Finite Group Databasebeta

← #29677161

Subgroups — #29677161

Order 15616.

622 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458850C211yesmaximal, characteristic, complemented
2#21458738C211yesmaximal, characteristic, complemented
3#21457461C211yesmaximal, characteristic
4#21445436C211yesmaximal, characteristic, complemented
5#21445334C211yesmaximal, characteristic, complemented
6#21445332C211yesmaximal, characteristic, complemented
7#21445311C211yesmaximal, characteristic, complemented
8#21445306C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445067C211yesmaximal, characteristic, complemented
11#21445060C211yesmaximal, characteristic, complemented
12#21445054C211yesmaximal, characteristic
13#21444710C211yesmaximal, characteristic, complemented
14#21444707C211yesmaximal, characteristic, complemented
15C61×#3353C211yesmaximal, characteristic
16C2×#14519807—21no—
17#16840491C2211yescharacteristic
18D4×Dic122C2211yescharacteristic
19#16840169—21no—
20#16840167C2211yescharacteristic
21#16840165C2211yescharacteristic
22#16840165C2211yescharacteristic
23#16840157—21no—
24#16840141C2211yescharacteristic
25#16840141C2211yescharacteristic
26#16840060—21no—
27#16840055—21no—
28#16840047C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840018—21no—
31#16839981—21no—
32#16839972—21no—
33#16839969C2211yescharacteristic
34#16839969C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839967C2211yescharacteristic
37#16839924—21no—
38#16839917—21no—
39#16839893C2211yescharacteristic
40#16839892C2211yescharacteristic
41#16839867—21no—
42#16839863—21no—
43C4×#11758200C2211yescharacteristic
44#16839840C2211yescharacteristic
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839508C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#484—21no—
60C61×#482—21no—
61C61×#475C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C61×#468—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#428—21no—
67C22×Dic122—21no—
68#14519807—44no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758202—21no—
73C2×#11758202—21no—
74C2×#11758202—21no—
75C2×#11758200—21no—
76C2×#11758200—21no—
77C2×#11758200D411yescharacteristic
78C2×#11758194—21no—
79#14519777—21no—
80#14519777C2311yescharacteristic
81#14519777C2311yescharacteristic
82#14519776—21no—
83#14519768—21no—
84#14519768—41no—
85#14519756—21no—
86#14519754—41no—
87Q8×Dic61—21no—
88C4×Dic122—21no—
89C4×Dic122C2311yescharacteristic
90D4×Dic61—21no—
91#14519711—21no—
92#14519711—21no—
93#14519710—21no—
94#14519710—41no—
95#14519710—41no—
96#14519708—21no—
97#14519708D411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102#14519706—21no—
103#14519701—21no—
104#14519701—21no—
105#14519701—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110#14519698D411yescharacteristic
111C22⋊#92418—21no—
112#14519688—21no—
113#14519687—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#126×C61—41no—
122#124×C61—21no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61—21no—
135#107×C61—21no—
136#106×C61—21no—
137#106×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61—21no—
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×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—41no—
156C22×Dic61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—42no—
160C2×Dic122—41no—
161C2×Dic122—81no—
162C2×Dic122C2×D411yescharacteristic
163SD16×C61—22no—
164M16×C61—42no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C42×C61—21no—
184C42×C61—41no—
185C42×C61C2411yescharacteristic
186C22⋊Dic61—41no—
187#11758202—42no—
188#11758202—42no—
189#11758202—42no—
190#11758202—81no—
191#11758202—81no—
192#11758202—81no—
193#11758200—22no—
194#11758200—42no—
195#11758200—81no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—41no—
201C4⋊Dic61—41no—
202C4⋊Dic61C2×D411yescharacteristic
203#11758196—21no—
204#11758196—41no—
205#11758196—41no—
206C4×Dic61—21no—
207C4×Dic61—41no—
208#11758194—42no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418C2×D411yescharacteristic
214C2×#92418C2×D411yescharacteristic
215C23×C61—21no—
216C23×C61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—82no—
228C2×C4×C61—21no—
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—82no—
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61H(5,𝔽2)11yescharacteristic
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—82no—
247Dic122—21no—
248Dic122—21no—
249Dic122—41no—
250Dic122—41no—
251Dic122—41no—
252Dic122—41no—
253Dic122—82no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61#13712yescomplemented
257#92418—22no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418AGL(1,ℤ/8)12yes—
263#20311—611nomaximal, Sylow
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61D4211yescharacteristic
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C61C2×#13711yescharacteristic
280C4×C61#57611yescharacteristic
281C4×C61#57811yescharacteristic
282Dic61—41no—
283Dic61—41no—
284Dic61—81no—
285Dic61—81no—
286#3398—611no—
287#3386—611no—
288#3353D6111yescharacteristic
289#3276—611no—
290#1713—611no—
291#1694—611no—
292#1693—611no—
293#1690—611no—
294#1689—611no—
295#1650—611no—
296#1649—611no—
297#1648—611no—
298#1647—611no—
299#1590—611no—
300#1590—611no—
301C2×C61—81no—
302C2×C61—81no—
303C2×C61#327411yescharacteristic
304C2×C61#327611yescharacteristic
305C2×C61#329311yescharacteristic
306C2×#137—1221no—
307#557—611no—
308#556C2×D6111yescharacteristic
309D4×Q8—611no—
310#547C2×D6111yescharacteristic
311#501—1221no—
312#500—611no—
313#500—611no—
314#500—611no—
315#500C2×D6111yescharacteristic
316#497—1221no—
317#494—611no—
318#494—611no—
319#484—21no—
320#482—21no—
321#478—1221no—
322#477—1221no—
323#475—611no—
324#475C2×D6111yescharacteristic
325#474—611no—
326#474C2×D6111yescharacteristic
327#470—1221no—
328#468—21no—
329#464—1221no—
330#462—611no—
331#462—611no—
332#462—1221no—
333#461—611no—
334#461—611no—
335#452—1221no—
336#451—1221no—
337#446—611no—
338#446—611no—
339#441—1221no—
340#440—1221no—
341C4×SD16—611no—
342C4×SD16C2×D6111yescharacteristic
343#436—611no—
344#436C2×D6111yescharacteristic
345#428—21no—
346#334—611no—
347#334—611no—
348#332—611no—
349#332—611no—
350#332—611no—
351#332—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356C82—611no—
357C61#2031111yescharacteristic, complemented, Sylow
358C2×#41—21no—
359C22×Q8—1221no—
360#137—2444no—
361C2×Q16—1221no—
362C2×Q16—1221no—
363C2×Q16—1221no—
364C2×Q16—1221no—
365C2×Q16—1221no—
366C2×Q16—1221no—
367C2×SD16—611no—
368C2×SD16—1221no—
369C2×SD16—1221no—
370C2×SD16C22⋊D6111yescharacteristic
371C2×M16—21no—
372C2×M16—1221no—
373C4⋊Q8—611no—
374C4⋊Q8—611no—
375C4⋊Q8—1221no—
376C4⋊Q8—1221no—
377C4⋊Q8C22×D6111yescharacteristic
378C4⋊Q8C22×D6111yescharacteristic
379#126—41no—
380#125—1221no—
381#125—2441no—
382#124—21no—
383#123—41no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—1221no—
387C22⋊Q8—2441no—
388#121—21no—
389C4×Q8—21no—
390C4×Q8—611no—
391C4×Q8—1221no—
392C4×Q8—1221no—
393C4×Q8C22×D6111yescharacteristic
394C4×D4—1221no—
395C4×D4C22×D6111yescharacteristic
396C4×D4C22×D6111yescharacteristic
397#117—21no—
398C2×C4⋊C4—21no—
399#107—21no—
400#107—21no—
401#107—21no—
402#107—1221no—
403#107—1221no—
404#107—1221no—
405#107—2441no—
406#107—2441no—
407#106—21no—
408#106—611no—
409#106—1221no—
410#106C22⋊D6111yescharacteristic
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417#103—21no—
418#103—611no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103C22⋊D6111yescharacteristic
425#102—21no—
426#102—611no—
427#102—1221no—
428#102C22⋊D6111yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—1221no—
431#97—1221no—
432#97—1221no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8C22×D6111yescharacteristic
436#41—42no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—611no—
441C2×Q8—1221no—
442C2×Q8—1221no—
443C2×Q8—4881no—
444C2×Q8—2441no—
445C2×Q8—2442no—
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×D4—41no—
448C2×D4D4×D6111yescharacteristic
449C2×D4C2×C22⋊D6111yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4—2441no—
454Q16—4881no—
455Q16—4881no—
456Q16—4881no—
457Q16—2442no—
458Q16—2442no—
459Q16—2442no—
460SD16—22no—
461SD16—1222no—
462SD16—4881no—
463SD16—2442no—
464M16—42no—
465M16—2442no—
466C2×C8—21no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—611no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—2441no—
489C4⋊C4—2441no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4D4×D6111yescharacteristic
493C4⋊C4C2×C22⋊D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—2441no—
501C42—21no—
502C42—41no—
503C42—1221no—
504C42—2441no—
505C42C23×D6111yescharacteristic
506C23—21no—
507C23—21no—
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—1221no—
515Q8—1221no—
516Q8—4882no—
517Q8—2441no—
518Q8—2441no—
519Q8—2441no—
520Q8—2441no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—82no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—4882no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4C2×D4×D6111yescharacteristic
543C2×C4C22×C22⋊D6111yescharacteristic
544C2×C4#1451982211yescharacteristic
545C8—21no—
546C8—41no—
547C8—612no—
548C8—1222no—
549C8—1221no—
550C8—2441no—
551C8—2441no—
552C8—2441no—
553C8#1451980712yescomplemented
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D4×C22⋊D6111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—4881no—
569C4—4881no—
570C4—2441no—
571C4—2441no—
572C4AGL(1,ℤ/8)×D6111yescharacteristic
573C4C2×#1451980711yescharacteristic
574C4#1684056611yescharacteristic
575C4#1684057711yescharacteristic
576C2—81no—
577C2—81no—
578C2#2145743311yescharacteristic
579C2#2145746111yescharacteristic
580C2#2145762111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3353C2
socleC22×C61D42
prime radicalC61×#547C22
hypercenter#3353D61
hypocenterC61#20311
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3353

Complements

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

NH ≅ G/Ntype
1. #21458850C2semidirect
2. #21458738C2semidirect
4. #21445436C2semidirect
5. #21445334C2semidirect
6. #21445332C2semidirect
7. #21445311C2semidirect
8. #21445306C2semidirect
9. #21445075C2semidirect
10. #21445067C2semidirect
11. #21445060C2semidirect
13. #21444710C2semidirect
14. #21444707C2semidirect
256. C8×C61#137semidirect
357. C61#20311semidirect
553. C8#14519807semidirect

Maximal subgroups

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

subgroupindex
#214588502
#214587382
#214574612
#214454362
#214453342
#214453322
#214453112
#214453062
#214450752
#214450672
#214450602
#214450542
#214447102
#214447072
C61×#33532
#2031161