Finite Group Databasebeta

← #29665451

Subgroups — #29665451

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456754C211yesmaximal, characteristic, complemented
2#21455970C211yesmaximal, characteristic, complemented
3#21455879C211yesmaximal, characteristic, complemented
4#21445277C211yesmaximal, characteristic, complemented
5#21445270C211yesmaximal, characteristic, complemented
6#21445235C211yesmaximal, characteristic, complemented
7#21445228C211yesmaximal, characteristic, complemented
8#21445179C211yesmaximal, characteristic, complemented
9#21445174C211yesmaximal, characteristic, complemented
10#21445167C211yesmaximal, characteristic, complemented
11#21445160C211yesmaximal, characteristic, complemented
12#21444599C211yesmaximal, characteristic, complemented
13#21444512C211yesmaximal, characteristic, complemented
14#21444469C211yesmaximal, characteristic, complemented
15C61×#2988C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840312C2211yescharacteristic
18#16840139C2211yescharacteristic
19#16840135C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840109C2211yescharacteristic
22#16840086—21no—
23#16840086—21no—
24#16840057C2211yescharacteristic
25#16840052C2211yescharacteristic
26#16840047C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16839978—21no—
29#16839978—21no—
30#16839962C2211yescharacteristic
31#16839962C2211yescharacteristic
32#16839957C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839909—21no—
35#16839909—21no—
36#16839907—21no—
37#16839907—21no—
38#16839872—21no—
39#16839860—21no—
40C4×#11758201—21no—
41C4×#11758199—21no—
42#16839819C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839505C2211yescharacteristic
53#16839505C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C8×Q8×C61C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C8×D4×C61—21no—
60C8×D4×C61—21no—
61C8×D4×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#431—21no—
64C61×#431C2211yescharacteristic
65C2×C4⋊C8×C61—21no—
66C2×C4⋊C8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758222—21no—
69C2×#11758190—21no—
70C2×#11758190—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×D488—21no—
74C2×D488—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519774C2311yescharacteristic
80#14519774C2311yescharacteristic
81#14519765—21no—
82#14519765—21no—
83#14519751—21no—
84#14519751—21no—
85#14519751—21no—
86#14519751—21no—
87C4×D244—21no—
88C4×D244—21no—
89C4×D244—21no—
90C4×D244—21no—
91#14519710—21no—
92#14519710—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519699—21no—
104#14519699—21no—
105#14519698—21no—
106#14519698—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519688—21no—
114C4×#92418—21no—
115C2×#41×C61D411yescharacteristic
116C22×C8×C61—21no—
117C22×C8×C61—21no—
118C22×C8×C61—21no—
119C4×Q8×C61D411yescharacteristic
120C4×Q8×C61C2311yescharacteristic
121C4×D4×C61—21no—
122C4×D4×C61—21no—
123C4×D4×C61D411yescharacteristic
124C4×D4×C61C2311yescharacteristic
125#117×C61—21no—
126#117×C61D411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—41no—
156C2×C22⋊D61—41no—
157#11758222—81no—
158#11758222—81no—
159#11758222—82no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×C4×D61—41no—
167C2×C4×D61—41no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—81no—
173C2×C8×C61—81no—
174C2×C8×C61—81no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61C2×D411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61#4111yescharacteristic
192C42×C61C2411yescharacteristic
193#11758201—42no—
194#11758201—42no—
195#11758199—42no—
196#11758199—42no—
197#11758198—41no—
198#11758198—41no—
199#11758198—41no—
200#11758198—41no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209D488—81no—
210D488—81no—
211#11758190—81no—
212#11758190—81no—
213C23×C61—21no—
214C23×C61#12111yescharacteristic
215C22×D61—41no—
216C22×D61—41no—
217Q8×C61—21no—
218Q8×C61#13512yes—
219D4×C61—24no—
220D4×C61—21no—
221D4×C61#13512yes—
222C2×C4×C61—24no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—81no—
234C2×C4×C61#12111yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C22⋊D61—82no—
241C22⋊D61—82no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244D244—41no—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250D244—41no—
251D244—41no—
252D244—81no—
253D244—81no—
254C4×D61—82no—
255C4×D61—82no—
256Dic122—41no—
257Dic122—41no—
258Dic122—81no—
259C8×C61—21no—
260C8×C61—21no—
261C8×C61—21no—
262C8×C61—21no—
263C8×C61—41no—
264C8×C61—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#19412—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—22no—
273C22×C61—21no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×#12111yescharacteristic
277C2×D61—81no—
278C2×D61—81no—
279C2×D61—81no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—22no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61C2×#13511yescharacteristic
291C4×C61C2×#13511yescharacteristic
292C4×C61#57611yescharacteristic
293C4×C61#57711yescharacteristic
294Dic61—81no—
295Dic61—81no—
296#3207—611no—
297#3115—611no—
298#3106—611no—
299#2988D6111yescharacteristic, complemented
300#1684—611no—
301#1683—611no—
302#1678—611no—
303#1677—611no—
304#1668—611no—
305#1667—611no—
306#1666—611no—
307#1665—611no—
308#1572—611no—
309#1551—611no—
310#1540—611no—
311C2×C61—41no—
312C2×C61—42no—
313C2×C61#304511yescharacteristic
314C2×C61#305011yescharacteristic
315C2×C61#306811yescharacteristic
316D61—161no—
317D61—161no—
318#532—611no—
319#532—611no—
320C4×#41C2×D6111yescharacteristic
321#493—611no—
322#492—611no—
323#487—611no—
324#486—611no—
325#482—1221no—
326#482—1221no—
327#477—611no—
328#476—611no—
329#475—611no—
330#474—611no—
331#463—1221no—
332#463—1221no—
333#460—611no—
334#460—611no—
335#459—611no—
336#459—611no—
337#449—1221no—
338#449—1221no—
339#449—1221no—
340#449—1221no—
341C8×Q8C2×D6111yescharacteristic
342C8×Q8C2×D6111yescharacteristic
343#442—1221no—
344#440—1221no—
345C4×SD16—1221no—
346C4×D8—1221no—
347C8×D4—21no—
348C8×D4—21no—
349C8×D4C2×D6111yescharacteristic
350C8×D4C2×D6111yescharacteristic
351#432—611no—
352#431—21no—
353#431—611no—
354#431C2×D6111yescharacteristic
355C2×C4⋊C8—21no—
356C2×C4⋊C8C2×D6111yescharacteristic
357#335—611no—
358#335—611no—
359#334—611no—
360#334—611no—
361#333—611no—
362#333—611no—
363#332—611no—
364#332—611no—
365#331—611no—
366#331—611no—
367#331—611no—
368#331—611no—
369C61#1941211yescharacteristic, complemented, Sylow
370C2×#41—1221no—
371C2×#41—1221no—
372C2×#41D24411yescharacteristic
373C2×SD16—1221no—
374C2×SD16—1221no—
375C2×SD16—1221no—
376C2×SD16—1221no—
377C2×D8—1221no—
378C2×D8—1221no—
379C2×D8—1221no—
380C2×D8—1221no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C4⋊Q8—611no—
385C4⋊Q8—611no—
386#127—611no—
387#127—611no—
388#124—1221no—
389#124—1221no—
390#121—1221no—
391#121—1221no—
392#121—1221no—
393#121—1221no—
394C4×Q8D24411yescharacteristic
395C4×Q8C22×D6111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—1221no—
399C4×D4—1221no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4D24411yescharacteristic
403C4×D4C22×D6111yescharacteristic
404#117—21no—
405#117D24411yescharacteristic
406C2×C42—21no—
407C2×C42C22×D6111yescharacteristic
408#107—1221no—
409#107—1221no—
410#106—1221no—
411#106—1221no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—611no—
418C4⋊C8—611no—
419C4⋊C8C22⋊D6111yescharacteristic
420C4⋊C8C22⋊D6111yescharacteristic
421C4⋊C8C22×D6111yescharacteristic
422C4⋊C8C22×D6111yescharacteristic
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#103—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8C22⋊D6111yescharacteristic
440C22⋊C8C22⋊D6111yescharacteristic
441#97—1221no—
442C4×C8—21no—
443C4×C8—21no—
444C4×C8—1221no—
445C4×C8C22×D6111yescharacteristic
446C4×C8C22×D6111yescharacteristic
447#41—22no—
448#41—22no—
449#41—4881no—
450#41—4881no—
451#41—4882no—
452C2×Q8—1221no—
453C2×Q8—1221no—
454C2×Q8C2×D24411yescharacteristic
455C2×D4—21no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—2441no—
463C2×D4—2441no—
464C2×D4C2×D24411yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4C2×D24411yescharacteristic
471C22×C4#1175822211yescharacteristic
472C22×C4C2×C22⋊D6111yescharacteristic
473SD16—4881no—
474SD16—4881no—
475SD16—2442no—
476SD16—2442no—
477D8—4881no—
478D8—4881no—
479D8—2442no—
480D8—2442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—81no—
484C2×C8—81no—
485C2×C8—81no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8C2×C22⋊D6111yescharacteristic
491C2×C8C2×C22⋊D6111yescharacteristic
492C2×C8C2×C22⋊D6111yescharacteristic
493C2×C8C2×C22⋊D6111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—1221no—
500C4⋊C4C2×D24411yescharacteristic
501C4⋊C4C2×D24411yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—2441no—
506C22⋊C4—2441no—
507C22⋊C4—2441no—
508C22⋊C4—2441no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42C2×D24411yescharacteristic
513C42#1175822211yescharacteristic
514C42C2×C22⋊D6111yescharacteristic
515C42C23×D6111yescharacteristic
516C23—21no—
517C23—2441no—
518C23—2441no—
519C23#1451975111yescharacteristic
520Q8—21no—
521Q8—4881no—
522Q8—2441no—
523Q8—2441no—
524Q8#1451979912yes—
525D4—24no—
526D4—21no—
527D4—4881no—
528D4—4881no—
529D4—4882no—
530D4—4882no—
531D4—2441no—
532D4—2441no—
533D4—2441no—
534D4—2441no—
535D4—2441no—
536D4—2441no—
537D4—2441no—
538D4—2441no—
539D4#1451979912yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—81no—
552C2×C4—4882no—
553C2×C4—4882no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4#1451975111yescharacteristic
557C2×C4#1451975111yescharacteristic
558C2×C4#1451975111yescharacteristic
559C2×C4C22×C22⋊D6111yescharacteristic
560C2×C4C22×D24411yescharacteristic
561C2×C4C2×#1175822211yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—2441no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C22—21no—
573C22—22no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—4881no—
579C22—4881no—
580C22—4881no—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22C2×#1451975111yescharacteristic
585C4—21no—
586C4—22no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—4881no—
593C4—4881no—
594C4C2×#1451979911yescharacteristic
595C4C2×#1451979911yescharacteristic
596C4#1684056511yescharacteristic
597C4#1684057011yescharacteristic
598C2—41no—
599C2—42no—
600C2—9761no—
601C2—9761no—
602C2#2145535811yescharacteristic
603C2#2145540011yescharacteristic
604C2#2145554711yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2988C2
socleC22×C61C2×#121
hypercenter#2988D61
hypocenterC61#19412
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #21456754C2semidirect
2. #21455970C2semidirect
3. #21455879C2semidirect
4. #21445277C2semidirect
5. #21445270C2semidirect
6. #21445235C2semidirect
7. #21445228C2semidirect
8. #21445179C2semidirect
9. #21445174C2semidirect
10. #21445167C2semidirect
11. #21445160C2semidirect
12. #21444599C2semidirect
13. #21444512C2semidirect
14. #21444469C2semidirect
15. C61×#2988C2semidirect
299. #2988D61semidirect
369. C61#19412semidirect

Maximal subgroups

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

subgroupindex
#214567542
#214559702
#214558792
#214452772
#214452702
#214452352
#214452282
#214451792
#214451742
#214451672
#214451602
#214445992
#214445122
#214444692
C61×#29882
#1941261