Finite Group Databasebeta

← #29671448

Subgroups — #29671448

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458747C211yesmaximal, characteristic, complemented
2#21458459C211yesmaximal, characteristic, complemented
3#21457485C211yesmaximal, characteristic
4#21445419C211yesmaximal, characteristic, complemented
5#21445320C211yesmaximal, characteristic, complemented
6#21445289C211yesmaximal, characteristic, complemented
7#21445249C211yesmaximal, characteristic, complemented
8#21445232C211yesmaximal, characteristic, complemented
9#21445040C211yesmaximal, characteristic, complemented
10#21445019C211yesmaximal, characteristic
11#21444983C211yesmaximal, characteristic, complemented
12#21444913C211yesmaximal, characteristic, complemented
13#21444710C211yesmaximal, characteristic, complemented
14C8×#11758202C211yesmaximal, characteristic, complemented
15C61×#3362C211yesmaximal, characteristic
16C2×#14519807—21no—
17#16840490C2211yescharacteristic
18D4×Dic122C2211yescharacteristic
19#16840168—21no—
20#16840158C2211yescharacteristic
21#16840134C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840111—21no—
25#16840108C2211yescharacteristic
26#16840069—21no—
27#16840054C2211yescharacteristic
28#16840047C2211yescharacteristic
29#16840047C2211yescharacteristic
30#16840046—21no—
31#16840044—21no—
32#16840006—21no—
33#16839972C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839965—21no—
36#16839959C2211yescharacteristic
37#16839924—21no—
38#16839900—21no—
39#16839893C2211yescharacteristic
40C8×Dic122C2211yescharacteristic
41#16839867—21no—
42C4×#11758202C2211yescharacteristic
43#16839853—21no—
44#16839840C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839509C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56Q82×C61C2211yescharacteristic
57C61×#550C2211yescharacteristic
58C61×#486—21no—
59C61×#486C2211yescharacteristic
60C61×#476—21no—
61C61×#476C2211yescharacteristic
62C61×#460—21no—
63C61×#460C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×SD16×C61—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×Dic122—21no—
68#14519807—44no—
69C2×#11758202—21no—
70C2×#11758202D411yescharacteristic
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—21no—
75C2×#11758194—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519776—21no—
79#14519775—21no—
80#14519769—21no—
81#14519767—41no—
82#14519756—21no—
83#14519754—41no—
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87D4×Dic61—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—41no—
104#14519701D411yescharacteristic
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110#14519698—41no—
111C22⋊#92418—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C8×Dic61—21no—
116C2×#41×C61—21no—
117C2×SD16×C61—21no—
118C2×SD16×C61D411yescharacteristic
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61—41no—
122C4⋊Q8×C61C2311yescharacteristic
123#127×C61—21no—
124#127×C61C2311yescharacteristic
125#121×C61—21no—
126#121×C61—41no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×D4×C61—21no—
132C4×D4×C61C2311yescharacteristic
133#106×C61—21no—
134#106×C61D411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C4×C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61C2×D411yescharacteristic
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×Dic61—41no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—42no—
163C2×Dic122—41no—
164C2×Dic122—81no—
165C2×Dic122C2×D411yescharacteristic
166SD16×C61—41no—
167SD16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61C2×D411yescharacteristic
170C2×C8×C61C2×D411yescharacteristic
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×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—41no—
185C42×C61C2411yescharacteristic
186C22⋊Dic61—41no—
187#11758202—42no—
188#11758202SD1614yescomplemented
189#11758200—42no—
190#11758200—42no—
191#11758200—42no—
192#11758200—81no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—41no—
200#11758196—41no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—21no—
204C4×Dic61—41no—
205#11758194—42no—
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—81no—
218Q8×C61—161no—
219Q8×C61C2×SD1612yes—
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—
245C2×Dic61—82no—
246Dic122—21no—
247Dic122—41no—
248Dic122—41no—
249Dic122—41no—
250Dic122—41no—
251Dic122—82no—
252Dic122C2×SD1612yes—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256#92418—21no—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418C2×SD1612yes—
262#19896—611nomaximal, Sylow
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—81no—
267C22×C61—81no—
268C22×C61—81no—
269C22×C61D4211yescharacteristic
270C4×C61—22no—
271C4×C61—21no—
272C4×C61—41no—
273C4×C61—41no—
274C4×C61—41no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61C22×SD1611yescharacteristic
278C4×C61#57511yescharacteristic
279C4×C61#57711yescharacteristic
280C4×C61#57811yescharacteristic
281Dic61—22no—
282Dic61—41no—
283Dic61—81no—
284Dic61—81no—
285#3387—611no—
286#3362D6111yescharacteristic
287#3359—611no—
288#3278—611no—
289#1708—611no—
290#1691—611no—
291#1686—611no—
292#1680—611no—
293#1678—611no—
294#1645—611no—
295#1642—611no—
296#1637—611no—
297#1626—611no—
298#1590—611no—
299C8×Q16—611no—
300C2×C61—81no—
301C2×C61—161no—
302C2×C61#327711yescharacteristic
303C2×C61D4×SD1611yescharacteristic
304C2×C61#329011yescharacteristic
305C2×#137—1221no—
306Q82C2×D6111yescharacteristic
307#557—611no—
308#550C2×D6111yescharacteristic
309D4×Q8—611no—
310#501—1221no—
311#498—611no—
312#492—611no—
313#487—611no—
314#487—611no—
315#487—1221no—
316#486—21no—
317#486—611no—
318#486C2×D6111yescharacteristic
319#479—1221no—
320#477—611no—
321#476—21no—
322#476C2×D6111yescharacteristic
323#475—611no—
324#475—611no—
325#475—1221no—
326#475—1221no—
327#468—1221no—
328#462—611no—
329#461—611no—
330#461—1221no—
331#460—21no—
332#460—611no—
333#460C2×D6111yescharacteristic
334#452—1221no—
335#448—1221no—
336#446—611no—
337C8×Q8—611no—
338C8×Q8C2×D6111yescharacteristic
339#441—1221no—
340C4×Q16—611no—
341C4×SD16—21no—
342C4×SD16—1221no—
343C4×SD16C2×D6111yescharacteristic
344#436—611no—
345#335—611no—
346#334—611no—
347#333—611no—
348#332—611no—
349#332—611no—
350#331—611no—
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353Q8⋊C8—611no—
354D4⋊C8—611no—
355C82—611no—
356C61#1989611yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C22×Q8—1221no—
359#137—2444no—
360C2×Q16—611no—
361C2×Q16—1221no—
362C2×SD16—21no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×SD16—1221no—
367C2×SD16C22⋊D6111yescharacteristic
368C2×M16—1221no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—41no—
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376C4⋊Q8C22×D6111yescharacteristic
377#127—21no—
378#127C22×D6111yescharacteristic
379#125—1221no—
380#125—2441no—
381C22⋊Q8—1221no—
382C22⋊Q8—2441no—
383#121—21no—
384#121—41no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—611no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8C22×D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—1221no—
394C4×D4C22×D6111yescharacteristic
395#107—611no—
396#107—1221no—
397#106—21no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402#106C22⋊D6111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—1221no—
408C4⋊C8—1221no—
409C4⋊C8C22×D6111yescharacteristic
410#103—611no—
411#103—611no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—2441no—
420#103C22⋊D6111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—1221no—
426#102—2441no—
427#102C22⋊D6111yescharacteristic
428C22⋊C8—1221no—
429#97—1221no—
430C4×C8—21no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—1221no—
434C4×C8C22×D6111yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—41no—
439C2×Q8—611no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8—4881no—
443C2×Q8—2441no—
444C2×Q8—2442no—
445C2×Q8D4×D6111yescharacteristic
446C2×Q8C2×C22⋊D6111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4C2×C22⋊D6111yescharacteristic
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—2441no—
456Q16—614no—
457Q16—2442no—
458SD16—41no—
459SD16—42no—
460SD16—4881no—
461SD16—2442no—
462SD16—2442no—
463SD16—2442no—
464M16—2442no—
465C2×C8—21no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—611no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—2441no—
487C4⋊C4—2441no—
488C4⋊C4—2441no—
489C4⋊C4—2441no—
490C4⋊C4D4×D6111yescharacteristic
491C4⋊C4C2×C22⋊D6111yescharacteristic
492C4⋊C4C2×C22⋊D6111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—41no—
495C22⋊C4—2441no—
496C42—21no—
497C42—21no—
498C42—41no—
499C42—1221no—
500C42—2441no—
501C42C23×D6111yescharacteristic
502C23—21no—
503C23—41no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—81no—
508Q8—161no—
509Q8—612no—
510Q8—1221no—
511Q8—4882no—
512Q8—2441no—
513Q8—2441no—
514Q8—2441no—
515Q8—2441no—
516Q8SD16×D6112yes—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—82no—
524D4—81no—
525D4—161no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—4882no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4C22×C22⋊D6111yescharacteristic
542C2×C4#1451982211yescharacteristic
543C8—21no—
544C8—21no—
545C8—41no—
546C8—612no—
547C8—1221no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22D4×C22⋊D6111yescharacteristic
559C4—22no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—81no—
566C4—1222no—
567C4—4881no—
568C4—4881no—
569C4—2441no—
570C4C2×SD16×D6111yescharacteristic
571C4#1684056011yescharacteristic
572C4#1684056811yescharacteristic
573C4#1684057711yescharacteristic
574C2—81no—
575C2—161no—
576C2#2145747211yescharacteristic
577C2SD16×C22⋊D6111yescharacteristic
578C2#2145760111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3362C2
socleC22×C61D42
prime radicalC61×#550C22
hypercenter#3362D61
hypocenterC61#19896
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3362

Complements

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

NH ≅ G/Ntype
1. #21458747C2semidirect
2. #21458459C2semidirect
4. #21445419C2semidirect
5. #21445320C2semidirect
6. #21445289C2semidirect
7. #21445249C2semidirect
8. #21445232C2semidirect
9. #21445040C2semidirect
11. #21444983C2semidirect
12. #21444913C2semidirect
13. #21444710C2semidirect
14. C8×#11758202C2semidirect
188. #11758202SD16semidirect
356. C61#19896semidirect

Maximal subgroups

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

subgroupindex
#214587472
#214584592
#214574852
#214454192
#214453202
#214452892
#214452492
#214452322
#214450402
#214450192
#214449832
#214449132
#214447102
C8×#117582022
C61×#33622
#1989661