Finite Group Databasebeta

← #29665109

Subgroups — #29665109

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457186C211yesmaximal, characteristic, complemented
2#21456837C211yesmaximal, characteristic
3#21454823C211yesmaximal, characteristic, complemented
4#21445384C211yesmaximal, characteristic, complemented
5#21445377C211yesmaximal, characteristic, complemented
6#21445356C211yesmaximal, characteristic, complemented
7#21445349C211yesmaximal, characteristic, complemented
8#21445260C211yesmaximal, characteristic, complemented
9#21445253C211yesmaximal, characteristic, complemented
10#21445232C211yesmaximal, characteristic, complemented
11#21445225C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444529C211yesmaximal, characteristic, complemented
14#21444487C211yesmaximal, characteristic, complemented
15C61×#3138C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840149—21no—
18#16840126—21no—
19#16840069—21no—
20#16840054C2211yescharacteristic, complemented
21#16840049C2211yescharacteristic, complemented
22#16840018—21no—
23#16840010—21no—
24#16839984—21no—
25#16839969C2211yescharacteristic, complemented
26#16839964C2211yescharacteristic, complemented
27#16839959C2211yescharacteristic
28#16839959C2211yescharacteristic
29#16839954C2211yescharacteristic
30#16839954C2211yescharacteristic
31#16839913—21no—
32#16839896—21no—
33#16839892C2211yescharacteristic, complemented
34C8×Dic122C2211yescharacteristic, complemented
35#16839841C2211yescharacteristic, complemented
36#16839838—21no—
37#16839831—21no—
38C8×D244C2211yescharacteristic, complemented
39#16839824—21no—
40#16839819C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839786C2211yescharacteristic
43#16839719—21no—
44#16839515C2211yescharacteristic, complemented
45#16839515C2211yescharacteristic, complemented
46#16839513C2211yescharacteristic, complemented
47#16839513C2211yescharacteristic, complemented
48#16839511C2211yescharacteristic, complemented
49#16839511C2211yescharacteristic, complemented
50#16839508C2211yescharacteristic, complemented
51#16839508C2211yescharacteristic, complemented
52#16839506C2211yescharacteristic
53#16839506C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C2×#127×C61C2211yescharacteristic
58C61×#490—21no—
59C61×#490—21no—
60C61×#486C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#486C2211yescharacteristic
63C61×#486C2211yescharacteristic
64C61×#418—21no—
65C61×#418—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199—21no—
72C2×#11758199—21no—
73C2×#11758194—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76#14519771—21no—
77#14519769D411yescharacteristic
78#14519765D411yescharacteristic
79#14519760—21no—
80#14519756D411yescharacteristic
81#14519751D411yescharacteristic
82C4×Dic122C2311yescharacteristic
83C4×D244C2311yescharacteristic
84C4×C22⋊D61—21no—
85#14519734—21no—
86#14519710—21no—
87#14519708—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519689—21no—
108#14519689—21no—
109#14519688—21no—
110#14519687—21no—
111C4×#92418—21no—
112C8×Dic61—21no—
113C22×D4×C61—21no—
114C22×D4×C61—21no—
115C22×D4×C61—21no—
116C2×M16×C61D411yescharacteristic
117C2×M16×C61D411yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61—21no—
121#127×C61—21no—
122#127×C61—21no—
123#127×C61C2311yescharacteristic
124#127×C61C2311yescharacteristic
125#125×C61—21no—
126C22⋊Q8×C61—21no—
127C22⋊Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130#117×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#102×C61—21no—
133#102×C61—21no—
134#102×C61—21no—
135#102×C61—21no—
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C24×C61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61—82no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61#4111yescharacteristic
164C2×C22⋊D61—21no—
165C2×D244C2×D411yescharacteristic
166C2×C4×D61—21no—
167C2×Dic122C2×D411yescharacteristic
168M16×C61—41no—
169M16×C61—41no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C42×C61—41no—
182C42×C61C2×D411yescharacteristic
183C42×C61C2×D411yescharacteristic
184C42×C61#4111yescharacteristic
185C42×C61C2411yescharacteristic
186C22⋊Dic61—21no—
187#11758202—81no—
188#11758201—81no—
189#11758200—81no—
190#11758200—81no—
191#11758199—81no—
192#11758199—81no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196#11758198—21no—
197C4⋊Dic61C2×D411yescharacteristic
198C4⋊Dic61C2×D411yescharacteristic
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202#11758196—21no—
203C4×Dic61—21no—
204#11758194—81no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211#11758189—42no—
212C8×D61—42no—
213C23×C61—41no—
214C23×C61—41no—
215C23×C61—82no—
216C23×C61—82no—
217C23×C61—82no—
218C23×C61#12111yescharacteristic
219C22×D61—21no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—81no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—41no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61—81no—
232D4×C61—81no—
233D4×C61—82no—
234D4×C61—82no—
235D4×C61—82no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12111yescharacteristic
245C2×C4×C61#12111yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C22⋊D61—81no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253D244—21no—
254D244—21no—
255C4×D61—41no—
256C4×D61—41no—
257Dic122—21no—
258Dic122—21no—
259C8×C61—21no—
260C8×C61—21no—
261C8×C61—21no—
262C8×C61—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#19380—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61—81no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—164no—
280C22×C61C2×#12111yescharacteristic
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—81no—
289C4×C61—81no—
290C4×C61#57511yescharacteristic
291C4×C61#57511yescharacteristic
292C4×C61#57611yescharacteristic
293C4×C61#57711yescharacteristic
294Dic61—41no—
295Dic61—41no—
296Dic61—41no—
297#3252—611no—
298#3217—611no—
299#3138D6111yescharacteristic, complemented
300#2969—611no—
301#1702—611no—
302#1701—611no—
303#1698—611no—
304#1697—611no—
305#1682—611no—
306#1681—611no—
307#1678—611no—
308#1677—611no—
309#1569—611no—
310#1554—611no—
311#1545—611no—
312C2×C61—41no—
313C2×C61—161no—
314C2×C61—161no—
315C2×C61#304011yescharacteristic
316C2×C61#306211yescharacteristic
317C2×C61#306811yescharacteristic
318D61—81no—
319#533C2×D6111yescharacteristic
320C2×#127C2×D6111yescharacteristic
321#529—611no—
322#496—1221no—
323#490—21no—
324#490—21no—
325#490—1221no—
326#486C2×D6111yescharacteristic
327#486C2×D6111yescharacteristic
328#486C2×D6111yescharacteristic
329#486C2×D6111yescharacteristic
330#479—1221no—
331#477—611no—
332#476—611no—
333#470—1221no—
334#468—1221no—
335#464—1221no—
336#462—611no—
337#461—611no—
338#460—611no—
339#460—611no—
340#459—611no—
341#459—611no—
342#450—1221no—
343#447—1221no—
344#446—611no—
345C8×Q8—611no—
346#436—611no—
347#436—1221no—
348#435—1221no—
349C8×D4—611no—
350#433—1221no—
351#432—611no—
352#431—611no—
353#423—611no—
354#418—21no—
355#418—21no—
356#405—1221no—
357C4×M16C2×D6111yescharacteristic
358#335—611no—
359#335—611no—
360#334—611no—
361#334—611no—
362#333—611no—
363#333—611no—
364#332—611no—
365#332—611no—
366#331—611no—
367#331—611no—
368#331—611no—
369#331—611no—
370C61#1938011yescharacteristic, complemented, Sylow
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—1221no—
375C2×SD16—1221no—
376C2×SD16—1221no—
377C2×SD16—1221no—
378C2×D8—1221no—
379C2×D8—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16C22⋊D6111yescharacteristic
383C2×M16C22⋊D6111yescharacteristic
384C22×C8—1221no—
385C4⋊Q8C22×D6111yescharacteristic
386C4⋊Q8C22×D6111yescharacteristic
387#127—21no—
388#127—21no—
389#127—21no—
390#127C22×D6111yescharacteristic
391#127C22×D6111yescharacteristic
392#126—1221no—
393#125—21no—
394#125—611no—
395#124—611no—
396#123—1221no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—611no—
400#121—611no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—611no—
404C4×D4—611no—
405C4×D4—1221no—
406#117—21no—
407#117—1221no—
408C2×C42C22×D6111yescharacteristic
409#107—1221no—
410#106—1221no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419C4⋊C8—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—1221no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435#102—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440#97—1221no—
441#97—1221no—
442#97C22⋊D6111yescharacteristic
443#97C22⋊D6111yescharacteristic
444C4×C8—1221no—
445C4×C8—1221no—
446C4×C8C22×D6111yescharacteristic
447C4×C8C22×D6111yescharacteristic
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—611no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—81no—
464C2×D4—81no—
465C2×D4—82no—
466C2×D4—611no—
467C2×D4—1221no—
468C22×C4—1221no—
469C22×C4D4×D6111yescharacteristic
470C22×C4#1175822411yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472Q16—4881no—
473SD16—4881no—
474SD16—4881no—
475SD16—4881no—
476D8—4881no—
477D8—4881no—
478M16—41no—
479M16—41no—
480M16—4881no—
481M16—2442no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—2442no—
489C2×C8C2×C22⋊D6111yescharacteristic
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C2×C8C2×C22⋊D6111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—611no—
500C4⋊C4—611no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C22⋊C4—41no—
506C22⋊C4—1221no—
507C22⋊C4—1221no—
508C22⋊C4—1221no—
509C22⋊C4—1221no—
510C22⋊C4—1221no—
511C42—41no—
512C42—1221no—
513C42D4×D6111yescharacteristic
514C42#1175822411yescharacteristic
515C42C2×C22⋊D6111yescharacteristic
516C42C23×D6111yescharacteristic
517C23—41no—
518C23—41no—
519C23—82no—
520C23—82no—
521C23—82no—
522C23—1221no—
523C23#1451974811yescharacteristic
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—1221no—
528Q8—1221no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—81no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—1221no—
543D4—1221no—
544D4—4881no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—1221no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4#1451974811yescharacteristic
558C2×C4#1451974811yescharacteristic
559C2×C4#1451974811yescharacteristic
560C2×C4C2×D4×D6111yescharacteristic
561C2×C4C22×C22⋊D6111yescharacteristic
562C2×C4C2×#1175822411yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—2441no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—164no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22C2×#1451974811yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—81no—
592C4—81no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4#1684056011yescharacteristic
597C4#1684056011yescharacteristic
598C4#1684056611yescharacteristic
599C4#1684057211yescharacteristic
600C2—41no—
601C2—161no—
602C2—161no—
603C2—4881no—
604C2#2145530911yescharacteristic
605C2#2145549311yescharacteristic
606C2#2145554311yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3138C2
socleC22×C61C2×#121
prime radical#21456837C2
hypercenter#3138D61
hypocenterC61#19380
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3138

Complements

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

NH ≅ G/Ntype
1. #21457186C2semidirect
3. #21454823C2semidirect
4. #21445384C2semidirect
5. #21445377C2semidirect
6. #21445356C2semidirect
7. #21445349C2semidirect
8. #21445260C2semidirect
9. #21445253C2semidirect
10. #21445232C2semidirect
11. #21445225C2semidirect
12. #21444586C2semidirect
13. #21444529C2semidirect
14. #21444487C2semidirect
15. C61×#3138C2semidirect
20. #16840054C22semidirect
21. #16840049C22semidirect
25. #16839969C22semidirect
26. #16839964C22semidirect
33. #16839892C22semidirect
34. C8×Dic122C22semidirect
35. #16839841C22semidirect
38. C8×D244C22semidirect
44. #16839515C22semidirect
45. #16839515C22semidirect
46. #16839513C22semidirect
47. #16839513C22semidirect
48. #16839511C22semidirect
49. #16839511C22semidirect
50. #16839508C22semidirect
51. #16839508C22semidirect
299. #3138D61semidirect
370. C61#19380semidirect

Maximal subgroups

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

subgroupindex
#214571862
#214568372
#214548232
#214453842
#214453772
#214453562
#214453492
#214452602
#214452532
#214452322
#214452252
#214445862
#214445292
#214444872
C61×#31382
#1938061