Finite Group Databasebeta

← #29665154

Subgroups — #29665154

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457175C211yesmaximal, characteristic
2#21456846C211yesmaximal, characteristic, complemented
3#21454823C211yesmaximal, characteristic, complemented
4#21445384C211yesmaximal, characteristic, complemented
5#21445377C211yesmaximal, characteristic, complemented
6#21445370C211yesmaximal, characteristic, complemented
7#21445363C211yesmaximal, characteristic, complemented
8#21445260C211yesmaximal, characteristic, complemented
9#21445253C211yesmaximal, characteristic, complemented
10#21445246C211yesmaximal, characteristic, complemented
11#21445239C211yesmaximal, characteristic, complemented
12#21444586C211yesmaximal, characteristic, complemented
13#21444524C211yesmaximal, characteristic, complemented
14#21444491C211yesmaximal, characteristic, complemented
15C61×#3141C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840154—21no—
18#16840130—21no—
19#16840062—21no—
20#16840044C2211yescharacteristic
21#16840039C2211yescharacteristic
22#16840013—21no—
23#16840006—21no—
24#16839977—21no—
25#16839969C2211yescharacteristic
26#16839969C2211yescharacteristic
27#16839964C2211yescharacteristic
28#16839964C2211yescharacteristic
29#16839959C2211yescharacteristic
30#16839954C2211yescharacteristic
31#16839918—21no—
32#16839901—21no—
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839838—21no—
37#16839831—21no—
38C8×D244C2211yescharacteristic
39#16839824—21no—
40#16839819C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839786C2211yescharacteristic
43#16839719—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#532C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#489—21no—
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#486C2211yescharacteristic
63C61×#486C2211yescharacteristic
64C61×#417—21no—
65C61×#417—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758199—21no—
73C2×#11758194—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76#14519771—21no—
77#14519769D411yescharacteristic
78#14519765D411yescharacteristic
79#14519760—21no—
80#14519756D411yescharacteristic
81#14519751D411yescharacteristic
82C4×Dic122C2311yescharacteristic
83C4×D244C2311yescharacteristic
84C4×C22⋊D61—21no—
85#14519734—21no—
86#14519710—21no—
87#14519708—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519700—21no—
102#14519698—21no—
103#14519698—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519689—21no—
108#14519689—21no—
109#14519688—21no—
110#14519687—21no—
111C4×#92418—21no—
112C8×Dic61—21no—
113C2×#41×C61—21no—
114C22×Q8×C61—21no—
115C2×M16×C61D411yescharacteristic
116C2×M16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#127×C61C2311yescharacteristic
124#124×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#103×C61—21no—
133#103×C61—21no—
134#103×C61—21no—
135#103×C61—21no—
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—42no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—41no—
150C2×Q8×C61—81no—
151C2×Q8×C61—81no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—41no—
156C22×C4×C61—41no—
157C22×C4×C61—41no—
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C2×C22⋊D61—21no—
162C2×D244C2×D411yescharacteristic
163C2×C4×D61—21no—
164C2×Dic122C2×D411yescharacteristic
165M16×C61—41no—
166M16×C61—41no—
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
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—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C42×C61C2×D411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61#4111yescharacteristic
184C42×C61C2411yescharacteristic
185C22⋊Dic61—21no—
186#11758202—81no—
187#11758202—81no—
188#11758201—81no—
189#11758201—81no—
190#11758200—81no—
191#11758199—81no—
192#11758198—21no—
193#11758198—21no—
194#11758198—21no—
195#11758198—21no—
196C4⋊Dic61C2×D411yescharacteristic
197C4⋊Dic61C2×D411yescharacteristic
198#11758196—21no—
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202C4×Dic61—21no—
203#11758194—81no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210#11758189—42no—
211C8×D61—42no—
212C23×C61—41no—
213C23×C61#12111yescharacteristic
214C22×D61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—82no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—81no—
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—82no—
237C2×C4×C61—82no—
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C22⋊D61—81no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248D244—21no—
249D244—21no—
250C4×D61—41no—
251C4×D61—41no—
252Dic122—21no—
253Dic122—21no—
254C8×C61—21no—
255C8×C61—21no—
256C8×C61—21no—
257C8×C61—21no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#19383—611nomaximal, Sylow
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—81no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61C2×#12111yescharacteristic
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61#57511yescharacteristic
283C4×C61#57511yescharacteristic
284C4×C61#57611yescharacteristic
285C4×C61#57711yescharacteristic
286Dic61—41no—
287Dic61—41no—
288Dic61—41no—
289#3251—611no—
290#3218—611no—
291#3141D6111yescharacteristic, complemented
292#2969—611no—
293#1702—611no—
294#1701—611no—
295#1700—611no—
296#1699—611no—
297#1682—611no—
298#1681—611no—
299#1680—611no—
300#1679—611no—
301#1569—611no—
302#1553—611no—
303#1546—611no—
304C2×C61—41no—
305C2×C61—161no—
306C2×C61#304011yescharacteristic
307C2×C61#306211yescharacteristic
308C2×C61#306911yescharacteristic
309D61—81no—
310#532C2×D6111yescharacteristic
311C2×C4⋊Q8C2×D6111yescharacteristic
312#529—611no—
313#497—1221no—
314#491—1221no—
315#489—21no—
316#489—21no—
317#487C2×D6111yescharacteristic
318#487C2×D6111yescharacteristic
319#486C2×D6111yescharacteristic
320#486C2×D6111yescharacteristic
321#478—1221no—
322#475—611no—
323#474—611no—
324#469—1221no—
325#468—1221no—
326#463—1221no—
327#462—611no—
328#462—611no—
329#461—611no—
330#461—611no—
331#460—611no—
332#459—611no—
333#451—1221no—
334#448—1221no—
335#446—611no—
336C8×Q8—611no—
337#436—611no—
338#436—1221no—
339#435—1221no—
340C8×D4—611no—
341#433—1221no—
342#432—611no—
343#431—611no—
344#423—611no—
345#417—21no—
346#417—21no—
347#405—1221no—
348C4×M16C2×D6111yescharacteristic
349#335—611no—
350#335—611no—
351#334—611no—
352#334—611no—
353#332—611no—
354#332—611no—
355#332—611no—
356#332—611no—
357#332—611no—
358#332—611no—
359#331—611no—
360#331—611no—
361C61#1938311yescharacteristic, complemented, Sylow
362C2×#41—21no—
363C22×Q8—21no—
364C2×Q16—1221no—
365C2×Q16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×D8—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16C22⋊D6111yescharacteristic
373C2×M16C22⋊D6111yescharacteristic
374C22×C8—1221no—
375C4⋊Q8—21no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8C22×D6111yescharacteristic
379C4⋊Q8C22×D6111yescharacteristic
380C4⋊Q8C22×D6111yescharacteristic
381#127C22×D6111yescharacteristic
382#126—1221no—
383#125—611no—
384#124—21no—
385#124—611no—
386#123—1221no—
387C22⋊Q8—611no—
388#121—21no—
389#121—21no—
390#121—611no—
391C4×Q8—611no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—611no—
395C4×D4—1221no—
396#117—1221no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C42C22×D6111yescharacteristic
400#107—1221no—
401#106—1221no—
402C4⋊C8—611no—
403C4⋊C8—611no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8—1221no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#103—1221no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427C22⋊C8—1221no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—1221no—
432#97—1221no—
433#97C22⋊D6111yescharacteristic
434#97C22⋊D6111yescharacteristic
435C4×C8—1221no—
436C4×C8—1221no—
437C4×C8C22×D6111yescharacteristic
438C4×C8C22×D6111yescharacteristic
439#41—42no—
440#41—42no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—81no—
446C2×Q8—81no—
447C2×Q8—611no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—611no—
453C2×D4—1221no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—1221no—
457C22×C4D4×D6111yescharacteristic
458C22×C4#1175822411yescharacteristic
459C22×C4C2×C22⋊D6111yescharacteristic
460Q16—4881no—
461Q16—4881no—
462SD16—4881no—
463SD16—4881no—
464SD16—4881no—
465D8—4881no—
466M16—41no—
467M16—41no—
468M16—4881no—
469M16—2442no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—2442no—
477C2×C8C2×C22⋊D6111yescharacteristic
478C2×C8C2×C22⋊D6111yescharacteristic
479C2×C8C2×C22⋊D6111yescharacteristic
480C2×C8C2×C22⋊D6111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—611no—
490C4⋊C4—611no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—1221no—
498C22⋊C4—1221no—
499C22⋊C4—1221no—
500C22⋊C4—1221no—
501C22⋊C4—1221no—
502C42—1221no—
503C42D4×D6111yescharacteristic
504C42#1175822411yescharacteristic
505C42C2×C22⋊D6111yescharacteristic
506C42C23×D6111yescharacteristic
507C23—41no—
508C23—1221no—
509C23#1451974811yescharacteristic
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—82no—
517Q8—1221no—
518Q8—1221no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525D4—1221no—
526D4—1221no—
527D4—4881no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4#1451974811yescharacteristic
544C2×C4#1451974811yescharacteristic
545C2×C4#1451974811yescharacteristic
546C2×C4C2×D4×D6111yescharacteristic
547C2×C4C22×C22⋊D6111yescharacteristic
548C2×C4C2×#1175822411yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22C2×#1451974811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—2441no—
577C4—2441no—
578C4—2441no—
579C4#1684056011yescharacteristic
580C4#1684056011yescharacteristic
581C4#1684056611yescharacteristic
582C4#1684057211yescharacteristic
583C2—41no—
584C2—161no—
585C2—4881no—
586C2#2145530911yescharacteristic
587C2#2145549311yescharacteristic
588C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3141C2
socleC22×C61C2×#121
prime radical#21457175C2
hypercenter#3141D61
hypocenterC61#19383
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #21456846C2semidirect
3. #21454823C2semidirect
4. #21445384C2semidirect
5. #21445377C2semidirect
6. #21445370C2semidirect
7. #21445363C2semidirect
8. #21445260C2semidirect
9. #21445253C2semidirect
10. #21445246C2semidirect
11. #21445239C2semidirect
12. #21444586C2semidirect
13. #21444524C2semidirect
14. #21444491C2semidirect
15. C61×#3141C2semidirect
291. #3141D61semidirect
361. C61#19383semidirect

Maximal subgroups

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

subgroupindex
#214571752
#214568462
#214548232
#214453842
#214453772
#214453702
#214453632
#214452602
#214452532
#214452462
#214452392
#214445862
#214445242
#214444912
C61×#31412
#1938361