×C4×C4⋊C4—473no—
288C2×C4×C22⋊C4—473no—
289C2×#376—471no—
290C2×C47—42no—
291C2×C47C22×#12611yescharacteristic
292C2×C47C2×#52913yes—
293C2×C47C2×#52913yes—
294D47—42no—
295D47#240118yesdirect product factor
296C24×C4—471no—
297C22×C4⋊C4—473no—
298C22×C4⋊C4—473no—
299C22×C22⋊C4—473no—
300C22×C22⋊C4—473no—
301C22×C42—473no—
302C22×C42—473no—
303#401—473no—
304#401—473no—
305#401—471no—
306#401C2×D4711yescharacteristic, complemented
307#400—473no—
308#400—473no—
309#400—473no—
310#400—473no—
311#400—473no—
312#400—473no—
313#400—473no—
314#400C2×D4713yescomplemented
315#397—473no—
316#397—473no—
317#397—473no—
318#397—473no—
319#397—473no—
320#397—473no—
321#397—473no—
322#397C2×D4713yes—
323#396—473no—
324#396—473no—
325#396—471no—
326#396C2×D4711yescharacteristic
327C4×C4⋊C4—473no—
328C4×C4⋊C4—473no—
329C4×C4⋊C4—473no—
330C4×C4⋊C4—473no—
331C4×C4⋊C4—473no—
332C4×C4⋊C4—473no—
333C4×C4⋊C4—473no—
334C4×C4⋊C4C2×D4713yescomplemented
335C4×C22⋊C4—473no—
336C4×C22⋊C4—473no—
337C4×C22⋊C4—473no—
338C4×C22⋊C4—473no—
339C4×C22⋊C4—473no—
340C4×C22⋊C4—473no—
341C4×C22⋊C4—473no—
342C4×C22⋊C4C2×D4713yes—
343#376—473no—
344#376—473no—
345#376—471no—
346#376C2×D4711yescharacteristic, complemented
347C2×#95—471no—
348C2×#95—473no—
349C2×#95—473no—
350C2×#95—473no—
351C2×#95—473no—
352C2×#95—473no—
353C47C2×#240111yescharacteristic, complemented, Sylow
354C25—471no—
355C23×C4—471no—
356C23×C4—473no—
357C23×C4—471no—
358C23×C4—473no—
359C23×C4—473no—
360C23×C4—473no—
361C23×C4—471no—
362C23×C4—471no—
363C23×C4—471no—
364C23×C4—9412no—
365C23×C4C22×D4711yescharacteristic
366C2×C4⋊C4—473no—
367C2×C4⋊C4—473no—
368C2×C4⋊C4—473no—
369C2×C4⋊C4—473no—
370C2×C4⋊C4—473no—
371C2×C4⋊C4—473no—
372C2×C4⋊C4—9412no—
373C2×C4⋊C4—9412no—
374C2×C4⋊C4C22×D4713yes—
375C2×C4⋊C4C22×D4713yes—
376C2×C22⋊C4—473no—
377C2×C22⋊C4—473no—
378C2×C22⋊C4—473no—
379C2×C22⋊C4—473no—
380C2×C22⋊C4—473no—
381C2×C22⋊C4—473no—
382C2×C22⋊C4—9412no—
383C2×C22⋊C4—9412no—
384C2×C22⋊C4C22×D4713yes—
385C2×C22⋊C4C22×D4713yes—
386C2×C42—473no—
387C2×C42—473no—
388C2×C42—473no—
389C2×C42—473no—
390C2×C42—473no—
391C2×C42—473no—
392C2×C42—9412no—
393C2×C42—9412no—
394C2×C42C22×D4713yes—
395C2×C42C22×D4713yes—
396#95—473no—
397#95—473no—
398#95—473no—
399#95—473no—
400#95—473no—
401#95—473no—
402#95—473no—
403#95—473no—
404#95—473no—
405#95—473no—
406#95—473no—
407#95—473no—
408#95—473no—
409#95—473no—
410#95—473no—
411#95—473no—
412#95C22×D4711yescharacteristic
413#95C22×D4713yes—
414#95C22×D4713yes—
415#95C22×D4713yes—
416#95C22×D4713yes—
417#95C22×D4713yes—
418C24—471no—
419C24—474no—
420C24—471no—
421C24—946no—
422C24—946no—
423C24C23×D4711yescharacteristic
424C22×C4—26no—
425C22×C4—471no—
426C22×C4—4712no—
427C22×C4—473no—
428C22×C4—4712no—
429C22×C4—471no—
430C22×C4—473no—
431C22×C4—473no—
432C22×C4—473no—
433C22×C4—946no—
434C22×C4—946no—
435C22×C4—946no—
436C22×C4—946no—
437C22×C4—946no—
438C22×C4—946no—
439C22×C4—946no—
440C22×C4—946no—
441C22×C4—946no—
442C22×C4—946no—
443C22×C4—946no—
444C22×C4—946no—
445C22×C4—946no—
446C22×C4—946no—
447C22×C4—946no—
448C22×C4—18816no—
449C22×C4C23×D4711yescharacteristic
450C22×C4C23×D4713yes—
451C22×C4C23×D4713yes—
452C22×C4C23×D4713yes—
453C22×C4C23×D4713yes—
454C22×C4C23×D4711yescharacteristic
455C4⋊C4—26no—
456C4⋊C4—26no—
457C4⋊C4—946no—
458C4⋊C4—946no—
459C4⋊C4—946no—
460C4⋊C4—946no—
461C4⋊C4—946no—
462C4⋊C4—946no—
463C22⋊C4—26no—
464C22⋊C4—26no—
465C22⋊C4—946no—
466C22⋊C4—946no—
467C22⋊C4—946no—
468C22⋊C4—946no—
469C22⋊C4—946no—
470C22⋊C4—946no—
471C42—26no—
472C42—26no—
473C42—946no—
474C42—946no—
475C42—946no—
476C42—946no—
477C42—946no—
478C42—946no—
479C23—23no—
480C23—23no—
481C23—476no—
482C23—476no—
483C23—472no—
484C23—472no—
485C23—9424no—
486C23—943no—
487C23—943no—
488C23—1884no—
489C23—18812no—
490C23#41×D4712yes—
491C23C24×D4711yescharacteristic
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—44no—
505C2×C4—476no—
506C2×C4—4716no—
507C2×C4—476no—
508C2×C4—9424no—
509C2×C4—943no—
510C2×C4—943no—
511C2×C4—943no—
512C2×C4—943no—
513C2×C4—943no—
514C2×C4—943no—
515C2×C4—943no—
516C2×C4—943no—
517C2×C4—943no—
518C2×C4—943no—
519C2×C4—943no—
520C2×C4—943no—
521C2×C4—1884no—
522C2×C4—18812no—
523C2×C4—18812no—
524C2×C4—18812no—
525C2×C4—1884no—
526C2×C4—1884no—
527C2×C4—1884no—
528C2×C4#41×D4716yes—
529C2×C4#41×D4716yes—
530C22—26no—
531C22—41no—
532C22—43no—
533C22—474no—
534C22—4712no—
535C22—4712no—
536C22—946no—
537C22—18816no—
538C22—1881no—
539C22—1883no—
540C22C2×#41×D4713yes—
541C22C2×#41×D4711yescharacteristic
542C22C2×#41×D4713yes—
543C4—26no—
544C4—41no—
545C4—43no—
546C4—43no—
547C4—43no—
548C4—474no—
549C4—946no—
550C4—1881no—
551C4—1883no—
552C4—1883no—
553C4—1883no—
554C4#126×D4714yes—
555C2—42no—
556C2—478no—
557C2—1882no—
558C2C2×#126×D4711yescharacteristic
559C2#529×D4713yes—
560C2#529×D4713yes—
subgroupG/H
centerC22×C4C23×D47
commutator, socle, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC47×#2401C2
prime radicalC24×D47C23
hypercenter#2401D47
hypocenterC47C2×#2401
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2401

Complements

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

NH ≅ G/Ntype
1. #20246691C2semidirect
2. #20246690C2semidirect
3. #20246689C2semidirect
4. #20246688C2semidirect
5. #20246687C2semidirect
6. #20246686C2semidirect
7. #20246685C2semidirect
8. #401×D47C2semidirect
9. #400×D47C2semidirect
12. C4×C4⋊C4×D47C2semidirect
14. #376×D47C2semidirect
15. C47×#2401C2semidirect
23. C47⋊#401C22semidirect
24. C47⋊#401C22semidirect
25. C47⋊#401C22semidirect
26. #15689065C22semidirect
27. #15689065C22semidirect
28. #15689064C22semidirect
29. #15689064C22semidirect
30. #15689063C22semidirect
31. #15689062C22semidirect
32. #15689061C22semidirect
43. C4⋊C4×Dic47C22semidirect
44. C4⋊C4×Dic47C22semidirect
45. C4×Dic47⋊C4C22semidirect
46. C4×Dic47⋊C4C22semidirect
47. C4×C4⋊Dic47C22semidirect
48. #15688974C22semidirect
49. #15688974C22semidirect
57. #15688969C22semidirect
58. #15688968C22semidirect
59. #15688968C22semidirect
66. C47×#401C22semidirect
67. C47×#400C22semidirect
70. C4×C4⋊C4×C47C22semidirect
72. C47×#376C22semidirect
282. #2401D47direct (N × H)
295. D47#2401direct (N × H)
306. #401C2×D47semidirect
314. #400C2×D47semidirect
334. C4×C4⋊C4C2×D47semidirect
346. #376C2×D47semidirect
353. C47C2×#2401semidirect

Maximal subgroups

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

subgroupindex
#202466912
#202466902
#202466892
#202466882
#202466872
#202466862
#202466852
#401×D472
#400×D472
#397×D472
#396×D472
C4×C4⋊C4×D472
C4×C22⋊C4×D472
#376×D472
C47×#24012
C2×#240147