Finite Group Databasebeta

← #29671489

Subgroups — #29671489

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458118C211yesmaximal, characteristic, complemented
2#21458055C211yesmaximal, characteristic, complemented
3#21457634C211yesmaximal, characteristic, complemented
4#21445432C211yesmaximal, characteristic, complemented
5#21445368C211yesmaximal, characteristic, complemented
6#21445354C211yesmaximal, characteristic, complemented
7#21445267C211yesmaximal, characteristic, complemented
8#21445256C211yesmaximal, characteristic, complemented
9#21445047C211yesmaximal, characteristic, complemented
10#21444996C211yesmaximal, characteristic, complemented
11#21444969C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444704C211yesmaximal, characteristic, complemented
14C8×#11758199C211yesmaximal, characteristic, complemented
15C61×#3303C211yesmaximal, characteristic, complemented
16#16840417C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840114C2211yescharacteristic, complemented
19#16840112C2211yescharacteristic, complemented
20#16840110C2211yescharacteristic
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840097—21no—
24#16840086—21no—
25#16840077—21no—
26#16840049C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16840039C2211yescharacteristic
29#16840013—21no—
30#16840006—21no—
31#16839997—21no—
32#16839967C2211yescharacteristic, complemented
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839905—21no—
36#16839895—21no—
37#16839894—21no—
38C4×#11758199C2211yescharacteristic
39#16839840C2211yescharacteristic
40#16839840C2211yescharacteristic, complemented
41C8×D244C2211yescharacteristic
42#16839766—21no—
43#16839761—21no—
44#102×D61—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57C61×#547C2211yescharacteristic, complemented
58C61×#487C2211yescharacteristic, complemented
59C61×#485—21no—
60C61×#476C2211yescharacteristic, complemented
61C61×#465—21no—
62C61×#461C2211yescharacteristic
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic, complemented
66C61×#416—21no—
67C2×#11758222—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×#11758200—21no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758199D411yescharacteristic
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×C8×D61—21no—
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519759—41no—
80#14519756—21no—
81#14519752—21no—
82#14519751—21no—
83#14519748—21no—
84#14519747—41no—
85C4×D244C2311yescharacteristic
86C4⋊C4×D61—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519701—41no—
95#14519700—21no—
96#14519700—21no—
97#14519700—21no—
98#14519699—21no—
99#14519699—21no—
100#14519698—21no—
101#14519698D411yescharacteristic
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—41no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×SD16×C61—21no—
117C2×D8×C61D411yescharacteristic
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#124×C61—41no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160D4×D61—42no—
161D4×D61—81no—
162#11758222—42no—
163#11758222—81no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—42no—
168C2×D244—41no—
169C2×D244—81no—
170C2×D244C2×D411yescharacteristic
171C2×C4×D61—21no—
172C2×C4×D61—41no—
173C2×Dic122—21no—
174SD16×C61—81no—
175D8×C61—41no—
176C2×C8×C61—21no—
177C2×C8×C61—81no—
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—41no—
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C42×C61—41no—
195C42×C61C2411yescharacteristic
196C22⋊Dic61—41no—
197#11758200—81no—
198#11758199—22no—
199#11758199—81no—
200#11758199—81no—
201#11758198—21no—
202#11758198—41no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61C2×D411yescharacteristic
206#11758196—41no—
207#11758194—81no—
208#11758194—81no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215C8×D61—81no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C22×D61—21no—
220C22×D61—41no—
221C22×D61—82no—
222C22×D61—82no—
223C22×D61—161no—
224Q8×C61—41no—
225Q8×C61—41no—
226Q8×C61—81no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—82no—
234D4×C61—161no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—82no—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61H(5,𝔽2)11yescharacteristic
250C22⋊D61—82no—
251C22⋊D61—82no—
252C2×Dic61—21no—
253C2×Dic61—41no—
254D244—21no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—41no—
259D244—81no—
260D244—82no—
261D244#13512yes—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—82no—
265Dic122—41no—
266Dic122—41no—
267C8×C61—21no—
268C8×C61—21no—
269C8×C61—41no—
270#92418—21no—
271#92418—21no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#19899—611nomaximal, Sylow
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61D4211yescharacteristic
287C2×D61—22no—
288C2×D61—41no—
289C2×D61—41no—
290C2×D61—81no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61—164no—
294C4×C61—21no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—81no—
299C4×C61—81no—
300C4×C61C2×#13511yescharacteristic
301C4×C61#57511yescharacteristic
302C4×C61#57611yescharacteristic
303C4×C61#57611yescharacteristic
304Dic61—41no—
305Dic61—81no—
306#3330—611no—
307#3325—611no—
308#3303D6111yescharacteristic, complemented
309#3294—611no—
310#1711—611no—
311#1699—611no—
312#1697—611no—
313#1683—611no—
314#1681—611no—
315#1646—611no—
316#1639—611no—
317#1635—611no—
318#1625—611no—
319#1589—611no—
320C8×D8—611no—
321C2×C61—81no—
322C2×C61—81no—
323C2×C61—81no—
324C2×C61#327311yescharacteristic
325C2×C61#328011yescharacteristic
326C2×C61#329011yescharacteristic
327D61—42no—
328D61—161no—
329#555C2×D6111yescharacteristic
330#547—611no—
331#547C2×D6111yescharacteristic, complemented
332D42—611no—
333#487—611no—
334#487—611no—
335#487C2×D6111yescharacteristic, complemented
336#486—611no—
337#486—611no—
338#486—611no—
339#485—21no—
340#484—1221no—
341#482—1221no—
342#480—1221no—
343#476—611no—
344#476C2×D6111yescharacteristic, complemented
345#474—611no—
346#474—611no—
347#469—1221no—
348#468—1221no—
349#466—1221no—
350#465—21no—
351#461—611no—
352#461C2×D6111yescharacteristic
353#459—611no—
354#459—611no—
355#449—21no—
356#449—1221no—
357#447—1221no—
358#447—1221no—
359C4×D8—611no—
360C4×D8C2×D6111yescharacteristic
361#436—611no—
362#436—611no—
363C8×D4—611no—
364C8×D4C2×D6111yescharacteristic, complemented
365#418—1221no—
366#417—1221no—
367#416—21no—
368C2×#102—1221no—
369#335—611no—
370#335—611no—
371#333—611no—
372#332—611no—
373#332—611no—
374#331—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377D4⋊C8—611no—
378D4⋊C8—611no—
379C82—611no—
380C61#1989911yescharacteristic, complemented, Sylow
381C2×#41—21no—
382C2×#41—1221no—
383C22×D4—1221no—
384C22×D4—1221no—
385C2×SD16—21no—
386C2×SD16—1221no—
387C2×D8—611no—
388C2×D8—1221no—
389C2×D8—1221no—
390C2×D8C22⋊D6111yescharacteristic
391C2×M16—1221no—
392C2×M16—1221no—
393C22×C8—21no—
394C22×C8—1221no—
395C4⋊Q8—611no—
396C4⋊Q8C22×D6111yescharacteristic
397C4⋊Q8C22×D6111yescharacteristic
398#127—611no—
399#124—41no—
400#123—41no—
401#123—2441no—
402C22⋊Q8—21no—
403C22⋊Q8—1221no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—1221no—
408#121—1221no—
409#121—1221no—
410#120—2441no—
411C4×D4—611no—
412C4×D4C22×D6111yescharacteristic
413C4×D4C22×D6111yescharacteristic
414C4×D4C22×D6111yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—1221no—
419#107—611no—
420#107—1221no—
421#107—1221no—
422#107C22⋊D6111yescharacteristic
423#106—21no—
424#106—1221no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8C22×D6111yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—1221no—
433#103—1221no—
434#103—1221no—
435#103—2441no—
436#102—21no—
437#102—611no—
438#102—611no—
439#102—1221no—
440#102—1221no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—2441no—
449#102C22⋊D6111yescharacteristic
450#102C22⋊D6111yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—1221no—
453C22⋊C8—1221no—
454C22⋊C8—1221no—
455C4×C8—611no—
456C4×C8—611no—
457C4×C8C22×D6111yescharacteristic
458C24—2441no—
459#41—42no—
460#41—81no—
461#41—4881no—
462#41—2442no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—1221no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—611no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—4881no—
473C2×D4—4881no—
474C2×D4—2441no—
475C2×D4—2442no—
476C2×D4—2441no—
477C2×D4—2442no—
478C2×D4—2441no—
479C2×D4D4×D6111yescharacteristic
480C2×D4C2×C22⋊D6111yescharacteristic
481C2×D4C2×C22⋊D6111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—41no—
486C22×C4—1221no—
487C22×C4—2441no—
488SD16—81no—
489SD16—4881no—
490D8—41no—
491D8—1222no—
492D8—4881no—
493D8—4881no—
494M16—4881no—
495M16—4881no—
496C2×C8—21no—
497C2×C8—81no—
498C2×C8—611no—
499C2×C8—611no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—1221no—
503C2×C8—1221no—
504C2×C8—4881no—
505C2×C8C2×C22⋊D6111yescharacteristic
506C2×C8C2×C22⋊D6111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—611no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—2441no—
516C4⋊C4D4×D6111yescharacteristic
517C4⋊C4C2×C22⋊D6111yescharacteristic
518C4⋊C4C2×C22⋊D6111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—1221no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C42—41no—
529C42C23×D6111yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—1221no—
534C23—9761no—
535C23—4882no—
536C23—4882no—
537C23—2441no—
538Q8—41no—
539Q8—41no—
540Q8—81no—
541Q8—2441no—
542Q8—2441no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—82no—
550D4—161no—
551D4—612no—
552D4—1221no—
553D4—4881no—
554D4—4882no—
555D4—4882no—
556D4—4882no—
557D4—2441no—
558D4—2441no—
559D4—2441no—
560D4—2441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—1221no—
574C2×C4—4882no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4C2×D4×D6111yescharacteristic
579C2×C4C22×C22⋊D6111yescharacteristic
580C2×C4#1451982211yescharacteristic
581C8—21no—
582C8—21no—
583C8—41no—
584C8—1221no—
585C8—1221no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C8—2441no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—1222no—
600C22—9764no—
601C22—4881no—
602C22—4881no—
603C22—4881no—
604C22—2441no—
605C22—2441no—
606C22D4×C22⋊D6111yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4—4881no—
614C4—2441no—
615C4#135×D6111yescharacteristic
616C4#1684056011yescharacteristic
617C4#1684056411yescharacteristic
618C4#1684056511yescharacteristic
619C2—81no—
620C2—81no—
621C2—81no—
622C2—9761no—
623C2—2442no—
624C2#2145742611yescharacteristic
625C2#2145749811yescharacteristic
626C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3303C2
socleC22×C61D42
hypercenter#3303D61
hypocenterC61#19899
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3303

Complements

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

NH ≅ G/Ntype
1. #21458118C2semidirect
2. #21458055C2semidirect
3. #21457634C2semidirect
4. #21445432C2semidirect
5. #21445368C2semidirect
6. #21445354C2semidirect
7. #21445267C2semidirect
8. #21445256C2semidirect
9. #21445047C2semidirect
10. #21444996C2semidirect
11. #21444969C2semidirect
12. #21444908C2semidirect
13. #21444704C2semidirect
14. C8×#11758199C2semidirect
15. C61×#3303C2semidirect
18. #16840114C22semidirect
19. #16840112C22semidirect
32. #16839967C22semidirect
40. #16839840C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839511C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
57. C61×#547C22semidirect
58. C61×#487C22semidirect
60. C61×#476C22semidirect
65. C8×D4×C61C22semidirect
308. #3303D61semidirect
331. #547C2×D61semidirect
335. #487C2×D61semidirect
344. #476C2×D61semidirect
364. C8×D4C2×D61semidirect
380. C61#19899semidirect

Maximal subgroups

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

subgroupindex
#214581182
#214580552
#214576342
#214454322
#214453682
#214453542
#214452672
#214452562
#214450472
#214449962
#214449692
#214449082
#214447042
C8×#117581992
C61×#33032
#1989961