Finite Group Databasebeta

← #30610638

Subgroups — #30610638

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462740C211yesmaximal, characteristic, complemented
2#21462623C211yesmaximal, characteristic, complemented
3#21461180C212yesmaximal, complemented
4#21461177C212yesmaximal, complemented
5#21461173C212yesmaximal, complemented
6#21461166C212yesmaximal, complemented
7#21461120C211yesmaximal, characteristic, complemented
8#21461116C211yesmaximal, characteristic, complemented
9#21461112C211yesmaximal, characteristic, complemented
10C2×#16840610C211yesmaximal, characteristic, complemented
11#21459242C211yesmaximal, characteristic
12#16840812—21no—
13#16840811—21no—
14#16840796—21no—
15#16840791—22no—
16#16840790—21no—
17#16840789—22no—
18#16840784C2212yescomplemented
19#16840780C2212yescomplemented
20#16840778C2211yescharacteristic
21#16840778C2211yescharacteristic
22#16840766C2212yescomplemented
23C2×C4⋊#92420C2211yescharacteristic
24C4×D61⋊C8C2212yescomplemented
25C2×C4×#92420C2211yescharacteristic
26#16840612C2211yescharacteristic, complemented
27#16840612C2211yescharacteristic, complemented
28#16840612C2212yescomplemented
29#16840610C2212yes—
30#16840610C2212yes—
31#16840610C2212yes—
32#16840610C2212yes—
33#16840610C2211yescharacteristic, complemented
34#16840610C2211yescharacteristic, complemented
35#16840610C2212yescomplemented
36#16840386—21no—
37#16840386C412yes—
38#16840368—21no—
39#16840368C412yes—
40#16840352—22no—
41#16840343C411yescharacteristic
42#16840331C411yescharacteristic
43#16840331C411yescharacteristic
44#16840313—21no—
45#16840313C2212yes—
46#16840297—21no—
47#16840297C2212yes—
48#16840275—22no—
49#16840230C2211yescharacteristic
50#16840230C2211yescharacteristic
51C2×#14519739C2211yescharacteristic
52C61×#544C411yescharacteristic
53C2×#11758213—22no—
54C2×D61⋊C8—22no—
55C22×#92420—21no—
56C22×#92420—21no—
57#14519844—22no—
58C4⋊#92420—21no—
59C4⋊#92420—22no—
60C4⋊#92420—21no—
61C4⋊#92420C2312yes—
62C4⋊#92420C2311yescharacteristic
63C4⋊#92420C2311yescharacteristic
64#14519834—22no—
65#14519834—22no—
66C22⋊#92420—21no—
67C22⋊#92420—21no—
68#14519832—22no—
69C4×#92420—21no—
70C4×#92420—22no—
71C4×#92420—21no—
72C4×#92420C2311yescharacteristic
73C4×#92420C2311yescharacteristic
74C4×#92420C2312yes—
75C2×#11758226—22no—
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222C2×C411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C22×C4×D61—21no—
80#14519774—21no—
81#14519774C2×C412yes—
82#14519772—22no—
83#14519772—22no—
84#14519766—22no—
85#14519766—22no—
86#14519765—21no—
87#14519765C2×C412yes—
88#14519762—22no—
89#14519762—22no—
90#14519762—22no—
91#14519762—22no—
92#14519757—21no—
93#14519757C2×C412yes—
94#14519753—22no—
95#14519752—21no—
96#14519752—22no—
97#14519752—21no—
98#14519752—21no—
99#14519752—22no—
100#14519752—22no—
101#14519752C2×C412yes—
102#14519752C2×C412yes—
103#14519752C2×C412yes—
104#14519751—22no—
105#14519747—22no—
106#14519747—22no—
107#14519742C2×C411yescharacteristic
108#14519742D411yescharacteristic
109#14519742D411yescharacteristic
110#14519742C2311yescharacteristic
111#14519739—22no—
112#14519739—21no—
113#14519739—21no—
114#14519739—22no—
115#14519739C2×C412yes—
116#14519739C2×C411yescharacteristic
117#14519739D411yescharacteristic
118#14519739D411yescharacteristic
119#14519739C2312yes—
120#14519739C2311yescharacteristic
121#14519737—21no—
122#14519737—21no—
123#14519737D412yes—
124#14519737D412yes—
125#14519735—22no—
126#14519734—21no—
127#14519734C2×C412yes—
128C2×#11758198—21no—
129C2×C4×Dic61C2311yescharacteristic
130C42×D61—21no—
131C42×D61C2312yes—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2×C412yes—
134#125×C61—21no—
135#125×C61C2×C412yes—
136C22⋊Q8×C61—22no—
137#117×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C23×D61—21no—
141C2×Q8×C61—22no—
142C22×C4×C61—21no—
143C22×C4×C61C22×C411yescharacteristic
144C2×C22⋊D61—21no—
145C2×C22⋊D61C22⋊C412yes—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148#11758226—82no—
149#11758226—82no—
150#11758222—24no—
151#11758222—24no—
152C2×D244—24no—
153C2×D244—21no—
154C2×D244—22no—
155C2×D244—22no—
156C2×D244—22no—
157C2×D244—22no—
158C2×D244—22no—
159C2×D244C22⋊C411yescharacteristic
160C2×D244C22×C412yes—
161C2×D244C22×C411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—22no—
164C2×C4×D61—21no—
165C2×C4×D61—22no—
166C2×C4×D61—21no—
167C2×C4×D61—81no—
168C2×C4×D61—81no—
169C2×C4×D61C22×C412yes—
170C2×C4×D61C2×D412yes—
171C2×C4×D61C2×D412yes—
172C2×Dic122C22⋊C411yescharacteristic
173C2×Dic122C22×C411yescharacteristic
174C2×#92420—21no—
175C2×#92420—22no—
176C2×#92420—21no—
177C2×#92420—21no—
178C2×#92420—21no—
179C2×#92420—22no—
180C2×#92420—42no—
181C2×#92420—81no—
182#11758213—82no—
183D61⋊C8—44no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61C22⋊C411yescharacteristic
189C4⋊C4×C61C22⋊C411yescharacteristic
190C4⋊C4×C61C22×C412yes—
191C4⋊C4×C61C22×C411yescharacteristic
192C4⋊C4×C61C22×C411yescharacteristic
193C22⋊C4×C61—21no—
194C22⋊C4×C61C22⋊C412yes—
195C42×C61—21no—
196C42×C61C22×C412yes—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—21no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—22no—
206#11758198—21no—
207#11758198C22⋊C412yes—
208#11758198C22⋊C412yes—
209C4⋊Dic61—22no—
210#11758196—21no—
211#11758196—21no—
212#11758196C22⋊C412yes—
213#11758196C22⋊C412yes—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D412yes—
220C4×Dic61C2×D412yes—
221C4×Dic61C2411yescharacteristic
222C23×C61C2×C22⋊C411yescharacteristic
223C22×D61—22no—
224C22×D61—21no—
225C22×D61—42no—
226C22×D61—81no—
227C22×D61—81no—
228C22×D61C2×C22⋊C412yes—
229Q8×C61—82no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—22no—
233C2×C4×C61—81no—
234C2×C4×C61C2×C22⋊C412yes—
235C2×C4×C61C2×C22⋊C412yes—
236C2×C4×C61C2×C22⋊C411yescharacteristic
237C2×C4×C61#13114yes—
238C2×C4×C61C23×C411yescharacteristic
239C22⋊D61—24no—
240C22⋊D61—42no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—41no—
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C411yescharacteristic
247C2×Dic61C2×C22⋊C412yes—
248C2×Dic61C22×D411yescharacteristic
249C2×Dic61C22×D411yescharacteristic
250D244—24no—
251D244—22no—
252D244—22no—
253D244—42no—
254D244—82no—
255D244—82no—
256D244—82no—
257D244—82no—
258D244—82no—
259C4×D61—24no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—41no—
266C4×D61—42no—
267C4×D61—41no—
268C4×D61—81no—
269C4×D61—82no—
270Dic122—22no—
271Dic122—22no—
272#92420—22no—
273#92420—42no—
274#92420—41no—
275#92420—41no—
276#92420—42no—
277#92420—41no—
278#17483—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—21no—
281C22×C61#40812yes—
282C22×C61C22×C22⋊C411yescharacteristic
283C2×D61—22no—
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—41no—
287C2×D61—42no—
288C2×D61—42no—
289C2×D61—41no—
290C2×D61—41no—
291C2×D61—42no—
292C2×D61—84no—
293C4×C61—22no—
294C4×C61—22no—
295C4×C61—42no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61#40812yes—
299C4×C61C2×#13112yes—
300Dic61—22no—
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61—41no—
305Dic61#57611yescharacteristic
306Dic61#57711yescharacteristic
307#3460—611no—
308#2989—611no—
309C8×#41—611no—
310#1496—612no—
311#1495—612no—
312#1494—612no—
313#1492—612no—
314#1478—611no—
315#1477—611no—
316#1476—611no—
317C2×D4⋊C8—611no—
318C2×C61—22no—
319C2×C61C2×#40811yescharacteristic
320C2×C61#289711yescharacteristic
321C2×C61#290111yescharacteristic
322D61—42no—
323D61—81no—
324D61—82no—
325#544#692311yescharacteristic
326#542—612no—
327#542—1221no—
328#540—612no—
329#540—1221no—
330#538—1222no—
331#537—611no—
332#535—611no—
333#535—611no—
334#532—612no—
335#532—1221no—
336#529—612no—
337#529—1221no—
338#525—1222no—
339C4×#41—611no—
340C4×#41—611no—
341C2×C4×D4—611no—
342#446—1221no—
343C8×Q8—1221no—
344#436—1221no—
345#435—1222no—
346C8×D4—1222no—
347C8×D4—1221no—
348#432—612no—
349#431—611no—
350#431—612no—
351#431—611no—
352#423—612no—
353C2×C4⋊C8—611no—
354C2×C4×C8—611no—
355C2×C4×C8—612no—
356Q8⋊C8—611no—
357Q8⋊C8—611no—
358Q8⋊C8—612no—
359D4⋊C8—612no—
360D4⋊C8—612no—
361D4⋊C8—612no—
362D4⋊C8—612no—
363D4⋊C8—611no—
364D4⋊C8—611no—
365D4⋊C8—612no—
366C61#1748311yescharacteristic, complemented, Sylow
367C2×#41—611no—
368C2×#41—611no—
369C2×#41—1222no—
370C22×D4—611no—
371C23×C4—1221no—
372C2×M16—1222no—
373C22×C8—1221no—
374C22×C8—1221no—
375C22×C8—1222no—
376C4⋊Q8—21no—
377C4⋊Q8C2×#692312yes—
378#127—612no—
379#127—1221no—
380#126—1222no—
381#126—1222no—
382#125—21no—
383#125C2×#692312yes—
384#124—612no—
385#124—1221no—
386#124—1222no—
387#124—1222no—
388#123—1222no—
389#123—1222no—
390#123—1222no—
391#123—1222no—
392C22⋊Q8—22no—
393C22⋊Q8—612no—
394C22⋊Q8—1221no—
395C22⋊Q8—1222no—
396#121—612no—
397#121—612no—
398#121—612no—
399#121—1222no—
400#121—1222no—
401#121—1222no—
402#121—1221no—
403#121—1222no—
404#121—1221no—
405#121—1221no—
406#120—1222no—
407#120—1222no—
408C4×Q8—611no—
409C4×Q8—611no—
410C4×Q8—611no—
411C4×Q8—611no—
412C4×D4—611no—
413C4×D4—611no—
414C4×D4—612no—
415C4×D4—612no—
416C4×D4—612no—
417C4×D4—612no—
418C4×D4—611no—
419C4×D4—611no—
420C4×D4—1221no—
421C4×D4—1221no—
422C4×D4—1222no—
423C4×D4—1221no—
424C4×D4—1221no—
425C4×D4—1222no—
426#117—612no—
427#117—1221no—
428#117—1222no—
429#117C2×#692311yescharacteristic
430#117C2×#692311yescharacteristic
431C2×C4⋊C4C2×#692311yescharacteristic
432C2×C22⋊C4—1221no—
433C2×C42—611no—
434C2×C42—612no—
435C2×C42—1221no—
436C4⋊C8—612no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—1221no—
440C4⋊C8—1222no—
441C4⋊C8—1221no—
442C4⋊C8—1222no—
443C22⋊C8—1221no—
444C22⋊C8—1221no—
445C22⋊C8—1222no—
446C22⋊C8—1222no—
447#97—1222no—
448C4×C8—611no—
449C4×C8—611no—
450C4×C8—612no—
451C4×C8—1221no—
452C4×C8—1222no—
453C4×C8—1221no—
454C24—1221no—
455#41—1224no—
456#41—1224no—
457#41—4882no—
458#41—4882no—
459C2×Q8—22no—
460C2×Q8—611no—
461C2×Q8—611no—
462C2×D4—612no—
463C2×D4—611no—
464C2×D4—612no—
465C2×D4—611no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C2×D4—1221no—
470C2×D4—1222no—
471C2×D4—1222no—
472C2×D4—1221no—
473C2×D4—1224no—
474C22×C4—21no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—1221no—
481C22×C4—1222no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—4881no—
486C22×C4—4881no—
487C22×C4C22×#692311yescharacteristic
488M16—4882no—
489C2×C8—1221no—
490C2×C8—1222no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1222no—
495C2×C8—4881no—
496C2×C8—2444no—
497C2×C8—2442no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—612no—
503C4⋊C4—612no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1222no—
507C4⋊C4C22⋊#692311yescharacteristic
508C4⋊C4C22⋊#692311yescharacteristic
509C4⋊C4C22×#692312yes—
510C4⋊C4C22×#692311yescharacteristic
511C4⋊C4C22×#692311yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—612no—
514C22⋊C4—612no—
515C22⋊C4—1222no—
516C22⋊C4—1222no—
517C22⋊C4—1221no—
518C22⋊C4—1221no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4C22⋊#692312yes—
526C42—21no—
527C42—611no—
528C42—611no—
529C42—612no—
530C42—612no—
531C42—611no—
532C42—611no—
533C42—1221no—
534C42—1221no—
535C42C22×#692312yes—
536C23—612no—
537C23—1222no—
538C23—1221no—
539C23—4881no—
540C23—4881no—
541C23—2442no—
542C23C2×C22⋊#692311yescharacteristic
543Q8—82no—
544Q8—1222no—
545Q8—1222no—
546D4—1224no—
547D4—1222no—
548D4—1224no—
549D4—1222no—
550D4—4882no—
551D4—4882no—
552D4—4882no—
553D4—4882no—
554D4—4882no—
555D4—2442no—
556D4—2442no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—81no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—612no—
565C2×C4—611no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1224no—
571C2×C4—1221no—
572C2×C4—4881no—
573C2×C4—4882no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2442no—
581C2×C4C2×C22⋊#692312yes—
582C2×C4C2×C22⋊#692312yes—
583C2×C4C2×C22⋊#692311yescharacteristic
584C2×C4#1451986514yes—
585C2×C4C23×#692311yescharacteristic
586C8—1222no—
587C8—2441no—
588C8—2442no—
589C8—2441no—
590C8—2442no—
591C8—2441no—
592C22—21no—
593C22—21no—
594C22—1222no—
595C22—1222no—
596C22—1222no—
597C22—4884no—
598C22—2441no—
599C22—2442no—
600C22—2442no—
601C22—2441no—
602C22—2441no—
603C22—2442no—
604C22#1684073712yes—
605C22C22×C22⋊#692311yescharacteristic
606C4—22no—
607C4—22no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—611no—
612C4—611no—
613C4—1222no—
614C4—1221no—
615C4—1221no—
616C4—1221no—
617C4—2441no—
618C4#1684073712yes—
619C4C2×#1451986512yes—
620C2—22no—
621C2—4882no—
622C2—4881no—
623C2—2442no—
624C2C2×#1684073711yescharacteristic
625C2#2146244011yescharacteristic
626C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radical#21459242C2
cosocleC4×Dic61C24
hypercenter#544#6923
hypocenterC61#17483
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
1. #21462740C2semidirect
2. #21462623C2semidirect
3. #21461180C2semidirect
4. #21461177C2semidirect
5. #21461173C2semidirect
6. #21461166C2semidirect
7. #21461120C2semidirect
8. #21461116C2semidirect
9. #21461112C2semidirect
10. C2×#16840610C2semidirect
18. #16840784C22semidirect
19. #16840780C22semidirect
22. #16840766C22semidirect
24. C4×D61⋊C8C22semidirect
26. #16840612C22semidirect
27. #16840612C22semidirect
28. #16840612C22semidirect
33. #16840610C22semidirect
34. #16840610C22semidirect
35. #16840610C22semidirect
366. C61#17483semidirect

Maximal subgroups

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

subgroupindex
#214627402
#214626232
#214611802
#214611772
#214611732
#214611662
#214611202
#214611162
#214611122
C2×#168406102
#214592422
#1748361