Finite Group Databasebeta

← #26123503

Subgroups — #26123503

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20251905C211yesmaximal, characteristic
2C2×#15689122C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4C2×#15688893C211yesmaximal, characteristic, complemented
5#20243107C211yesmaximal, characteristic, complemented
6#20243097C211yesmaximal, characteristic, complemented
7C47×#2317C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689131—21no—
13#15689127—21no—
14#15689122—22no—
15#15689122—21no—
16#15689122—21no—
17#15689122—22no—
18#15689117—22no—
19C2×#13093947—21no—
20C2×#13093944—21no—
21#15689096—22no—
22#15689096C414yescomplemented
23C2×#13093938—22no—
24#15688893—22no—
25#15688885—22no—
26#15688882—22no—
27C2×#117×C47C2211yescharacteristic
28C2×#117×C47C2211yescharacteristic
29C22×C4⋊C4×C47C2211yescharacteristic
30C47×#389—22no—
31C47×#385—22no—
32C47×#384—21no—
33C47×#382—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350C2×C412yes—
45C2×#10625350Q812yes—
46C22×Dic94D411yescharacteristic
47C22×D188D411yescharacteristic
48C22×C22⋊D47—21no—
49C22×C4×D47—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329D412yes—
62C22×C47⋊C8—21no—
63C22×C47⋊C8D412yes—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67#13093983C2×C412yes—
68C2×C4⋊Dic47—21no—
69C2×C22⋊Dic47—21no—
70C2×C4×Dic47—21no—
71#13093947—24no—
72#13093947—22no—
73#13093947—22no—
74#13093944—24no—
75#13093944—22no—
76#13093944—22no—
77#13093938—28no—
78C23×C4×C47—21no—
79C23×C4×C47C2311yescharacteristic
80#117×C47—21no—
81#117×C47—21no—
82#117×C47—21no—
83#117×C47—21no—
84#117×C47—21no—
85#117×C47—21no—
86#117×C47C2×C412yes—
87#117×C47D412yes—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
93C2×C4⋊C4×C47—21no—
94C2×C4⋊C4×C47—24no—
95C2×C4⋊C4×C47D412yes—
96C2×C4⋊C4×C47D411yescharacteristic
97C2×C4⋊C4×C47D411yescharacteristic
98C2×C22⋊C4×C47—21no—
99C2×C22⋊C4×C47D412yes—
100C2×C42×C47—21no—
101C2×C42×C47—21no—
102#95×C47—24no—
103C24×C47C2×D411yescharacteristic
104C23×D47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—22no—
109C22×C4×C47—41no—
110C22×C4×C47—41no—
111C22×C4×C47—82no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×C4×C47C2×D411yescharacteristic
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D411yescharacteristic
119C22×C4×C47C2×Q811yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47#4111yescharacteristic
123C22×C4×C47#4111yescharacteristic
124C22×C4×C47#4111yescharacteristic
125C22×C4×C47#4111yescharacteristic
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—41no—
129C2×C22⋊D47—41no—
130C2×C22⋊D47—41no—
131C2×C22⋊D47—41no—
132C22×Dic47—21no—
133C22×Dic47—41no—
134#10625350—22no—
135#10625350—22no—
136#10625350—22no—
137#10625350—22no—
138#10625350—22no—
139#10625350—22no—
140#10625350—22no—
141#10625350—22no—
142#10625350—41no—
143#10625350—41no—
144#10625350—41no—
145#10625350—41no—
146#10625350—41no—
147#10625350—41no—
148#10625350—41no—
149#10625350—41no—
150C2×D188—21no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188C4⋊C412yescomplemented
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×C4×D47—41no—
159C2×C4×D47—41no—
160C2×C4×D47—41no—
161C2×C4×D47—41no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164C2×Dic94—21no—
165C2×Dic94—21no—
166C2×Dic94—21no—
167C2×Dic94C4⋊C412yescomplemented
168C4⋊C4×C47—22no—
169C4⋊C4×C47—22no—
170C4⋊C4×C47—22no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—41no—
177C4⋊C4×C47—41no—
178C4⋊C4×C47—84no—
179C22⋊C4×C47—22no—
180C22⋊C4×C47—41no—
181C22⋊C4×C47—41no—
182C22⋊C4×C47C22⋊C414yes—
183C42×C47—22no—
184C42×C47—22no—
185C42×C47—41no—
186C42×C47—41no—
187C22⋊Dic47—22no—
188C22⋊Dic47—41no—
189C4⋊Dic47—22no—
190C4⋊Dic47—41no—
191C4×Dic47—22no—
192C4×Dic47—41no—
193#10625329—22no—
194#10625329—22no—
195#10625329—41no—
196#10625329—41no—
197#10625329—41no—
198#10625329—41no—
199#10625329—41no—
200#10625329—41no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—41no—
206C2×C47⋊C8—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47C2×C22⋊C411yescharacteristic
210C23×C47#12011yescharacteristic
211C23×C47#12111yescharacteristic
212C23×C47C22⋊Q811yescharacteristic
213C23×C47#12311yescharacteristic
214C23×C47#12411yescharacteristic
215C23×C47#12711yescharacteristic
216C22×D47—22no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47—81no—
220C22×D47—81no—
221C2×C4×C47—24no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—44no—
226C2×C4×C47—42no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—42no—
230C2×C4×C47—82no—
231C2×C4×C47—82no—
232C2×C4×C47C2×C4⋊C411yescharacteristic
233C2×C4×C47#11711yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C4×D411yescharacteristic
237C2×C4×C47C4×D411yescharacteristic
238C2×C4×C47#12011yescharacteristic
239C2×C4×C47#12011yescharacteristic
240C2×C4×C47#12111yescharacteristic
241C2×C4×C47#12111yescharacteristic
242C2×C4×C47#12111yescharacteristic
243C2×C4×C47#12111yescharacteristic
244C2×C4×C47#12111yescharacteristic
245C2×C4×C47#12111yescharacteristic
246C2×C4×C47#12111yescharacteristic
247C2×C4×C47C22⋊Q811yescharacteristic
248C2×C4×C47C22⋊Q811yescharacteristic
249C2×C4×C47C22⋊Q811yescharacteristic
250C2×C4×C47C22⋊Q811yescharacteristic
251C2×C4×C47C22⋊Q811yescharacteristic
252C2×C4×C47#12311yescharacteristic
253C2×C4×C47#12311yescharacteristic
254C2×C4×C47#12311yescharacteristic
255C2×C4×C47#12311yescharacteristic
256C2×C4×C47#12411yescharacteristic
257C2×C4×C47#12411yescharacteristic
258C2×C4×C47#12611yescharacteristic
259C2×C4×C47#12611yescharacteristic
260C22⋊D47—42no—
261C22⋊D47—42no—
262C22⋊D47—42no—
263C22⋊D47—42no—
264C2×Dic47—22no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—42no—
268C2×Dic47—81no—
269C2×Dic47—81no—
270D188—22no—
271D188—22no—
272D188—41no—
273D188—41no—
274C4×D47—42no—
275C4×D47—42no—
276C4×D47—42no—
277C4×D47—42no—
278Dic94—22no—
279Dic94—22no—
280Dic94—41no—
281Dic94—41no—
282C47⋊C8—42no—
283C47⋊C8—42no—
284#11093—471nomaximal, Sylow
285C22×C47—21no—
286C22×C47—21no—
287C22×C47—21no—
288C22×C47—21no—
289C22×C47—21no—
290C22×C47—21no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47—41no—
294C22×C47—41no—
295C22×C47#38011yescharacteristic
296C22×C47#38611yescharacteristic
297C22×C47#39011yescharacteristic
298C22×C47#39211yescharacteristic
299C22×C47#39311yescharacteristic
300C22×C47#39711yescharacteristic
301C22×C47#39911yescharacteristic
302C2×D47—42no—
303C2×D47—82no—
304C2×D47—81no—
305C2×D47—81no—
306C2×D47—82no—
307C4×C47—44no—
308C4×C47—81no—
309C4×C47—82no—
310C4×C47—81no—
311C4×C47#38511yescharacteristic
312C4×C47#38511yescharacteristic
313C4×C47#38811yescharacteristic
314C4×C47#38811yescharacteristic
315C4×C47#39411yescharacteristic
316C4×C47#39411yescharacteristic
317C4×C47#39611yescharacteristic
318C4×C47#39611yescharacteristic
319Dic47—42no—
320Dic47—82no—
321#2896—471no—
322C2×#417—471no—
323C2×#410—471no—
324#2317D4711yescharacteristic, complemented
325C2×#344—471no—
326#1736—471no—
327#1733—471no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47—21no—
331C2×C47—21no—
332C2×C47—21no—
333C2×C47—21no—
334C2×C47#143911yescharacteristic
335C2×C47#200811yescharacteristic
336C2×C47#200911yescharacteristic
337D47—82no—
338C22×#41—471no—
339C22×M16—471no—
340C22×M16—471no—
341C2×#117—471no—
342C2×#117C2×D4711yescharacteristic
343C2×#117C2×D4711yescharacteristic
344C22×C4⋊C4C2×D4711yescharacteristic
345#419—941no—
346#418—941no—
347#417—942no—
348#417—942no—
349#417—941no—
350#417—941no—
351#416—942no—
352C2×#103—941no—
353C2×#102—941no—
354#410—474no—
355#410—942no—
356C2×#99—942no—
357#389—22no—
358#385—22no—
359#384—21no—
360#382—21no—
361#344—942no—
362#340—942no—
363#339—942no—
364C47#1109311yescharacteristic, complemented, Sylow
365C2×#41—472no—
366C2×#41—472no—
367C2×#41—941no—
368C2×#41—941no—
369C2×#41—941no—
370C2×#41—941no—
371C2×#41—941no—
372C2×#41—941no—
373C2×#41—941no—
374C2×#41—941no—
375C2×#41—941no—
376C2×#41—941no—
377C22×Q8—471no—
378C22×D4—471no—
379C22×D4—941no—
380C23×C4—21no—
381C23×C4—941no—
382C23×C4C22×D4711yescharacteristic
383C2×M16—472no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16—941no—
390C2×M16—941no—
391C2×M16—941no—
392C2×M16—941no—
393C2×M16—941no—
394C2×M16—941no—
395C22×C8—472no—
396C22×C8—941no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—472no—
404#117—941no—
405#117—941no—
406#117—941no—
407#117C4×D4712yes—
408#117D18812yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—941no—
417C2×C4⋊C4C22⋊D4712yes—
418C2×C4⋊C4C22⋊D4711yescharacteristic
419C2×C4⋊C4C22⋊D4711yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—941no—
422C2×C22⋊C4C22⋊D4712yes—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—941no—
426#103—944no—
427#103—942no—
428#103—942no—
429#102—944no—
430#102—942no—
431#102—942no—
432#99—948no—
433#95—24no—
434C24—941no—
435C24C2×C22⋊D4711yescharacteristic
436#41—942no—
437#41—942no—
438#41—942no—
439#41—942no—
440#41—942no—
441#41—942no—
442#41—942no—
443#41—942no—
444#41—1881no—
445#41—1881no—
446#41—1881no—
447#41—1881no—
448#41—1881no—
449#41—1881no—
450#41—1881no—
451#41—1881no—
452C2×Q8—472no—
453C2×Q8—941no—
454C2×Q8—941no—
455C2×Q8—941no—
456C2×Q8—941no—
457C2×Q8—941no—
458C2×D4—472no—
459C2×D4—942no—
460C2×D4—942no—
461C2×D4—941no—
462C2×D4—941no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4—941no—
466C2×D4—1881no—
467C2×D4—1881no—
468C2×D4—1881no—
469C2×D4—1881no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—82no—
477C22×C4—941no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—1881no—
481C22×C4—1881no—
482C22×C4—1881no—
483C22×C4—1881no—
484C22×C4—1881no—
485C22×C4C2×C4×D4711yescharacteristic
486C22×C4C2×D18811yescharacteristic
487C22×C4#1062535011yescharacteristic
488C22×C4#1062535011yescharacteristic
489C22×C4D4×D4711yescharacteristic
490C22×C4D4×D4711yescharacteristic
491C22×C4D4×D4711yescharacteristic
492C22×C4#1062535211yescharacteristic
493C22×C4Q8×D4711yescharacteristic
494C22×C4#1062535411yescharacteristic
495C22×C4#1062535411yescharacteristic
496C22×C4#1062535411yescharacteristic
497C22×C4C2×C22⋊D4711yescharacteristic
498C22×C4C2×C22⋊D4711yescharacteristic
499M16—942no—
500M16—942no—
501M16—1881no—
502M16—1881no—
503M16—1881no—
504M16—1881no—
505M16—1881no—
506M16—1881no—
507C2×C8—942no—
508C2×C8—942no—
509C2×C8—942no—
510C2×C8—942no—
511C2×C8—1881no—
512C2×C8—1881no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—84no—
524C4⋊C4—942no—
525C4⋊C4—1881no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—942no—
530C22⋊C4—1881no—
531C22⋊C4(C2×D47)⋊C414yes—
532C42—22no—
533C42—22no—
534C42—41no—
535C42—41no—
536C42—942no—
537C42—1881no—
538C23—41no—
539C23—41no—
540C23—942no—
541C23—3761no—
542C23—3761no—
543C23—1881no—
544C23—1881no—
545C23C2×(C2×D47)⋊C411yescharacteristic
546C23#1309399311yescharacteristic
547C23#1309399511yescharacteristic
548C23#1309400011yescharacteristic
549C23#1309400711yescharacteristic
550C23#1309401311yescharacteristic
551C23#1309402011yescharacteristic
552Q8—942no—
553Q8—942no—
554Q8—1881no—
555Q8—1881no—
556D4—942no—
557D4—942no—
558D4—1882no—
559D4—1882no—
560D4—1882no—
561D4—1882no—
562D4—1881no—
563D4—1881no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—942no—
576C2×C4—3761no—
577C2×C4—3761no—
578C2×C4—1882no—
579C2×C4—1881no—
580C2×C4—1881no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4—1882no—
584C2×C4—1882no—
585C2×C4C4⋊C4×D4711yescharacteristic
586C2×C4#1309398211yescharacteristic
587C2×C4C4×C22⋊D4711yescharacteristic
588C2×C4C4×C22⋊D4711yescharacteristic
589C2×C4#1309398611yescharacteristic
590C2×C4#1309398611yescharacteristic
591C2×C4#1309399211yescharacteristic
592C2×C4#1309399211yescharacteristic
593C2×C4#1309399611yescharacteristic
594C2×C4#1309399611yescharacteristic
595C2×C4#1309399811yescharacteristic
596C2×C4#1309399811yescharacteristic
597C2×C4#1309399911yescharacteristic
598C2×C4#1309399911yescharacteristic
599C2×C4#1309399911yescharacteristic
600C2×C4#1309400011yescharacteristic
601C2×C4#1309400011yescharacteristic
602C2×C4#1309400211yescharacteristic
603C2×C4#1309400211yescharacteristic
604C2×C4#1309400411yescharacteristic
605C2×C4#1309400911yescharacteristic
606C2×C4#1309400911yescharacteristic
607C2×C4#1309400911yescharacteristic
608C2×C4#1309400911yescharacteristic
609C2×C4#1309401311yescharacteristic
610C2×C4#1309401311yescharacteristic
611C2×C4#1309401911yescharacteristic
612C2×C4#1309401911yescharacteristic
613C8—1882no—
614C8—1882no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—3762no—
626C22—3762no—
627C22—3761no—
628C22—3761no—
629C22—1882no—
630C22#1568898011yescharacteristic
631C22#1568900211yescharacteristic
632C22#1568902411yescharacteristic
633C22#1568903111yescharacteristic
634C22#1568903411yescharacteristic
635C22#1568904911yescharacteristic
636C22#1568905811yescharacteristic
637C4—44no—
638C4—82no—
639C4—81no—
640C4—81no—
641C4—3762no—
642C4—1882no—
643C4#1568899411yescharacteristic
644C4#1568899411yescharacteristic
645C4#1568901311yescharacteristic
646C4#1568901311yescharacteristic
647C4#1568904011yescharacteristic
648C4#1568904011yescharacteristic
649C4#1568904511yescharacteristic
650C4#1568904511yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—3762no—
658C2#2024163011yescharacteristic
659C2#2024444111yescharacteristic
660C2#2024444811yescharacteristic
subgroupG/H
centerC22#15689031
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#2317C2
socleC22×C47#392
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#2317D47
hypocenterC47#11093
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. C2×#15688893C2semidirect
5. #20243107C2semidirect
6. #20243097C2semidirect
7. C47×#2317C2semidirect
22. #15689096C4semidirect
155. C2×D188C4⋊C4semidirect
167. C2×Dic94C4⋊C4semidirect
324. #2317D47semidirect
364. C47#11093semidirect

Maximal subgroups

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

subgroupindex
#202519052
C2×#156891222
C2×#156890962
C2×#156888932
#202431072
#202430972
C47×#23172
#1109347