Finite Group Databasebeta

← #29670914

Subgroups — #29670914

Order 15616.

656 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#21458168C211yesmaximal, characteristic, complemented
2#21457741C211yesmaximal, characteristic, complemented
3#21457537C211yesmaximal, characteristic, complemented
4#21445493C211yesmaximal, characteristic, complemented
5#21445332C211yesmaximal, characteristic, complemented
6#21445272C211yesmaximal, characteristic, complemented
7#21445191C211yesmaximal, characteristic, complemented
8#21445182C211yesmaximal, characteristic, complemented
9#21445054C211yesmaximal, characteristic, complemented
10#21445053C211yesmaximal, characteristic, complemented
11#21445047C211yesmaximal, characteristic, complemented
12#21444969C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3354C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840417C2211yescharacteristic
18#16840417C2211yescharacteristic
19#16840167C2211yescharacteristic
20#16840165C2211yescharacteristic
21#16840141C2211yescharacteristic
22#16840114C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840103—21no—
25#16840074—21no—
26#16840074—21no—
27#16840049C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840001—21no—
31#16839995—21no—
32#16839989—21no—
33#16839967C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839964C2211yescharacteristic
36#16839924—21no—
37#16839922—21no—
38#16839905—21no—
39C4×#11758199C2211yescharacteristic
40C8×D244C2211yescharacteristic
41D4×#92418C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#107×D61—21no—
44#16839756—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839507C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#555C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#482—21no—
60C61×#481—21no—
61C61×#476C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C61×#469—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#428—21no—
67C2×#11758222—21no—
68C2×#11758222—21no—
69#14519797—44no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75C2×#11758199D411yescharacteristic
76C22×#92418—21no—
77C22×#92418—21no—
78C2×C8×D61—21no—
79#14519777C2311yescharacteristic
80#14519777C2311yescharacteristic
81#14519759—41no—
82#14519759—41no—
83#14519756—21no—
84#14519756—21no—
85#14519748—21no—
86#14519748—21no—
87C4×D244C2311yescharacteristic
88C4⋊C4×D61—21no—
89C4⋊C4×D61—21no—
90#14519711—21no—
91#14519711—21no—
92#14519710—21no—
93#14519710—21no—
94#14519710—41no—
95#14519710D411yescharacteristic
96#14519708—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519701—21no—
101#14519701—41no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698D411yescharacteristic
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×D8×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#124×C61—41no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137#106×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160#11758222—42no—
161#11758222—42no—
162#11758222—81no—
163#11758222—81no—
164C2×D244C2×D411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—41no—
167C2×C4×D61—41no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170D8×C61—22no—
171M16×C61—42no—
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×C61C2×D411yescharacteristic
181C4⋊C4×C61C2×D411yescharacteristic
182C4⋊C4×C61C2×D411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61—21no—
185C22⋊C4×C61—21no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C42×C61—41no—
190C42×C61C2411yescharacteristic
191C22⋊Dic61—41no—
192C22⋊Dic61—41no—
193#11758202—42no—
194#11758202—81no—
195#11758201—42no—
196#11758200—42no—
197#11758200—81no—
198#11758199—22no—
199#11758198—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61C2×D411yescharacteristic
205#11758196—41no—
206#11758196—41no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—42no—
212C2×#92418—81no—
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215C8×D61—42no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—21no—
219C22×D61—21no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—81no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—21no—
228D4×C61—21no—
229D4×C61—82no—
230D4×C61—161no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
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—41no—
241C2×C4×C61—41no—
242C2×C4×C61—82no—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C22⋊D61—82no—
247C22⋊D61—82no—
248C2×Dic61—21no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251D244—21no—
252D244AGL(1,ℤ/8)12yes—
253C4×D61—41no—
254C4×D61—41no—
255C4×D61—82no—
256C4×D61—82no—
257Dic122—41no—
258Dic122—41no—
259Dic122—41no—
260Dic122—41no—
261C8×C61—21no—
262C8×C61—41no—
263C8×C61#13512yescomplemented
264#92418—21no—
265#92418—21no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#92418—41no—
270#19859—611nomaximal, Sylow
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61D4211yescharacteristic
281C2×D61—22no—
282C2×D61—41no—
283C2×D61—41no—
284C4×C61—21no—
285C4×C61—41no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—81no—
289C4×C61—81no—
290C4×C61C2×#13511yescharacteristic
291C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C61#57611yescharacteristic
293C4×C61#57811yescharacteristic
294Dic61—41no—
295Dic61—81no—
296Dic61—81no—
297#3354D6111yescharacteristic, complemented
298#3334—611no—
299#3303—611no—
300#3283—611no—
301#1723—611no—
302#1693—611no—
303#1683—611no—
304#1671—611no—
305#1669—611no—
306#1647—611no—
307#1647—611no—
308#1646—611no—
309#1635—611no—
310#1581—611no—
311#1580—611no—
312C2×C61—81no—
313C2×C61—81no—
314C2×C61—81no—
315C2×C61#326411yescharacteristic
316C2×C61#328311yescharacteristic
317C2×C61#328911yescharacteristic
318D61—42no—
319C2×#135—1221no—
320#555C2×D6111yescharacteristic
321#547—611no—
322#547—611no—
323#547C2×D6111yescharacteristic
324#500—611no—
325#500—611no—
326#498C2×D6111yescharacteristic
327#494—611no—
328#487—611no—
329#487—611no—
330#485—1221no—
331#482—21no—
332#481—21no—
333#480—1221no—
334#480—1221no—
335#476—611no—
336#476C2×D6111yescharacteristic
337#474—611no—
338#474—611no—
339#474C2×D6111yescharacteristic
340#469—21no—
341#467—1221no—
342#466—1221no—
343#465—1221no—
344#461—611no—
345#461—611no—
346#461—611no—
347#452—1221no—
348#452—1221no—
349#449—1221no—
350C4×D8—611no—
351C4×D8C2×D6111yescharacteristic
352#436C2×D6111yescharacteristic
353C8×D4—611no—
354C8×D4—611no—
355C8×D4—611no—
356#428—21no—
357C2×#107—1221no—
358#416—1221no—
359#335—611no—
360#334—611no—
361#333—611no—
362#332—611no—
363#332—611no—
364#332—611no—
365D4⋊C8—611no—
366D4⋊C8—611no—
367D4⋊C8—611no—
368D4⋊C8—611no—
369#322—611no—
370C61#1985911yescharacteristic, complemented, Sylow
371C2×#41—21no—
372C2×#41—1221no—
373C2×#41—1221no—
374#135—2444no—
375C2×Q16—1221no—
376C2×Q16—1221no—
377C2×SD16—1221no—
378C2×SD16—1221no—
379C2×SD16—1221no—
380C2×D8—611no—
381C2×D8C22⋊D6111yescharacteristic
382C2×M16—21no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8—1221no—
386C4⋊Q8—611no—
387C4⋊Q8—611no—
388C4⋊Q8C22×D6111yescharacteristic
389C4⋊Q8C22×D6111yescharacteristic
390#124—41no—
391#123—41no—
392#123—2441no—
393#123—2441no—
394C22⋊Q8—21no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—1221no—
401#121—1221no—
402C4×D4—611no—
403C4×D4C22×D6111yescharacteristic
404C4×D4C22×D6111yescharacteristic
405C4×D4C22×D6111yescharacteristic
406#117—21no—
407#117—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—1221no—
417#107—2441no—
418#107C22⋊D6111yescharacteristic
419#106—21no—
420#106—21no—
421#106—21no—
422#106—1221no—
423C4⋊C8—611no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8C22×D6111yescharacteristic
427#103—1221no—
428#103—1221no—
429#103—1221no—
430#103—1221no—
431#103—1221no—
432#103—2441no—
433#102—21no—
434#102—21no—
435#102—611no—
436#102—611no—
437#102—1221no—
438#102—1221no—
439#102—1221no—
440#102C22⋊D6111yescharacteristic
441#102C22⋊D6111yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1221no—
446C4×C8—611no—
447C4×C8—611no—
448C4×C8C22×D6111yescharacteristic
449#41—42no—
450#41—81no—
451#41—4881no—
452#41—4881no—
453#41—2442no—
454#41—2442no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—1221no—
458C2×Q8—1221no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—611no—
462C2×D4—2441no—
463C2×D4—2441no—
464C2×D4D4×D6111yescharacteristic
465C2×D4C2×C22⋊D6111yescharacteristic
466C2×D4C2×C22⋊D6111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—1221no—
472C22×C4—2441no—
473C22×C4—2441no—
474Q16—4881no—
475Q16—2442no—
476SD16—4881no—
477SD16—2442no—
478SD16—2442no—
479D8—22no—
480D8—1222no—
481M16—42no—
482C2×C8—21no—
483C2×C8—611no—
484C2×C8—611no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1221no—
489C2×C8—4881no—
490C2×C8—2442no—
491C2×C8—2442no—
492C2×C8C2×C22⋊D6111yescharacteristic
493C2×C8C2×C22⋊D6111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—611no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—2441no—
505C4⋊C4—2441no—
506C4⋊C4D4×D6111yescharacteristic
507C4⋊C4C2×C22⋊D6111yescharacteristic
508C4⋊C4C2×C22⋊D6111yescharacteristic
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—1221no—
516C22⋊C4—2441no—
517C22⋊C4—2441no—
518C42—41no—
519C42C23×D6111yescharacteristic
520C23—21no—
521C23—21no—
522C23—21no—
523C23—1221no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527Q8—2441no—
528Q8—2441no—
529Q8—2441no—
530Q8—2441no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—82no—
538D4—161no—
539D4—612no—
540D4—1221no—
541D4—4882no—
542D4—4882no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—82no—
555C2×C4—1221no—
556C2×C4—4882no—
557C2×C4—4882no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4C2×D4×D6111yescharacteristic
563C2×C4C22×C22⋊D6111yescharacteristic
564C2×C4#1451982211yescharacteristic
565C8—21no—
566C8—41no—
567C8—1221no—
568C8—1221no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C8#1451979712yescomplemented
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—1222no—
584C22—2441no—
585C22—2441no—
586C22D4×C22⋊D6111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—4881no—
594C4—4881no—
595C4—2441no—
596C4C2×#1451979711yescharacteristic
597C4AGL(1,ℤ/8)×D6111yescharacteristic
598C4#1684056611yescharacteristic
599C4#1684057711yescharacteristic
600C2—81no—
601C2—81no—
602C2—81no—
603C2—2442no—
604C2#2145729311yescharacteristic
605C2#2145753711yescharacteristic
606C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3354C2
socleC22×C61D42
hypercenter#3354D61
hypocenterC61#19859
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3354

Complements

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

NH ≅ G/Ntype
1. #21458168C2semidirect
2. #21457741C2semidirect
3. #21457537C2semidirect
4. #21445493C2semidirect
5. #21445332C2semidirect
6. #21445272C2semidirect
7. #21445191C2semidirect
8. #21445182C2semidirect
9. #21445054C2semidirect
10. #21445053C2semidirect
11. #21445047C2semidirect
12. #21444969C2semidirect
13. #21444646C2semidirect
14. #21444643C2semidirect
15. C61×#3354C2semidirect
263. C8×C61#135semidirect
297. #3354D61semidirect
370. C61#19859semidirect
573. C8#14519797semidirect

Maximal subgroups

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

subgroupindex
#214581682
#214577412
#214575372
#214454932
#214453322
#214452722
#214451912
#214451822
#214450542
#214450532
#214450472
#214449692
#214446462
#214446432
C61×#33542
#1985961