Finite Group Databasebeta

← D47×#2852 #26422151

Subgroups — D47×#2852 #26422151

Order 12032.

3354 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#126×D47C211yesmaximal, characteristic, complemented
2C22×C42×D47C211yesmaximal, characteristic, complemented
3#20251706C213yesmaximal, complemented
4#20251705C213yesmaximal, complemented
5#20251704C211yesmaximal, characteristic, complemented
6#20251703C211yesmaximal, characteristic, complemented
7#20251702C213yesmaximal, complemented
8#20251701C213yesmaximal, complemented
9#20251700C211yesmaximal, characteristic, complemented
10#388×D47C213yesmaximal, complemented
11#387×D47C213yesmaximal, complemented
12#386×D47C213yesmaximal
13#385×D47C213yesmaximal, complemented
14#383×D47C211yesmaximal, characteristic, complemented
15C47×#2852C211yesmaximal, characteristic, complemented
16C22×D4×D47C2211yescharacteristic
17C23×C4×D47C2213yes—
18C2×#13094019C2213yescomplemented
19C2×#13094018C2211yescharacteristic, complemented
20C2×#13094017C2213yescomplemented
21#126×D47—28no—
22C2×C4⋊C4×D47C2213yes—
23C2×C4⋊C4×D47C2213yes—
24C2×C22⋊C4×D47C2213yes—
25C2×C22⋊C4×D47C2213yes—
26C2×C22⋊C4×D47C2213yes—
27C22×C4×Dic47C2213yescomplemented
28C2×C42×D47—28no—
29C2×C42×D47C2213yes—
30C2×C42×D47C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic, complemented
32C2×C42×D47C2213yescomplemented
33#15689017C2213yescomplemented
34#15689016C2213yescomplemented
35#15689015C2213yescomplemented
36#15689014C2213yescomplemented
37#15689013C2213yescomplemented
38#15689012C2213yescomplemented
39#15689011C2213yescomplemented
40#15689010C2213yescomplemented
41#15689009C2213yescomplemented
42#15689008C2213yescomplemented
43#15689007C2213yescomplemented
44#15689006C2213yescomplemented
45#15689005C2213yescomplemented
46#15689004C2213yescomplemented
47#15689003C2213yes—
48#15689002C2213yes—
49#15689001C2213yes—
50#15689001C2213yes—
51#15689000C2213yes—
52#15688999C2213yes—
53#15688999C2213yes—
54#15688998C2213yescomplemented
55#15688997C2213yescomplemented
56#15688997C2213yescomplemented
57#15688996C2213yescomplemented
58#15688995C2213yescomplemented
59#15688994C2213yescomplemented
60#15688994C2213yescomplemented
61#15688991C2211yescharacteristic, complemented
62#15688990C2213yescomplemented
63#15688990C2213yescomplemented
64#95×D47C2213yes—
65#95×D47C2213yes—
66#95×D47C2213yes—
67#95×D47C2213yes—
68C2×#126×C47C2211yescharacteristic, complemented
69C22×C42×C47C2211yescharacteristic, complemented
70C47×#388C2213yescomplemented
71C47×#387C2213yescomplemented
72C47×#386C2213yes—
73C47×#385C2213yescomplemented
74C47×#383C2211yescharacteristic, complemented
75C24×D47C2311yescharacteristic
76C24×D47C2311yescharacteristic
77C22×D188C2311yescharacteristic
78C22×C22⋊D47C2311yescharacteristic
79C22×C22⋊D47C2311yescharacteristic
80C2×D4×D47—212no—
81C23×Dic47C2313yes—
82C22×C4×D47—212no—
83C22×C4×D47—212no—
84C22×C4×D47—212no—
85C22×C4×D47C2311yescharacteristic
86C22×C4×D47C2313yes—
87C22×C4×D47C2313yes—
88C22×C4×D47C2313yes—
89C22×C4×D47C2313yes—
90C22×C4×D47C2313yes—
91C22×C4×D47C2313yes—
92#13094019—212no—
93#13094018—24no—
94#13094017—212no—
95C2×C4⋊Dic47C2313yes—
96C2×C4⋊Dic47C2313yes—
97C2×Dic47⋊C4C2313yes—
98C2×Dic47⋊C4C2313yes—
99C2×Dic47⋊C4C2313yes—
100C2×Dic47⋊C4C2313yes—
101C4⋊C4×D47—212no—
102C4⋊C4×D47—212no—
103C2×C22⋊Dic47C2313yes—
104C2×C22⋊Dic47C2313yes—
105C2×C22⋊Dic47C2313yes—
106C2×(C2×D47)⋊C4C2313yes—
107C2×(C2×D47)⋊C4C2313yes—
108C2×(C2×D47)⋊C4C2313yes—
109C2×(C2×D47)⋊C4C2313yes—
110C2×(C2×D47)⋊C4C2313yes—
111C2×(C2×D47)⋊C4C2313yes—
112C22⋊C4×D47—212no—
113C22⋊C4×D47—212no—
114C22⋊C4×D47—212no—
115C2×C4×Dic47—212no—
116C2×C4×Dic47C2313yes—
117C2×C4×Dic47C2313yes—
118C2×C4×Dic47C2313yes—
119C2×C4×Dic47C2313yes—
120C42×D47—212no—
121C42×D47—24no—
122C42×D47—212no—
123C42×D47D418yescomplemented
124C47⋊#95C2313yes—
125C47⋊#95C2313yes—
126C47⋊#95C2313yes—
127C47⋊#95C2313yes—
128C47⋊#95C2313yes—
129C47⋊#95C2313yes—
130C47⋊#95C2313yes—
131C47⋊#95C2313yes—
132C47⋊#95C2313yes—
133C47⋊#95C2313yes—
134C47⋊#95C2313yes—
135C47⋊#95C2313yes—
136C22×D4×C47C2311yescharacteristic
137C23×C4×C47C2313yes—
138#126×C47—24no—
139C2×C4⋊C4×C47C2313yes—
140C2×C4⋊C4×C47C2313yes—
141C2×C22⋊C4×C47C2313yes—
142C2×C22⋊C4×C47C2313yes—
143C2×C22⋊C4×C47C2313yes—
144C2×C42×C47—24no—
145C2×C42×C47C2313yes—
146C2×C42×C47C2311yescharacteristic
147#95×C47C2313yes—
148#95×C47C2313yes—
149#95×C47C2313yes—
150#95×C47C2313yes—
151C24×C47C2411yescharacteristic
152C24×C47C2411yescharacteristic
153C23×D47—22no—
154C23×D47—26no—
155C23×D47—22no—
156C23×D47—26no—
157C23×D47—26no—
158C23×D47#41112yes—
159C23×D47C2411yescharacteristic
160C23×D47C2411yescharacteristic
161C23×D47C2411yescharacteristic
162C2×D4×C47—26no—
163C22×C4×C47—26no—
164C22×C4×C47—26no—
165C22×C4×C47—26no—
166C22×C4×C47C2413yes—
167C22×C4×C47C2413yes—
168C22×C4×C47C2411yescharacteristic
169C22×C4×C47C2413yes—
170C22×C4×C47C2413yes—
171C2×C22⋊D47—26no—
172C2×C22⋊D47—26no—
173C22×Dic47—26no—
174C22×Dic47—26no—
175C22×Dic47—26no—
176C22×Dic47C2411yescharacteristic
177C22×Dic47C2413yes—
178C22×Dic47C2413yes—
179C22×Dic47C2413yes—
180C22×Dic47C2413yes—
181D4×D47—416no—
182C2×D188—26no—
183C2×C4×D47—296no—
184C2×C4×D47—26no—
185C2×C4×D47—26no—
186C2×C4×D47—26no—
187C2×C4×D47—26no—
188C2×C4×D47—26no—
189C2×C4×D47—26no—
190C2×C4×D47—26no—
191C2×C4×D47—26no—
192C2×C4×D47—26no—
193C2×C4×D47—26no—
194C2×C4×D47—26no—
195C2×C4×D47—26no—
196C2×C4×D47—26no—
197C2×C4×D47—26no—
198C2×C4×D47—26no—
199C2×C4×D47—26no—
200C2×C4×D47—26no—
201C2×C4×D47C2×D4112yes—
202C2×C4×D47#41112yes—
203C4⋊C4×C47—26no—
204C4⋊C4×C47—26no—
205C22⋊C4×C47—26no—
206C22⋊C4×C47—26no—
207C22⋊C4×C47—26no—
208C42×C47—26no—
209C42×C47C2×D414yescomplemented
210C22⋊Dic47—26no—
211C22⋊Dic47—26no—
212C22⋊Dic47—26no—
213(C2×D47)⋊C4—26no—
214(C2×D47)⋊C4—26no—
215(C2×D47)⋊C4—26no—
216(C2×D47)⋊C4—26no—
217(C2×D47)⋊C4—26no—
218(C2×D47)⋊C4—26no—
219C4⋊Dic47—26no—
220C4⋊Dic47—26no—
221Dic47⋊C4—26no—
222Dic47⋊C4—26no—
223Dic47⋊C4—26no—
224Dic47⋊C4—26no—
225C4×Dic47—26no—
226C4×Dic47—26no—
227C4×Dic47—26no—
228C4×Dic47C2×D4112yescomplemented
229C23×C47—21no—
230C23×C47—23no—
231C23×C47—21no—
232C23×C47—23no—
233C23×C47—23no—
234C23×C47C2×#4116yes—
235C23×C47C2511yescharacteristic
236C22×D47—21no—
237C22×D47—23no—
238C22×D47—224no—
239C22×D47—224no—
240C22×D47—21no—
241C22×D47—23no—
242C22×D47—23no—
243C22×D47—412no—
244C22×D47—44no—
245C22×D47—412no—
246C22×D47#126116yescomplemented
247C22×D47C22×D412yes—
248C22×D47C2×#4116yes—
249C22×D47C2×#4116yes—
250C22×D47C2×#4116yes—
251D4×C47—44no—
252C2×C4×C47—224no—
253C2×C4×C47—23no—
254C2×C4×C47—23no—
255C2×C4×C47—23no—
256C2×C4×C47—23no—
257C2×C4×C47—23no—
258C2×C4×C47—23no—
259C2×C4×C47—23no—
260C2×C4×C47—23no—
261C2×C4×C47—23no—
262C2×C4×C47—23no—
263C2×C4×C47—23no—
264C2×C4×C47C22×D416yes—
265C2×C4×C47C2×#4116yes—
266C22⋊D47—44no—
267C22⋊D47—44no—
268C2×Dic47—224no—
269C2×Dic47—23no—
270C2×Dic47—23no—
271C2×Dic47—23no—
272C2×Dic47—23no—
273C2×Dic47—23no—
274C2×Dic47—23no—
275C2×Dic47—23no—
276C2×Dic47—23no—
277C2×Dic47—23no—
278C2×Dic47—23no—
279C2×Dic47—23no—
280C2×Dic47C22×D416yes—
281C2×Dic47C2×#4116yes—
282D188—44no—
283C4×D47—224no—
284C4×D47—224no—
285C4×D47—224no—
286C4×D47—224no—
287C4×D47—412no—
288C4×D47—44no—
289C4×D47—412no—
290C2×#2852—471nomaximal, Sylow
291C22×C47—26no—
292C22×C47—26no—
293C22×C47—43no—
294C22×C47—41no—
295C22×C47—43no—
296C22×C47C2×#12614yescomplemented
297C22×C47C23×D411yescharacteristic
298C22×C47C22×#4113yes—
299C22×C47C22×#4113yes—
300C2×D47—26no—
301C2×D47—26no—
302C2×D47—232no—
303C2×D47—43no—
304C2×D47—41no—
305C2×D47—43no—
306C2×D47—88no—
307C2×D47#525112yes—
308C2×D47C2×#12614yes—
309C2×D47C2×#12614yescomplemented
310C2×D47#529112yes—
311C4×C47—26no—
312C4×C47—26no—
313C4×C47—43no—
314C4×C47—41no—
315C4×C47—43no—
316Dic47—26no—
317Dic47—26no—
318Dic47—43no—
319Dic47—41no—
320Dic47—43no—
321C22×#126—471no—
322C23×C42—471no—
323#2852—471no—
324#2852—473no—
325#2852—473no—
326#2852—473no—
327#2852—473no—
328#2852—471no—
329#2852—471no—
330#2852D4711yescharacteristic, direct product factor
331C2×#388—473no—
332C2×#387—473no—
333C2×#386—473no—
334C2×#385—473no—
335C2×#383—471no—
336C2×C47—24no—
337C2×C47—81no—
338C2×C47C2×#52513yes—
339C2×C47C22×#12611yescharacteristic
340C2×C47C2×#52913yes—
341D47—24no—
342D47—81no—
343D47#285218yesdirect product factor
344C23×D4—471no—
345C24×C4—473no—
346C2×#126—473no—
347C2×#126—473no—
348C2×#126—471no—
349C2×#126—948no—
350C2×#126C2×D4711yescharacteristic, complemented
351C22×C4⋊C4—473no—
352C22×C4⋊C4—473no—
353C22×C22⋊C4—473no—
354C22×C22⋊C4—473no—
355C22×C22⋊C4—473no—
356C22×C42—471no—
357C22×C42—473no—
358C22×C42—473no—
359C22×C42—471no—
360C22×C42—473no—
361C22×C42—948no—
362C22×C42C2×D4711yescharacteristic, complemented
363#388—473no—
364#388—473no—
365#388—473no—
366#388—473no—
367#388—473no—
368#388—473no—
369#388—473no—
370#388C2×D4713yescomplemented
371#387—473no—
372#387—473no—
373#387—473no—
374#387—473no—
375#387—473no—
376#387—473no—
377#387—473no—
378#387C2×D4713yescomplemented
379#386—473no—
380#386—473no—
381#386—473no—
382#386—473no—
383#386—473no—
384#386—473no—
385#386—473no—
386#386C2×D4713yes—
387#385—473no—
388#385—473no—
389#385—473no—
390#385—473no—
391#385—473no—
392#385—473no—
393#385—473no—
394#385C2×D4713yescomplemented
395#383—471no—
396#383—473no—
397#383—473no—
398#383C2×D4711yescharacteristic, complemented
399C2×#95—473no—
400C2×#95—473no—
401C2×#95—473no—
402C2×#95—473no—
403C47C2×#285211yescharacteristic, complemented, Sylow
404C25—471no—
405C25—471no—
406C22×D4—471no—
407C22×D4—471no—
408C22×D4—471no—
409C22×D4—9412no—
410C22×D4C22×D4711yescharacteristic
411C23×C4—473no—
412C23×C4—473no—
413C23×C4—473no—
414C23×C4—473no—
415C23×C4—473no—
416C23×C4—473no—
417C23×C4—473no—
418C23×C4—471no—
419C23×C4—9412no—
420C23×C4—9412no—
421C23×C4—9412no—
422C23×C4C22×D4713yes—
423#126—24no—
424#126—9412no—
425#126—9412no—
426#126—944no—
427C2×C4⋊C4—473no—
428C2×C4⋊C4—473no—
429C2×C4⋊C4—473no—
430C2×C4⋊C4—473no—
431C2×C4⋊C4—473no—
432C2×C4⋊C4—473no—
433C2×C4⋊C4—9412no—
434C2×C4⋊C4—9412no—
435C2×C4⋊C4C22×D4713yes—
436C2×C4⋊C4C22×D4713yes—
437C2×C22⋊C4—473no—
438C2×C22⋊C4—473no—
439C2×C22⋊C4—473no—
440C2×C22⋊C4—473no—
441C2×C22⋊C4—473no—
442C2×C22⋊C4—473no—
443C2×C22⋊C4—473no—
444C2×C22⋊C4—473no—
445C2×C22⋊C4—473no—
446C2×C22⋊C4—9412no—
447C2×C22⋊C4—9412no—
448C2×C22⋊C4—9412no—
449C2×C22⋊C4C22×D4713yes—
450C2×C22⋊C4C22×D4713yes—
451C2×C22⋊C4C22×D4713yes—
452C2×C42—24no—
453C2×C42—473no—
454C2×C42—478no—
455C2×C42—473no—
456C2×C42—473no—
457C2×C42—473no—
458C2×C42—9412no—
459C2×C42—9412no—
460C2×C42—9412no—
461C2×C42—944no—
462C2×C42C22×D4713yes—
463C2×C42C22×D4711yescharacteristic
464#95—473no—
465#95—473no—
466#95—473no—
467#95—473no—
468#95—473no—
469#95—473no—
470#95—473no—
471#95—473no—
472#95—473no—
473#95—473no—
474#95—473no—
475#95—473no—
476#95C22×D4713yes—
477#95C22×D4713yes—
478#95C22×D4713yes—
479#95C22×D4713yes—
480C24—471no—
481C24—4712no—
482C24—471no—
483C24—471no—
484C24—942no—
485C24—946no—
486C24—942no—
487C24—946no—
488C24—946no—
489C24C23×D4711yescharacteristic
490C24C23×D4711yescharacteristic
491C2×D4—26no—
492C2×D4—946no—
493C2×D4—946no—
494C2×D4—946no—
495C2×D4—18816no—
496C22×C4—26no—
497C22×C4—26no—
498C22×C4—26no—
499C22×C4—473no—
500C22×C4—473no—
501C22×C4—4712no—
502C22×C4—4712no—
503C22×C4—471no—
504C22×C4—473no—
505C22×C4—473no—
506C22×C4—946no—
507C22×C4—946no—
508C22×C4—946no—
509C22×C4—946no—
510C22×C4—946no—
511C22×C4—946no—
512C22×C4—946no—
513C22×C4—946no—
514C22×C4—9496no—
515C22×C4—946no—
516C22×C4—946no—
517C22×C4—946no—
518C22×C4—946no—
519C22×C4—946no—
520C22×C4—946no—
521C22×C4—946no—
522C22×C4—946no—
523C22×C4—946no—
524C22×C4—946no—
525C22×C4—946no—
526C22×C4—946no—
527C22×C4C23×D4711yescharacteristic
528C22×C4C23×D4713yes—
529C22×C4C23×D4713yes—
530C22×C4C23×D4713yes—
531C22×C4C23×D4713yes—
532C4⋊C4—26no—
533C4⋊C4—26no—
534C4⋊C4—946no—
535C4⋊C4—946no—
536C4⋊C4—946no—
537C4⋊C4—946no—
538C4⋊C4—946no—
539C4⋊C4—946no—
540C22⋊C4—26no—
541C22⋊C4—26no—
542C22⋊C4—26no—
543C22⋊C4—946no—
544C22⋊C4—946no—
545C22⋊C4—946no—
546C22⋊C4—946no—
547C22⋊C4—946no—
548C22⋊C4—946no—
549C22⋊C4—946no—
550C22⋊C4—946no—
551C22⋊C4—946no—
552C42—26no—
553C42—4712no—
554C42—946no—
555C42—946no—
556C42—946no—
557C42D4×D4714yescomplemented
558C23—21no—
559C23—23no—
560C23—21no—
561C23—23no—
562C23—23no—
563C23—472no—
564C23—476no—
565C23—476no—
566C23—4716no—
567C23—476no—
568C23—9424no—
569C23—9424no—
570C23—941no—
571C23—943no—
572C23—941no—
573C23—943no—
574C23—943no—
575C23—1884no—
576C23—18812no—
577C23—18812no—
578C23#41×D4716yes—
579C23C24×D4711yescharacteristic
580D4—44no—
581D4—1884no—
582D4—1884no—
583D4—1884no—
584C2×C4—224no—
585C2×C4—23no—
586C2×C4—23no—
587C2×C4—23no—
588C2×C4—23no—
589C2×C4—23no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—23no—
596C2×C4—476no—
597C2×C4—476no—
598C2×C4—9424no—
599C2×C4—9424no—
600C2×C4—9424no—
601C2×C4—9424no—
602C2×C4—9424no—
603C2×C4—943no—
604C2×C4—943no—
605C2×C4—943no—
606C2×C4—943no—
607C2×C4—943no—
608C2×C4—943no—
609C2×C4—943no—
610C2×C4—943no—
611C2×C4—943no—
612C2×C4—943no—
613C2×C4—943no—
614C2×C4—18812no—
615C2×C4—18812no—
616C2×C4—1884no—
617C2×C4C2×D4×D4716yes—
618C2×C4#41×D4716yes—
619C22—26no—
620C22—26no—
621C22—43no—
622C22—41no—
623C22—43no—
624C22—4712no—
625C22—474no—
626C22—4712no—
627C22—474no—
628C22—9432no—
629C22—946no—
630C22—946no—
631C22—3768no—
632C22—1883no—
633C22—1881no—
634C22—1883no—
635C22#126×D4714yescomplemented
636C22C22×D4×D4711yescharacteristic
637C22C2×#41×D4713yes—
638C22C2×#41×D4713yes—
639C4—26no—
640C4—26no—
641C4—43no—
642C4—41no—
643C4—43no—
644C4—946no—
645C4—946no—
646C4—1883no—
647C4—1881no—
648C4—1883no—
649C2—24no—
650C2—81no—
651C2—478no—
652C2—944no—
653C2—3761no—
654C2#525×D4713yes—
655C2C2×#126×D4711yescharacteristic
656C2#529×D4713yes—
subgroupG/H
center, FrattiniC23C24×D47
commutator, socle, cosocleC23×C47C25
FittingC47×#2852C2
prime radicalC22×D4×D47C22
hypercenter#2852D47
hypocenterC47C2×#2852
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #2852

Complements

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

NH ≅ G/Ntype
1. C2×#126×D47C2semidirect
2. C22×C42×D47C2semidirect
3. #20251706C2semidirect
4. #20251705C2semidirect
5. #20251704C2semidirect
6. #20251703C2semidirect
7. #20251702C2semidirect
8. #20251701C2semidirect
9. #20251700C2semidirect
10. #388×D47C2semidirect
11. #387×D47C2semidirect
13. #385×D47C2semidirect
14. #383×D47C2semidirect
15. C47×#2852C2semidirect
18. C2×#13094019C22semidirect
19. C2×#13094018C22semidirect
20. C2×#13094017C22semidirect
27. C22×C4×Dic47C22semidirect
31. C2×C42×D47C22semidirect
32. C2×C42×D47C22semidirect
33. #15689017C22semidirect
34. #15689016C22semidirect
35. #15689015C22semidirect
36. #15689014C22semidirect
37. #15689013C22semidirect
38. #15689012C22semidirect
39. #15689011C22semidirect
40. #15689010C22semidirect
41. #15689009C22semidirect
42. #15689008C22semidirect
43. #15689007C22semidirect
44. #15689006C22semidirect
45. #15689005C22semidirect
46. #15689004C22semidirect
54. #15688998C22semidirect
55. #15688997C22semidirect
56. #15688997C22semidirect
57. #15688996C22semidirect
58. #15688995C22semidirect
59. #15688994C22semidirect
60. #15688994C22semidirect
61. #15688991C22semidirect
62. #15688990C22semidirect
63. #15688990C22semidirect
68. C2×#126×C47C22semidirect
69. C22×C42×C47C22semidirect
70. C47×#388C22semidirect
71. C47×#387C22semidirect
73. C47×#385C22semidirect
74. C47×#383C22semidirect
123. C42×D47D4semidirect
209. C42×C47C2×D4semidirect
228. C4×Dic47C2×D4semidirect
246. C22×D47#126semidirect
296. C22×C47C2×#126semidirect
309. C2×D47C2×#126semidirect
330. #2852D47direct (N × H)
343. D47#2852direct (N × H)
350. C2×#126C2×D47semidirect
362. C22×C42C2×D47semidirect
370. #388C2×D47semidirect
378. #387C2×D47semidirect
394. #385C2×D47semidirect
398. #383C2×D47semidirect
403. C47C2×#2852semidirect
557. C42D4×D47semidirect
635. C22#126×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#126×D472
C22×C42×D472
#202517062
#202517052
#202517042
#202517032
#202517022
#202517012
#202517002
#388×D472
#387×D472
#386×D472
#385×D472
#383×D472
C47×#28522
C2×#285247