Finite Group Databasebeta

← #29670320

Subgroups — #29670320

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#21458063C211yesmaximal, characteristic, complemented
2#21457769C211yesmaximal, characteristic, complemented
3D4×#11758201C211yesmaximal, characteristic, complemented
4#21445459C211yesmaximal, characteristic, complemented
5#21445377C211yesmaximal, characteristic, complemented
6#21445235C211yesmaximal, characteristic, complemented
7#21445226C211yesmaximal, characteristic, complemented
8#21445162C211yesmaximal, characteristic, complemented
9#21445046C211yesmaximal, characteristic, complemented
10#21444984C211yesmaximal, characteristic, complemented
11#21444884C211yesmaximal, characteristic, complemented
12#21444872C211yesmaximal, characteristic, complemented
13#21444662C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3358C211yesmaximal, characteristic, complemented
16C22×#11758201—21no—
17#16840477C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840136C2211yescharacteristic
21#16840114C2211yescharacteristic, complemented
22#16840109C2211yescharacteristic
23#16840108C2211yescharacteristic, complemented
24#16840089—21no—
25#16840083—21no—
26#16840057C2211yescharacteristic, complemented
27#16840052C2211yescharacteristic
28#16840014—21no—
29#16839996—21no—
30#16839993—21no—
31#16839964C2211yescharacteristic
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839954C2211yescharacteristic
35#16839912—21no—
36#16839907—21no—
37#16839901—21no—
38#16839894—21no—
39C4×#11758201C2211yescharacteristic
40#16839841C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic, complemented
43#16839765—21no—
44#16839758—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#550C2211yescharacteristic, complemented
57D4×Q8×C61C2211yescharacteristic
58C61×#486—21no—
59C61×#486C2211yescharacteristic, complemented
60C61×#474—21no—
61C61×#474C2211yescharacteristic, complemented
62C61×#459—21no—
63C61×#459C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic, complemented
65C4×D8×C61—21no—
66C4×D8×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758201—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758201—44no—
74C2×#11758201D411yescharacteristic
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199—41no—
78C2×#11758189—21no—
79C22×#92418—21no—
80C22×#92418—21no—
81#14519777C2311yescharacteristic
82#14519774C2311yescharacteristic
83#14519763—41no—
84#14519752—21no—
85#14519751—21no—
86#14519751—21no—
87#14519748—21no—
88#14519747—41no—
89C4×D244C2311yescharacteristic
90#14519736—21no—
91#14519735—21no—
92#14519710—21no—
93#14519708—21no—
94#14519708D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—21no—
99#14519701—21no—
100#14519701D411yescharacteristic
101#14519700—41no—
102#14519699—21no—
103#14519699—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×Q8×C61—21no—
118C2×D8×C61—21no—
119C2×D8×C61D411yescharacteristic
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61—21no—
123#127×C61C2311yescharacteristic
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126#121×C61—21no—
127#121×C61—41no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#107×C61—21no—
134#107×C61D411yescharacteristic
135C4⋊C8×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
143C4×C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146#41×C61—42no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×Q8×C61—41no—
150C2×Q8×C61—42no—
151C2×Q8×C61—81no—
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61C2×D411yescharacteristic
159C2×D4×C61C2×D411yescharacteristic
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C2×C22⋊D61—41no—
165C2×C22⋊D61—41no—
166D4×D61—42no—
167D4×D61—81no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—42no—
172C2×D244—41no—
173C2×D244—81no—
174C2×D244C2×D411yescharacteristic
175C2×C4×D61—21no—
176C2×Dic122—21no—
177D8×C61—22no—
178D8×C61—42no—
179C2×C8×C61—21no—
180C2×C8×C61C2×D411yescharacteristic
181C2×C8×C61C2×D411yescharacteristic
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—41no—
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—
193C42×C61—21no—
194C42×C61C2411yescharacteristic
195C22⋊Dic61—41no—
196#11758201—22no—
197#11758201—42no—
198#11758201—42no—
199#11758201—42no—
200#11758201—81no—
201#11758199—81no—
202#11758199—81no—
203#11758199—82no—
204#11758198—21no—
205#11758198—41no—
206#11758198—41no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61C2×D411yescharacteristic
210C4×Dic61—41no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—42no—
216C2×#92418—81no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219#11758189—81no—
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—41no—
230Q8×C61—41no—
231Q8×C61—82no—
232Q8×C61AGL(1,ℤ/8)12yes—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—41no—
239D4×C61—41no—
240D4×C61—82no—
241D4×C61—81no—
242D4×C61—161no—
243D4×C61#13512yes—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—82no—
254C2×C4×C61—82no—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C22⋊D61—82no—
259C22⋊D61—161no—
260C2×Dic61—21no—
261C2×Dic61—41no—
262D244—21no—
263D244—21no—
264D244—41no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—81no—
269D244—82no—
270C4×D61—41no—
271C4×D61—41no—
272Dic122—81no—
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—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61D4211yescharacteristic
293C2×D61—41no—
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#3358D6111yescharacteristic, complemented
313#3325—611no—
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—161no—
330C2×C61#326411yescharacteristic
331C2×C61#328211yescharacteristic
332C2×C61#328811yescharacteristic
333D61—81no—
334D61—161no—
335C22×SD16—1221no—
336#555—611no—
337#550C2×D6111yescharacteristic, complemented
338D4×Q8C2×D6111yescharacteristic
339D42—611no—
340#493—611no—
341#492—611no—
342#487—611no—
343#486—21no—
344#486—611no—
345#486—611no—
346#486C2×D6111yescharacteristic, complemented
347#482—1221no—
348#482—1221no—
349#477—611no—
350#476—611no—
351#474—21no—
352#474C2×D6111yescharacteristic, complemented
353#469—1221no—
354#466—1221no—
355#465—1221no—
356#461—611no—
357#460—611no—
358#459—21no—
359#459—611no—
360#459—611no—
361#459C2×D6111yescharacteristic
362#450—1221no—
363#449—1221no—
364#448—1221no—
365#447—1221no—
366C8×Q8C2×D6111yescharacteristic, complemented
367C4×SD16—611no—
368C4×D8—21no—
369C4×D8C2×D6111yescharacteristic
370#436—611no—
371C8×D4—611no—
372C8×D4—611no—
373#418—1221no—
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—21no—
388C22×Q8—21no—
389C22×D4—1221no—
390C22×D4—1221no—
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—1221no—
403C22×C8—1221no—
404C22×C8—1221no—
405C4⋊Q8—21no—
406C4⋊Q8—611no—
407C4⋊Q8C22×D6111yescharacteristic
408#127—21no—
409#127—611no—
410#127C22×D6111yescharacteristic
411#124—2441no—
412C22⋊Q8—21no—
413C22⋊Q8—41no—
414#121—21no—
415#121—41no—
416#121—1221no—
417#121—1221no—
418#121—1221no—
419#121—1221no—
420#120—2441no—
421C4×Q8C22×D6111yescharacteristic
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—611no—
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427#117—1221no—
428#117—1221no—
429#107—21no—
430#107—1221no—
431#107C22⋊D6111yescharacteristic
432#106—611no—
433#106—1221no—
434C4⋊C8—21no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
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—1221no—
459C22⋊C8—1221no—
460C22⋊C8—1221no—
461C4×C8—21no—
462C4×C8—611no—
463C4×C8—611no—
464C4×C8C22×D6111yescharacteristic
465C24—2441no—
466#41—42no—
467#41—81no—
468C2×Q8—21no—
469C2×Q8—41no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×Q8—1221no—
473C2×Q8D4×D6111yescharacteristic
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—41no—
478C2×D4—41no—
479C2×D4—611no—
480C2×D4—1221no—
481C2×D4—1221no—
482C2×D4—1221no—
483C2×D4—4881no—
484C2×D4—4881no—
485C2×D4—2441no—
486C2×D4—2442no—
487C2×D4—2441no—
488C2×D4—2441no—
489C2×D4—2442no—
490C2×D4C2×C22⋊D6111yescharacteristic
491C2×D4C2×C22⋊D6111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—1221no—
497SD16—1222no—
498SD16—4881no—
499SD16—2442no—
500SD16—2442no—
501SD16—2442no—
502D8—22no—
503D8—42no—
504D8—4881no—
505D8—4881no—
506D8—4882no—
507M16—4881no—
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—21no—
522C4⋊C4—41no—
523C4⋊C4—611no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
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—1221no—
534C22⋊C4—2441no—
535C22⋊C4—2441no—
536C22⋊C4—2441no—
537C42—21no—
538C42—2441no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—21no—
542C23—41no—
543C23—1221no—
544C23—9761no—
545C23—4882no—
546C23—4882no—
547C23—2441no—
548Q8—21no—
549Q8—41no—
550Q8—41no—
551Q8—82no—
552Q8—4881no—
553Q8#1451980112yes—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—82no—
562D4—81no—
563D4—161no—
564D4—1221no—
565D4—1221no—
566D4—9761no—
567D4—4881no—
568D4—4882no—
569D4—4882no—
570D4—2441no—
571D4—2441no—
572D4—2441no—
573D4—2441no—
574D4#1451979712yes—
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—82no—
586C2×C4—1221no—
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—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—9764no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22D4×C22⋊D6111yescharacteristic
619C4—22no—
620C4—21no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—4881no—
626C4—2441no—
627C4C2×#1451979711yescharacteristic
628C4C2×#1451980111yescharacteristic
629C4#1684056311yescharacteristic
630C4#1684057011yescharacteristic
631C2—42no—
632C2—81no—
633C2—161no—
634C2—9761no—
635C2—4881no—
636C2#2145729911yescharacteristic
637C2#2145752711yescharacteristic
638C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3358C2
socleC22×C61D42
hypercenter#3358D61
hypocenterC61#19819
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3358

Complements

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

NH ≅ G/Ntype
1. #21458063C2semidirect
2. #21457769C2semidirect
3. D4×#11758201C2semidirect
4. #21445459C2semidirect
5. #21445377C2semidirect
6. #21445235C2semidirect
7. #21445226C2semidirect
8. #21445162C2semidirect
9. #21445046C2semidirect
10. #21444984C2semidirect
11. #21444884C2semidirect
12. #21444872C2semidirect
13. #21444662C2semidirect
14. #21444643C2semidirect
15. C61×#3358C2semidirect
21. #16840114C22semidirect
23. #16840108C22semidirect
26. #16840057C22semidirect
42. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. #16839483C22semidirect
56. C61×#550C22semidirect
59. C61×#486C22semidirect
61. C61×#474C22semidirect
64. C8×Q8×C61C22semidirect
312. #3358D61semidirect
337. #550C2×D61semidirect
346. #486C2×D61semidirect
352. #474C2×D61semidirect
366. C8×Q8C2×D61semidirect
386. C61#19819semidirect

Maximal subgroups

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

subgroupindex
#214580632
#214577692
D4×#117582012
#214454592
#214453772
#214452352
#214452262
#214451622
#214450462
#214449842
#214448842
#214448722
#214446622
#214446432
C61×#33582
#1981961