Finite Group Databasebeta

← #29669866

Subgroups — #29669866

Order 15616.

680 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#21458611C211yesmaximal, characteristic, complemented
2#21458477C211yesmaximal, characteristic, complemented
3#21457643C211yesmaximal, characteristic, complemented
4#21445456C211yesmaximal, characteristic, complemented
5#21445357C211yesmaximal, characteristic, complemented
6#21445258C211yesmaximal, characteristic, complemented
7#21445228C211yesmaximal, characteristic, complemented
8#21445164C211yesmaximal, characteristic, complemented
9#21445024C211yesmaximal, characteristic, complemented
10#21444984C211yesmaximal, characteristic, complemented
11#21444877C211yesmaximal, characteristic, complemented
12#21444873C211yesmaximal, characteristic
13#21444656C211yesmaximal, characteristic, complemented
14#21444631C211yesmaximal, characteristic, complemented
15D4×SD16×C61C211yesmaximal, characteristic, complemented
16#16840497C2211yescharacteristic, complemented
17#16840469C2211yescharacteristic
18#16840138C2211yescharacteristic
19#16840124—21no—
20#16840118—21no—
21#16840114C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic
25#16840078—21no—
26#16840061—21no—
27#16840057C2211yescharacteristic, complemented
28#16840052C2211yescharacteristic
29#16840049—21no—
30#16840044C2211yescharacteristic, complemented
31#16839989—21no—
32#16839979—21no—
33#16839977—21no—
34#16839959C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839957C2211yescharacteristic
37#16839913—21no—
38#16839893C2211yescharacteristic, complemented
39C8×Dic122C2211yescharacteristic, complemented
40#16839872—21no—
41C4×#11758200C2211yescharacteristic
42#16839842—21no—
43D4×#92418C2211yescharacteristic
44C2×#14519698—21no—
45#16839514C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52#16839492C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic, complemented
56C22×SD16×C61—21no—
57D4×Q8×C61C2211yescharacteristic
58D42×C61C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#465—21no—
61C61×#461C2211yescharacteristic
62C61×#460C2211yescharacteristic
63C61×#450—21no—
64C61×#448—21no—
65C4×SD16×C61C2211yescharacteristic
66C8×D4×C61C2211yescharacteristic
67C2×#11758200—21no—
68C2×#11758200D411yescharacteristic
69C2×#11758199—21no—
70C2×#11758199—21no—
71C2×#11758199—41no—
72C22×#92418—21no—
73#14519777C2311yescharacteristic
74#14519774C2311yescharacteristic
75#14519768—21no—
76#14519766—21no—
77#14519765—21no—
78#14519762—41no—
79#14519756—21no—
80#14519754—41no—
81C4×Dic122C2311yescharacteristic
82C4×D244—21no—
83D4×Dic61—21no—
84#14519739—21no—
85C2×C4⋊Dic61—21no—
86#14519710—21no—
87#14519708—21no—
88#14519708—21no—
89#14519708D411yescharacteristic
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94#14519706—21no—
95#14519701—21no—
96#14519700—21no—
97#14519700—41no—
98#14519700D411yescharacteristic
99#14519699—21no—
100#14519699—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698D411yescharacteristic
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110C22⋊#92418—21no—
111#14519688—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C22×Q8×C61—21no—
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61—44no—
123C2×SD16×C61D411yescharacteristic
124C22×C8×C61—21no—
125C4⋊Q8×C61—21no—
126C4⋊Q8×C61C2311yescharacteristic
127#127×C61C2311yescharacteristic
128C22⋊Q8×C61—21no—
129C22⋊Q8×C61—41no—
130#121×C61—21no—
131#121×C61—21no—
132#120×C61—41no—
133C4×Q8×C61C2311yescharacteristic
134C4×D4×C61—21no—
135C4×D4×C61C2311yescharacteristic
136C4×D4×C61C2311yescharacteristic
137#106×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C2×Q8×C61—21no—
147C2×Q8×C61—41no—
148C2×Q8×C61—42no—
149C2×Q8×C61—81no—
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—41no—
165C22×Dic61—41no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×C4×D61—41no—
170C2×Dic122—21no—
171C2×Dic122C2×D411yescharacteristic
172SD16×C61—22no—
173SD16×C61—42no—
174SD16×C61—42no—
175SD16×C61—42no—
176SD16×C61—81no—
177C2×C8×C61—21no—
178C2×C8×C61—42no—
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
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—41no—
191C22⋊C4×C61—41no—
192C42×C61—21no—
193C42×C61C2411yescharacteristic
194C22⋊Dic61—41no—
195#11758200—22no—
196#11758200—81no—
197#11758199—42no—
198#11758199—42no—
199#11758199—82no—
200#11758198—41no—
201#11758198—41no—
202#11758198—41no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—41no—
206C4⋊Dic61C2×D411yescharacteristic
207#11758196—21no—
208#11758196—41no—
209C4×Dic61—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—81no—
215C2×#92418C2×D411yescharacteristic
216C2×#92418C2×D411yescharacteristic
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—41no—
220C23×C61—82no—
221C23×C61—82no—
222C23×C61—161no—
223C22×D61—41no—
224Q8×C61—21no—
225Q8×C61—21no—
226Q8×C61—41no—
227Q8×C61—41no—
228Q8×C61—82no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—41no—
232D4×C61—41no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—81no—
236D4×C61—82no—
237D4×C61—82no—
238D4×C61#13512yes—
239D4×C61AGL(1,ℤ/8)12yes—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—82no—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—41no—
256C2×Dic61—161no—
257D244—41no—
258D244—41no—
259D244—41no—
260D244—41no—
261D244—81no—
262C4×D61—161no—
263Dic122—21no—
264Dic122—21no—
265Dic122—81no—
266C8×C61—21no—
267C8×C61—21no—
268C8×C61—41no—
269#92418—21no—
270#92418—21no—
271#92418—41no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#19789—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—22no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61—81no—
285C22×C61—164no—
286C22×C61D4211yescharacteristic
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—81no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—81no—
296C4×C61C2×#13511yescharacteristic
297C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
298C4×C61#57711yescharacteristic
299C4×C61#57711yescharacteristic
300Dic61—41no—
301Dic61—41no—
302Dic61—81no—
303#3373—611no—
304#3361—611no—
305#3295—611no—
306D4×SD16D6111yescharacteristic, complemented
307#1717—611no—
308#1698—611no—
309#1681—611no—
310#1677—611no—
311#1666—611no—
312#1643—611no—
313#1637—611no—
314#1620—611no—
315#1619—611no—
316#1582—611no—
317SD16⋊C8—611no—
318C2×C61—42no—
319C2×C61—42no—
320C2×C61—161no—
321C2×C61#326511yescharacteristic
322C2×C61#328211yescharacteristic
323C2×C61#328811yescharacteristic
324D61—161no—
325C22×SD16—21no—
326#559—611no—
327#554—611no—
328D4×Q8C2×D6111yescharacteristic
329D42C2×D6111yescharacteristic
330#493—611no—
331#492C2×D6111yescharacteristic
332#489—1221no—
333#488—1221no—
334#487—611no—
335#486—611no—
336#486—611no—
337#486—611no—
338#481—1221no—
339#478—1221no—
340#477—611no—
341#476—611no—
342#476—1221no—
343#475—611no—
344#465—21no—
345#465—1221no—
346#463—1221no—
347#463—1221no—
348#461C2×D6111yescharacteristic
349#460—611no—
350#460C2×D6111yescharacteristic
351#459—611no—
352#459—611no—
353#450—21no—
354#450—1221no—
355#448—21no—
356#446—611no—
357C8×Q8—611no—
358#442—1221no—
359C4×SD16—611no—
360C4×SD16C2×D6111yescharacteristic
361C4×D8—1221no—
362C8×D4—611no—
363C8×D4C2×D6111yescharacteristic
364C2×#102—1221no—
365#335—611no—
366#334—611no—
367#333—611no—
368#332—611no—
369#331—611no—
370#331—611no—
371Q8⋊C8—611no—
372Q8⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375#322—611no—
376C61#1978911yescharacteristic, complemented, Sylow
377C22×Q8—21no—
378C22×D4—21no—
379C22×D4—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—44no—
385C2×SD16—611no—
386C2×SD16—1221no—
387C2×SD16C22⋊D6111yescharacteristic
388C2×D8—1221no—
389C2×D8—1221no—
390C2×D8—2441no—
391C22×C8—21no—
392C22×C8—1221no—
393C4⋊Q8—21no—
394C4⋊Q8—611no—
395C4⋊Q8C22×D6111yescharacteristic
396#127—611no—
397#127C22×D6111yescharacteristic
398#125—1221no—
399#124—1221no—
400#124—1221no—
401#123—2441no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—1221no—
405C22⋊Q8—2441no—
406#121—21no—
407#121—21no—
408#120—41no—
409C4×Q8—611no—
410C4×Q8C22×D6111yescharacteristic
411C4×D4—21no—
412C4×D4—1221no—
413C4×D4—1221no—
414C4×D4—1221no—
415C4×D4C22×D6111yescharacteristic
416C4×D4C22×D6111yescharacteristic
417C2×C4⋊C4—1221no—
418#107—1221no—
419#106—611no—
420#106—1221no—
421#106—1221no—
422#106C22⋊D6111yescharacteristic
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—1221no—
427C4⋊C8—1221no—
428C4⋊C8C22×D6111yescharacteristic
429#103—21no—
430#103—611no—
431#103—1221no—
432#103—1221no—
433#103—2441no—
434#103C22⋊D6111yescharacteristic
435#102—21no—
436#102—611no—
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#102—1221no—
446#102—1221no—
447#102C22⋊D6111yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—1221no—
450#97—1221no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—1221no—
454C4×C8C22×D6111yescharacteristic
455C24—41no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—611no—
461C2×Q8—1221no—
462C2×Q8C2×C22⋊D6111yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4—1221no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4D4×D6111yescharacteristic
476C2×D4C2×C22⋊D6111yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—41no—
480C22×C4—2441no—
481C22×C4—2441no—
482SD16—22no—
483SD16—42no—
484SD16—42no—
485SD16—42no—
486SD16—81no—
487SD16—1222no—
488SD16—4881no—
489D8—4882no—
490D8—2442no—
491D8—2442no—
492C2×C8—21no—
493C2×C8—42no—
494C2×C8—611no—
495C2×C8—611no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—4881no—
501C2×C8C2×C22⋊D6111yescharacteristic
502C2×C8C2×C22⋊D6111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—611no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—2441no—
512C4⋊C4—2441no—
513C4⋊C4D4×D6111yescharacteristic
514C4⋊C4C2×C22⋊D6111yescharacteristic
515C4⋊C4C2×C22⋊D6111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—2441no—
521C22⋊C4—2441no—
522C22⋊C4—2441no—
523C22⋊C4—2441no—
524C42—21no—
525C42—1221no—
526C42C23×D6111yescharacteristic
527C23—21no—
528C23—21no—
529C23—41no—
530C23—82no—
531C23—82no—
532C23—161no—
533C23—2441no—
534Q8—21no—
535Q8—21no—
536Q8—41no—
537Q8—41no—
538Q8—82no—
539Q8—1221no—
540Q8—1221no—
541Q8—4881no—
542D4—21no—
543D4—21no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—4881no—
552D4—2441no—
553D4—2441no—
554D4—2441no—
555D4—2441no—
556D4#1451979812yes—
557D4#1451980312yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—82no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—9761no—
571C2×C4—9761no—
572C2×C4—2441no—
573C2×C4C2×D4×D6111yescharacteristic
574C2×C4C22×C22⋊D6111yescharacteristic
575C2×C4#1451982211yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—1221no—
580C8—1221no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C8—2441no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—164no—
595C22—4881no—
596C22—4881no—
597C22—4881no—
598C22D4×C22⋊D6111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—4881no—
606C4—2441no—
607C4—2441no—
608C4C2×#1451979811yescharacteristic
609C4C2×#1451980311yescharacteristic
610C4#1684056811yescharacteristic
611C4#1684057311yescharacteristic
612C2—42no—
613C2—42no—
614C2—161no—
615C2—9761no—
616C2#2145731011yescharacteristic
617C2#2145752611yescharacteristic
618C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingD4×SD16×C61C2
socleC22×C61D42
prime radical#21444873C2
hypercenterD4×SD16D61
hypocenterC61#19789
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4×SD16

Complements

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

NH ≅ G/Ntype
1. #21458611C2semidirect
2. #21458477C2semidirect
3. #21457643C2semidirect
4. #21445456C2semidirect
5. #21445357C2semidirect
6. #21445258C2semidirect
7. #21445228C2semidirect
8. #21445164C2semidirect
9. #21445024C2semidirect
10. #21444984C2semidirect
11. #21444877C2semidirect
13. #21444656C2semidirect
14. #21444631C2semidirect
15. D4×SD16×C61C2semidirect
16. #16840497C22semidirect
21. #16840114C22semidirect
22. #16840110C22semidirect
23. #16840109C22semidirect
27. #16840057C22semidirect
30. #16840044C22semidirect
38. #16839893C22semidirect
39. C8×Dic122C22semidirect
45. #16839514C22semidirect
46. #16839513C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
52. #16839492C22semidirect
55. #16839484C22semidirect
306. D4×SD16D61semidirect
376. C61#19789semidirect

Maximal subgroups

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

subgroupindex
#214586112
#214584772
#214576432
#214454562
#214453572
#214452582
#214452282
#214451642
#214450242
#214449842
#214448772
#214448732
#214446562
#214446312
D4×SD16×C612
#1978961