Finite Group Databasebeta

← #26372732

Subgroups — #26372732

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×#15689559C211yesmaximal, characteristic, complemented
2C22×#13093965C211yesmaximal, characteristic, complemented
3#20255075C211yesmaximal, characteristic, complemented
4#20245652C211yesmaximal, characteristic, complemented
5#20245489C211yesmaximal, characteristic, complemented
6#20245482C211yesmaximal, characteristic, complemented
7#20245443C211yesmaximal, characteristic, complemented
8#20245420C211yesmaximal, characteristic, complemented
9#20245317C211yesmaximal, characteristic, complemented
10#20245309C211yesmaximal, characteristic, complemented
11#20245300C211yesmaximal, characteristic, complemented
12#20245299C211yesmaximal, characteristic, complemented
13#20245262C211yesmaximal, characteristic, complemented
14#20245214C211yesmaximal, characteristic, complemented
15D4×D8×C47C211yesmaximal, characteristic, complemented
16C2×#13094046C2211yescharacteristic, complemented
17C22×D376C2211yescharacteristic, complemented
18#15689769—21no—
19#15689559—24no—
20C2×#13093968C2211yescharacteristic, complemented
21C2×#13093968C2211yescharacteristic, complemented
22C2×#13093968C2211yescharacteristic, 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#15689507C2211yescharacteristic, complemented
33#15689364C2211yescharacteristic, complemented
34#15689359C2211yescharacteristic, complemented
35#15689339—21no—
36#15689276—21no—
37#15689270—21no—
38C4×D376C2211yescharacteristic, complemented
39#15688950C2211yescharacteristic, complemented
40C4⋊(C47⋊C16)C2211yescharacteristic, complemented
41#15688926C2211yescharacteristic, complemented
42#15688924C2211yescharacteristic, complemented
43#15688924C2211yescharacteristic, complemented
44#15688924C2211yescharacteristic, complemented
45#15688923C2211yescharacteristic, complemented
46#15688923C2211yescharacteristic, complemented
47C22⋊(C47⋊C16)C2211yescharacteristic, complemented
48C22⋊(C47⋊C16)C2211yescharacteristic, complemented
49#15688899C2211yescharacteristic, complemented
50C22×D8×C47C2211yescharacteristic
51C22×D8×C47C2211yescharacteristic, complemented
52D42×C47—21no—
53C47×#493C2211yescharacteristic, complemented
54C47×#466C2211yescharacteristic
55C47×#466C2211yescharacteristic, complemented
56C47×#459—21no—
57C47×#447—21no—
58C47×#447—21no—
59C4×D8×C47C2211yescharacteristic, complemented
60C8×D4×C47C2211yescharacteristic
61C2×#10625350—21no—
62C22×D188—21no—
63#13094046—22no—
64#13094046—41no—
65C2×Dic188C2311yescharacteristic
66C2×#10625325—21no—
67C2×#10625325—21no—
68C2×D376—22no—
69C2×D376—21no—
70C2×D376—41no—
71C2×D376C2311yescharacteristic
72C2×D376C2311yescharacteristic
73#13094012—21no—
74#13094009—41no—
75#13094003—21no—
76#13093998—21no—
77#13093997—41no—
78#13093992—41no—
79C4×D188—21no—
80C22⋊C4×D47—41no—
81#13093968—22no—
82#13093968—22no—
83#13093968—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#13093949—21no—
98#13093946—21no—
99#13093946—21no—
100C22×D4×C47—21no—
101C22×D4×C47—21no—
102C22×D4×C47—41no—
103C2×D8×C47—22no—
104C2×D8×C47—22no—
105C2×D8×C47—21no—
106C2×D8×C47—21no—
107C2×D8×C47—21no—
108C2×D8×C47—41no—
109C2×D8×C47—41no—
110C2×D8×C47C2311yescharacteristic
111C2×D8×C47C2311yescharacteristic
112C2×D8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115#127×C47—21no—
116#121×C47—21no—
117#121×C47—21no—
118#121×C47—41no—
119#120×C47—41no—
120#120×C47—41no—
121C4×D4×C47—21no—
122C4×D4×C47D411yescharacteristic
123#107×C47C2311yescharacteristic
124C4⋊C8×C47D411yescharacteristic
125#102×C47—21no—
126#102×C47—21no—
127#102×C47—21no—
128C22⋊C8×C47D411yescharacteristic
129C22⋊C8×C47D411yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C24×C47—41no—
132C24×C47—41no—
133C23×D47—41no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47—42no—
138C2×D4×C47—42no—
139C2×D4×C47—41no—
140C2×D4×C47—41no—
141C2×D4×C47—41no—
142C2×D4×C47—41no—
143C2×D4×C47—41no—
144C2×D4×C47—41no—
145C2×D4×C47—81no—
146C2×D4×C47—81no—
147C2×D4×C47—84no—
148C2×D4×C47D811yescharacteristic
149C22×C4×C47—41no—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C2×C22⋊D47—41no—
153C2×C22⋊D47—41no—
154#10625350—42no—
155#10625350—81no—
156C2×D188—21no—
157C2×D188—21no—
158C2×D188—42no—
159C2×D188—41no—
160C2×D188—81no—
161C2×C4×D47—41no—
162C2×C4×D47—41no—
163C2×Dic94—21no—
164D8×C47—21no—
165D8×C47—21no—
166D8×C47—21no—
167D8×C47—21no—
168D8×C47—21no—
169D8×C47—42no—
170D8×C47—42no—
171D8×C47—81no—
172D8×C47C2×D412yes—
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×C47D811yescharacteristic
183C22⋊C4×C47—41no—
184C22⋊C4×C47—41no—
185C22⋊C4×C47—41no—
186C22⋊C4×C47D811yescharacteristic
187C22⋊C4×C47D811yescharacteristic
188C42×C47C2×D411yescharacteristic
189C22⋊Dic47—41no—
190(C2×D47)⋊C4—41no—
191(C2×D47)⋊C4—41no—
192(C2×D47)⋊C4—41no—
193(C2×D47)⋊C4—41no—
194C4⋊Dic47—21no—
195Dic47⋊C4—41no—
196Dic188—21no—
197Dic188—21no—
198D376—21no—
199D376—21no—
200D376—21no—
201D376—42no—
202D376C2×D412yescomplemented
203#10625325—42no—
204#10625325—81no—
205C47⋊C16—21no—
206C47⋊C16—21no—
207C47⋊C16—21no—
208C47⋊C16C2×D412yescomplemented
209C23×C47—41no—
210C23×C47—41no—
211C23×C47—41no—
212C23×C47—82no—
213C23×C47—82no—
214C23×C47—82no—
215C23×C47—82no—
216C23×C47—161no—
217C23×C47—161no—
218C23×C47C2×D811yescharacteristic
219C23×C47C2×D811yescharacteristic
220C22×D47—41no—
221C22×D47—41no—
222C22×D47—82no—
223C22×D47—82no—
224C22×D47—161no—
225D4×C47—22no—
226D4×C47—22no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—41no—
230D4×C47—41no—
231D4×C47—41no—
232D4×C47—82no—
233D4×C47—82no—
234D4×C47—82no—
235D4×C47—82no—
236D4×C47—82no—
237D4×C47—161no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—41no—
243C2×C4×C47—82no—
244C2×C4×C47C2×D811yescharacteristic
245C2×C4×C47C2×D811yescharacteristic
246C2×C4×C47C2×D811yescharacteristic
247C2×C4×C47C2×D811yescharacteristic
248C2×C4×C47C22×D411yescharacteristic
249C22⋊D47—82no—
250C22⋊D47—161no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253D188—22no—
254D188—41no—
255D188—41no—
256D188—41no—
257D188—82no—
258C4×D47—82no—
259C4×D47—161no—
260Dic94—41no—
261Dic94—41no—
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—81no—
280C22×C47—81no—
281C22×C47—81no—
282C22×C47—164no—
283C22×C47—164no—
284C22×C47#50912yescomplemented
285C22×C47C22×D811yescharacteristic
286C2×D47—42no—
287C2×D47—81no—
288C2×D47—81no—
289C2×D47—81no—
290C2×D47—81no—
291C2×D47—81no—
292C2×D47—164no—
293C4×C47—21no—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—81no—
298C4×C47D4211yescharacteristic
299C4×C47#57611yescharacteristic
300Dic47—81no—
301Dic47—81no—
302C2×#509—471no—
303C22×D16—471no—
304#3280—471no—
305D4×D8D4711yescharacteristic, complemented
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×C47—161no—
322C2×C47D4×D811yescharacteristic
323C2×C47C2×#50911yescharacteristic
324C2×C47#341511yescharacteristic
325D47—82no—
326D47—161no—
327C2×#135—471no—
328C22×D8—471no—
329C22×D8C2×D4711yescharacteristic
330C22×D8C2×D4711yescharacteristic, complemented
331#546—941no—
332D42—21no—
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#495—471no—
347#493C2×D4711yescharacteristic, complemented
348#467—471no—
349#466—471no—
350#466C2×D4711yescharacteristic
351#466C2×D4711yescharacteristic, complemented
352#463—941no—
353#459—21no—
354#450—941no—
355#449—941no—
356#447—21no—
357#447—21no—
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—941no—
374C22×D4—21no—
375C22×D4—21no—
376C22×D4—41no—
377C22×D4—941no—
378#135—942no—
379#135—1881no—
380C2×Q16—471no—
381C2×SD16—941no—
382C2×SD16—941no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—41no—
389C2×D8—41no—
390C2×D8—471no—
391C2×D8—471no—
392C2×D8—942no—
393C2×D8—941no—
394C2×D8—1881no—
395C2×D8C22×D4711yescharacteristic
396C2×D8C22×D4711yescharacteristic
397C2×D8C22×D4711yescharacteristic
398C22×C8C22×D4711yescharacteristic
399C22×C8C22×D4711yescharacteristic
400#127—21no—
401#124—941no—
402#123—1881no—
403C22⋊Q8—941no—
404#121—21no—
405#121—21no—
406#121—41no—
407#121—941no—
408#121—1881no—
409#120—41no—
410#120—41no—
411#120—1881no—
412C4×D4—21no—
413C4×D4—941no—
414C4×D4C22⋊D4711yescharacteristic
415C2×C22⋊C4—1881no—
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—941no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—941no—
439#102—941no—
440C22⋊C8C22⋊D4711yescharacteristic
441C22⋊C8C22⋊D4711yescharacteristic
442C4×C8C22×D4711yescharacteristic
443C24—41no—
444C24—41no—
445C24—1881no—
446#41—3761no—
447#41—1882no—
448C2×Q8—941no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4—84no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4—3761no—
466C2×D4—1882no—
467C2×D4—1881no—
468C2×D4—1881no—
469C2×D4—1881no—
470C2×D4#1062533411yescharacteristic
471C22×C4—41no—
472C22×C4—1881no—
473C22×C4—1881no—
474C22×C4C2×C22⋊D4711yescharacteristic
475C22×C4C2×C22⋊D4711yescharacteristic
476Q16—941no—
477Q16—941no—
478SD16—3761no—
479SD16—1882no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—21no—
485D8—42no—
486D8—42no—
487D8—81no—
488D8—472no—
489D8—941no—
490D8—941no—
491D8—941no—
492D8—1882no—
493D8D4×D4712yes—
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—941no—
504C4⋊C4—1881no—
505C4⋊C4#1062533411yescharacteristic
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—1881no—
510C22⋊C4—1881no—
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—41no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—161no—
530C23—3762no—
531C23—3762no—
532C23—1881no—
533C23—1881no—
534C23—7521no—
535C23C2×#1062533411yescharacteristic
536C23C2×#1062533411yescharacteristic
537Q8—1881no—
538Q8—1881no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—82no—
547D4—82no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—942no—
553D4—3762no—
554D4—3762no—
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—82no—
565C2×C4—3762no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—7521no—
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—81no—
591C22—81no—
592C22—81no—
593C22—164no—
594C22—164no—
595C22—3761no—
596C22—3761no—
597C22—3761no—
598C22—3761no—
599C22—3761no—
600C22—1882no—
601C22—7524no—
602C22#1568955912yescomplemented
603C22C22×#1062533411yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—81no—
609C4—3761no—
610C4—3761no—
611C4D4×C22⋊D4711yescharacteristic
612C4#1568992611yescharacteristic
613C2—22no—
614C2—41no—
615C2—82no—
616C2—161no—
617C2—161no—
618C2—3762no—
619C2—7521no—
620C2D4×#1062533411yescharacteristic
621C2C2×#1568955911yescharacteristic
622C2#2025652711yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingD4×D8×C47C2
socleC22×C47C22×D8
hypercenterD4×D8D47
hypocenterC47#33830
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#15689559C2semidirect
2. C22×#13093965C2semidirect
3. #20255075C2semidirect
4. #20245652C2semidirect
5. #20245489C2semidirect
6. #20245482C2semidirect
7. #20245443C2semidirect
8. #20245420C2semidirect
9. #20245317C2semidirect
10. #20245309C2semidirect
11. #20245300C2semidirect
12. #20245299C2semidirect
13. #20245262C2semidirect
14. #20245214C2semidirect
15. D4×D8×C47C2semidirect
16. C2×#13094046C22semidirect
17. C22×D376C22semidirect
20. C2×#13093968C22semidirect
21. C2×#13093968C22semidirect
22. C2×#13093968C22semidirect
26. C2×#13093965C22semidirect
27. C2×#13093965C22semidirect
28. C2×#13093965C22semidirect
29. C2×#13093965C22semidirect
30. C2×#13093964C22semidirect
31. C22×C47⋊C16C22semidirect
32. #15689507C22semidirect
33. #15689364C22semidirect
34. #15689359C22semidirect
38. C4×D376C22semidirect
39. #15688950C22semidirect
40. C4⋊(C47⋊C16)C22semidirect
41. #15688926C22semidirect
42. #15688924C22semidirect
43. #15688924C22semidirect
44. #15688924C22semidirect
45. #15688923C22semidirect
46. #15688923C22semidirect
47. C22⋊(C47⋊C16)C22semidirect
48. C22⋊(C47⋊C16)C22semidirect
49. #15688899C22semidirect
51. C22×D8×C47C22semidirect
53. C47×#493C22semidirect
55. C47×#466C22semidirect
59. C4×D8×C47C22semidirect
89. #13093965D4semidirect
202. D376C2×D4semidirect
208. C47⋊C16C2×D4semidirect
284. C22×C47#509semidirect
305. D4×D8D47semidirect
330. C22×D8C2×D47semidirect
347. #493C2×D47semidirect
351. #466C2×D47semidirect
359. C4×D8C2×D47semidirect
372. C47#33830semidirect
602. C22#15689559semidirect

Maximal subgroups

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

subgroupindex
C2×#156895592
C22×#130939652
#202550752
#202456522
#202454892
#202454822
#202454432
#202454202
#202453172
#202453092
#202453002
#202452992
#202452622
#202452142
D4×D8×C472
#3383047