Finite Group Databasebeta

← #29677113

Subgroups — #29677113

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458837C211yesmaximal, characteristic
2#21458151C211yesmaximal, characteristic, complemented
3#21458102C211yesmaximal, characteristic, complemented
4#21445421C211yesmaximal, characteristic, complemented
5#21445364C211yesmaximal, characteristic, complemented
6#21445354C211yesmaximal, characteristic, complemented
7#21445322C211yesmaximal, characteristic, complemented
8#21445291C211yesmaximal, characteristic, complemented
9#21445026C211yesmaximal, characteristic, complemented
10#21445011C211yesmaximal, characteristic, complemented
11#21444989C211yesmaximal, characteristic, complemented
12#21444922C211yesmaximal, characteristic, complemented
13#21444714C211yesmaximal, characteristic, complemented
14#21444704C211yesmaximal, characteristic, complemented
15C61×#3384C211yesmaximal, characteristic, complemented
16#16840482C2211yescharacteristic
17#16840433C2211yescharacteristic
18#16840150—21no—
19#16840135C2211yescharacteristic
20#16840112C2211yescharacteristic
21#16840112C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840100—21no—
25#16840075—21no—
26#16840054C2211yescharacteristic
27#16840047C2211yescharacteristic
28#16840018—21no—
29#16840010—21no—
30#16839976—21no—
31#16839969C2211yescharacteristic
32#16839967C2211yescharacteristic
33#16839962C2211yescharacteristic
34#16839961—21no—
35#16839957C2211yescharacteristic
36#16839922—21no—
37#16839918—21no—
38#16839892C2211yescharacteristic
39#16839861—21no—
40C4×#11758202C2211yescharacteristic
41#16839840C2211yescharacteristic
42#16839840C2211yescharacteristic
43#16839771—21no—
44#16839761—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#554C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#501—21no—
59C61×#498C2211yescharacteristic
60C61×#478—21no—
61C61×#476—21no—
62C61×#476C2211yescharacteristic
63C61×#474C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#442—21no—
66C4×D8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758202D411yescharacteristic
70C2×#11758190—21no—
71C2×#11758190—21no—
72C2×#11758200—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77#14519777C2311yescharacteristic
78#14519774C2311yescharacteristic
79#14519773—21no—
80#14519770—41no—
81#14519764—21no—
82#14519756—21no—
83#14519751—21no—
84#14519750—41no—
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519739—21no—
88#14519736—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—41no—
101#14519701D411yescharacteristic
102#14519700—21no—
103#14519700—21no—
104#14519700D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×D8×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120#125×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—41no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61C2311yescharacteristic
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61D411yescharacteristic
133#106×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—41no—
155C22×C4×C61—41no—
156C2×C22⋊D61—41no—
157C2×C22⋊D61—41no—
158#11758222—42no—
159#11758222—81no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×C4×D61—41no—
164C2×Dic122—21no—
165C2×Dic122C2×D411yescharacteristic
166D8×C61—22no—
167C2×C8×C61—21no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C4⋊C4×C61C2×D411yescharacteristic
181C22⋊C4×C61—21no—
182C22⋊C4×C61—21no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C42×C61—21no—
186C42×C61C2411yescharacteristic
187C22⋊Dic61—41no—
188C22⋊Dic61—41no—
189#11758202—41no—
190#11758202—81no—
191#11758201—81no—
192#11758200—81no—
193#11758199—81no—
194#11758198—41no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—41no—
200C4×Dic61—21no—
201C4×Dic61—41no—
202#11758194—81no—
203#11758194—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210#11758190—42no—
211#11758190—81no—
212C23×C61—21no—
213C23×C61—21no—
214C22×D61—41no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—81no—
220Q8×C61—82no—
221D4×C61—21no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—82no—
236C2×C4×C61—161no—
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61H(5,𝔽2)11yescharacteristic
240C22⋊D61—82no—
241C22⋊D61—161no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—41no—
245D244—41no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—81no—
250C4×D61—82no—
251Dic122—21no—
252Dic122—21no—
253Dic122—41no—
254Dic122—41no—
255C8×C61—21no—
256C8×C61—41no—
257C8×C61#13712yes—
258#92418—21no—
259#92418—21no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#20307—611nomaximal, Sylow
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61D4211yescharacteristic
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61C2×#13711yescharacteristic
283C4×C61#57511yescharacteristic
284C4×C61#57611yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—41no—
287Dic61—41no—
288Dic61—81no—
289#3397—611no—
290#3384D6111yescharacteristic, complemented
291#3333—611no—
292#3328—611no—
293#1708—611no—
294#1699—611no—
295#1697—611no—
296#1692—611no—
297#1686—611no—
298#1643—611no—
299#1641—611no—
300#1638—611no—
301#1627—611no—
302#1591—611no—
303#1589—611no—
304C2×C61—81no—
305C2×C61—81no—
306C2×C61#327311yescharacteristic
307C2×C61#327811yescharacteristic
308C2×C61#329011yescharacteristic
309D61—161no—
310#556—611no—
311#554C2×D6111yescharacteristic
312#550—611no—
313D4×Q8C2×D6111yescharacteristic
314#501—21no—
315#498C2×D6111yescharacteristic
316#496—1221no—
317#492—611no—
318#487—611no—
319#487—611no—
320#486—611no—
321#486—611no—
322#485—1221no—
323#480—1221no—
324#478—21no—
325#477—611no—
326#476—21no—
327#476C2×D6111yescharacteristic
328#475—611no—
329#474C2×D6111yescharacteristic
330#470—1221no—
331#468—1221no—
332#463—1221no—
333#462—611no—
334#461—611no—
335#460—611no—
336#460—1221no—
337#459—611no—
338#452—1221no—
339#451—1221no—
340#446—611no—
341#446C2×D6111yescharacteristic
342#442—21no—
343#440—1221no—
344C4×Q16—611no—
345C4×D8C2×D6111yescharacteristic
346#436—611no—
347#436—611no—
348#419—1221no—
349#417—1221no—
350#335—611no—
351#335—611no—
352#333—611no—
353#332—611no—
354#332—611no—
355#331—611no—
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358D4⋊C8—611no—
359D4⋊C8—611no—
360C82—611no—
361C61#2030711yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C22×Q8—21no—
364C2×Q16—611no—
365C2×Q16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×SD16—1221no—
370C2×D8—1221no—
371C2×D8C22⋊D6111yescharacteristic
372C2×M16—1221no—
373C2×M16—1221no—
374C4⋊Q8—21no—
375C4⋊Q8—611no—
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378#127—611no—
379#127—1221no—
380#126—2441no—
381#125—21no—
382#124—1221no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386C22⋊Q8—41no—
387C22⋊Q8—1221no—
388#121—1221no—
389#121—2441no—
390C4×Q8—611no—
391C4×Q8—1221no—
392C4×Q8C22×D6111yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—1221no—
396C4×D4C22×D6111yescharacteristic
397C4×D4C22×D6111yescharacteristic
398#117—1221no—
399C2×C4⋊C4—21no—
400#107—21no—
401#107—611no—
402#107—1221no—
403#107C22⋊D6111yescharacteristic
404#106—21no—
405#106—21no—
406#106—21no—
407#106—1221no—
408C4⋊C8—21no—
409C4⋊C8—611no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—1221no—
413C4⋊C8C22×D6111yescharacteristic
414#103—611no—
415#103—611no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—2441no—
423#102—21no—
424#102—21no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—2441no—
430#102C22⋊D6111yescharacteristic
431#102C22⋊D6111yescharacteristic
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434#97—21no—
435#97—1221no—
436C4×C8—611no—
437C4×C8—611no—
438C4×C8C22×D6111yescharacteristic
439#41—4881no—
440#41—2442no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—41no—
444C2×Q8—42no—
445C2×Q8—81no—
446C2×Q8—611no—
447C2×Q8—1221no—
448C2×Q8D4×D6111yescharacteristic
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4—2441no—
453C2×D4—2441no—
454C2×D4C2×C22⋊D6111yescharacteristic
455C2×D4C2×C22⋊D6111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—2441no—
461Q16—4881no—
462Q16—2441no—
463SD16—4881no—
464SD16—4881no—
465SD16—4881no—
466SD16—2442no—
467D8—22no—
468D8—4881no—
469M16—4881no—
470M16—4881no—
471C2×C8—21no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8C2×C22⋊D6111yescharacteristic
479C2×C8C2×C22⋊D6111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—611no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—2441no—
493C4⋊C4D4×D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C4⋊C4C2×C22⋊D6111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C42—21no—
504C42—1221no—
505C42—2441no—
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—21no—
509C23—2441no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—81no—
515Q8—82no—
516Q8—1221no—
517Q8—1221no—
518Q8—2441no—
519Q8—2441no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—9761no—
525D4—4881no—
526D4—4882no—
527D4—2441no—
528D4—2441no—
529D4—2441no—
530D4—2441no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—161no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—4882no—
546C2×C4—2441no—
547C2×C4C2×D4×D6111yescharacteristic
548C2×C4C22×C22⋊D6111yescharacteristic
549C2×C4#1451982211yescharacteristic
550C8—21no—
551C8—41no—
552C8—1221no—
553C8—1221no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8#1451980812yes—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—4881no—
566C22—4881no—
567C22—4881no—
568C22D4×C22⋊D6111yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—4881no—
577C4—2441no—
578C4—2441no—
579C4C2×#1451980811yescharacteristic
580C4#1684055811yescharacteristic
581C4#1684056611yescharacteristic
582C4#1684057011yescharacteristic
583C2—81no—
584C2—81no—
585C2—9761no—
586C2#2145742411yescharacteristic
587C2#2145748111yescharacteristic
588C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3384C2
socleC22×C61D42
prime radical#21458837C2
hypercenter#3384D61
hypocenterC61#20307
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3384

Complements

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

NH ≅ G/Ntype
2. #21458151C2semidirect
3. #21458102C2semidirect
4. #21445421C2semidirect
5. #21445364C2semidirect
6. #21445354C2semidirect
7. #21445322C2semidirect
8. #21445291C2semidirect
9. #21445026C2semidirect
10. #21445011C2semidirect
11. #21444989C2semidirect
12. #21444922C2semidirect
13. #21444714C2semidirect
14. #21444704C2semidirect
15. C61×#3384C2semidirect
290. #3384D61semidirect
361. C61#20307semidirect

Maximal subgroups

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

subgroupindex
#214588372
#214581512
#214581022
#214454212
#214453642
#214453542
#214453222
#214452912
#214450262
#214450112
#214449892
#214449222
#214447142
#214447042
C61×#33842
#2030761