Finite Group Databasebeta

← #29669840

Subgroups — #29669840

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458535C211yesmaximal, characteristic, complemented
2#21457736C211yesmaximal, characteristic, complemented
3D4×#11758200C211yesmaximal, characteristic, complemented
4#21445469C211yesmaximal, characteristic, complemented
5#21445384C211yesmaximal, characteristic, complemented
6#21445242C211yesmaximal, characteristic, complemented
7#21445240C211yesmaximal, characteristic, complemented
8#21445158C211yesmaximal, characteristic, complemented
9#21445067C211yesmaximal, characteristic, complemented
10#21445054C211yesmaximal, characteristic, complemented
11#21444998C211yesmaximal, characteristic, complemented
12#21444927C211yesmaximal, characteristic, complemented
13#21444655C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3294C211yesmaximal, characteristic
16C22×#11758200—21no—
17#16840482C2211yescharacteristic, complemented
18D4×Dic122C2211yescharacteristic
19#16840165C2211yescharacteristic, complemented
20#16840134C2211yescharacteristic
21#16840120—21no—
22#16840113C2211yescharacteristic, complemented
23#16840112C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic
25#16840100—21no—
26#16840056—21no—
27#16840042C2211yescharacteristic
28#16840042C2211yescharacteristic, complemented
29#16840001—21no—
30#16839989—21no—
31#16839975—21no—
32#16839969C2211yescharacteristic, complemented
33#16839967C2211yescharacteristic
34#16839967C2211yescharacteristic
35#16839959C2211yescharacteristic
36#16839924—21no—
37#16839913—21no—
38#16839900—21no—
39#16839892C2211yescharacteristic, complemented
40#16839859—21no—
41C4×#11758200C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43D4×#92418C2211yescharacteristic, complemented
44#16839758—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839509C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839507C2211yescharacteristic, complemented
50#16839506C2211yescharacteristic
51#16839492C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic, complemented
55#16839483C2211yescharacteristic, complemented
56C61×#547C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#480—21no—
60C61×#474C2211yescharacteristic
61C61×#466—21no—
62C61×#459C2211yescharacteristic
63C61×#447—21no—
64C4×D8×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#102×C61—21no—
67C22×Dic122—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758200—21no—
71C2×#11758200—21no—
72C2×#11758200—21no—
73C2×#11758200—21no—
74C2×#11758200—44no—
75C2×#11758200D411yescharacteristic
76C22×#92418—21no—
77C22×#92418—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519776—21no—
81#14519770—41no—
82#14519764—21no—
83#14519756—21no—
84#14519756—21no—
85#14519754—41no—
86C4×Dic122C2311yescharacteristic
87#14519742—21no—
88D4×Dic61—21no—
89#14519736—21no—
90#14519710—21no—
91#14519710—21no—
92#14519710—41no—
93#14519708D411yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519702—21no—
99#14519702—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700D411yescharacteristic
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—41no—
110#14519698D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519687—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C22×D4×C61—21no—
118C22×D4×C61—21no—
119C2×D8×C61—21no—
120C2×D8×C61D411yescharacteristic
121C22×C8×C61—21no—
122C4⋊Q8×C61C2311yescharacteristic
123#127×C61C2311yescharacteristic
124#123×C61—41no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129#120×C61—41no—
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—21no—
134#107×C61—21no—
135#107×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146#41×C61—42no—
147#41×C61—81no—
148C2×Q8×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61—42no—
155C2×D4×C61—42no—
156C2×D4×C61—41no—
157C2×D4×C61—81no—
158C2×D4×C61—81no—
159C2×D4×C61C2×D411yescharacteristic
160C2×D4×C61C2×D411yescharacteristic
161C2×D4×C61C2×D411yescharacteristic
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—41no—
166C22×Dic61—41no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—42no—
170C2×Dic122—41no—
171C2×Dic122—81no—
172C2×Dic122C2×D411yescharacteristic
173D8×C61—22no—
174D8×C61—81no—
175C2×C8×C61—21no—
176C2×C8×C61—81no—
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—41no—
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C42×C61C2411yescharacteristic
191C22⋊Dic61—41no—
192C22⋊Dic61—41no—
193C22⋊Dic61—41no—
194#11758202—81no—
195#11758200—22no—
196#11758200—42no—
197#11758200—42no—
198#11758200—42no—
199#11758200—42no—
200#11758200—81no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61C2×D411yescharacteristic
206#11758196—21no—
207#11758196—41no—
208#11758196—41no—
209C4×Dic61—21no—
210C4×Dic61—41no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—42no—
216C2×#92418—81no—
217C2×#92418C2×D411yescharacteristic
218C2×#92418C2×D411yescharacteristic
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—41no—
223C23×C61—82no—
224C23×C61—82no—
225C23×C61—161no—
226Q8×C61—41no—
227Q8×C61—41no—
228D4×C61—21no—
229D4×C61—21no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—41no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—81no—
237D4×C61—82no—
238D4×C61—82no—
239D4×C61—82no—
240D4×C61#13512yes—
241D4×C61AGL(1,ℤ/8)12yes—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—82no—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C22×D411yescharacteristic
255C2×C4×C61H(5,𝔽2)11yescharacteristic
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—82no—
261Dic122—21no—
262Dic122—21no—
263Dic122—41no—
264Dic122—41no—
265Dic122—41no—
266Dic122—41no—
267Dic122—82no—
268C8×C61—21no—
269C8×C61—21no—
270C8×C61—41no—
271#92418—21no—
272#92418—21no—
273#92418—41no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#19787—611nomaximal, Sylow
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—81no—
288C22×C61—81no—
289C22×C61—81no—
290C22×C61—164no—
291C22×C61D4211yescharacteristic
292C4×C61—21no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—81no—
297C4×C61C2×#13511yescharacteristic
298C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C61#57611yescharacteristic
300C4×C61#57711yescharacteristic
301Dic61—41no—
302Dic61—41no—
303Dic61—81no—
304Dic61—81no—
305#3367—611no—
306#3302—611no—
307#3294D6111yescharacteristic
308D4×SD16—611no—
309#1719—611no—
310#1702—611no—
311#1679—611no—
312#1679—611no—
313#1665—611no—
314#1649—611no—
315#1647—611no—
316#1639—611no—
317#1628—611no—
318#1582—611no—
319#1580—611no—
320C2×C61—42no—
321C2×C61—42no—
322C2×C61—81no—
323C2×C61—161no—
324C2×C61#326411yescharacteristic
325C2×C61#328211yescharacteristic
326C2×C61#328911yescharacteristic
327C22×SD16—1221no—
328#556—611no—
329D4×Q8—611no—
330#547C2×D6111yescharacteristic
331D42C2×D6111yescharacteristic
332#500—611no—
333#492—611no—
334#489—1221no—
335#487—611no—
336#487—611no—
337#486—611no—
338#486C2×D6111yescharacteristic
339#485—1221no—
340#480—21no—
341#477—1221no—
342#474—611no—
343#474—611no—
344#474C2×D6111yescharacteristic
345#467—1221no—
346#466—21no—
347#465—1221no—
348#463—1221no—
349#462—611no—
350#461—611no—
351#461—611no—
352#460—611no—
353#459C2×D6111yescharacteristic
354#452—1221no—
355#450—1221no—
356#448—1221no—
357#447—21no—
358#446—611no—
359#440—1221no—
360C4×SD16—611no—
361C4×D8C2×D6111yescharacteristic
362C8×D4—611no—
363C8×D4—611no—
364C8×D4C2×D6111yescharacteristic
365#416—1221no—
366C2×#102—21no—
367#334—611no—
368#334—611no—
369#332—611no—
370#332—611no—
371#332—611no—
372#331—611no—
373Q8⋊C8—611no—
374D4⋊C8—611no—
375D4⋊C8—611no—
376D4⋊C8—611no—
377#322—611no—
378C61#1978711yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C22×Q8—1221no—
381C22×D4—21no—
382C22×D4—21no—
383C2×Q16—1221no—
384C2×SD16—611no—
385C2×SD16—1221no—
386C2×SD16—1221no—
387C2×SD16—1221no—
388C2×SD16—1221no—
389C2×SD16—1221no—
390C2×SD16—2444no—
391C2×D8—21no—
392C2×D8C22⋊D6111yescharacteristic
393C22×C8—21no—
394C22×C8—1221no—
395C22×C8—1221no—
396C4⋊Q8—611no—
397C4⋊Q8—611no—
398C4⋊Q8—1221no—
399C4⋊Q8C22×D6111yescharacteristic
400#127C22×D6111yescharacteristic
401#126—2441no—
402#124—1221no—
403#123—41no—
404C22⋊Q8—21no—
405C22⋊Q8—1221no—
406C22⋊Q8—1221no—
407C22⋊Q8—2441no—
408#121—21no—
409#121—21no—
410#121—21no—
411#120—41no—
412C4×Q8—611no—
413C4×Q8—1221no—
414C4×D4—1221no—
415C4×D4C22×D6111yescharacteristic
416C4×D4C22×D6111yescharacteristic
417C4×D4C22×D6111yescharacteristic
418#117—1221no—
419C2×C4⋊C4—21no—
420#107—21no—
421#107—1221no—
422#107—1221no—
423#107—2441no—
424#107C22⋊D6111yescharacteristic
425#106—611no—
426C4⋊C8—611no—
427C4⋊C8—611no—
428C4⋊C8—611no—
429C4⋊C8—1221no—
430C4⋊C8C22×D6111yescharacteristic
431#103—611no—
432#103—1221no—
433#103—1221no—
434#103—1221no—
435#103—1221no—
436#103—1221no—
437#103—1221no—
438#103—1221no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—611no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#102—2441no—
448#102C22⋊D6111yescharacteristic
449#102C22⋊D6111yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—1221no—
452C22⋊C8—1221no—
453#97—1221no—
454C4×C8—611no—
455C4×C8—611no—
456C4×C8C22×D6111yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—611no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—4881no—
465C2×Q8—2441no—
466C2×Q8—2442no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—41no—
475C2×D4—81no—
476C2×D4—81no—
477C2×D4D4×D6111yescharacteristic
478C2×D4C2×C22⋊D6111yescharacteristic
479C2×D4C2×C22⋊D6111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—2441no—
485Q16—4881no—
486SD16—1222no—
487SD16—4881no—
488SD16—2442no—
489SD16—2442no—
490SD16—2442no—
491SD16—2442no—
492D8—22no—
493D8—81no—
494C2×C8—21no—
495C2×C8—81no—
496C2×C8—611no—
497C2×C8—611no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C2×C8—4881no—
503C2×C8—2442no—
504C2×C8C2×C22⋊D6111yescharacteristic
505C2×C8C2×C22⋊D6111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—41no—
509C4⋊C4—611no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—2441no—
516C4⋊C4—2441no—
517C4⋊C4D4×D6111yescharacteristic
518C4⋊C4C2×C22⋊D6111yescharacteristic
519C4⋊C4C2×C22⋊D6111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—2441no—
526C22⋊C4—2441no—
527C22⋊C4—2441no—
528C42—1221no—
529C42—2441no—
530C42C23×D6111yescharacteristic
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—1221no—
541Q8—1221no—
542Q8—4882no—
543Q8—2441no—
544Q8—2441no—
545Q8—2441no—
546Q8—2441no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—81no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4#1451979712yes—
560D4#1451980112yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—82no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—4882no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4C2×D4×D6111yescharacteristic
578C2×C4C22×C22⋊D6111yescharacteristic
579C2×C4#1451982211yescharacteristic
580C8—21no—
581C8—21no—
582C8—41no—
583C8—1221no—
584C8—1221no—
585C8—2441no—
586C8—2441no—
587C8—2441no—
588C8—2441no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D4×C22⋊D6111yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—81no—
608C4—4881no—
609C4—4881no—
610C4—2441no—
611C4—2441no—
612C4C2×#1451979711yescharacteristic
613C4C2×#1451980111yescharacteristic
614C4#1684056311yescharacteristic
615C4#1684057311yescharacteristic
616C2—42no—
617C2—42no—
618C2—81no—
619C2—161no—
620C2#2145729911yescharacteristic
621C2#2145752211yescharacteristic
622C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3294C2
socleC22×C61D42
hypercenter#3294D61
hypocenterC61#19787
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3294

Complements

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

NH ≅ G/Ntype
1. #21458535C2semidirect
2. #21457736C2semidirect
3. D4×#11758200C2semidirect
4. #21445469C2semidirect
5. #21445384C2semidirect
6. #21445242C2semidirect
7. #21445240C2semidirect
8. #21445158C2semidirect
9. #21445067C2semidirect
10. #21445054C2semidirect
11. #21444998C2semidirect
12. #21444927C2semidirect
13. #21444655C2semidirect
14. #21444643C2semidirect
17. #16840482C22semidirect
19. #16840165C22semidirect
22. #16840113C22semidirect
23. #16840112C22semidirect
28. #16840042C22semidirect
32. #16839969C22semidirect
39. #16839892C22semidirect
43. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839509C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
51. #16839492C22semidirect
54. D4⋊#92418C22semidirect
55. #16839483C22semidirect
378. C61#19787semidirect

Maximal subgroups

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

subgroupindex
#214585352
#214577362
D4×#117582002
#214454692
#214453842
#214452422
#214452402
#214451582
#214450672
#214450542
#214449982
#214449272
#214446552
#214446432
C61×#32942
#1978761