Finite Group Databasebeta

← #26372737

Subgroups — #26372737

Order 12032.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689558C211yesmaximal, characteristic, complemented
2C22×#13093965C211yesmaximal, characteristic, complemented
3D4×D376C211yesmaximal, characteristic, complemented
4#20245655C211yesmaximal, characteristic, complemented
5#20245489C211yesmaximal, characteristic, complemented
6#20245486C211yesmaximal, characteristic, complemented
7#20245440C211yesmaximal, characteristic, complemented
8#20245423C211yesmaximal, characteristic, complemented
9#20245316C211yesmaximal, characteristic, complemented
10#20245311C211yesmaximal, characteristic, complemented
11#20245300C211yesmaximal, characteristic, complemented
12#20245299C211yesmaximal, characteristic, complemented
13#20245262C211yesmaximal, characteristic, complemented
14#20245214C211yesmaximal, characteristic, complemented
15C47×#3280C211yesmaximal, characteristic, complemented
16C22×D376C2211yescharacteristic
17C22×D376C2211yescharacteristic, complemented
18D4×D188—21no—
19#15689558—24no—
20C2×#13093967C2211yescharacteristic, complemented
21C2×#13093967C2211yescharacteristic, complemented
22C2×#13093967C2211yescharacteristic, complemented
23C2×#13093965—24no—
24C2×#13093965C2211yescharacteristic
25C2×#13093965C2211yescharacteristic
26C2×#13093965C2211yescharacteristic, complemented
27C2×#13093965C2211yescharacteristic, complemented
28C2×#13093965C2211yescharacteristic, complemented
29C2×#13093965C2211yescharacteristic, complemented
30C2×#13093964C2211yescharacteristic, complemented
31C22×C47⋊C16C2211yescharacteristic, complemented
32#15689500C2211yescharacteristic, complemented
33#15689359C2211yescharacteristic
34#15689359C2211yescharacteristic, complemented
35#15689319—21no—
36#15689259—21no—
37#15689259—21no—
38C4×D376C2211yescharacteristic, complemented
39#15688950C2211yescharacteristic, complemented
40C4⋊(C47⋊C16)C2211yescharacteristic, complemented
41#15688927C2211yescharacteristic, complemented
42#15688924C2211yescharacteristic, complemented
43#15688924C2211yescharacteristic, complemented
44#15688923C2211yescharacteristic, complemented
45#15688923C2211yescharacteristic, complemented
46#15688923C2211yescharacteristic, complemented
47C22⋊(C47⋊C16)C2211yescharacteristic, complemented
48C22⋊(C47⋊C16)C2211yescharacteristic, complemented
49#15688899C2211yescharacteristic, complemented
50C2×#135×C47C2211yescharacteristic, complemented
51C22×D8×C47C2211yescharacteristic, complemented
52C47×#546—21no—
53C47×#495C2211yescharacteristic, complemented
54C47×#467C2211yescharacteristic, complemented
55C47×#466C2211yescharacteristic, complemented
56C47×#463—21no—
57C47×#450—21no—
58C47×#449—21no—
59C4×D8×C47C2211yescharacteristic, complemented
60C8×D4×C47C2211yescharacteristic
61C22×D188—21no—
62C22×D188—21no—
63C2×D4×D47—41no—
64C2×D376—22no—
65C2×D376—22no—
66C2×D376—21no—
67C2×D376—21no—
68C2×D376—21no—
69C2×D376—41no—
70C2×D376—41no—
71C2×D376C2311yescharacteristic
72C2×D376C2311yescharacteristic
73C2×D376C2311yescharacteristic
74#13094021—21no—
75#13093999—41no—
76#13093998—21no—
77#13093998—21no—
78#13093994—41no—
79#13093994—41no—
80C4×D188—21no—
81#13093967—22no—
82#13093967—22no—
83#13093967—41no—
84#13093965—22no—
85#13093965—22no—
86#13093965—22no—
87#13093965—22no—
88#13093965—41no—
89#13093965D414yescomplemented
90#13093964—22no—
91C2×C47⋊C16—22no—
92C2×C47⋊C16C2311yescharacteristic
93C2×C47⋊C16C2311yescharacteristic
94C2×C47⋊C16C2311yescharacteristic
95C2×C47⋊C16C2311yescharacteristic
96#13093958C2311yescharacteristic
97#13093946—21no—
98#13093946—21no—
99#13093946—21no—
100C2×#41×C47—21no—
101C22×D4×C47—21no—
102#135×C47—22no—
103#135×C47—41no—
104C2×Q16×C47C2311yescharacteristic
105C2×SD16×C47—21no—
106C2×SD16×C47—21no—
107C2×D8×C47—22no—
108C2×D8×C47—21no—
109C2×D8×C47—41no—
110C2×D8×C47C2311yescharacteristic
111C2×D8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114#124×C47—21no—
115#123×C47—41no—
116C22⋊Q8×C47—21no—
117#121×C47—21no—
118#121×C47—41no—
119#120×C47—41no—
120C4×D4×C47—21no—
121C4×D4×C47D411yescharacteristic
122C2×C22⋊C4×C47—41no—
123#107×C47C2311yescharacteristic
124C4⋊C8×C47D411yescharacteristic
125#103×C47—21no—
126#102×C47—21no—
127#102×C47—21no—
128C22⋊C8×C47D411yescharacteristic
129C22⋊C8×C47D411yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C24×C47—41no—
132C23×D47—41no—
133C23×D47—41no—
134#41×C47—42no—
135#41×C47—81no—
136C2×Q8×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47—42no—
140C2×D4×C47—41no—
141C2×D4×C47—41no—
142C2×D4×C47—41no—
143C2×D4×C47—81no—
144C2×D4×C47D811yescharacteristic
145C22×C4×C47—41no—
146C22×C4×C47—41no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C2×C22⋊D47—41no—
150C2×C22⋊D47—41no—
151D4×D47—84no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188—42no—
156C2×D188—42no—
157C2×D188—41no—
158C2×D188—41no—
159C2×D188—41no—
160C2×D188—41no—
161C2×D188—81no—
162C2×D188—81no—
163C2×C4×D47—41no—
164Q16×C47—21no—
165Q16×C47—21no—
166SD16×C47—42no—
167SD16×C47—81no—
168D8×C47—21no—
169D8×C47—21no—
170D8×C47—21no—
171D8×C47—42no—
172D8×C47C2×D412yescomplemented
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2411yescharacteristic
181C4⋊C4×C47—21no—
182C4⋊C4×C47—41no—
183C4⋊C4×C47D811yescharacteristic
184C22⋊C4×C47—41no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47—41no—
187C22⋊C4×C47—41no—
188C22⋊C4×C47—41no—
189C22⋊C4×C47D811yescharacteristic
190C22⋊C4×C47D811yescharacteristic
191C42×C47C2×D411yescharacteristic
192(C2×D47)⋊C4—41no—
193(C2×D47)⋊C4—41no—
194(C2×D47)⋊C4—41no—
195C4⋊Dic47—21no—
196D376—21no—
197D376—21no—
198D376—21no—
199D376—21no—
200D376—21no—
201D376—42no—
202D376—42no—
203D376—81no—
204D376C2×D412yes—
205C47⋊C16—21no—
206C47⋊C16—21no—
207C47⋊C16—21no—
208C47⋊C16C2×D412yescomplemented
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—82no—
212C23×C47—82no—
213C23×C47—161no—
214C23×C47C2×D811yescharacteristic
215C23×C47C2×D811yescharacteristic
216C22×D47—41no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47—82no—
220C22×D47—82no—
221C22×D47—82no—
222C22×D47—82no—
223C22×D47—161no—
224C22×D47—161no—
225Q8×C47—41no—
226Q8×C47—41no—
227D4×C47—22no—
228D4×C47—22no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—82no—
233D4×C47—82no—
234D4×C47—161no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—82no—
242C2×C4×C47—161no—
243C2×C4×C47C2×D811yescharacteristic
244C2×C4×C47C2×D811yescharacteristic
245C2×C4×C47C2×D811yescharacteristic
246C2×C4×C47C2×D811yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C22⋊D47—82no—
249C22⋊D47—82no—
250C2×Dic47—41no—
251D188—22no—
252D188—41no—
253D188—41no—
254D188—41no—
255D188—41no—
256D188—41no—
257D188—82no—
258D188—82no—
259D188—82no—
260D188—161no—
261C4×D47—82no—
262C8×C47—21no—
263C8×C47—21no—
264C8×C47—21no—
265C8×C47C22×D411yescharacteristic
266C8×C47H(5,𝔽2)11yescharacteristic
267#33830—471nomaximal, Sylow
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—42no—
274C22×C47—81no—
275C22×C47—81no—
276C22×C47—81no—
277C22×C47—81no—
278C22×C47—81no—
279C22×C47—164no—
280C22×C47#50912yescomplemented
281C22×C47C22×D811yescharacteristic
282C2×D47—42no—
283C2×D47—81no—
284C2×D47—81no—
285C2×D47—81no—
286C2×D47—81no—
287C2×D47—81no—
288C2×D47—81no—
289C2×D47—81no—
290C2×D47—81no—
291C2×D47—164no—
292C2×D47—164no—
293C4×C47—21no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—81no—
298C4×C47—81no—
299C4×C47D4211yescharacteristic
300C4×C47#57611yescharacteristic
301Dic47—81no—
302C2×#509—471no—
303C22×D16—471no—
304#3280D4711yescharacteristic, complemented
305D4×D8—471no—
306#2250—471no—
307#2218—471no—
308#2217—471no—
309#2210—471no—
310#2206—471no—
311#2187—471no—
312#2186—471no—
313#2184—471no—
314#2184—471no—
315#2177—471no—
316#2168—471no—
317C2×C47—22no—
318C2×C47—41no—
319C2×C47—82no—
320C2×C47—161no—
321C2×C47D4×D811yescharacteristic
322C2×C47C2×#50911yescharacteristic
323C2×C47#341511yescharacteristic
324D47—82no—
325D47—161no—
326D47—161no—
327C2×#135C2×D4711yescharacteristic, complemented
328C22×D8—471no—
329C22×D8—471no—
330C22×D8C2×D4711yescharacteristic, complemented
331#546—21no—
332D42—941no—
333#509—944no—
334C2×SD32—471no—
335C2×SD32—471no—
336C2×SD32—471no—
337C2×D16—471no—
338C2×D16—471no—
339C2×D16—471no—
340C2×D16—471no—
341C2×D16—471no—
342C2×D16—471no—
343C2×D16—944no—
344C2×M32—471no—
345C22×C16—471no—
346#495C2×D4711yescharacteristic, complemented
347#493—471no—
348#467C2×D4711yescharacteristic, complemented
349#466—471no—
350#466—471no—
351#466C2×D4711yescharacteristic, complemented
352#463—21no—
353#459—941no—
354#450—21no—
355#449—21no—
356#447—941no—
357#447—941no—
358C4×D8—471no—
359C4×D8C2×D4711yescharacteristic, complemented
360C8×D4C2×D4711yescharacteristic
361#367—471no—
362C4⋊C16—471no—
363#358—471no—
364#357—471no—
365#357—471no—
366#357—471no—
367#357—471no—
368#357—471no—
369C22⋊C16—471no—
370C22⋊C16—471no—
371#346—471no—
372C47#3383011yescharacteristic, complemented, Sylow
373C2×#41—21no—
374C22×D4—21no—
375C22×D4—941no—
376C22×D4—941no—
377C22×D4—1881no—
378#135—22no—
379#135—41no—
380C2×Q16C22×D4711yescharacteristic
381C2×SD16—21no—
382C2×SD16—21no—
383C2×D8—22no—
384C2×D8—21no—
385C2×D8—41no—
386C2×D8—471no—
387C2×D8—471no—
388C2×D8—471no—
389C2×D8—942no—
390C2×D8—942no—
391C2×D8—941no—
392C2×D8—941no—
393C2×D8—941no—
394C2×D8—1881no—
395C2×D8—1881no—
396C2×D8C22×D4711yescharacteristic
397C2×D8C22×D4711yescharacteristic
398C22×C8C22×D4711yescharacteristic
399C22×C8C22×D4711yescharacteristic
400#127—941no—
401#124—21no—
402#123—41no—
403C22⋊Q8—21no—
404#121—21no—
405#121—41no—
406#121—941no—
407#121—941no—
408#121—1881no—
409#120—41no—
410#120—1881no—
411#120—1881no—
412C4×D4—21no—
413C4×D4—941no—
414C4×D4C22⋊D4711yescharacteristic
415C2×C22⋊C4—41no—
416SD32—942no—
417SD32—942no—
418SD32—1881no—
419D16—474no—
420D16—942no—
421D16—942no—
422D16—942no—
423D16—942no—
424D16—1881no—
425M32—942no—
426C2×C16—471no—
427C2×C16—471no—
428C2×C16—471no—
429C2×C16—471no—
430C2×C16—942no—
431#107—471no—
432#107C22×D4711yescharacteristic
433C4⋊C8C22⋊D4711yescharacteristic
434#103—21no—
435#102—21no—
436#102—21no—
437#102—941no—
438#102—941no—
439#102—941no—
440C22⋊C8C22⋊D4711yescharacteristic
441C22⋊C8C22⋊D4711yescharacteristic
442C4×C8C22×D4711yescharacteristic
443C24—41no—
444C24—1881no—
445C24—1881no—
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—81no—
456C2×D4—941no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4—3761no—
460C2×D4—3761no—
461C2×D4—3764no—
462C2×D4—1882no—
463C2×D4—1882no—
464C2×D4—1881no—
465C2×D4—1881no—
466C2×D4—1881no—
467C2×D4—1881no—
468C2×D4—1881no—
469C2×D4—1881no—
470C2×D4#1062533411yescharacteristic
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—1881no—
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C2×C22⋊D4711yescharacteristic
476Q16—21no—
477Q16—21no—
478SD16—42no—
479SD16—81no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—42no—
484D8—472no—
485D8—941no—
486D8—941no—
487D8—941no—
488D8—941no—
489D8—941no—
490D8—3761no—
491D8—1882no—
492D8—1882no—
493D8D4×D4712yescomplemented
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C2×C22⋊D4711yescharacteristic
499C2×C8C2×C22⋊D4711yescharacteristic
500C2×C8C2×C22⋊D4711yescharacteristic
501C2×C8C23×D4711yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—941no—
505C4⋊C4#1062533411yescharacteristic
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—1881no—
512C22⋊C4—1881no—
513C22⋊C4—1881no—
514C22⋊C4#1062533411yescharacteristic
515C22⋊C4#1062533411yescharacteristic
516C42C2×C22⋊D4711yescharacteristic
517C16—472no—
518C16—941no—
519C16—941no—
520C16—941no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526C23—3762no—
527C23—3762no—
528C23—3762no—
529C23—3762no—
530C23—1881no—
531C23—1881no—
532C23—1881no—
533C23—7521no—
534C23—7521no—
535C23C2×#1062533411yescharacteristic
536C23C2×#1062533411yescharacteristic
537Q8—41no—
538Q8—41no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—82no—
545D4—82no—
546D4—161no—
547D4—942no—
548D4—3762no—
549D4—3762no—
550D4—3762no—
551D4—3762no—
552D4—3762no—
553D4—1881no—
554D4—1881no—
555D4—1881no—
556D4—1881no—
557D4—1881no—
558D4—7521no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—3762no—
568C2×C4—1881no—
569C2×C4C2×#1062533411yescharacteristic
570C2×C4C2×#1062533411yescharacteristic
571C2×C4C2×#1062533411yescharacteristic
572C2×C4C2×#1062533411yescharacteristic
573C2×C4C22×C22⋊D4711yescharacteristic
574C8—21no—
575C8—21no—
576C8—21no—
577C8C2×D4×D4711yescharacteristic
578C8#1309406911yescharacteristic
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—164no—
591C22—3761no—
592C22—3761no—
593C22—3761no—
594C22—3761no—
595C22—3761no—
596C22—3761no—
597C22—3761no—
598C22—3761no—
599C22—1882no—
600C22—7524no—
601C22—7524no—
602C22#1568955812yescomplemented
603C22C22×#1062533411yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—81no—
609C4—81no—
610C4—3761no—
611C4D4×C22⋊D4711yescharacteristic
612C4#1568992611yescharacteristic
613C2—22no—
614C2—41no—
615C2—82no—
616C2—161no—
617C2—3762no—
618C2—7521no—
619C2—7521no—
620C2D4×#1062533411yescharacteristic
621C2C2×#1568955811yescharacteristic
622C2#2025652711yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3280C2
socleC22×C47C22×D8
hypercenter#3280D47
hypocenterC47#33830
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#15689558C2semidirect
2. C22×#13093965C2semidirect
3. D4×D376C2semidirect
4. #20245655C2semidirect
5. #20245489C2semidirect
6. #20245486C2semidirect
7. #20245440C2semidirect
8. #20245423C2semidirect
9. #20245316C2semidirect
10. #20245311C2semidirect
11. #20245300C2semidirect
12. #20245299C2semidirect
13. #20245262C2semidirect
14. #20245214C2semidirect
15. C47×#3280C2semidirect
17. C22×D376C22semidirect
20. C2×#13093967C22semidirect
21. C2×#13093967C22semidirect
22. C2×#13093967C22semidirect
26. C2×#13093965C22semidirect
27. C2×#13093965C22semidirect
28. C2×#13093965C22semidirect
29. C2×#13093965C22semidirect
30. C2×#13093964C22semidirect
31. C22×C47⋊C16C22semidirect
32. #15689500C22semidirect
34. #15689359C22semidirect
38. C4×D376C22semidirect
39. #15688950C22semidirect
40. C4⋊(C47⋊C16)C22semidirect
41. #15688927C22semidirect
42. #15688924C22semidirect
43. #15688924C22semidirect
44. #15688923C22semidirect
45. #15688923C22semidirect
46. #15688923C22semidirect
47. C22⋊(C47⋊C16)C22semidirect
48. C22⋊(C47⋊C16)C22semidirect
49. #15688899C22semidirect
50. C2×#135×C47C22semidirect
51. C22×D8×C47C22semidirect
53. C47×#495C22semidirect
54. C47×#467C22semidirect
55. C47×#466C22semidirect
59. C4×D8×C47C22semidirect
89. #13093965D4semidirect
172. D8×C47C2×D4semidirect
208. C47⋊C16C2×D4semidirect
280. C22×C47#509semidirect
304. #3280D47semidirect
327. C2×#135C2×D47semidirect
330. C22×D8C2×D47semidirect
346. #495C2×D47semidirect
348. #467C2×D47semidirect
351. #466C2×D47semidirect
359. C4×D8C2×D47semidirect
372. C47#33830semidirect
493. D8D4×D47semidirect
602. C22#15689558semidirect

Maximal subgroups

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

subgroupindex
C2×#156895582
C22×#130939652
D4×D3762
#202456552
#202454892
#202454862
#202454402
#202454232
#202453162
#202453112
#202453002
#202452992
#202452622
#202452142
C47×#32802
#3383047