Finite Group Databasebeta

← #29670321

Subgroups — #29670321

Order 15616.

702 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458450C211yesmaximal, characteristic, complemented
2#21458055C211yesmaximal, characteristic, complemented
3SD16×D244C211yesmaximal, characteristic, complemented
4#21445460C211yesmaximal, characteristic, complemented
5#21445378C211yesmaximal, characteristic, complemented
6#21445237C211yesmaximal, characteristic, complemented
7#21445225C211yesmaximal, characteristic, complemented
8#21445160C211yesmaximal, characteristic, complemented
9#21445047C211yesmaximal, characteristic, complemented
10#21444982C211yesmaximal, characteristic, complemented
11#21444884C211yesmaximal, characteristic, complemented
12#21444872C211yesmaximal, characteristic, complemented
13#21444663C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic, complemented
15C61×#3305C211yesmaximal, characteristic, complemented
16C2×SD16×D61—21no—
17Q8×D244C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840135C2211yescharacteristic
21#16840112C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic
23#16840108—21no—
24#16840108C2211yescharacteristic, complemented
25#16840086—21no—
26#16840049C2211yescharacteristic
27#16840042—21no—
28#16840042C2211yescharacteristic, complemented
29#16840013—21no—
30#16839992—21no—
31#16839967C2211yescharacteristic
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839954—21no—
35#16839954C2211yescharacteristic
36#16839914—21no—
37#16839902—21no—
38#16839895—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758199—21no—
41C4×#11758199C2211yescharacteristic
42#16839840C2211yescharacteristic
43C8×D244C2211yescharacteristic
44#16839766—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839509C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57C61×#550C2211yescharacteristic, complemented
58C61×#486C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#477C2211yescharacteristic, complemented
61C61×#466—21no—
62C61×#459C2211yescharacteristic
63C61×#449—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic, complemented
66C61×#416—21no—
67C2×Q8×D61—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70C2×#11758190—21no—
71C2×#11758190—21no—
72C2×#11758200—21no—
73C2×#11758201—21no—
74SD16×D61—44no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—41no—
78C2×#11758199D411yescharacteristic
79C2×#11758194—21no—
80C2×C8×D61—21no—
81#14519777—21no—
82#14519777C2311yescharacteristic
83#14519774C2311yescharacteristic
84#14519757—21no—
85#14519757—41no—
86#14519752—21no—
87#14519751—21no—
88#14519747—41no—
89C4×D244—21no—
90C4×D244C2311yescharacteristic
91#14519710—21no—
92#14519710D411yescharacteristic
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—41no—
99#14519700—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×D8×C61—21no—
119C22×C8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61—21no—
122#127×C61C2311yescharacteristic
123#124×C61—41no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—41no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—21no—
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134#107×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61—21no—
138#103×C61D411yescharacteristic
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146#41×C61—42no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61C2×D411yescharacteristic
157C2×D4×C61C2×D411yescharacteristic
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—41no—
161C2×C22⋊D61—41no—
162Q8×D61—42no—
163Q8×D61—81no—
164D4×D61—42no—
165D4×D61—81no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—42no—
170C2×D244—41no—
171C2×D244—81no—
172C2×D244C2×D411yescharacteristic
173C2×C4×D61—21no—
174C2×C4×D61—41no—
175C2×Dic122—21no—
176C2×Dic122—41no—
177SD16×C61—22no—
178D8×C61—81no—
179C2×C8×C61—21no—
180C2×C8×C61—81no—
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C4⋊C4×C61C2×D411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C42×C61—21no—
195C42×C61—41no—
196C42×C61C2411yescharacteristic
197#11758201—42no—
198#11758200—42no—
199#11758199—22no—
200#11758199—42no—
201#11758199—81no—
202#11758199—82no—
203#11758198—21no—
204#11758198—41no—
205#11758198—41no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—41no—
209C4⋊Dic61C2×D411yescharacteristic
210#11758194—81no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418C2×D411yescharacteristic
216C2×#92418C2×D411yescharacteristic
217#11758190—42no—
218#11758190—81no—
219C8×D61—42no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—41no—
223C22×D61—21no—
224C22×D61—41no—
225C22×D61—82no—
226C22×D61—82no—
227C22×D61—161no—
228Q8×C61—21no—
229Q8×C61—81no—
230Q8×C61AGL(1,ℤ/8)12yes—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—82no—
240D4×C61—81no—
241D4×C61—161no—
242D4×C61—161no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—82no—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C22⋊D61—82no—
257C2×Dic61—21no—
258C2×Dic61—41no—
259D244—21no—
260D244—41no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—81no—
265D244—82no—
266D244#13512yes—
267C4×D61—41no—
268C4×D61—41no—
269C4×D61—82no—
270Dic122—41no—
271Dic122—41no—
272Dic122—82no—
273C8×C61—21no—
274C8×C61—21no—
275C8×C61—41no—
276#92418—21no—
277#92418—21no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#19819—611nomaximal, Sylow
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61D4211yescharacteristic
293C2×D61—22no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—81no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—164no—
300C4×C61—22no—
301C4×C61—21no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61C2×#13511yescharacteristic
307C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C61#57611yescharacteristic
309C4×C61#57711yescharacteristic
310Dic61—41no—
311Dic61—81no—
312#3358—611no—
313#3325—611no—
314#3305D6111yescharacteristic, complemented
315D4×SD16—611no—
316#1717—611no—
317#1701—611no—
318#1678—611no—
319#1677—611no—
320#1665—611no—
321#1646—611no—
322#1637—611no—
323#1621—611no—
324#1619—611no—
325#1583—611no—
326#1580—611no—
327C2×C61—81no—
328C2×C61—81no—
329C2×C61—161no—
330C2×C61#326411yescharacteristic
331C2×C61#328211yescharacteristic
332C2×C61#328811yescharacteristic
333D61—42no—
334D61—161no—
335C22×SD16—1221no—
336#555C2×D6111yescharacteristic
337#550C2×D6111yescharacteristic, complemented
338D4×Q8—611no—
339D42—611no—
340#493—611no—
341#492—611no—
342#487—611no—
343#486—611no—
344#486—611no—
345#486—1221no—
346#486C2×D6111yescharacteristic, complemented
347#482—21no—
348#482—1221no—
349#477C2×D6111yescharacteristic, complemented
350#476—611no—
351#474—611no—
352#474—1221no—
353#469—1221no—
354#466—21no—
355#465—1221no—
356#461—611no—
357#460—611no—
358#459—611no—
359#459—611no—
360#459—1221no—
361#459C2×D6111yescharacteristic
362#450—1221no—
363#449—21no—
364#448—1221no—
365#447—1221no—
366C8×Q8—611no—
367C4×SD16C2×D6111yescharacteristic
368C4×D8—611no—
369C4×D8—1221no—
370#436—611no—
371C8×D4—611no—
372C8×D4C2×D6111yescharacteristic, complemented
373#418—1221no—
374#416—21no—
375#334—611no—
376#334—611no—
377#333—611no—
378#332—611no—
379#331—611no—
380#331—611no—
381Q8⋊C8—611no—
382D4⋊C8—611no—
383D4⋊C8—611no—
384D4⋊C8—611no—
385#322—611no—
386C61#1981911yescharacteristic, complemented, Sylow
387C2×#41—21no—
388C22×Q8—1221no—
389C22×D4—1221no—
390C22×D4—1221no—
391C2×SD16—1221no—
392C2×SD16—1221no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—2444no—
396C2×SD16C22⋊D6111yescharacteristic
397C2×D8—21no—
398C2×D8—611no—
399C2×D8—1221no—
400C2×D8—1221no—
401C2×D8—2441no—
402C2×M16—1221no—
403C22×C8—21no—
404C22×C8—1221no—
405C4⋊Q8—611no—
406C4⋊Q8—1221no—
407C4⋊Q8C22×D6111yescharacteristic
408#127—21no—
409#127—611no—
410#127C22×D6111yescharacteristic
411#124—41no—
412C22⋊Q8—1221no—
413C22⋊Q8—2441no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121—41no—
418#121—1221no—
419#121—1221no—
420#120—2441no—
421C4×Q8C22×D6111yescharacteristic
422C4×D4—21no—
423C4×D4—611no—
424C4×D4—1221no—
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427#117—21no—
428#117—21no—
429#107—21no—
430#107—611no—
431#107—1221no—
432#106—1221no—
433#106C22⋊D6111yescharacteristic
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—1221no—
438C4⋊C8C22×D6111yescharacteristic
439#103—21no—
440#103—1221no—
441#103—2441no—
442#103C22⋊D6111yescharacteristic
443#102—21no—
444#102—21no—
445#102—21no—
446#102—611no—
447#102—611no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102C22⋊D6111yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—1221no—
460C22⋊C8—1221no—
461C4×C8—611no—
462C4×C8—611no—
463C4×C8—1221no—
464C4×C8C22×D6111yescharacteristic
465C24—2441no—
466#41—42no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8—1221no—
470C2×Q8—4881no—
471C2×Q8—2441no—
472C2×Q8—2442no—
473C2×Q8C2×C22⋊D6111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4—611no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—4881no—
485C2×D4—4881no—
486C2×D4—2441no—
487C2×D4—2442no—
488C2×D4—2441no—
489C2×D4—2442no—
490C2×D4D4×D6111yescharacteristic
491C2×D4C2×C22⋊D6111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—1221no—
496C22×C4—2441no—
497SD16—22no—
498SD16—4881no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502D8—81no—
503D8—1222no—
504D8—4881no—
505D8—4882no—
506D8—2442no—
507M16—4881no—
508C2×C8—21no—
509C2×C8—81no—
510C2×C8—611no—
511C2×C8—611no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—2442no—
517C2×C8C2×C22⋊D6111yescharacteristic
518C2×C8C2×C22⋊D6111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—611no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—2441no—
526C4⋊C4D4×D6111yescharacteristic
527C4⋊C4C2×C22⋊D6111yescharacteristic
528C4⋊C4C2×C22⋊D6111yescharacteristic
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—1221no—
535C22⋊C4—2441no—
536C22⋊C4—2441no—
537C42—21no—
538C42—41no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—21no—
542C23—41no—
543C23—1221no—
544C23—9761no—
545C23—4882no—
546C23—4882no—
547C23—2441no—
548Q8—21no—
549Q8—81no—
550Q8—4882no—
551Q8—2441no—
552Q8—2441no—
553Q8#1451980212yes—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—21no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—82no—
563D4—81no—
564D4—161no—
565D4—161no—
566D4—612no—
567D4—1221no—
568D4—4881no—
569D4—4882no—
570D4—4882no—
571D4—2441no—
572D4—2441no—
573D4—2441no—
574D4—2441no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
585C2×C4—1221no—
586C2×C4—4882no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4C22×C22⋊D6111yescharacteristic
592C2×C4#1451982211yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—1221no—
597C8—1221no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C8—2441no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—1222no—
612C22—9764no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—2441no—
617C22—2441no—
618C22D4×C22⋊D6111yescharacteristic
619C4—22no—
620C4—21no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—4881no—
626C4—2441no—
627C4#135×D6111yescharacteristic
628C4C2×#1451980211yescharacteristic
629C4#1684056511yescharacteristic
630C4#1684056911yescharacteristic
631C2—81no—
632C2—81no—
633C2—161no—
634C2—9761no—
635C2—2442no—
636C2#2145730011yescharacteristic
637C2#2145752011yescharacteristic
638C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3305C2
socleC22×C61D42
hypercenter#3305D61
hypocenterC61#19819
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3305

Complements

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

NH ≅ G/Ntype
1. #21458450C2semidirect
2. #21458055C2semidirect
3. SD16×D244C2semidirect
4. #21445460C2semidirect
5. #21445378C2semidirect
6. #21445237C2semidirect
7. #21445225C2semidirect
8. #21445160C2semidirect
9. #21445047C2semidirect
10. #21444982C2semidirect
11. #21444884C2semidirect
12. #21444872C2semidirect
13. #21444663C2semidirect
14. #21444641C2semidirect
15. C61×#3305C2semidirect
21. #16840112C22semidirect
24. #16840108C22semidirect
28. #16840042C22semidirect
39. Q8×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839509C22semidirect
49. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839484C22semidirect
57. C61×#550C22semidirect
58. C61×#486C22semidirect
60. C61×#477C22semidirect
65. C8×D4×C61C22semidirect
314. #3305D61semidirect
337. #550C2×D61semidirect
346. #486C2×D61semidirect
349. #477C2×D61semidirect
372. C8×D4C2×D61semidirect
386. C61#19819semidirect

Maximal subgroups

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

subgroupindex
#214584502
#214580552
SD16×D2442
#214454602
#214453782
#214452372
#214452252
#214451602
#214450472
#214449822
#214448842
#214448722
#214446632
#214446412
C61×#33052
#1981961