Finite Group Databasebeta

← #29669669

Subgroups — #29669669

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458162C211yesmaximal, characteristic, complemented
2#21457749C211yesmaximal, characteristic, complemented
3#21457747C211yesmaximal, characteristic, complemented
4#21445466C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445268C211yesmaximal, characteristic, complemented
7#21445239C211yesmaximal, characteristic, complemented
8#21445206C211yesmaximal, characteristic, complemented
9#21445103C211yesmaximal, characteristic, complemented
10#21445102C211yesmaximal, characteristic, complemented
11#21445045C211yesmaximal, characteristic, complemented
12#21444970C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3330C211yesmaximal, characteristic, complemented
16#16840477C2211yescharacteristic
17#16840416C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840114C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840112C2211yescharacteristic
23#16840105—21no—
24#16840100—21no—
25#16840075—21no—
26#16840073—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840039C2211yescharacteristic
31#16839996—21no—
32#16839993—21no—
33#16839990—21no—
34#16839967C2211yescharacteristic
35#16839964C2211yescharacteristic
36#16839907—21no—
37#16839904—21no—
38C4×#11758199C2211yescharacteristic
39C8×D244C2211yescharacteristic
40D4×#92418C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42C2×#14519710—21no—
43#16839758—21no—
44#16839755—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
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×#11758224—21no—
68C2×#11758200—21no—
69C2×#11758201—21no—
70C2×#11758199D411yescharacteristic
71C22×#92418—21no—
72C22×#92418—21no—
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519763—41no—
77#14519761—41no—
78#14519757—21no—
79#14519751—21no—
80#14519751—21no—
81#14519748—21no—
82C4×D244C2311yescharacteristic
83#14519736—21no—
84#14519735—21no—
85C2×C4⋊Dic61—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92#14519708—21no—
93#14519708—41no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519700—21no—
103#14519700—41no—
104#14519698—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—
165C2×D244C2×D411yescharacteristic
166C2×C4×D61—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169SD16×C61—81no—
170D8×C61—22no—
171M16×C61—81no—
172C2×C8×C61—21no—
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—41no—
180C4⋊C4×C61—41no—
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C42×C61C2411yescharacteristic
190C22⋊Dic61—41no—
191#11758201—81no—
192#11758200—81no—
193#11758199—41no—
194#11758198—21no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—41no—
202C4⋊Dic61C2×D411yescharacteristic
203C4×Dic61—41no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—42no—
209C2×#92418—81no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C8×D61—81no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61—21no—
216C22×D61—21no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—82no—
227D4×C61—82no—
228D4×C61#13512yes—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—82no—
241C2×C4×C61—82no—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61H(5,𝔽2)11yescharacteristic
245C22⋊D61—82no—
246C22⋊D61—161no—
247C2×Dic61—21no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—82no—
251D244—21no—
252D244—21no—
253C4×D61—41no—
254C4×D61—41no—
255Dic122—41no—
256Dic122—41no—
257Dic122—81no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61—41no—
261#92418—21no—
262#92418—21no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#19776—611nomaximal, Sylow
268C22×C61—22no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61D4211yescharacteristic
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C4×C61—21no—
282C4×C61—41no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61C2×#13511yescharacteristic
288C4×C61#57511yescharacteristic
289C4×C61#57611yescharacteristic
290C4×C61#57711yescharacteristic
291Dic61—41no—
292Dic61—81no—
293Dic61—81no—
294#3334—611no—
295#3330D6111yescharacteristic, complemented
296#3303—611no—
297#3303—611no—
298#1718—611no—
299#1703—611no—
300#1683—611no—
301#1679—611no—
302#1673—611no—
303#1654—611no—
304#1654—611no—
305#1646—611no—
306#1635—611no—
307#1581—611no—
308#1580—611no—
309C2×C61—42no—
310C2×C61—81no—
311C2×C61—81no—
312C2×C61#326711yescharacteristic
313C2×C61#328011yescharacteristic
314C2×C61#328911yescharacteristic
315D61—81no—
316#555—611no—
317#547—611no—
318#547C2×D6111yescharacteristic
319#547C2×D6111yescharacteristic
320#500—611no—
321#498—611no—
322#487—611no—
323#487—611no—
324#487—611no—
325#487C2×D6111yescharacteristic
326#485—1221no—
327#485—1221no—
328#484—21no—
329#480—1221no—
330#480—1221no—
331#476—611no—
332#476—611no—
333#474—611no—
334#474—611no—
335#474C2×D6111yescharacteristic
336#468—21no—
337#466—1221no—
338#465—1221no—
339#465—1221no—
340#461—611no—
341#461—611no—
342#461C2×D6111yescharacteristic
343#449—21no—
344#449—1221no—
345#449—1221no—
346C4×D8—611no—
347C4×D8C2×D6111yescharacteristic
348#436C2×D6111yescharacteristic
349C8×D4—611no—
350C8×D4—611no—
351C8×D4—611no—
352C2×#107—1221no—
353#417—21no—
354#416—1221no—
355#416—1221no—
356#335—611no—
357#334—611no—
358#333—611no—
359#332—611no—
360#332—611no—
361#332—611no—
362D4⋊C8—611no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—611no—
366#322—611no—
367C61#1977611yescharacteristic, complemented, Sylow
368C2×#41—21no—
369C2×#41—21no—
370C2×#41—1221no—
371C2×SD16—21no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×D8—611no—
375C2×D8C22⋊D6111yescharacteristic
376C2×M16—21no—
377C22×C8—1221no—
378C22×C8—1221no—
379C22×C8—1221no—
380C4⋊Q8—611no—
381C4⋊Q8—611no—
382C4⋊Q8C22×D6111yescharacteristic
383C4⋊Q8C22×D6111yescharacteristic
384#124—2441no—
385#123—41no—
386#123—41no—
387#123—2441no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390C22⋊Q8—1221no—
391#121—21no—
392#121—21no—
393#121—1221no—
394#121—1221no—
395#121—1221no—
396C4×D4—611no—
397C4×D4C22×D6111yescharacteristic
398C4×D4C22×D6111yescharacteristic
399C4×D4C22×D6111yescharacteristic
400#117—1221no—
401#117—1221no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—1221no—
405#107—21no—
406#107—611no—
407#107—1221no—
408#107—1221no—
409#107—1221no—
410#107—1221no—
411#107C22⋊D6111yescharacteristic
412#106—1221no—
413#106—1221no—
414#106—2441no—
415C4⋊C8—611no—
416C4⋊C8—611no—
417C4⋊C8—611no—
418C4⋊C8C22×D6111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#103—1221no—
427#103—1221no—
428#103—2441no—
429#102—21no—
430#102—611no—
431#102—611no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435#102—1221no—
436#102C22⋊D6111yescharacteristic
437#102C22⋊D6111yescharacteristic
438C22⋊C8—21no—
439C22⋊C8—1221no—
440C22⋊C8—1221no—
441C22⋊C8—1221no—
442C4×C8—611no—
443C4×C8—611no—
444C4×C8C22×D6111yescharacteristic
445#41—42no—
446#41—42no—
447#41—81no—
448#41—81no—
449#41—4881no—
450#41—2442no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—611no—
458C2×D4—2441no—
459C2×D4—2441no—
460C2×D4D4×D6111yescharacteristic
461C2×D4C2×C22⋊D6111yescharacteristic
462C2×D4C2×C22⋊D6111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—1221no—
469C22×C4—2441no—
470SD16—81no—
471SD16—4881no—
472SD16—4881no—
473D8—22no—
474D8—2441no—
475M16—81no—
476C2×C8—21no—
477C2×C8—611no—
478C2×C8—611no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—4881no—
484C2×C8—4881no—
485C2×C8—2442no—
486C2×C8C2×C22⋊D6111yescharacteristic
487C2×C8C2×C22⋊D6111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—611no—
495C4⋊C4—1221no—
496C4⋊C4—1221no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C4⋊C4—2441no—
500C4⋊C4D4×D6111yescharacteristic
501C4⋊C4C2×C22⋊D6111yescharacteristic
502C4⋊C4C2×C22⋊D6111yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—1221no—
509C22⋊C4—2441no—
510C22⋊C4—2441no—
511C22⋊C4—2441no—
512C42—2441no—
513C42C23×D6111yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23—1221no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—4881no—
523Q8—2441no—
524Q8—2441no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—82no—
531D4—82no—
532D4—1221no—
533D4—1221no—
534D4—9761no—
535D4—4882no—
536D4#1451979712yes—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—1221no—
551C2×C4—4882no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4C2×D4×D6111yescharacteristic
557C2×C4C22×C22⋊D6111yescharacteristic
558C2×C4#1451982211yescharacteristic
559C8—21no—
560C8—21no—
561C8—41no—
562C8—1221no—
563C8—1221no—
564C8—2441no—
565C8—2441no—
566C8—2441no—
567C8—2441no—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22D4×C22⋊D6111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—4881no—
588C4—4881no—
589C4—2441no—
590C4C2×#1451979711yescharacteristic
591C4#1684055811yescharacteristic
592C4#1684056511yescharacteristic
593C4#1684057211yescharacteristic
594C2—42no—
595C2—81no—
596C2—81no—
597C2—4881no—
598C2#2145733811yescharacteristic
599C2#2145750011yescharacteristic
600C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3330C2
socleC22×C61D42
hypercenter#3330D61
hypocenterC61#19776
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. #21458162C2semidirect
2. #21457749C2semidirect
3. #21457747C2semidirect
4. #21445466C2semidirect
5. #21445394C2semidirect
6. #21445268C2semidirect
7. #21445239C2semidirect
8. #21445206C2semidirect
9. #21445103C2semidirect
10. #21445102C2semidirect
11. #21445045C2semidirect
12. #21444970C2semidirect
13. #21444646C2semidirect
14. #21444643C2semidirect
15. C61×#3330C2semidirect
295. #3330D61semidirect
367. C61#19776semidirect

Maximal subgroups

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

subgroupindex
#214581622
#214577492
#214577472
#214454662
#214453942
#214452682
#214452392
#214452062
#214451032
#214451022
#214450452
#214449702
#214446462
#214446432
C61×#33302
#1977661