Finite Group Databasebeta

← #29677082

Subgroups — #29677082

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458126C211yesmaximal, characteristic, complemented
2#21458124C211yesmaximal, characteristic, complemented
3#21458118C211yesmaximal, characteristic, complemented
4#21445427C211yesmaximal, characteristic, complemented
5#21445368C211yesmaximal, characteristic, complemented
6#21445366C211yesmaximal, characteristic, complemented
7#21445364C211yesmaximal, characteristic, complemented
8#21445363C211yesmaximal, characteristic, complemented
9#21445054C211yesmaximal, characteristic, complemented
10#21445054C211yesmaximal, characteristic, complemented
11#21445053C211yesmaximal, characteristic, complemented
12#21445052C211yesmaximal, characteristic, complemented
13#21444704C211yesmaximal, characteristic, complemented
14#21444702C211yesmaximal, characteristic, complemented
15C61×#3330C211yesmaximal, characteristic, complemented
16#16840417C2211yescharacteristic
17#16840416C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840099—21no—
24#16840097—21no—
25#16840095—21no—
26#16840042C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16840039C2211yescharacteristic
29#16840010—21no—
30#16840007—21no—
31#16840006—21no—
32#16839967C2211yescharacteristic
33#16839967C2211yescharacteristic
34#16839964C2211yescharacteristic
35#16839907—21no—
36#16839905—21no—
37#16839904—21no—
38C4×#11758199C2211yescharacteristic
39#16839841C2211yescharacteristic
40#16839840C2211yescharacteristic
41#16839840C2211yescharacteristic
42#16839763—21no—
43#16839761—21no—
44#16839760—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#547C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#484—21no—
60C61×#474C2211yescharacteristic
61C61×#468—21no—
62C61×#461C2211yescharacteristic
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#417—21no—
67C2×#11758222—21no—
68C2×#11758224—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758201—21no—
72C2×#11758199D411yescharacteristic
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758189—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519761—41no—
79#14519759—41no—
80#14519757—21no—
81#14519756—21no—
82#14519751—21no—
83#14519748—21no—
84C4×D244C2311yescharacteristic
85C2×C4⋊Dic61—21no—
86C4⋊C4×D61—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—41no—
91#14519710—41no—
92#14519710D411yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519702—21no—
97#14519702—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519700—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698D411yescharacteristic
108#14519697—21no—
109#14519697D411yescharacteristic
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×SD16×C61—21no—
118C2×D8×C61D411yescharacteristic
119C2×M16×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#123×C61—41no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—42no—
146#41×C61—81no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C22×Dic61—41no—
163#11758224—42no—
164#11758224—81no—
165#11758222—42no—
166#11758222—81no—
167C2×D244C2×D411yescharacteristic
168C2×C4×D61—21no—
169C2×C4×D61—41no—
170C2×Dic122—21no—
171C2×Dic122—21no—
172SD16×C61—81no—
173D8×C61—41no—
174M16×C61—81no—
175C2×C8×C61—21no—
176C2×C8×C61C2×D411yescharacteristic
177C2×C8×C61C2×D411yescharacteristic
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—41no—
183C4⋊C4×C61—41no—
184C4⋊C4×C61C2×D411yescharacteristic
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—41no—
191C22⋊C4×C61—41no—
192C42×C61C2411yescharacteristic
193C22⋊Dic61—41no—
194#11758201—81no—
195#11758200—81no—
196#11758200—81no—
197#11758199—41no—
198#11758198—21no—
199#11758198—41no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—41no—
205C4⋊Dic61C2×D411yescharacteristic
206#11758196—41no—
207#11758194—81no—
208#11758194—81no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215#11758189—81no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C22×D61—21no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—82no—
231D4×C61—82no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—82no—
244C2×C4×C61—82no—
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61H(5,𝔽2)11yescharacteristic
248C22⋊D61—82no—
249C22⋊D61—82no—
250C2×Dic61—21no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—82no—
254D244—21no—
255D244—21no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—82no—
259Dic122—41no—
260Dic122—41no—
261Dic122—41no—
262Dic122—41no—
263C8×C61—21no—
264C8×C61—21no—
265C8×C61—41no—
266#92418—22no—
267#92418—21no—
268#92418—21no—
269#92418—41no—
270#92418—41no—
271#92418—41no—
272#20304—611nomaximal, Sylow
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61D4211yescharacteristic
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C4×C61—21no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—81no—
291C4×C61—81no—
292C4×C61#57511yescharacteristic
293C4×C61#57511yescharacteristic
294C4×C61#57611yescharacteristic
295C4×C61#57611yescharacteristic
296Dic61—41no—
297Dic61—81no—
298Dic61—81no—
299#3330—611no—
300#3330—611no—
301#3330—611no—
302#3330D6111yescharacteristic, complemented
303#1710—611no—
304#1699—611no—
305#1699—611no—
306#1699—611no—
307#1699—611no—
308#1647—611no—
309#1647—611no—
310#1647—611no—
311#1647—611no—
312#1589—611no—
313#1589—611no—
314C2×C61—81no—
315C2×C61—81no—
316C2×C61—81no—
317C2×C61#327311yescharacteristic
318C2×C61#327311yescharacteristic
319C2×C61#329311yescharacteristic
320D61—81no—
321#547—611no—
322#547—611no—
323#547C2×D6111yescharacteristic
324#547C2×D6111yescharacteristic
325#500—611no—
326#500—611no—
327#487—611no—
328#487—611no—
329#487—611no—
330#487C2×D6111yescharacteristic
331#484—21no—
332#484—1221no—
333#484—1221no—
334#484—1221no—
335#474—611no—
336#474—611no—
337#474—611no—
338#474C2×D6111yescharacteristic
339#468—21no—
340#468—1221no—
341#468—1221no—
342#468—1221no—
343#461—611no—
344#461—611no—
345#461—611no—
346#461C2×D6111yescharacteristic
347#449—21no—
348#449—1221no—
349#449—1221no—
350#449—1221no—
351C4×D8—611no—
352C4×D8C2×D6111yescharacteristic
353#436—611no—
354#436—611no—
355#436—611no—
356#436C2×D6111yescharacteristic
357#417—21no—
358#417—1221no—
359#417—1221no—
360#417—1221no—
361#335—611no—
362#335—611no—
363#332—611no—
364#332—611no—
365#332—611no—
366#332—611no—
367D4⋊C8—611no—
368D4⋊C8—611no—
369D4⋊C8—611no—
370D4⋊C8—611no—
371C82—611no—
372C61#2030411yescharacteristic, complemented, Sylow
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—1221no—
376C2×#41—1221no—
377C2×SD16—21no—
378C2×SD16—1221no—
379C2×SD16—1221no—
380C2×SD16—1221no—
381C2×D8—611no—
382C2×D8C22⋊D6111yescharacteristic
383C2×M16—21no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C4⋊Q8—611no—
388C4⋊Q8—611no—
389C4⋊Q8C22×D6111yescharacteristic
390C4⋊Q8C22×D6111yescharacteristic
391#123—41no—
392#123—41no—
393#123—2441no—
394#123—2441no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—1221no—
398C22⋊Q8—1221no—
399#121—21no—
400#121—21no—
401#121—1221no—
402#121—1221no—
403C4×D4—611no—
404C4×D4C22×D6111yescharacteristic
405C4×D4C22×D6111yescharacteristic
406C4×D4C22×D6111yescharacteristic
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4—1221no—
411#107—21no—
412#107—611no—
413#107—1221no—
414#107—1221no—
415#107—1221no—
416#107—2441no—
417#107—2441no—
418#107C22⋊D6111yescharacteristic
419C4⋊C8—611no—
420C4⋊C8—611no—
421C4⋊C8—611no—
422C4⋊C8C22×D6111yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—1221no—
427#103—1221no—
428#103—1221no—
429#103—1221no—
430#103—1221no—
431#103—1221no—
432#103—1221no—
433#103—1221no—
434#103—1221no—
435#102—21no—
436#102—611no—
437#102—611no—
438#102—1221no—
439#102—1221no—
440#102—1221no—
441#102C22⋊D6111yescharacteristic
442#102C22⋊D6111yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C22⋊C8—1221no—
447C4×C8—611no—
448C4×C8—611no—
449C4×C8C22×D6111yescharacteristic
450#41—42no—
451#41—42no—
452#41—81no—
453#41—81no—
454#41—4881no—
455#41—4881no—
456#41—2442no—
457#41—2442no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—1221no—
461C2×Q8—1221no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—611no—
465C2×D4—2441no—
466C2×D4—2441no—
467C2×D4D4×D6111yescharacteristic
468C2×D4C2×C22⋊D6111yescharacteristic
469C2×D4C2×C22⋊D6111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—1221no—
476C22×C4—2441no—
477C22×C4—2441no—
478SD16—81no—
479SD16—4881no—
480SD16—4881no—
481SD16—4881no—
482D8—41no—
483D8—2441no—
484M16—81no—
485M16—4881no—
486M16—4881no—
487M16—4881no—
488C2×C8—21no—
489C2×C8—611no—
490C2×C8—611no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8C2×C22⋊D6111yescharacteristic
496C2×C8C2×C22⋊D6111yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—611no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—2441no—
509C4⋊C4—2441no—
510C4⋊C4D4×D6111yescharacteristic
511C4⋊C4C2×C22⋊D6111yescharacteristic
512C4⋊C4C2×C22⋊D6111yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—1221no—
519C22⋊C4—2441no—
520C22⋊C4—2441no—
521C42C23×D6111yescharacteristic
522C23—21no—
523C23—21no—
524C23—21no—
525C23—1221no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—2441no—
531Q8—2441no—
532Q8—2441no—
533Q8—2441no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—82no—
541D4—82no—
542D4—1221no—
543D4—1221no—
544D4—4882no—
545D4—4882no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—1221no—
560C2×C4—4882no—
561C2×C4—4882no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4C2×D4×D6111yescharacteristic
567C2×C4C22×C22⋊D6111yescharacteristic
568C2×C4#1451982211yescharacteristic
569C8—21no—
570C8—21no—
571C8—41no—
572C8—1222no—
573C8—1221no—
574C8—1221no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—2441no—
588C22—2441no—
589C22—2441no—
590C22D4×C22⋊D6111yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—81no—
596C4—81no—
597C4—4881no—
598C4—4881no—
599C4—2441no—
600C4#1684055811yescharacteristic
601C4#1684056011yescharacteristic
602C4#1684056511yescharacteristic
603C4#1684056611yescharacteristic
604C2—81no—
605C2—81no—
606C2—81no—
607C2—4881no—
608C2#2145742411yescharacteristic
609C2#2145742611yescharacteristic
610C2#2145762111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3330C2
socleC22×C61D42
hypercenter#3330D61
hypocenterC61#20304
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #21458126C2semidirect
2. #21458124C2semidirect
3. #21458118C2semidirect
4. #21445427C2semidirect
5. #21445368C2semidirect
6. #21445366C2semidirect
7. #21445364C2semidirect
8. #21445363C2semidirect
9. #21445054C2semidirect
10. #21445054C2semidirect
11. #21445053C2semidirect
12. #21445052C2semidirect
13. #21444704C2semidirect
14. #21444702C2semidirect
15. C61×#3330C2semidirect
302. #3330D61semidirect
372. C61#20304semidirect

Maximal subgroups

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

subgroupindex
#214581262
#214581242
#214581182
#214454272
#214453682
#214453662
#214453642
#214453632
#214450542
#214450532
#214450522
#214447042
#214447022
C61×#33302
#2030461