Finite Group Databasebeta

← #29671066

Subgroups — #29671066

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458850C211yesmaximal, characteristic, complemented
2#21458800C211yesmaximal, characteristic
3#21458708C211yesmaximal, characteristic, complemented
4#21445492C211yesmaximal, characteristic, complemented
5#21445289C211yesmaximal, characteristic, complemented
6#21445260C211yesmaximal, characteristic, complemented
7#21445208C211yesmaximal, characteristic, complemented
8#21445187C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445060C211yesmaximal, characteristic, complemented
11#21445019C211yesmaximal, characteristic
12#21444914C211yesmaximal, characteristic, complemented
13#21444670C211yesmaximal, characteristic, complemented
14#21444631C211yesmaximal, characteristic, complemented
15C61×#3304C211yesmaximal, characteristic
16#16840491C2211yescharacteristic
17#16840491C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840163—21no—
21#16840157—21no—
22#16840141C2211yescharacteristic
23#16840134—21no—
24#16840134C2211yescharacteristic
25#16840108C2211yescharacteristic
26#16840071—21no—
27#16840071—21no—
28#16840047C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16839981—21no—
31#16839972—21no—
32#16839969C2211yescharacteristic
33#16839967—21no—
34#16839967C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839959—21no—
37#16839959C2211yescharacteristic
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41#16839867—21no—
42Q16×Dic61—21no—
43C4×#11758200—21no—
44C4×#11758200C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839508C2211yescharacteristic
48#16839507C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#550C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#482—21no—
60C61×#475C2211yescharacteristic
61C61×#465—21no—
62C61×#460C2211yescharacteristic
63C61×#452—21no—
64C4×Q16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C61×#416—21no—
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758200D411yescharacteristic
76#14519777—21no—
77#14519777—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519768—21no—
81#14519768—21no—
82#14519768—41no—
83#14519768—41no—
84Q8×Dic61—21no—
85Q8×Dic61—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122C2311yescharacteristic
89#14519711—21no—
90#14519711—21no—
91#14519710—41no—
92#14519708—21no—
93#14519708—21no—
94#14519708D411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519706—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519700—21no—
105#14519700—21no—
106#14519700D411yescharacteristic
107#14519698—21no—
108#14519698—41no—
109#14519698D411yescharacteristic
110#14519688—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×Q16×C61D411yescharacteristic
117C2×SD16×C61—21no—
118C22×C8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61—21no—
121#127×C61C2311yescharacteristic
122#126×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125#121×C61—21no—
126#121×C61—41no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61D411yescharacteristic
138#103×C61D411yescharacteristic
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122C2×D411yescharacteristic
160Q16×C61—22no—
161SD16×C61—81no—
162C2×C8×C61—21no—
163C2×C8×C61—81no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C22⋊C4×C61—21no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—41no—
181C42×C61C2411yescharacteristic
182#11758202—42no—
183#11758202—81no—
184#11758202—81no—
185#11758200—22no—
186#11758200—42no—
187#11758200—81no—
188#11758200—81no—
189#11758200—81no—
190#11758200—81no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—41no—
196C4⋊Dic61—41no—
197C4⋊Dic61—41no—
198C4⋊Dic61—41no—
199C4⋊Dic61C2×D411yescharacteristic
200#11758196—21no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—21no—
204C4×Dic61—41no—
205C4×Dic61—41no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C23×C61—21no—
213C23×C61—41no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61#13712yes—
220D4×C61—21no—
221D4×C61—21no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—82no—
227D4×C61—81no—
228D4×C61—161no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
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—82no—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245Dic122—21no—
246Dic122—21no—
247Dic122—41no—
248Dic122—41no—
249Dic122—41no—
250Dic122—41no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—41no—
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#92418—41no—
259#92418#13512yes—
260#19869—611nomaximal, Sylow
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—81no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61D4211yescharacteristic
268C4×C61—22no—
269C4×C61—21no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—81no—
275C4×C61C2×#13511yescharacteristic
276C4×C61C2×#13711yescharacteristic
277C4×C61#57611yescharacteristic
278C4×C61#57711yescharacteristic
279Dic61—41no—
280Dic61—41no—
281Dic61—81no—
282Dic61—81no—
283#3398—611no—
284#3392—611no—
285#3383—611no—
286#3304D6111yescharacteristic
287#1722—611no—
288#1686—611no—
289#1682—611no—
290#1673—611no—
291#1670—611no—
292#1650—611no—
293#1648—611no—
294#1642—611no—
295#1626—611no—
296#1584—611no—
297SD16⋊C8—611no—
298C2×C61—81no—
299C2×C61—161no—
300C2×C61#326611yescharacteristic
301C2×C61#328711yescharacteristic
302C2×C61#328911yescharacteristic
303#557—611no—
304#557—611no—
305#556C2×D6111yescharacteristic
306#550C2×D6111yescharacteristic
307#500—611no—
308#500—611no—
309#499—1221no—
310#497—1221no—
311#494—611no—
312#492—611no—
313#492—1221no—
314#486—611no—
315#486C2×D6111yescharacteristic
316#482—21no—
317#479—1221no—
318#479—1221no—
319#475—611no—
320#475—611no—
321#475C2×D6111yescharacteristic
322#465—21no—
323#464—1221no—
324#462—611no—
325#462—1221no—
326#461—611no—
327#461—611no—
328#461—1221no—
329#460—611no—
330#460—1221no—
331#460C2×D6111yescharacteristic
332#452—21no—
333#446—611no—
334C8×Q8—611no—
335C8×Q8—611no—
336#441—1221no—
337C4×Q16—1221no—
338C4×Q16C2×D6111yescharacteristic
339C4×SD16—611no—
340C4×SD16—1221no—
341C8×D4C2×D6111yescharacteristic
342#416—21no—
343#335—611no—
344#335—611no—
345#332—611no—
346#332—611no—
347#332—611no—
348#331—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352D4⋊C8—611no—
353#322—611no—
354C61#1986911yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C2×Q16—1221no—
357C2×Q16—1221no—
358C2×Q16—1221no—
359C2×Q16C22⋊D6111yescharacteristic
360C2×SD16—21no—
361C2×SD16—611no—
362C2×SD16—1221no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×SD16—1221no—
367C22×C8—21no—
368C4⋊Q8—611no—
369C4⋊Q8—611no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8C22×D6111yescharacteristic
373#127—21no—
374#127C22×D6111yescharacteristic
375#126—41no—
376#125—1221no—
377#125—1221no—
378#125—2441no—
379#125—2441no—
380#124—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—41no—
384C4×Q8—21no—
385C4×Q8—611no—
386C4×Q8—1221no—
387C4×Q8—1221no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8C22×D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4C22×D6111yescharacteristic
394#117—21no—
395#107—1221no—
396#107—1221no—
397#107—2441no—
398#107C22⋊D6111yescharacteristic
399#106—21no—
400#106—611no—
401#106—1221no—
402#106—1221no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—1221no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410#103—21no—
411#103—611no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103C22⋊D6111yescharacteristic
418#103C22⋊D6111yescharacteristic
419#102—21no—
420#102—21no—
421#102—21no—
422#102—611no—
423#102—1221no—
424#102—2441no—
425C22⋊C8—21no—
426#97—1221no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8—1221no—
430C4×C8—1221no—
431C4×C8C22×D6111yescharacteristic
432#41—42no—
433#41—81no—
434C2×Q8—21no—
435C2×Q8—611no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8C2×C22⋊D6111yescharacteristic
439C2×Q8C2×C22⋊D6111yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4D4×D6111yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448Q16—22no—
449Q16—4881no—
450Q16—4881no—
451Q16—2442no—
452SD16—81no—
453SD16—1222no—
454SD16—4881no—
455SD16—4881no—
456SD16—4881no—
457SD16—4881no—
458SD16—2442no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8—611no—
462C2×C8—611no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8C2×C22⋊D6111yescharacteristic
468C2×C8C2×C22⋊D6111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—611no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—2441no—
481C4⋊C4—2441no—
482C4⋊C4—2441no—
483C4⋊C4—2441no—
484C4⋊C4—2441no—
485C4⋊C4—2441no—
486C4⋊C4D4×D6111yescharacteristic
487C4⋊C4C2×C22⋊D6111yescharacteristic
488C4⋊C4C2×C22⋊D6111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C42—21no—
494C42—21no—
495C42—41no—
496C42—1221no—
497C42—2441no—
498C42—2441no—
499C42C23×D6111yescharacteristic
500C23—21no—
501C23—41no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—1221no—
508Q8—1221no—
509Q8—2441no—
510Q8—2441no—
511Q8—2441no—
512Q8—2441no—
513Q8#1451980712yes—
514D4—21no—
515D4—21no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—82no—
521D4—81no—
522D4—161no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4C2×D4×D6111yescharacteristic
537C2×C4C22×C22⋊D6111yescharacteristic
538C2×C4#1451982211yescharacteristic
539C8—21no—
540C8—21no—
541C8—41no—
542C8—612no—
543C8—1221no—
544C8—2441no—
545C8—2441no—
546C8—2441no—
547C8—2441no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22D4×C22⋊D6111yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—4881no—
563C4—4881no—
564C4—2441no—
565C4—2441no—
566C4#135×D6111yescharacteristic
567C4C2×#1451980711yescharacteristic
568C4#1684056411yescharacteristic
569C4#1684057311yescharacteristic
570C2—81no—
571C2—161no—
572C2#2145732511yescharacteristic
573C2#2145757311yescharacteristic
574C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3304C2
socleC22×C61D42
prime radicalC61×#550C22
hypercenter#3304D61
hypocenterC61#19869
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3304

Complements

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

NH ≅ G/Ntype
1. #21458850C2semidirect
3. #21458708C2semidirect
4. #21445492C2semidirect
5. #21445289C2semidirect
6. #21445260C2semidirect
7. #21445208C2semidirect
8. #21445187C2semidirect
9. #21445075C2semidirect
10. #21445060C2semidirect
12. #21444914C2semidirect
13. #21444670C2semidirect
14. #21444631C2semidirect
354. C61#19869semidirect

Maximal subgroups

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

subgroupindex
#214588502
#214588002
#214587082
#214454922
#214452892
#214452602
#214452082
#214451872
#214450752
#214450602
#214450192
#214449142
#214446702
#214446312
C61×#33042
#1986961