Finite Group Databasebeta

← #26243759

Subgroups — #26243759

Order 12032.

1610 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689634C211yesmaximal, characteristic
2C2×#15689159C211yesmaximal, characteristic, complemented
3C2×#15689117C211yesmaximal, characteristic, complemented
4C2×#15689117C211yesmaximal, characteristic, complemented
5C22×C22⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6#20244591C212yesmaximal, complemented
7#20244584C212yesmaximal, complemented
8#20244577C212yesmaximal, complemented
9#20244570C212yesmaximal, complemented
10#20243104C211yesmaximal, characteristic, complemented
11C47×#2280C211yesmaximal, characteristic, complemented
12C22×#10625350C2211yescharacteristic
13C23×C47⋊C8C2211yescharacteristic
14C23×C47⋊C8C2211yescharacteristic
15#15689634—24no—
16#15689634—24no—
17C2×#13094007—21no—
18C2×#13094003C2212yes—
19C2×#13093998C2212yes—
20C2×#13093993—21no—
21C2×C4×C22⋊D47—22no—
22C2×#13093983C2211yescharacteristic
23#15689159—24no—
24C2×#13093957C2212yescomplemented
25C2×#13093955C2212yescomplemented
26#15689117—24no—
27#15689117—24no—
28C2×#13093947C2211yescharacteristic, complemented
29C2×#13093947C2212yescomplemented
30C2×#13093947C2211yescharacteristic, complemented
31C2×#13093944C2211yescharacteristic, complemented
32C2×#13093944C2212yescomplemented
33C2×#13093944C2211yescharacteristic, complemented
34C2×C22⋊(C47⋊C8)—24no—
35C2×C22⋊(C47⋊C8)C2212yes—
36C2×C22⋊(C47⋊C8)C2212yes—
37#15688885C2212yescomplemented
38#15688885C2212yescomplemented
39C24×C4×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C2×#117×C47C2211yescharacteristic
42C47×#381—21no—
43C47×#380C2212yes—
44C47×#380C2212yes—
45C47×#379—21no—
46C4×C22⋊C4×C47—22no—
47C2×#10625350—22no—
48C2×#10625350—22no—
49C2×#10625350—22no—
50C2×#10625350—22no—
51C2×#10625350—22no—
52C2×#10625350D414yes—
53C22×Dic94C2311yescharacteristic
54C22×D188C2311yescharacteristic
55C22×C22⋊D47—22no—
56C22×C22⋊D47—21no—
57C22×C4×D47—21no—
58C22×C47⋊C8—22no—
59C22×C47⋊C8—22no—
60C22×C47⋊C8—22no—
61C22×C47⋊C8—22no—
62C22×C47⋊C8—22no—
63C22×C47⋊C8D414yescomplemented
64C22×C47⋊C8C2312yes—
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094007—28no—
68#13094003—24no—
69#13094003—24no—
70#13093998—24no—
71#13093998—24no—
72#13093993—28no—
73C4×C22⋊D47—216no—
74#13093983—22no—
75#13093983D414yes—
76C2×C4⋊Dic47C2312yes—
77C2×Dic47⋊C4—22no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—22no—
80C2×(C2×D47)⋊C4—22no—
81C2×C4×Dic47—21no—
82#13093957—24no—
83#13093955—24no—
84#13093947—24no—
85#13093947—22no—
86#13093947—22no—
87#13093944—24no—
88#13093944—22no—
89#13093944—22no—
90C22⋊(C47⋊C8)—24no—
91C22⋊(C47⋊C8)—24no—
92C25×C47D411yescharacteristic
93C23×C4×C47—22no—
94C23×C4×C47—22no—
95C23×C4×C47—22no—
96C23×C4×C47—22no—
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47D412yes—
100C23×C4×C47D411yescharacteristic
101C23×C4×C47C2312yes—
102C23×C4×C47C2311yescharacteristic
103#117×C47—22no—
104#117×C47—22no—
105#117×C47—22no—
106#117×C47—22no—
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2312yes—
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47—22no—
114C2×C42×C47—21no—
115C2×C42×C47—21no—
116#95×C47—22no—
117#95×C47—22no—
118C24×C47—22no—
119C24×C47—24no—
120C24×C47—22no—
121C24×C47—22no—
122C24×C47—42no—
123C24×C47C2×D412yes—
124C24×C47C2×D411yescharacteristic
125C23×D47—21no—
126C22×C4×C47—22no—
127C22×C4×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—24no—
130C22×C4×C47—24no—
131C22×C4×C47—24no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—44no—
142C22×C4×C47—44no—
143C22×C4×C47—44no—
144C22×C4×C47—44no—
145C22×C4×C47C2×D412yes—
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D412yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D412yes—
150C22×C4×C47#4112yes—
151C22×C4×C47#4112yes—
152C22×C4×C47#4112yes—
153C22×C4×C47C2411yescharacteristic
154C2×C22⋊D47—28no—
155C2×C22⋊D47—24no—
156C2×C22⋊D47—44no—
157C2×C22⋊D47—42no—
158C2×C22⋊D47—42no—
159C2×C22⋊D47—44no—
160C22×Dic47—22no—
161C22×Dic47—21no—
162#10625350—28no—
163#10625350—28no—
164#10625350—44no—
165#10625350—44no—
166C2×D188—21no—
167C2×D188—21no—
168C2×D188—21no—
169C2×D188—21no—
170C2×D188—21no—
171C2×D188C2×D412yes—
172C2×C4×D47—24no—
173C2×C4×D47—42no—
174C2×C4×D47—42no—
175C2×Dic94—21no—
176C2×Dic94—21no—
177C2×Dic94—21no—
178C2×Dic94—21no—
179C2×Dic94—21no—
180C2×Dic94C2×D412yes—
181C4⋊C4×C47—22no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—21no—
184C4⋊C4×C47—22no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C22⋊C4×C47—44no—
188C22⋊C4×C47—42no—
189C22⋊C4×C47—42no—
190C22⋊C4×C47—44no—
191C42×C47—42no—
192C42×C47—42no—
193C22⋊Dic47—28no—
194C22⋊Dic47—24no—
195(C2×D47)⋊C4—28no—
196C4⋊Dic47—22no—
197C4⋊Dic47C2×D414yes—
198Dic47⋊C4—28no—
199C4×Dic47—24no—
200C2×C47⋊C8—28no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—44no—
209C2×C47⋊C8C2×D412yes—
210C2×C47⋊C8C2×D412yes—
211C23×C47—22no—
212C23×C47—22no—
213C23×C47—28no—
214C23×C47—22no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—22no—
219C23×C47—22no—
220C23×C47—48no—
221C23×C47—48no—
222C23×C47—44no—
223C23×C47—44no—
224C23×C47#12012yes—
225C23×C47#12112yes—
226C23×C47#12312yes—
227C23×C47#13514yes—
228C23×C47C22×D411yescharacteristic
229C22×D47—22no—
230C22×D47—41no—
231C22×D47—41no—
232C22×D47—42no—
233C22×D47—42no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—44no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—42no—
241C2×C4×C47—42no—
242C2×C4×C47—48no—
243C2×C4×C47—42no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—42no—
249C2×C4×C47—42no—
250C2×C4×C47#12012yes—
251C2×C4×C47#12112yes—
252C2×C4×C47#12114yes—
253C2×C4×C47#12114yes—
254C2×C4×C47#12314yes—
255C2×C4×C47#12312yes—
256C2×C4×C47#12414yes—
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×C4×C47C22×D411yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C22⋊D47—416no—
264C22⋊D47—48no—
265C2×Dic47—24no—
266C2×Dic47—22no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271D188—22no—
272D188—22no—
273D188—41no—
274D188—41no—
275C4×D47—48no—
276Dic94—22no—
277Dic94—22no—
278Dic94—41no—
279Dic94—41no—
280C47⋊C8—22no—
281C47⋊C8—22no—
282C47⋊C8—42no—
283#23479—471nomaximal, Sylow
284C22×C47—24no—
285C22×C47—24no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—24no—
289C22×C47—24no—
290C22×C47—24no—
291C22×C47—416no—
292C22×C47—42no—
293C22×C47—42no—
294C22×C47—42no—
295C22×C47—42no—
296C22×C47#39414yes—
297C22×C47C2×#12011yescharacteristic
298C22×C47C2×#12111yescharacteristic
299C22×C47C2×#12311yescharacteristic
300C22×C47C2×#13512yes—
301C22×C47#57512yes—
302C2×D47—42no—
303C2×D47—44no—
304C2×D47—82no—
305C2×D47—81no—
306C2×D47—81no—
307C4×C47—42no—
308C4×C47—82no—
309C4×C47—81no—
310C4×C47—81no—
311C4×C47#39414yes—
312C4×C47C2×#12111yescharacteristic
313C4×C47C2×#12111yescharacteristic
314C4×C47C2×#12311yescharacteristic
315C4×C47C2×#12411yescharacteristic
316Dic47—42no—
317Dic47—44no—
318C2×#525—471no—
319C2×#427—471no—
320C2×#416—471no—
321C2×#416—471no—
322C22×C22⋊C8—471no—
323#2280D4711yescharacteristic, complemented
324#2036—472no—
325#2035—472no—
326#2034—472no—
327#2033—472no—
328#1735—471no—
329C2×C47—24no—
330C2×C47—44no—
331C2×C47C2×#39411yescharacteristic
332C2×C47#300212yes—
333C2×C47#305011yescharacteristic
334C2×C47#305411yescharacteristic
335C2×C47#309112yes—
336D47—82no—
337C22×#41—471no—
338C24×C4C2×D4711yescharacteristic
339C23×C8—471no—
340C23×C8—471no—
341#525—944no—
342#525—944no—
343C2×#123—941no—
344C2×C22⋊Q8—472no—
345C2×#121—472no—
346C2×#120—941no—
347C2×C4×D4—942no—
348C2×#117—471no—
349C2×#117C2×D4711yescharacteristic
350C2×#117C2×D4711yescharacteristic
351#427—944no—
352C2×#107—472no—
353C2×#106—472no—
354#416—944no—
355#416—944no—
356C2×#103—471no—
357C2×#103—472no—
358C2×#103—471no—
359C2×#102—471no—
360C2×#102—472no—
361C2×#102—471no—
362C2×C22⋊C8—472no—
363C2×C22⋊C8—472no—
364C2×C22⋊C8—944no—
365#381—21no—
366#380C2×D4712yes—
367#380C2×D4712yes—
368#379—21no—
369C4×C22⋊C4—22no—
370#340—472no—
371#340—472no—
372C47#2347911yescharacteristic, complemented, Sylow
373C25C22⋊D4711yescharacteristic
374C2×#41—474no—
375C2×#41—942no—
376C2×#41—942no—
377C2×#41—942no—
378C2×#41—942no—
379C2×#41—942no—
380C22×Q8—471no—
381C22×D4—471no—
382C22×D4—942no—
383C22×D4—941no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—941no—
391C23×C4C22⋊D4711yescharacteristic
392C23×C4C22⋊D4712yes—
393C23×C4C22×D4712yes—
394C23×C4C22×D4711yescharacteristic
395C22×C8—474no—
396C22×C8—471no—
397C22×C8—471no—
398C22×C8—472no—
399C22×C8—942no—
400C22×C8—942no—
401C22×C8—942no—
402C22×C8—942no—
403C22×C8—942no—
404#123—948no—
405C22⋊Q8—944no—
406C22⋊Q8—944no—
407#121—944no—
408#121—944no—
409#120—948no—
410C4×D4—9416no—
411#117—22no—
412#117—22no—
413#117—22no—
414#117—22no—
415#117—474no—
416#117—942no—
417C2×C4⋊C4—472no—
418C2×C4⋊C4—942no—
419C2×C4⋊C4C22×D4711yescharacteristic
420C2×C4⋊C4C22×D4711yescharacteristic
421C2×C4⋊C4C22×D4712yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—941no—
427C2×C22⋊C4—942no—
428C2×C22⋊C4—942no—
429C2×C42—21no—
430C2×C42—21no—
431C2×C42—941no—
432#107—944no—
433#106—944no—
434#103—942no—
435#103—942no—
436#103—944no—
437#102—942no—
438#102—942no—
439#102—944no—
440C22⋊C8—944no—
441C22⋊C8—944no—
442#95—22no—
443#95—22no—
444C24—22no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—42no—
449C24—941no—
450C24C2×C22⋊D4712yes—
451C24C2×C22⋊D4711yescharacteristic
452#41—948no—
453#41—948no—
454#41—1884no—
455#41—1884no—
456C2×Q8—472no—
457C2×Q8—941no—
458C2×Q8—941no—
459C2×Q8—941no—
460C2×Q8—941no—
461C2×Q8—941no—
462C2×D4—472no—
463C2×D4—948no—
464C2×D4—944no—
465C2×D4—941no—
466C2×D4—941no—
467C2×D4—941no—
468C2×D4—941no—
469C2×D4—941no—
470C2×D4—1884no—
471C2×D4—1882no—
472C2×D4—1882no—
473C2×D4—1884no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—942no—
494C22×C4—941no—
495C22×C4—944no—
496C22×C4—1882no—
497C22×C4—1882no—
498C22×C4#1062535012yes—
499C22×C4#1062535012yes—
500C22×C4D4×D4712yes—
501C22×C4D4×D4712yes—
502C22×C4D4×D4712yes—
503C22×C4#1062535212yes—
504C22×C4C2×C22⋊D4712yes—
505C22×C4C2×C22⋊D4711yescharacteristic
506C22×C4C23×D4711yescharacteristic
507C2×C8—472no—
508C2×C8—472no—
509C2×C8—948no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—942no—
515C2×C8—942no—
516C2×C8—942no—
517C2×C8—1884no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—474no—
525C4⋊C4—948no—
526C4⋊C4—942no—
527C22⋊C4—44no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—44no—
531C22⋊C4—948no—
532C22⋊C4—948no—
533C22⋊C4—944no—
534C42—42no—
535C42—42no—
536C42—944no—
537C23—22no—
538C23—22no—
539C23—28no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—48no—
547C23—48no—
548C23—44no—
549C23—44no—
550C23—942no—
551C23—1881no—
552C23—1881no—
553C23—1882no—
554C23—1882no—
555C23#1309399212yes—
556C23#1309399612yes—
557C23#1309400712yes—
558C23#1309404414yes—
559C23C22×C22⋊D4711yescharacteristic
560Q8—942no—
561Q8—942no—
562Q8—1881no—
563Q8—1881no—
564D4—942no—
565D4—942no—
566D4—18816no—
567D4—1888no—
568D4—1881no—
569D4—1881no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—44no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—944no—
587C2×C4—942no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4—1882no—
591C2×C4—1882no—
592C2×C4—1888no—
593C2×C4#1309399212yes—
594C2×C4#1309399612yes—
595C2×C4#1309399714yes—
596C2×C4#1309399714yes—
597C2×C4#1309400614yes—
598C2×C4#1309400712yes—
599C2×C4#1309401014yes—
600C2×C4C2×D4×D4711yescharacteristic
601C2×C4C2×D4×D4711yescharacteristic
602C2×C4C2×D4×D4711yescharacteristic
603C2×C4C2×#1062535211yescharacteristic
604C2×C4C2×#1062535011yescharacteristic
605C2×C4C2×#1062535011yescharacteristic
606C8—942no—
607C8—942no—
608C8—1882no—
609C22—22no—
610C22—22no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—416no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—3761no—
622C22—3761no—
623C22—3762no—
624C22—1882no—
625C22—1884no—
626C22#1568903814yes—
627C22C2×#1309399211yescharacteristic
628C22C2×#1309399611yescharacteristic
629C22C2×#1309400711yescharacteristic
630C22C2×#1309404412yes—
631C22#1568992112yes—
632C4—42no—
633C4—81no—
634C4—81no—
635C4—82no—
636C4—1882no—
637C4—1884no—
638C4#1568903814yes—
639C4C2×#1309399711yescharacteristic
640C4C2×#1309399711yescharacteristic
641C4C2×#1309400611yescharacteristic
642C4C2×#1309401011yescharacteristic
643C2—24no—
644C2—44no—
645C2—3762no—
646C2C2×#1568903811yescharacteristic
647C2#2025260412yes—
648C2#2025296611yescharacteristic
649C2#2025299411yescharacteristic
650C2#2025330112yes—
subgroupG/H
centerC22×C4C2×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2280C2
socleC23×C47C22×D4
prime radicalC2×#15689634C2
hypercenter#2280D47
hypocenterC47#23479
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#15689159C2semidirect
3. C2×#15689117C2semidirect
4. C2×#15689117C2semidirect
5. C22×C22⋊(C47⋊C8)C2semidirect
6. #20244591C2semidirect
7. #20244584C2semidirect
8. #20244577C2semidirect
9. #20244570C2semidirect
10. #20243104C2semidirect
11. C47×#2280C2semidirect
24. C2×#13093957C22semidirect
25. C2×#13093955C22semidirect
28. C2×#13093947C22semidirect
29. C2×#13093947C22semidirect
30. C2×#13093947C22semidirect
31. C2×#13093944C22semidirect
32. C2×#13093944C22semidirect
33. C2×#13093944C22semidirect
37. #15688885C22semidirect
38. #15688885C22semidirect
63. C22×C47⋊C8D4semidirect
323. #2280D47semidirect
372. C47#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#156896342
C2×#156891592
C2×#156891172
C22×C22⋊(C47⋊C8)2
#202445912
#202445842
#202445772
#202445702
#202431042
C47×#22802
#2347947