Finite Group Databasebeta

← #29662744

Subgroups — #29662744

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456378C211yesmaximal, characteristic, complemented
2#21455890C211yesmaximal, characteristic, complemented
3#21455879C211yesmaximal, characteristic
4#21445401C211yesmaximal, characteristic, complemented
5#21445394C211yesmaximal, characteristic, complemented
6#21445387C211yesmaximal, characteristic, complemented
7#21445380C211yesmaximal, characteristic, complemented
8#21445325C211yesmaximal, characteristic, complemented
9#21445318C211yesmaximal, characteristic, complemented
10#21445291C211yesmaximal, characteristic, complemented
11#21445284C211yesmaximal, characteristic, complemented
12#21444567C211yesmaximal, characteristic, complemented
13#21444483C211yesmaximal, characteristic, complemented
14#21444479C211yesmaximal, characteristic, complemented
15C61×#2965C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840312C2211yescharacteristic
18#16840160C2211yescharacteristic
19#16840135C2211yescharacteristic
20#16840113C2211yescharacteristic
21#16840109C2211yescharacteristic
22#16840103—21no—
23#16840086—21no—
24#16840057C2211yescharacteristic
25#16840052C2211yescharacteristic
26#16840047C2211yescharacteristic
27#16840042C2211yescharacteristic
28#16839991—21no—
29#16839991—21no—
30#16839972C2211yescharacteristic
31#16839967C2211yescharacteristic
32#16839962C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839924—21no—
35#16839907—21no—
36C4×#11758202—21no—
37C4×#11758190—21no—
38C4×#11758190—21no—
39C4×#11758201—21no—
40C4×#11758200—21no—
41C4×#11758199—21no—
42#16839815C2211yescharacteristic
43#16839815C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51#16839509C2211yescharacteristic
52#16839507C2211yescharacteristic
53#16839507C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C4×#41×C61C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C61×#446C2211yescharacteristic
59C61×#436C2211yescharacteristic
60C61×#436C2211yescharacteristic
61C61×#435—21no—
62C61×#435—21no—
63C61×#431—21no—
64C61×#431C2211yescharacteristic
65C4×M16×C61—21no—
66C2×C4×C8×C61C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758190—21no—
70C2×#11758190—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73C2×#11758199—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519769—21no—
79#14519765—21no—
80#14519756—21no—
81#14519756—21no—
82#14519751—21no—
83#14519751—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86C4×D244—21no—
87C4×D244—21no—
88#14519736—21no—
89#14519710—21no—
90#14519710—21no—
91#14519709—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519700—21no—
104#14519700—21no—
105#14519699—21no—
106#14519699—21no—
107#14519698—21no—
108#14519698—21no—
109#14519697—21no—
110#14519697—21no—
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113C4×#92418—21no—
114C4×#92418—21no—
115C2×#41×C61D411yescharacteristic
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C22×C8×C61D411yescharacteristic
119C22×C8×C61D411yescharacteristic
120C4×Q8×C61D411yescharacteristic
121C4×Q8×C61C2311yescharacteristic
122C4×D4×C61—21no—
123C4×D4×C61—21no—
124C4×D4×C61D411yescharacteristic
125C4×D4×C61C2311yescharacteristic
126#117×C61—21no—
127#117×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61—21no—
137#97×C61—21no—
138#97×C61—21no—
139C4×C8×C61—21no—
140C4×C8×C61D411yescharacteristic
141C4×C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—41no—
145#41×C61—41no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C2×C22⋊D61—41no—
156#11758222—82no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×C4×D61—41no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164M16×C61—42no—
165M16×C61—42no—
166C2×C8×C61—22no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—41no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C22⋊C4×C61—21no—
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61#4111yescharacteristic
187C42×C61C2411yescharacteristic
188C22⋊Dic61—41no—
189#11758202—42no—
190#11758201—42no—
191#11758200—42no—
192#11758199—42no—
193#11758198—41no—
194#11758198—41no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201#11758196—41no—
202#11758196—41no—
203C4×Dic61—41no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208#11758190—42no—
209#11758190—42no—
210C23×C61—21no—
211C23×C61#12111yescharacteristic
212C22×D61—41no—
213Q8×C61—21no—
214Q8×C61—21no—
215D4×C61—21no—
216D4×C61—21no—
217D4×C61—42no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—22no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—42no—
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C22⋊D61—82no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—41no—
244D244—81no—
245C4×D61—82no—
246Dic122—41no—
247Dic122—41no—
248Dic122—41no—
249Dic122—41no—
250Dic122—81no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—41no—
255C8×C61—41no—
256C8×C61#13512yes—
257#92418—41no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#19159—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61C2×#12111yescharacteristic
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61#47112yes—
279C4×C61C2×#13511yescharacteristic
280C4×C61#57511yescharacteristic
281C4×C61#57511yescharacteristic
282C4×C61#57511yescharacteristic
283Dic61—81no—
284Dic61—81no—
285Dic61—81no—
286#3167—611no—
287#3107—611no—
288#3106—611no—
289#2965D6111yescharacteristic, complemented
290#1704—611no—
291#1703—611no—
292#1702—611no—
293#1701—611no—
294#1692—611no—
295#1691—611no—
296#1686—611no—
297#1685—611no—
298#1564—611no—
299#1544—611no—
300#1543—611no—
301C2×C61—41no—
302C2×C61—81no—
303C2×C61#303511yescharacteristic
304C2×C61#305411yescharacteristic
305C2×C61C2×#47111yescharacteristic
306D61—161no—
307#533—611no—
308#532—611no—
309C4×#41C2×D6111yescharacteristic
310#498—611no—
311#492—611no—
312#487—611no—
313#486—611no—
314#485—1221no—
315#482—1221no—
316#477—611no—
317#476—611no—
318#475—611no—
319#474—611no—
320#465—1221no—
321#465—1221no—
322#462—611no—
323#461—611no—
324#460—611no—
325#459—611no—
326#452—1221no—
327#449—1221no—
328#446C2×D6111yescharacteristic
329#446C2×D6111yescharacteristic
330C4×Q16—1221no—
331C4×SD16—1221no—
332C4×SD16—1221no—
333C4×SD16—1221no—
334C4×SD16—1221no—
335C4×D8—1221no—
336#436C2×D6111yescharacteristic
337#436C2×D6111yescharacteristic
338#435—21no—
339#435—21no—
340#431—21no—
341#431—611no—
342#431—611no—
343#431C2×D6111yescharacteristic
344C4×M16—21no—
345C2×C4×C8C2×D6111yescharacteristic
346#335—611no—
347#335—611no—
348#334—611no—
349#334—611no—
350#333—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#331—611no—
357#331—611no—
358C61#1915911yescharacteristic, complemented, Sylow
359C2×#41—1221no—
360C2×#41D24411yescharacteristic
361C2×Q16—1221no—
362C2×SD16—1221no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×D8—1221no—
367C2×M16—21no—
368C2×M16—21no—
369C22×C8C22⋊D6111yescharacteristic
370C22×C8C22⋊D6111yescharacteristic
371C4⋊Q8—611no—
372C4⋊Q8—611no—
373C4⋊Q8—611no—
374#127—611no—
375#125—1221no—
376#124—1221no—
377C22⋊Q8—1221no—
378C22⋊Q8—1221no—
379#121—1221no—
380#121—1221no—
381C4×Q8—1221no—
382C4×Q8—1221no—
383C4×Q8D24411yescharacteristic
384C4×Q8C22×D6111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—1221no—
388C4×D4—1221no—
389C4×D4D24411yescharacteristic
390C4×D4C22×D6111yescharacteristic
391#117—21no—
392#117—1221no—
393#117D24411yescharacteristic
394C2×C42—21no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#107—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8C22×D6111yescharacteristic
409C4⋊C8C22×D6111yescharacteristic
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427#97—21no—
428#97—21no—
429C4×C8—21no—
430C4×C8—1221no—
431C4×C8—1221no—
432C4×C8C22⋊D6111yescharacteristic
433C4×C8C22⋊D6111yescharacteristic
434C4×C8C22×D6111yescharacteristic
435C4×C8C22×D6111yescharacteristic
436#41—41no—
437#41—41no—
438#41—4882no—
439C2×Q8—1221no—
440C2×Q8—1221no—
441C2×Q8—1221no—
442C2×Q8C2×D24411yescharacteristic
443C2×D4—21no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—2441no—
448C2×D4C2×D24411yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—2441no—
453C22×C4C2×D24411yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456Q16—2442no—
457SD16—2442no—
458SD16—2442no—
459SD16—2442no—
460SD16—2442no—
461D8—2442no—
462M16—42no—
463M16—42no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—41no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8C2×C22⋊D6111yescharacteristic
473C2×C8C2×C22⋊D6111yescharacteristic
474C2×C8C2×C22⋊D6111yescharacteristic
475C2×C8C2×C22⋊D6111yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—2441no—
485C4⋊C4—2441no—
486C4⋊C4C2×D24411yescharacteristic
487C4⋊C4C2×D24411yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—2441no—
492C22⋊C4—2441no—
493C22⋊C4—2441no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—2441no—
498C42C2×D24411yescharacteristic
499C42#1175822211yescharacteristic
500C42C2×C22⋊D6111yescharacteristic
501C42C23×D6111yescharacteristic
502C23—21no—
503C23—2441no—
504C23#1451975111yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—4881no—
508Q8—2441no—
509Q8—2441no—
510Q8—2441no—
511Q8—2441no—
512D4—21no—
513D4—21no—
514D4—42no—
515D4—4881no—
516D4—4882no—
517D4—2441no—
518D4—2441no—
519D4—2441no—
520D4—2441no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—4882no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4#1451975111yescharacteristic
538C2×C4#1451975111yescharacteristic
539C2×C4#1451975111yescharacteristic
540C2×C4C22×C22⋊D6111yescharacteristic
541C2×C4C22×D24411yescharacteristic
542C2×C4C2×#1175822211yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—2441no—
549C8—2441no—
550C8—2441no—
551C8—2441no—
552C8#1451979712yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—4881no—
560C22—4881no—
561C22—4881no—
562C22C2×#1451975111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—4881no—
570C4—4881no—
571C4—4881no—
572C4#1684002512yes—
573C4C2×#1451979711yescharacteristic
574C4#1684056011yescharacteristic
575C4#1684056211yescharacteristic
576C4#1684056211yescharacteristic
577C2—41no—
578C2—81no—
579C2—9761no—
580C2#2145527411yescharacteristic
581C2#2145542811yescharacteristic
582C2C2×#1684002511yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2965C2
socleC22×C61C2×#121
prime radical#21455879C2
hypercenter#2965D61
hypocenterC61#19159
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #21456378C2semidirect
2. #21455890C2semidirect
4. #21445401C2semidirect
5. #21445394C2semidirect
6. #21445387C2semidirect
7. #21445380C2semidirect
8. #21445325C2semidirect
9. #21445318C2semidirect
10. #21445291C2semidirect
11. #21445284C2semidirect
12. #21444567C2semidirect
13. #21444483C2semidirect
14. #21444479C2semidirect
15. C61×#2965C2semidirect
289. #2965D61semidirect
358. C61#19159semidirect

Maximal subgroups

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

subgroupindex
#214563782
#214558902
#214558792
#214454012
#214453942
#214453872
#214453802
#214453252
#214453182
#214452912
#214452842
#214445672
#214444832
#214444792
C61×#29652
#1915961