Finite Group Databasebeta

← #29670314

Subgroups — #29670314

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#21458452C211yesmaximal, characteristic, complemented
2#21457763C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4#21445455C211yesmaximal, characteristic, complemented
5#21445380C211yesmaximal, characteristic, complemented
6#21445232C211yesmaximal, characteristic, complemented
7#21445230C211yesmaximal, characteristic, complemented
8#21445158C211yesmaximal, characteristic, complemented
9#21445047C211yesmaximal, characteristic, complemented
10#21444983C211yesmaximal, characteristic, complemented
11#21444883C211yesmaximal, characteristic, complemented
12#21444873C211yesmaximal, characteristic, complemented
13#21444660C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3325C211yesmaximal, characteristic, complemented
16C22×#11758200—21no—
17#16840433C2211yescharacteristic, complemented
18D4×Dic122C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840134C2211yescharacteristic
21#16840112C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840107—21no—
25#16840086—21no—
26#16840054C2211yescharacteristic, complemented
27#16840042C2211yescharacteristic, complemented
28#16840041—21no—
29#16839996—21no—
30#16839989—21no—
31#16839967C2211yescharacteristic
32#16839959C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839955—21no—
36#16839913—21no—
37#16839905—21no—
38#16839900—21no—
39C8×Dic122C2211yescharacteristic, complemented
40C4×#11758200C2211yescharacteristic
41#16839842—21no—
42D4×#92418C2211yescharacteristic
43D4×#92418C2211yescharacteristic, complemented
44#16839756—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839507C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51#16839492C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#482—21no—
60C61×#476C2211yescharacteristic
61C61×#469—21no—
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#418—21no—
67C2×#11758222—21no—
68C22×Dic122—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—44no—
74C2×#11758200D411yescharacteristic
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—41no—
78C22×#92418—21no—
79C22×#92418—21no—
80#14519777C2311yescharacteristic
81#14519776—21no—
82#14519774C2311yescharacteristic
83#14519773—21no—
84#14519756—21no—
85#14519754—41no—
86#14519751—21no—
87#14519750—41no—
88C4×Dic122C2311yescharacteristic
89D4×Dic61—21no—
90#14519739—21no—
91#14519710—21no—
92#14519710—21no—
93#14519708D411yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519701—41no—
99#14519700—21no—
100#14519700—21no—
101#14519700D411yescharacteristic
102#14519699—21no—
103#14519699—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698D411yescharacteristic
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C8×Dic61—21no—
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×D8×C61—21no—
119C2×D8×C61D411yescharacteristic
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#124×C61—41no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C2×Q8×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61—42no—
153C2×D4×C61—42no—
154C2×D4×C61—41no—
155C2×D4×C61—81no—
156C2×D4×C61—81no—
157C2×D4×C61C2×D411yescharacteristic
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C2×C22⋊D61—41no—
164C2×C22⋊D61—41no—
165C22×Dic61—41no—
166#11758222—42no—
167#11758222—81no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×C4×D61—41no—
172C2×Dic122—21no—
173C2×Dic122—42no—
174C2×Dic122—41no—
175C2×Dic122—81no—
176C2×Dic122C2×D411yescharacteristic
177D8×C61—22no—
178D8×C61—81no—
179M16×C61—81no—
180C2×C8×C61—21no—
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
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—22no—
198#11758200—42no—
199#11758200—42no—
200#11758200—42no—
201#11758200—81no—
202#11758199—42no—
203#11758199—81no—
204#11758199—82no—
205#11758198—41no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61C2×D411yescharacteristic
209#11758196—21no—
210#11758196—41no—
211C4×Dic61—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—42no—
217C2×#92418—81no—
218C2×#92418C2×D411yescharacteristic
219C2×#92418C2×D411yescharacteristic
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—41no—
224C23×C61—82no—
225C23×C61—82no—
226C23×C61—161no—
227C22×D61—41no—
228Q8×C61—81no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—81no—
239D4×C61—82no—
240D4×C61—82no—
241D4×C61—161no—
242D4×C61#13512yes—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C22⋊D61—82no—
257C22⋊D61—161no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—41no—
261C2×Dic61—82no—
262D244—41no—
263D244—41no—
264D244—41no—
265D244—41no—
266D244—81no—
267C4×D61—82no—
268Dic122—21no—
269Dic122—41no—
270Dic122—41no—
271Dic122—82no—
272Dic122AGL(1,ℤ/8)12yes—
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—22no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—81no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61—164no—
296C22×C61D4211yescharacteristic
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C4×C61—21no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—81no—
305C4×C61C2×#13511yescharacteristic
306C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C61#57611yescharacteristic
308C4×C61#57711yescharacteristic
309Dic61—22no—
310Dic61—41no—
311Dic61—81no—
312#3358—611no—
313#3325D6111yescharacteristic, complemented
314#3305—611no—
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—42no—
328C2×C61—81no—
329C2×C61—81no—
330C2×C61—161no—
331C2×C61#326411yescharacteristic
332C2×C61#328211yescharacteristic
333C2×C61#328811yescharacteristic
334D61—161no—
335C22×SD16—1221no—
336#555C2×D6111yescharacteristic
337#550—611no—
338D4×Q8—611no—
339D42C2×D6111yescharacteristic
340#493—611no—
341#492—611no—
342#487—611no—
343#486—611no—
344#486—611no—
345#486—1221no—
346#486C2×D6111yescharacteristic
347#482—21no—
348#482—1221no—
349#477—611no—
350#476C2×D6111yescharacteristic
351#474—611no—
352#474—1221no—
353#469—21no—
354#466—1221no—
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—1221no—
364#448—1221no—
365#447—21no—
366C8×Q8—611no—
367C4×SD16—611no—
368C4×D8—1221no—
369C4×D8C2×D6111yescharacteristic
370#436C2×D6111yescharacteristic
371C8×D4—611no—
372C8×D4—611no—
373#418—21no—
374#416—1221no—
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—1221no—
388C22×Q8—1221no—
389C22×D4—21no—
390C22×D4—21no—
391C2×SD16—611no—
392C2×SD16—1221no—
393C2×SD16—1221no—
394C2×SD16—1221no—
395C2×SD16—1221no—
396C2×SD16—2444no—
397C2×D8—21no—
398C2×D8—1221no—
399C2×D8—1221no—
400C2×D8—2441no—
401C2×D8C22⋊D6111yescharacteristic
402C2×M16—21no—
403C22×C8—1221no—
404C22×C8—1221no—
405C4⋊Q8—611no—
406C4⋊Q8—1221no—
407C4⋊Q8C22×D6111yescharacteristic
408#127—611no—
409#127—1221no—
410#127C22×D6111yescharacteristic
411#124—41no—
412C22⋊Q8—1221no—
413C22⋊Q8—2441no—
414#121—21no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—1221no—
419#121—2441no—
420#120—41no—
421C4×Q8—611no—
422C4×D4—1221no—
423C4×D4—1221no—
424C4×D4C22×D6111yescharacteristic
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427#117—21no—
428#117—21no—
429#107—1221no—
430#107—1221no—
431#107C22⋊D6111yescharacteristic
432#106—21no—
433#106—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—1221no—
438C4⋊C8C22×D6111yescharacteristic
439#103—611no—
440#103—1221no—
441#103—1221no—
442#103—2441no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
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#102C22⋊D6111yescharacteristic
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—41no—
466#41—4881no—
467#41—2442no—
468C2×Q8—21no—
469C2×Q8—611no—
470C2×Q8—1221no—
471C2×Q8—4881no—
472C2×Q8—2441no—
473C2×Q8—2442no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—41no—
482C2×D4—81no—
483C2×D4—81no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—2441no—
488C2×D4—2441no—
489C2×D4D4×D6111yescharacteristic
490C2×D4C2×C22⋊D6111yescharacteristic
491C2×D4C2×C22⋊D6111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—2441no—
496C22×C4—2441no—
497SD16—1222no—
498SD16—4881no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502D8—22no—
503D8—81no—
504D8—4881no—
505D8—4882no—
506D8—2442no—
507M16—81no—
508C2×C8—21no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—4881no—
516C2×C8—2442no—
517C2×C8C2×C22⋊D6111yescharacteristic
518C2×C8C2×C22⋊D6111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—611no—
522C4⋊C4—1221no—
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—21no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—2441no—
536C22⋊C4—2441no—
537C42—41no—
538C42—1221no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—161no—
547C23—2441no—
548Q8—81no—
549Q8—612no—
550Q8—1221no—
551Q8—4882no—
552Q8—2441no—
553Q8—2441no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—81no—
564D4—82no—
565D4—82no—
566D4—161no—
567D4—9761no—
568D4—4881no—
569D4—4882no—
570D4—2441no—
571D4—2441no—
572D4—2441no—
573D4—2441no—
574D4#1451979712yes—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—4882no—
588C2×C4—4882no—
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—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—164no—
615C22—4881no—
616C22—4881no—
617C22—4881no—
618C22D4×C22⋊D6111yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—1222no—
625C4—4881no—
626C4—2441no—
627C4C2×#1451979711yescharacteristic
628C4AGL(1,ℤ/8)×D6111yescharacteristic
629C4#1684056611yescharacteristic
630C4#1684057311yescharacteristic
631C2—42no—
632C2—81no—
633C2—81no—
634C2—161no—
635C2—9761no—
636C2#2145729311yescharacteristic
637C2#2145752211yescharacteristic
638C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3325C2
socleC22×C61D42
hypercenter#3325D61
hypocenterC61#19819
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3325

Complements

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

NH ≅ G/Ntype
1. #21458452C2semidirect
2. #21457763C2semidirect
3. D4×#11758200C2semidirect
4. #21445455C2semidirect
5. #21445380C2semidirect
6. #21445232C2semidirect
7. #21445230C2semidirect
8. #21445158C2semidirect
9. #21445047C2semidirect
10. #21444983C2semidirect
11. #21444883C2semidirect
12. #21444873C2semidirect
13. #21444660C2semidirect
14. #21444643C2semidirect
15. C61×#3325C2semidirect
17. #16840433C22semidirect
21. #16840112C22semidirect
22. #16840110C22semidirect
23. #16840109C22semidirect
26. #16840054C22semidirect
27. #16840042C22semidirect
39. C8×Dic122C22semidirect
43. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839507C22semidirect
50. #16839505C22semidirect
51. #16839492C22semidirect
54. D4⋊#92418C22semidirect
55. #16839483C22semidirect
313. #3325D61semidirect
386. C61#19819semidirect

Maximal subgroups

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

subgroupindex
#214584522
#214577632
D4×#117582002
#214454552
#214453802
#214452322
#214452302
#214451582
#214450472
#214449832
#214448832
#214448732
#214446602
#214446432
C61×#33252
#1981961