Finite Group Databasebeta

← D47×#2847 #26422105

Subgroups — D47×#2847 #26422105

Order 12032.

8582 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D47C211yesmaximal, characteristic, complemented
2C2×#121×D47C213yesmaximal, complemented
3C2×#120×D47C212yesmaximal, complemented
4#20251671C213yesmaximal, complemented
5#20251670C211yesmaximal, characteristic, complemented
6#20251669C216yesmaximal, complemented
7#20251668C212yesmaximal, complemented
8#20251667C213yesmaximal, complemented
9#386×D47C216yesmaximal, complemented
10#380×D47C213yesmaximal, complemented
11C47×#2847C211yesmaximal, characteristic, complemented
12C25×D47C2211yescharacteristic
13C22×D4×D47C2216yes—
14C22×D4×D47C2211yescharacteristic, complemented
15C24×Dic47C2211yescharacteristic, complemented
16C23×C4×D47—224no—
17C23×C4×D47C2213yes—
18C23×C4×D47C2213yes—
19C23×C4×D47C2213yescomplemented
20C23×C4×D47C2213yescomplemented
21C2×#13093999C2213yescomplemented
22C2×#13093998C2213yescomplemented
23C2×#13093997C2216yescomplemented
24C2×#13093996C2216yescomplemented
25C2×#13093995C2213yescomplemented
26#121×D47—224no—
27C2×#13093994C2216yescomplemented
28C2×#13093993C2212yescomplemented
29C2×#13093992C2216yescomplemented
30#120×D47—216no—
31C2×C4⋊C4×D47C2213yescomplemented
32C2×C22⋊C4×D47C2216yes—
33C2×C22⋊C4×D47C2216yescomplemented
34#15689003C2216yescomplemented
35#15689002C2216yescomplemented
36#15689001C22112yescomplemented
37#15689000C2216yescomplemented
38#15688999C22112yescomplemented
39#15688983C2213yescomplemented
40#15688982C2216yescomplemented
41#15688981C2216yescomplemented
42#15688980C2216yescomplemented
43#95×D47C2216yescomplemented
44C24×C4×C47C2211yescharacteristic, complemented
45C2×#121×C47C2213yescomplemented
46C2×#120×C47C2212yescomplemented
47C47×#386C2216yescomplemented
48C47×#380C2213yescomplemented
49C24×D47—212no—
50C24×D47—212no—
51C24×D47D418yescomplemented
52C24×D47C2312yes—
53C24×D47C2313yes—
54C24×D47C2313yes—
55C22×D188C2316yes—
56C22×D188C2311yescharacteristic, complemented
57C22×C22⋊D47C2316yes—
58C22×C22⋊D47C2316yes—
59C22×C22⋊D47C2312yescomplemented
60C2×D4×D47—224no—
61C2×D4×D47—224no—
62C2×D4×D47—224no—
63C2×D4×D47—212no—
64C23×Dic47—212no—
65C23×Dic47C2313yes—
66C23×Dic47C2313yes—
67C22×C4×D47—2128no—
68C22×C4×D47—212no—
69C22×C4×D47—212no—
70C22×C4×D47—212no—
71C22×C4×D47—224no—
72C22×C4×D47—224no—
73C22×C4×D47—224no—
74C22×C4×D47—224no—
75C22×C4×D47D4124yescomplemented
76C22×C4×D47C2316yes—
77C22×C4×D47C2316yes—
78C22×C4×D47C2313yes—
79C22×C4×D47C2313yes—
80C22×C4×D47C2313yes—
81C22×C4×D47C2311yescharacteristic
82#13093999—212no—
83#13093998—212no—
84#13093997—224no—
85#13093996—224no—
86#13093995—212no—
87#13093994—224no—
88#13093993—28no—
89#13093992—224no—
90C2×C4⋊Dic47C2313yescomplemented
91C2×Dic47⋊C4C2316yescomplemented
92C4⋊C4×D47—212no—
93C2×C22⋊Dic47C2316yes—
94C2×C22⋊Dic47C2316yescomplemented
95C2×(C2×D47)⋊C4C23112yes—
96C2×(C2×D47)⋊C4C2316yescomplemented
97C2×(C2×D47)⋊C4C2316yescomplemented
98C22⋊C4×D47—224no—
99C22⋊C4×D47—224no—
100C47⋊#95C23112yescomplemented
101C47⋊#95C2316yescomplemented
102C25×C47C2311yescharacteristic
103C22×D4×C47C2316yes—
104C22×D4×C47C2311yescharacteristic, complemented
105C23×C4×C47—212no—
106C23×C4×C47C2313yes—
107C23×C4×C47C2313yes—
108#121×C47—212no—
109#120×C47—28no—
110C2×C4⋊C4×C47C2313yescomplemented
111C2×C22⋊C4×C47C2316yes—
112C2×C22⋊C4×C47C2316yescomplemented
113#95×C47C2316yescomplemented
114C24×C47—26no—
115C24×C47—26no—
116C24×C47C2×D414yescomplemented
117C24×C47C2412yes—
118C24×C47C2413yes—
119C23×D47—232no—
120C23×D47—296no—
121C23×D47—26no—
122C23×D47—26no—
123C23×D47—296no—
124C23×D47—212no—
125C23×D47—212no—
126C23×D47—212no—
127C23×D47—212no—
128C23×D47—212no—
129C23×D47—24no—
130C23×D47—212no—
131C23×D47C2×D4112yes—
132C23×D47C2×D4112yes—
133C23×D47C2×D4112yescomplemented
134C23×D47#41112yes—
135C23×D47C2412yes—
136C23×D47C2413yes—
137C23×D47C2411yescharacteristic
138C2×D4×C47—212no—
139C2×D4×C47—212no—
140C2×D4×C47—212no—
141C2×D4×C47—26no—
142C22×C4×C47—232no—
143C22×C4×C47—26no—
144C22×C4×C47—212no—
145C22×C4×C47—212no—
146C22×C4×C47C2×D4112yescomplemented
147C22×C4×C47C2416yes—
148C22×C4×C47C2413yes—
149C22×C4×C47C2411yescharacteristic
150C2×C22⋊D47—212no—
151C2×C22⋊D47—212no—
152C2×C22⋊D47—212no—
153C2×C22⋊D47—212no—
154C2×C22⋊D47—212no—
155C2×C22⋊D47—212no—
156C2×C22⋊D47—212no—
157C22×Dic47—232no—
158C22×Dic47—26no—
159C22×Dic47—212no—
160C22×Dic47—212no—
161C22×Dic47C2×D4112yescomplemented
162C22×Dic47C2416yes—
163C22×Dic47C2413yes—
164C22×Dic47C2411yescharacteristic
165D4×D47—496no—
166D4×D47—416no—
167C2×D188—212no—
168C2×D188—212no—
169C2×D188—212no—
170C2×D188—26no—
171C2×C4×D47—296no—
172C2×C4×D47—296no—
173C2×C4×D47—296no—
174C2×C4×D47—212no—
175C2×C4×D47—212no—
176C2×C4×D47—212no—
177C2×C4×D47—212no—
178C2×C4×D47—212no—
179C2×C4×D47—212no—
180C2×C4×D47—296no—
181C2×C4×D47—212no—
182C2×C4×D47—212no—
183C2×C4×D47—212no—
184C2×C4×D47C2×D4112yes—
185C2×C4×D47C2×D4112yes—
186C2×C4×D47C2×D4112yescomplemented
187C2×C4×D47C2×D4112yescomplemented
188C4⋊C4×C47—26no—
189C22⋊C4×C47—212no—
190C22⋊C4×C47—212no—
191C22⋊Dic47—212no—
192C22⋊Dic47—212no—
193(C2×D47)⋊C4—224no—
194(C2×D47)⋊C4—212no—
195(C2×D47)⋊C4—212no—
196C4⋊Dic47—26no—
197Dic47⋊C4—212no—
198C23×C47—28no—
199C23×C47—224no—
200C23×C47—224no—
201C23×C47—26no—
202C23×C47—26no—
203C23×C47—26no—
204C23×C47—22no—
205C23×C47—26no—
206C23×C47C22×D416yes—
207C23×C47C22×D416yes—
208C23×C47C2×#4116yes—
209C23×C47C2511yescharacteristic
210C22×D47—224no—
211C22×D47—248no—
212C22×D47—224no—
213C22×D47—2256no—
214C22×D47—224no—
215C22×D47—26no—
216C22×D47—26no—
217C22×D47—224no—
218C22×D47—248no—
219C22×D47—248no—
220C22×D47—224no—
221C22×D47—248no—
222C22×D47—26no—
223C22×D47—22no—
224C22×D47—26no—
225C22×D47—48no—
226C22×D47—424no—
227C22×D47—424no—
228C22×D47#121148yescomplemented
229C22×D47C22×D416yes—
230C22×D47C22×D416yes—
231C22×D47C22×D416yes—
232C22×D47C22×D412yes—
233C22×D47C2×#4116yes—
234C22×D47C2×#4116yes—
235D4×C47—424no—
236D4×C47—44no—
237C2×C4×C47—224no—
238C2×C4×C47—26no—
239C2×C4×C47—224no—
240C2×C4×C47—26no—
241C2×C4×C47—26no—
242C2×C4×C47—26no—
243C2×C4×C47C22×D416yes—
244C2×C4×C47C22×D416yes—
245C22⋊D47—424no—
246C22⋊D47—424no—
247C22⋊D47—48no—
248C2×Dic47—224no—
249C2×Dic47—26no—
250C2×Dic47—224no—
251C2×Dic47—26no—
252C2×Dic47—26no—
253C2×Dic47—26no—
254C2×Dic47C22×D416yes—
255C2×Dic47C22×D416yes—
256D188—424no—
257D188—44no—
258C4×D47—248no—
259C4×D47—224no—
260C4×D47—224no—
261C4×D47—224no—
262C4×D47—424no—
263C4×D47#120116yescomplemented
264C2×#2847—471nomaximal, Sylow
265C22×C47—232no—
266C22×C47—26no—
267C22×C47—212no—
268C22×C47—26no—
269C22×C47—212no—
270C22×C47—42no—
271C22×C47—46no—
272C22×C47—46no—
273C22×C47C2×#121112yescomplemented
274C22×C47C23×D413yes—
275C22×C47C23×D411yescharacteristic
276C22×C47C22×#4113yes—
277C2×D47—296no—
278C2×D47—26no—
279C2×D47—212no—
280C2×D47—26no—
281C2×D47—212no—
282C2×D47—296no—
283C2×D47—42no—
284C2×D47—46no—
285C2×D47—46no—
286C2×D47—816no—
287C2×D47C2×#12014yes—
288C2×D47C2×#121112yes—
289C2×D47C2×#121112yescomplemented
290C2×D47#525112yes—
291C4×C47—26no—
292C4×C47—46no—
293C4×C47C2×#12014yescomplemented
294Dic47—26no—
295Dic47—46no—
296Dic47C2×#12014yescomplemented
297C25×C4—471no—
298C22×#121—473no—
299C22×#120—472no—
300#2847—476no—
301#2847—473no—
302#2847—471no—
303#2847—473no—
304#2847—472no—
305#2847D4711yescharacteristic, direct product factor
306C2×#386—476no—
307C2×#380—473no—
308C2×C47—212no—
309C2×C47—82no—
310C2×C47C22×#12011yescharacteristic
311C2×C47C22×#12113yes—
312C2×C47C2×#52513yes—
313D47—212no—
314D47—82no—
315D47#284718yesdirect product factor
316C26—471no—
317C23×D4—476no—
318C23×D4—471no—
319C24×C4—473no—
320C24×C4—471no—
321C24×C4—473no—
322C24×C4—473no—
323C24×C4—473no—
324C24×C4—9424no—
325C24×C4C2×D4711yescharacteristic, complemented
326C2×#121—476no—
327C2×#121—473no—
328C2×#121—473no—
329C2×#121—473no—
330C2×#121—476no—
331C2×#121—9424no—
332C2×#121C2×D4713yescomplemented
333C2×#120—472no—
334C2×#120—476no—
335C2×#120—476no—
336C2×#120—9416no—
337C2×#120C2×D4712yescomplemented
338C22×C4⋊C4—473no—
339C22×C22⋊C4—476no—
340C22×C22⋊C4—476no—
341#386—476no—
342#386—476no—
343#386—476no—
344#386—4712no—
345#386—4712no—
346#386C2×D4716yescomplemented
347#380—473no—
348#380—476no—
349#380—476no—
350#380—476no—
351#380C2×D4713yescomplemented
352C2×#95—476no—
353C47C2×#284711yescharacteristic, complemented, Sylow
354C25—473no—
355C25—478no—
356C25—473no—
357C25—472no—
358C25—9412no—
359C25—9412no—
360C25C22×D4711yescharacteristic
361C22×D4—476no—
362C22×D4—476no—
363C22×D4—472no—
364C22×D4—476no—
365C22×D4—471no—
366C22×D4—9412no—
367C22×D4—9424no—
368C22×D4—9424no—
369C22×D4—9424no—
370C22×D4C22×D4716yes—
371C22×D4C22×D4711yescharacteristic, complemented
372C23×C4—212no—
373C23×C4—471no—
374C23×C4—473no—
375C23×C4—4724no—
376C23×C4—473no—
377C23×C4—473no—
378C23×C4—473no—
379C23×C4—473no—
380C23×C4—476no—
381C23×C4—476no—
382C23×C4—9412no—
383C23×C4—9424no—
384C23×C4—9424no—
385C23×C4—9424no—
386C23×C4—9424no—
387C23×C4—9412no—
388C23×C4—94128no—
389C23×C4—9412no—
390C23×C4—9412no—
391C23×C4C22×D4713yes—
392C23×C4C22×D4713yes—
393#121—212no—
394#121—9424no—
395#121—9412no—
396#121—9412no—
397#121—9424no—
398#121—9412no—
399#120—28no—
400#120—9424no—
401#120—9424no—
402#120—948no—
403C2×C4⋊C4—476no—
404C2×C4⋊C4—473no—
405C2×C4⋊C4—9412no—
406C2×C4⋊C4C22×D4713yescomplemented
407C2×C22⋊C4—476no—
408C2×C22⋊C4—476no—
409C2×C22⋊C4—4712no—
410C2×C22⋊C4—476no—
411C2×C22⋊C4—476no—
412C2×C22⋊C4—9424no—
413C2×C22⋊C4—9424no—
414C2×C22⋊C4C22×D4716yes—
415C2×C22⋊C4C22×D4716yescomplemented
416#95—4712no—
417#95—476no—
418#95C22×D4716yescomplemented
419C24—26no—
420C24—26no—
421C24—471no—
422C24—4712no—
423C24—4712no—
424C24—4712no—
425C24—473no—
426C24—4712no—
427C24—472no—
428C24—9412no—
429C24—9412no—
430C24—9496no—
431C24—9412no—
432C24—9412no—
433C24—9412no—
434C24—944no—
435C24—9412no—
436C24—9432no—
437C24—9496no—
438C24—946no—
439C24—946no—
440C24D4×D4714yescomplemented
441C24C23×D4712yes—
442C24C23×D4713yes—
443C2×D4—212no—
444C2×D4—212no—
445C2×D4—212no—
446C2×D4—26no—
447C2×D4—9412no—
448C2×D4—9412no—
449C2×D4—9412no—
450C2×D4—9412no—
451C2×D4—9412no—
452C2×D4—9412no—
453C2×D4—9412no—
454C2×D4—9412no—
455C2×D4—9412no—
456C2×D4—9412no—
457C2×D4—946no—
458C2×D4—18816no—
459C2×D4—18896no—
460C22×C4—232no—
461C22×C4—26no—
462C22×C4—212no—
463C22×C4—212no—
464C22×C4—471no—
465C22×C4—4712no—
466C22×C4—4712no—
467C22×C4—473no—
468C22×C4—4712no—
469C22×C4—4712no—
470C22×C4—4712no—
471C22×C4—476no—
472C22×C4—9412no—
473C22×C4—9412no—
474C22×C4—9496no—
475C22×C4—9412no—
476C22×C4—9412no—
477C22×C4—9496no—
478C22×C4—9496no—
479C22×C4—9496no—
480C22×C4—9412no—
481C22×C4—9412no—
482C22×C4—9412no—
483C22×C4—9412no—
484C22×C4—9412no—
485C22×C4—9432no—
486C22×C4—946no—
487C22×C4—9412no—
488C22×C4—9412no—
489C22×C4D4×D47112yescomplemented
490C22×C4C23×D4716yes—
491C22×C4C23×D4713yes—
492C22×C4C23×D4711yescharacteristic
493C4⋊C4—26no—
494C4⋊C4—9412no—
495C4⋊C4—946no—
496C22⋊C4—212no—
497C22⋊C4—212no—
498C22⋊C4—9412no—
499C22⋊C4—9424no—
500C22⋊C4—9412no—
501C22⋊C4—9412no—
502C22⋊C4—9412no—
503C23—28no—
504C23—224no—
505C23—224no—
506C23—26no—
507C23—26no—
508C23—26no—
509C23—22no—
510C23—26no—
511C23—476no—
512C23—472no—
513C23—476no—
514C23—4748no—
515C23—476no—
516C23—476no—
517C23—476no—
518C23—9424no—
519C23—9448no—
520C23—9448no—
521C23—9424no—
522C23—9448no—
523C23—9424no—
524C23—94256no—
525C23—9424no—
526C23—9448no—
527C23—9424no—
528C23—946no—
529C23—946no—
530C23—946no—
531C23—942no—
532C23—946no—
533C23—1888no—
534C23—18824no—
535C23—18824no—
536C23C2×D4×D4716yes—
537C23C2×D4×D4716yes—
538C23#41×D4716yes—
539C23C24×D4711yescharacteristic
540D4—424no—
541D4—44no—
542D4—18824no—
543D4—1888no—
544D4—18824no—
545D4—18824no—
546D4—1884no—
547C2×C4—224no—
548C2×C4—26no—
549C2×C4—224no—
550C2×C4—26no—
551C2×C4—26no—
552C2×C4—26no—
553C2×C4—476no—
554C2×C4—4716no—
555C2×C4—476no—
556C2×C4—9424no—
557C2×C4—9424no—
558C2×C4—9448no—
559C2×C4—9424no—
560C2×C4—9424no—
561C2×C4—946no—
562C2×C4—9424no—
563C2×C4—946no—
564C2×C4—946no—
565C2×C4—946no—
566C2×C4—18824no—
567C2×C4C2×D4×D4716yes—
568C2×C4C2×D4×D4716yes—
569C22—232no—
570C22—26no—
571C22—212no—
572C22—26no—
573C22—212no—
574C22—42no—
575C22—46no—
576C22—46no—
577C22—474no—
578C22—4712no—
579C22—4712no—
580C22—4712no—
581C22—9496no—
582C22—9496no—
583C22—946no—
584C22—9412no—
585C22—946no—
586C22—9412no—
587C22—37616no—
588C22—1882no—
589C22—1886no—
590C22—1886no—
591C22#121×D47112yescomplemented
592C22C22×D4×D4713yes—
593C22C22×D4×D4711yescharacteristic
594C22C2×#41×D4713yes—
595C4—26no—
596C4—46no—
597C4—474no—
598C4—946no—
599C4—1886no—
600C4#120×D4714yescomplemented
601C2—212no—
602C2—82no—
603C2—478no—
604C2—9412no—
605C2—3762no—
606C2C2×#120×D4711yescharacteristic
607C2C2×#121×D4713yes—
608C2#525×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2847C2
hypercenter#2847D47
hypocenterC47C2×#2847
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C24×C4×D47C2semidirect
2. C2×#121×D47C2semidirect
3. C2×#120×D47C2semidirect
4. #20251671C2semidirect
5. #20251670C2semidirect
6. #20251669C2semidirect
7. #20251668C2semidirect
8. #20251667C2semidirect
9. #386×D47C2semidirect
10. #380×D47C2semidirect
11. C47×#2847C2semidirect
14. C22×D4×D47C22semidirect
15. C24×Dic47C22semidirect
19. C23×C4×D47C22semidirect
20. C23×C4×D47C22semidirect
21. C2×#13093999C22semidirect
22. C2×#13093998C22semidirect
23. C2×#13093997C22semidirect
24. C2×#13093996C22semidirect
25. C2×#13093995C22semidirect
27. C2×#13093994C22semidirect
28. C2×#13093993C22semidirect
29. C2×#13093992C22semidirect
31. C2×C4⋊C4×D47C22semidirect
33. C2×C22⋊C4×D47C22semidirect
34. #15689003C22semidirect
35. #15689002C22semidirect
36. #15689001C22semidirect
37. #15689000C22semidirect
38. #15688999C22semidirect
39. #15688983C22semidirect
40. #15688982C22semidirect
41. #15688981C22semidirect
42. #15688980C22semidirect
43. #95×D47C22semidirect
44. C24×C4×C47C22semidirect
45. C2×#121×C47C22semidirect
46. C2×#120×C47C22semidirect
47. C47×#386C22semidirect
48. C47×#380C22semidirect
51. C24×D47D4semidirect
56. C22×D188C23semidirect
59. C22×C22⋊D47C23semidirect
75. C22×C4×D47D4semidirect
90. C2×C4⋊Dic47C23semidirect
91. C2×Dic47⋊C4C23semidirect
94. C2×C22⋊Dic47C23semidirect
96. C2×(C2×D47)⋊C4C23semidirect
97. C2×(C2×D47)⋊C4C23semidirect
100. C47⋊#95C23semidirect
101. C47⋊#95C23semidirect
104. C22×D4×C47C23semidirect
110. C2×C4⋊C4×C47C23semidirect
112. C2×C22⋊C4×C47C23semidirect
113. #95×C47C23semidirect
116. C24×C47C2×D4semidirect
133. C23×D47C2×D4semidirect
146. C22×C4×C47C2×D4semidirect
161. C22×Dic47C2×D4semidirect
186. C2×C4×D47C2×D4semidirect
187. C2×C4×D47C2×D4semidirect
228. C22×D47#121semidirect
263. C4×D47#120semidirect
273. C22×C47C2×#121semidirect
289. C2×D47C2×#121semidirect
293. C4×C47C2×#120semidirect
296. Dic47C2×#120semidirect
305. #2847D47direct (N × H)
315. D47#2847direct (N × H)
325. C24×C4C2×D47semidirect
332. C2×#121C2×D47semidirect
337. C2×#120C2×D47semidirect
346. #386C2×D47semidirect
351. #380C2×D47semidirect
353. C47C2×#2847semidirect
371. C22×D4C22×D47semidirect
406. C2×C4⋊C4C22×D47semidirect
415. C2×C22⋊C4C22×D47semidirect
418. #95C22×D47semidirect
440. C24D4×D47semidirect
489. C22×C4D4×D47semidirect
591. C22#121×D47semidirect
600. C4#120×D47semidirect

Maximal subgroups

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

subgroupindex
C24×C4×D472
C2×#121×D472
C2×#120×D472
#202516712
#202516702
#202516692
#202516682
#202516672
#386×D472
#380×D472
C47×#28472
C2×#284747