Finite Group Databasebeta

← #29669661

Subgroups — #29669661

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458055C211yesmaximal, characteristic, complemented
2#21457741C211yesmaximal, characteristic, complemented
3#21457634C211yesmaximal, characteristic, complemented
4#21445475C211yesmaximal, characteristic, complemented
5#21445396C211yesmaximal, characteristic, complemented
6#21445256C211yesmaximal, characteristic, complemented
7#21445230C211yesmaximal, characteristic, complemented
8#21445215C211yesmaximal, characteristic, complemented
9#21445047C211yesmaximal, characteristic, complemented
10#21444969C211yesmaximal, characteristic, complemented
11#21444934C211yesmaximal, characteristic, complemented
12#21444902C211yesmaximal, characteristic, complemented
13#21444649C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic, complemented
15C61×#3341C211yesmaximal, characteristic, complemented
16#16840417C2211yescharacteristic
17D4×D244C2211yescharacteristic
18#16840136C2211yescharacteristic
19#16840114C2211yescharacteristic, complemented
20#16840112C2211yescharacteristic, complemented
21#16840110C2211yescharacteristic
22#16840109C2211yescharacteristic
23#16840103—21no—
24#16840086—21no—
25#16840077—21no—
26#16840049C2211yescharacteristic
27#16840049C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16840013—21no—
30#16839997—21no—
31#16839989—21no—
32#16839967C2211yescharacteristic, complemented
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839905—21no—
36#16839895—21no—
37#16839894—21no—
38C4×#11758199C2211yescharacteristic
39#16839840C2211yescharacteristic
40C8×D244C2211yescharacteristic
41D4×#92418C2211yescharacteristic, complemented
42#16839766—21no—
43#16839756—21no—
44#102×D61—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839511C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57C61×#555C2211yescharacteristic, complemented
58C61×#500C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#482—21no—
61C61×#476C2211yescharacteristic
62C61×#476C2211yescharacteristic, complemented
63C61×#466—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic, complemented
66C61×#427—21no—
67C2×#11758222—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×#11758200—21no—
71C2×#11758201—41no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758199D411yescharacteristic
75C2×#11758194—21no—
76C22×#92418—21no—
77C2×C8×D61—21no—
78#14519777C2311yescharacteristic
79#14519774C2311yescharacteristic
80#14519759—41no—
81#14519756—21no—
82#14519752—21no—
83#14519751—21no—
84#14519748—21no—
85#14519747—41no—
86C4×D244C2311yescharacteristic
87C4⋊C4×D61—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91#14519708—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519701—41no—
96#14519700—21no—
97#14519700—21no—
98#14519700—21no—
99#14519699—21no—
100#14519699—21no—
101#14519698—21no—
102#14519698D411yescharacteristic
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×D8×C61D411yescharacteristic
116C22×C8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#124×C61—41no—
120#124×C61—41no—
121#121×C61—21no—
122#121×C61—21no—
123#121×C61—21no—
124#121×C61—21no—
125C4×D4×C61C2311yescharacteristic
126C4×D4×C61C2311yescharacteristic
127C4×D4×C61C2311yescharacteristic
128#117×C61—21no—
129#117×C61—21no—
130#117×C61—21no—
131#117×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C23×D61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×D4×C61—41no—
148C2×D4×C61—41no—
149C2×D4×C61C2×D411yescharacteristic
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157D4×D61—42no—
158D4×D61—81no—
159#11758222—42no—
160#11758222—81no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—42no—
165C2×D244—41no—
166C2×D244—81no—
167C2×D244C2×D411yescharacteristic
168C2×C4×D61—21no—
169C2×C4×D61—41no—
170C2×Dic122—21no—
171D8×C61—41no—
172C2×C8×C61—21no—
173C2×C8×C61—42no—
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C42×C61—41no—
191C42×C61—41no—
192C42×C61C2411yescharacteristic
193C22⋊Dic61—41no—
194#11758201—82no—
195#11758200—81no—
196#11758199—22no—
197#11758199—81no—
198#11758199—81no—
199#11758198—21no—
200#11758198—41no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61C2×D411yescharacteristic
204#11758196—41no—
205#11758194—81no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—81no—
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C8×D61—81no—
214C23×C61—21no—
215C23×C61—21no—
216C23×C61—21no—
217C22×D61—21no—
218C22×D61—41no—
219C22×D61—82no—
220C22×D61—82no—
221C22×D61—161no—
222Q8×C61—81no—
223Q8×C61—81no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—161no—
231D4×C61—161no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C22⋊D61—82no—
247C22⋊D61—82no—
248C2×Dic61—21no—
249C2×Dic61—41no—
250D244—21no—
251D244—41no—
252D244—41no—
253D244—41no—
254D244—41no—
255D244—81no—
256D244—82no—
257D244#13512yes—
258C4×D61—41no—
259C4×D61—41no—
260C4×D61—82no—
261Dic122—41no—
262Dic122—41no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—41no—
266#92418—21no—
267#92418—21no—
268#92418—41no—
269#92418—41no—
270#92418—41no—
271#92418—41no—
272#19775—611nomaximal, Sylow
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61D4211yescharacteristic
283C2×D61—22no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—164no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—81no—
295C4×C61—81no—
296C4×C61C2×#13511yescharacteristic
297C4×C61#57511yescharacteristic
298C4×C61#57611yescharacteristic
299C4×C61#57711yescharacteristic
300Dic61—41no—
301Dic61—81no—
302#3341D6111yescharacteristic, complemented
303#3325—611no—
304#3303—611no—
305#3294—611no—
306#1719—611no—
307#1703—611no—
308#1681—611no—
309#1677—611no—
310#1675—611no—
311#1646—611no—
312#1635—611no—
313#1629—611no—
314#1624—611no—
315#1581—611no—
316#1580—611no—
317C2×C61—81no—
318C2×C61—81no—
319C2×C61—81no—
320C2×C61#326711yescharacteristic
321C2×C61#328011yescharacteristic
322C2×C61#328811yescharacteristic
323D61—42no—
324D61—161no—
325#555C2×D6111yescharacteristic
326#555C2×D6111yescharacteristic, complemented
327#547—611no—
328D42—611no—
329#500C2×D6111yescharacteristic, complemented
330#492—611no—
331#487—611no—
332#487—611no—
333#486—611no—
334#486—611no—
335#485—1221no—
336#482—21no—
337#482—21no—
338#482—1221no—
339#480—1221no—
340#476—611no—
341#476—611no—
342#476C2×D6111yescharacteristic
343#476C2×D6111yescharacteristic, complemented
344#474—611no—
345#469—1221no—
346#466—21no—
347#466—1221no—
348#465—1221no—
349#461—611no—
350#459—611no—
351#459—611no—
352#449—1221no—
353#447—1221no—
354#447—1221no—
355C4×D8—611no—
356C4×D8C2×D6111yescharacteristic
357#436—611no—
358C8×D4—611no—
359C8×D4—611no—
360C8×D4C2×D6111yescharacteristic, complemented
361#427—21no—
362#418—1221no—
363#416—1221no—
364C2×#102—1221no—
365#335—611no—
366#334—611no—
367#333—611no—
368#333—611no—
369#332—611no—
370#331—611no—
371D4⋊C8—611no—
372D4⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375#322—611no—
376C61#1977511yescharacteristic, complemented, Sylow
377C2×#41—1221no—
378C22×D4—1221no—
379C22×D4—1221no—
380C2×SD16—1221no—
381C2×SD16—2441no—
382C2×D8—611no—
383C2×D8—1221no—
384C2×D8—1221no—
385C2×D8C22⋊D6111yescharacteristic
386C2×M16—1221no—
387C22×C8—21no—
388C22×C8—1221no—
389C22×C8—1221no—
390C4⋊Q8—611no—
391C4⋊Q8C22×D6111yescharacteristic
392C4⋊Q8C22×D6111yescharacteristic
393#127—611no—
394#124—41no—
395#124—41no—
396#123—2441no—
397C22⋊Q8—1221no—
398#121—21no—
399#121—21no—
400#121—21no—
401#121—21no—
402#121—1221no—
403#121—1221no—
404#121—1221no—
405#120—2441no—
406C4×D4—611no—
407C4×D4C22×D6111yescharacteristic
408C4×D4C22×D6111yescharacteristic
409C4×D4C22×D6111yescharacteristic
410#117—21no—
411#117—21no—
412#117—21no—
413#117—21no—
414C2×C4⋊C4—1221no—
415#107—21no—
416#107—21no—
417#107—611no—
418#107—1221no—
419#107C22⋊D6111yescharacteristic
420#106—21no—
421#106—21no—
422#106—1221no—
423#106—1221no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8C22×D6111yescharacteristic
428#103—1221no—
429#103—1221no—
430#103—1221no—
431#103—2441no—
432#102—21no—
433#102—21no—
434#102—611no—
435#102—611no—
436#102—1221no—
437#102—1221no—
438#102—1221no—
439#102—1221no—
440#102—1221no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102C22⋊D6111yescharacteristic
446#102C22⋊D6111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450C22⋊C8—1221no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8C22×D6111yescharacteristic
454C24—2441no—
455#41—4881no—
456#41—2442no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—1221no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—611no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—4881no—
467C2×D4—4881no—
468C2×D4—2441no—
469C2×D4—2442no—
470C2×D4—2441no—
471C2×D4—2442no—
472C2×D4—2441no—
473C2×D4D4×D6111yescharacteristic
474C2×D4C2×C22⋊D6111yescharacteristic
475C2×D4C2×C22⋊D6111yescharacteristic
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—1221no—
480C22×C4—2441no—
481SD16—4881no—
482SD16—4882no—
483D8—41no—
484D8—1222no—
485D8—4881no—
486D8—4881no—
487M16—4881no—
488C2×C8—21no—
489C2×C8—42no—
490C2×C8—611no—
491C2×C8—611no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—4881no—
497C2×C8—4881no—
498C2×C8C2×C22⋊D6111yescharacteristic
499C2×C8C2×C22⋊D6111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—611no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—2441no—
508C4⋊C4D4×D6111yescharacteristic
509C4⋊C4C2×C22⋊D6111yescharacteristic
510C4⋊C4C2×C22⋊D6111yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—1221no—
519C22⋊C4—2441no—
520C22⋊C4—2441no—
521C42—41no—
522C42—41no—
523C42C23×D6111yescharacteristic
524C23—21no—
525C23—21no—
526C23—21no—
527C23—1221no—
528C23—9761no—
529C23—4882no—
530C23—4882no—
531C23—2441no—
532Q8—81no—
533Q8—81no—
534Q8—2441no—
535Q8—2441no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—161no—
543D4—161no—
544D4—612no—
545D4—1221no—
546D4—4881no—
547D4—4882no—
548D4—4882no—
549D4—4882no—
550D4—2441no—
551D4—2441no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—1221no—
566C2×C4—4882no—
567C2×C4—2441no—
568C2×C4—2441no—
569C2×C4—2441no—
570C2×C4C2×D4×D6111yescharacteristic
571C2×C4C22×C22⋊D6111yescharacteristic
572C2×C4#1451982211yescharacteristic
573C8—21no—
574C8—21no—
575C8—41no—
576C8—1221no—
577C8—1221no—
578C8—2441no—
579C8—2441no—
580C8—2441no—
581C8—2441no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—1222no—
592C22—9764no—
593C22—4881no—
594C22—4881no—
595C22—4881no—
596C22—2441no—
597C22—2441no—
598C22D4×C22⋊D6111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—4881no—
606C4—2441no—
607C4#135×D6111yescharacteristic
608C4#1684056011yescharacteristic
609C4#1684056411yescharacteristic
610C4#1684057011yescharacteristic
611C2—81no—
612C2—81no—
613C2—81no—
614C2—9761no—
615C2—2442no—
616C2#2145734511yescharacteristic
617C2#2145749811yescharacteristic
618C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3341C2
socleC22×C61D42
hypercenter#3341D61
hypocenterC61#19775
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #21458055C2semidirect
2. #21457741C2semidirect
3. #21457634C2semidirect
4. #21445475C2semidirect
5. #21445396C2semidirect
6. #21445256C2semidirect
7. #21445230C2semidirect
8. #21445215C2semidirect
9. #21445047C2semidirect
10. #21444969C2semidirect
11. #21444934C2semidirect
12. #21444902C2semidirect
13. #21444649C2semidirect
14. #21444641C2semidirect
15. C61×#3341C2semidirect
19. #16840114C22semidirect
20. #16840112C22semidirect
32. #16839967C22semidirect
41. D4×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839511C22semidirect
49. #16839507C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839484C22semidirect
57. C61×#555C22semidirect
58. C61×#500C22semidirect
62. C61×#476C22semidirect
65. C8×D4×C61C22semidirect
302. #3341D61semidirect
326. #555C2×D61semidirect
329. #500C2×D61semidirect
343. #476C2×D61semidirect
360. C8×D4C2×D61semidirect
376. C61#19775semidirect

Maximal subgroups

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

subgroupindex
#214580552
#214577412
#214576342
#214454752
#214453962
#214452562
#214452302
#214452152
#214450472
#214449692
#214449342
#214449022
#214446492
#214446412
C61×#33412
#1977561