Finite Group Databasebeta

← #26372752

Subgroups — #26372752

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689558C211yesmaximal, characteristic, complemented
2C22×#13093967C211yesmaximal, characteristic, complemented
3D4×D376C211yesmaximal, characteristic, complemented
4#20245655C211yesmaximal, characteristic, complemented
5#20245503C211yesmaximal, characteristic, complemented
6#20245472C211yesmaximal, characteristic, complemented
7#20245440C211yesmaximal, characteristic, complemented
8#20245428C211yesmaximal, characteristic, complemented
9#20245316C211yesmaximal, characteristic, complemented
10#20245311C211yesmaximal, characteristic, complemented
11#20245305C211yesmaximal, characteristic, complemented
12#20245299C211yesmaximal, characteristic, complemented
13#20245250C211yesmaximal, characteristic, complemented
14#20245214C211yesmaximal, characteristic, complemented
15C47×#3285C211yesmaximal, characteristic, complemented
16C22×D376C2211yescharacteristic
17C22×D376C2211yescharacteristic
18D4×D188—21no—
19#15689558—24no—
20C2×#13093967—24no—
21C2×#13093967C2211yescharacteristic
22C2×#13093967C2211yescharacteristic
23C2×#13093967C2211yescharacteristic, complemented
24C2×#13093967C2211yescharacteristic, complemented
25C2×#13093967C2211yescharacteristic, complemented
26C2×#13093967C2211yescharacteristic, complemented
27C2×#13093965C2211yescharacteristic
28C2×#13093965C2211yescharacteristic, complemented
29C2×#13093965C2211yescharacteristic, complemented
30C2×#13093964C2211yescharacteristic, complemented
31C22×C47⋊C16C2211yescharacteristic, complemented
32#15689500C2211yescharacteristic
33#15689359C2211yescharacteristic
34#15689359C2211yescharacteristic
35#15689319—21no—
36#15689259—21no—
37#15689259—21no—
38C4×D376C2211yescharacteristic
39#15688948C2211yescharacteristic, complemented
40C4⋊(C47⋊C16)C2211yescharacteristic, complemented
41#15688927C2211yescharacteristic, complemented
42#15688927C2211yescharacteristic, complemented
43#15688924C2211yescharacteristic, complemented
44#15688923C2211yescharacteristic
45#15688923C2211yescharacteristic, complemented
46#15688923C2211yescharacteristic, complemented
47C22⋊(C47⋊C16)C2211yescharacteristic, complemented
48C22⋊(C47⋊C16)C2211yescharacteristic, complemented
49#15688899C2211yescharacteristic, complemented
50C2×#135×C47C2211yescharacteristic, complemented
51C22×Q16×C47C2211yescharacteristic, complemented
52C47×#548—21no—
53C47×#495C2211yescharacteristic, complemented
54C47×#467C2211yescharacteristic, complemented
55C47×#466C2211yescharacteristic, complemented
56C47×#464—21no—
57C47×#452—21no—
58C47×#448—21no—
59C4×Q16×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—22no—
84#13093967—22no—
85#13093967—41no—
86#13093967D414yescomplemented
87#13093965—22no—
88#13093965—22no—
89#13093965—41no—
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×Q8×C47—21no—
102#135×C47—22no—
103#135×C47—41no—
104C2×Q16×C47—22no—
105C2×Q16×C47—21no—
106C2×Q16×C47—41no—
107C2×Q16×C47C2311yescharacteristic
108C2×Q16×C47C2311yescharacteristic
109C2×SD16×C47—21no—
110C2×SD16×C47—21no—
111C2×D8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114#124×C47—21no—
115#124×C47—41no—
116C22⋊Q8×C47—21no—
117C22⋊Q8×C47—41no—
118#121×C47—21no—
119#121×C47—41no—
120C4×Q8×C47—21no—
121C4×D4×C47—41no—
122C4×D4×C47D411yescharacteristic
123#107×C47C2311yescharacteristic
124C4⋊C8×C47D411yescharacteristic
125#103×C47—21no—
126#103×C47—21no—
127#102×C47—21no—
128C22⋊C8×C47D411yescharacteristic
129C22⋊C8×C47D411yescharacteristic
130C4×C8×C47C2311yescharacteristic
131C23×D47—41no—
132C23×D47—41no—
133#41×C47—42no—
134#41×C47—81no—
135C2×Q8×C47—21no—
136C2×Q8×C47—21no—
137C2×Q8×C47—42no—
138C2×Q8×C47—41no—
139C2×Q8×C47—81no—
140C2×D4×C47—21no—
141C2×D4×C47—41no—
142C2×D4×C47—41no—
143C2×D4×C47D811yescharacteristic
144C22×C4×C47—41no—
145C22×C4×C47—41no—
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C2×C22⋊D47—41no—
149C2×C22⋊D47—41no—
150D4×D47—84no—
151C2×D188—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—42no—
155C2×D188—42no—
156C2×D188—41no—
157C2×D188—41no—
158C2×D188—41no—
159C2×D188—41no—
160C2×D188—81no—
161C2×D188—81no—
162C2×C4×D47—41no—
163Q16×C47—21no—
164Q16×C47—21no—
165Q16×C47—21no—
166Q16×C47—42no—
167Q16×C47C2×D412yescomplemented
168SD16×C47—42no—
169SD16×C47—81no—
170D8×C47—21no—
171D8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47C2×D411yescharacteristic
177C2×C8×C47C2×D411yescharacteristic
178C2×C8×C47C2×D411yescharacteristic
179C2×C8×C47C2411yescharacteristic
180C4⋊C4×C47—21no—
181C4⋊C4×C47—41no—
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×C47D811yescharacteristic
189C22⋊C4×C47D811yescharacteristic
190C42×C47—41no—
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×C47C2×D811yescharacteristic
211C23×C47C2×D811yescharacteristic
212C22×D47—41no—
213C22×D47—41no—
214C22×D47—41no—
215C22×D47—82no—
216C22×D47—82no—
217C22×D47—82no—
218C22×D47—82no—
219C22×D47—161no—
220C22×D47—161no—
221Q8×C47—22no—
222Q8×C47—41no—
223Q8×C47—41no—
224Q8×C47—41no—
225Q8×C47—82no—
226D4×C47—22no—
227D4×C47—41no—
228D4×C47—41no—
229D4×C47—82no—
230D4×C47—82no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—82no—
239C2×C4×C47—82no—
240C2×C4×C47C2×D811yescharacteristic
241C2×C4×C47C2×D811yescharacteristic
242C2×C4×C47C2×D811yescharacteristic
243C2×C4×C47C2×D811yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C22⋊D47—82no—
246C22⋊D47—82no—
247C2×Dic47—41no—
248D188—22no—
249D188—41no—
250D188—41no—
251D188—41no—
252D188—41no—
253D188—41no—
254D188—82no—
255D188—82no—
256D188—82no—
257D188—161no—
258C4×D47—82no—
259C8×C47—21no—
260C8×C47—21no—
261C8×C47—21no—
262C8×C47C22×D411yescharacteristic
263C8×C47H(5,𝔽2)11yescharacteristic
264#33831—471nomaximal, Sylow
265C22×C47—21no—
266C22×C47—21no—
267C22×C47—21no—
268C22×C47—21no—
269C22×C47—21no—
270C22×C47—81no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47#50912yescomplemented
274C22×C47C22×D811yescharacteristic
275C2×D47—42no—
276C2×D47—81no—
277C2×D47—81no—
278C2×D47—81no—
279C2×D47—81no—
280C2×D47—81no—
281C2×D47—81no—
282C2×D47—81no—
283C2×D47—81no—
284C2×D47—164no—
285C2×D47—164no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—21no—
289C4×C47—21no—
290C4×C47—42no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47D4211yescharacteristic
294C4×C47#57611yescharacteristic
295Dic47—81no—
296C2×#509—471no—
297C22×SD32—471no—
298#3285D4711yescharacteristic, complemented
299D4×D8—471no—
300#2250—471no—
301#2220—471no—
302#2215—471no—
303#2210—471no—
304#2207—471no—
305#2187—471no—
306#2186—471no—
307#2185—471no—
308#2184—471no—
309#2175—471no—
310#2168—471no—
311C2×C47—22no—
312C2×C47—41no—
313C2×C47—161no—
314C2×C47D4×D811yescharacteristic
315C2×C47C2×#50911yescharacteristic
316C2×C47#341611yescharacteristic
317D47—82no—
318D47—161no—
319D47—161no—
320C2×#135C2×D4711yescharacteristic, complemented
321C22×Q16C2×D4711yescharacteristic, complemented
322C22×D8—471no—
323C22×D8—471no—
324#548—21no—
325D42—941no—
326#509—944no—
327C2×SD32—471no—
328C2×SD32—471no—
329C2×SD32—471no—
330C2×SD32—471no—
331C2×SD32—471no—
332C2×SD32—471no—
333C2×SD32—944no—
334C2×D16—471no—
335C2×D16—471no—
336C2×D16—471no—
337C2×M32—471no—
338C22×C16—471no—
339#495C2×D4711yescharacteristic, complemented
340#493—471no—
341#467C2×D4711yescharacteristic, complemented
342#466—471no—
343#466—471no—
344#466C2×D4711yescharacteristic, complemented
345#464—21no—
346#459—941no—
347#452—21no—
348#448—21no—
349#447—941no—
350#447—941no—
351C4×Q16C2×D4711yescharacteristic, complemented
352C4×D8—471no—
353C8×D4C2×D4711yescharacteristic
354#366—471no—
355C4⋊C16—471no—
356#358—471no—
357#358—471no—
358#357—471no—
359#357—471no—
360#357—471no—
361#357—471no—
362C22⋊C16—471no—
363C22⋊C16—471no—
364#346—471no—
365C47#3383111yescharacteristic, complemented, Sylow
366C2×#41—21no—
367C22×Q8—21no—
368C22×D4—941no—
369C22×D4—941no—
370C22×D4—1881no—
371#135—22no—
372#135—41no—
373C2×Q16—22no—
374C2×Q16—21no—
375C2×Q16—41no—
376C2×Q16C22×D4711yescharacteristic
377C2×Q16C22×D4711yescharacteristic
378C2×SD16—21no—
379C2×SD16—21no—
380C2×D8—471no—
381C2×D8—471no—
382C2×D8—471no—
383C2×D8—942no—
384C2×D8—942no—
385C2×D8—941no—
386C2×D8—941no—
387C2×D8—941no—
388C2×D8—1881no—
389C2×D8—1881no—
390C2×D8C22×D4711yescharacteristic
391C22×C8C22×D4711yescharacteristic
392C22×C8C22×D4711yescharacteristic
393#127—941no—
394#124—21no—
395#124—41no—
396C22⋊Q8—21no—
397C22⋊Q8—41no—
398#121—21no—
399#121—41no—
400#121—941no—
401#121—941no—
402#121—1881no—
403#120—1881no—
404#120—1881no—
405C4×Q8—21no—
406C4×D4—41no—
407C4×D4—941no—
408C4×D4C22⋊D4711yescharacteristic
409SD32—474no—
410SD32—942no—
411SD32—942no—
412SD32—942no—
413SD32—942no—
414SD32—1881no—
415D16—942no—
416D16—942no—
417D16—1881no—
418M32—942no—
419C2×C16—471no—
420C2×C16—471no—
421C2×C16—471no—
422C2×C16—471no—
423C2×C16—942no—
424#107—471no—
425#107C22×D4711yescharacteristic
426C4⋊C8C22⋊D4711yescharacteristic
427#103—21no—
428#103—21no—
429#102—21no—
430#102—941no—
431#102—941no—
432#102—941no—
433C22⋊C8C22⋊D4711yescharacteristic
434C22⋊C8C22⋊D4711yescharacteristic
435C4×C8C22×D4711yescharacteristic
436C24—1881no—
437C24—1881no—
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—42no—
443C2×Q8—41no—
444C2×Q8—81no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—941no—
449C2×D4—941no—
450C2×D4—941no—
451C2×D4—3761no—
452C2×D4—3761no—
453C2×D4—3764no—
454C2×D4—1882no—
455C2×D4—1882no—
456C2×D4—1881no—
457C2×D4—1881no—
458C2×D4—1881no—
459C2×D4—1881no—
460C2×D4—1881no—
461C2×D4—1881no—
462C2×D4#1062533411yescharacteristic
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—1881no—
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C2×C22⋊D4711yescharacteristic
468Q16—21no—
469Q16—21no—
470Q16—21no—
471Q16—42no—
472Q16D4×D4712yescomplemented
473SD16—42no—
474SD16—81no—
475D8—21no—
476D8—21no—
477D8—472no—
478D8—941no—
479D8—941no—
480D8—941no—
481D8—941no—
482D8—941no—
483D8—3761no—
484D8—1882no—
485D8—1882no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8C2×C22⋊D4711yescharacteristic
491C2×C8C2×C22⋊D4711yescharacteristic
492C2×C8C2×C22⋊D4711yescharacteristic
493C2×C8C23×D4711yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—941no—
498C4⋊C4#1062533411yescharacteristic
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—1881no—
504C22⋊C4—1881no—
505C22⋊C4—1881no—
506C22⋊C4#1062533411yescharacteristic
507C22⋊C4#1062533411yescharacteristic
508C42—41no—
509C42C2×C22⋊D4711yescharacteristic
510C16—472no—
511C16—941no—
512C16—941no—
513C16—941no—
514C23—41no—
515C23—3762no—
516C23—3762no—
517C23—3762no—
518C23—3762no—
519C23—1881no—
520C23—1881no—
521C23—1881no—
522C23—7521no—
523C23—7521no—
524C23C2×#1062533411yescharacteristic
525C23C2×#1062533411yescharacteristic
526Q8—22no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—82no—
531D4—22no—
532D4—41no—
533D4—41no—
534D4—82no—
535D4—82no—
536D4—942no—
537D4—3762no—
538D4—3762no—
539D4—3762no—
540D4—3762no—
541D4—3762no—
542D4—1881no—
543D4—1881no—
544D4—1881no—
545D4—1881no—
546D4—1881no—
547D4—7521no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—82no—
556C2×C4—82no—
557C2×C4—3762no—
558C2×C4—1881no—
559C2×C4C2×#1062533411yescharacteristic
560C2×C4C2×#1062533411yescharacteristic
561C2×C4C2×#1062533411yescharacteristic
562C2×C4C2×#1062533411yescharacteristic
563C2×C4C22×C22⋊D4711yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8C2×D4×D4711yescharacteristic
568C8#1309406911yescharacteristic
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—3761no—
578C22—3761no—
579C22—3761no—
580C22—3761no—
581C22—3761no—
582C22—3761no—
583C22—3761no—
584C22—3761no—
585C22—1882no—
586C22—7524no—
587C22—7524no—
588C22#1568955812yescomplemented
589C22C22×#1062533411yescharacteristic
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—3761no—
598C4D4×C22⋊D4711yescharacteristic
599C4#1568992611yescharacteristic
600C2—22no—
601C2—41no—
602C2—161no—
603C2—3762no—
604C2—7521no—
605C2—7521no—
606C2D4×#1062533411yescharacteristic
607C2C2×#1568955811yescharacteristic
608C2#2025653211yescharacteristic
subgroupG/H
centerC22C22×#10625334
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC47×#3285C2
socleC22×C47C22×D8
hypercenter#3285D47
hypocenterC47#33831
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. C2×#15689558C2semidirect
2. C22×#13093967C2semidirect
3. D4×D376C2semidirect
4. #20245655C2semidirect
5. #20245503C2semidirect
6. #20245472C2semidirect
7. #20245440C2semidirect
8. #20245428C2semidirect
9. #20245316C2semidirect
10. #20245311C2semidirect
11. #20245305C2semidirect
12. #20245299C2semidirect
13. #20245250C2semidirect
14. #20245214C2semidirect
15. C47×#3285C2semidirect
23. C2×#13093967C22semidirect
24. C2×#13093967C22semidirect
25. C2×#13093967C22semidirect
26. C2×#13093967C22semidirect
28. C2×#13093965C22semidirect
29. C2×#13093965C22semidirect
30. C2×#13093964C22semidirect
31. C22×C47⋊C16C22semidirect
39. #15688948C22semidirect
40. C4⋊(C47⋊C16)C22semidirect
41. #15688927C22semidirect
42. #15688927C22semidirect
43. #15688924C22semidirect
45. #15688923C22semidirect
46. #15688923C22semidirect
47. C22⋊(C47⋊C16)C22semidirect
48. C22⋊(C47⋊C16)C22semidirect
49. #15688899C22semidirect
50. C2×#135×C47C22semidirect
51. C22×Q16×C47C22semidirect
53. C47×#495C22semidirect
54. C47×#467C22semidirect
55. C47×#466C22semidirect
59. C4×Q16×C47C22semidirect
86. #13093967D4semidirect
167. Q16×C47C2×D4semidirect
208. C47⋊C16C2×D4semidirect
273. C22×C47#509semidirect
298. #3285D47semidirect
320. C2×#135C2×D47semidirect
321. C22×Q16C2×D47semidirect
339. #495C2×D47semidirect
341. #467C2×D47semidirect
344. #466C2×D47semidirect
351. C4×Q16C2×D47semidirect
365. C47#33831semidirect
472. Q16D4×D47semidirect
588. 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×#130939672
D4×D3762
#202456552
#202455032
#202454722
#202454402
#202454282
#202453162
#202453112
#202453052
#202452992
#202452502
#202452142
C47×#32852
#3383147