Finite Group Databasebeta

← #29670734

Subgroups — #29670734

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458822C211yesmaximal, characteristic, complemented
2#21458502C211yesmaximal, characteristic, complemented
3#21457758C211yesmaximal, characteristic
4#21445480C211yesmaximal, characteristic, complemented
5#21445373C211yesmaximal, characteristic, complemented
6#21445261C211yesmaximal, characteristic, complemented
7#21445260C211yesmaximal, characteristic, complemented
8#21445182C211yesmaximal, characteristic, complemented
9#21445096C211yesmaximal, characteristic, complemented
10#21445088C211yesmaximal, characteristic, complemented
11#21445012C211yesmaximal, characteristic
12#21444914C211yesmaximal, characteristic, complemented
13#21444667C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3368C211yesmaximal, characteristic
16#16840491C2211yescharacteristic
17#16840482C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840141—21no—
20#16840141C2211yescharacteristic
21#16840115—21no—
22#16840113C2211yescharacteristic
23#16840108C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840083—21no—
26#16840072—21no—
27#16840047C2211yescharacteristic
28#16840042C2211yescharacteristic
29#16839989—21no—
30#16839982—21no—
31#16839972—21no—
32#16839972C2211yescharacteristic
33#16839972C2211yescharacteristic
34#16839969—21no—
35#16839969C2211yescharacteristic
36#16839959C2211yescharacteristic
37#16839924—21no—
38Q8×#92418C2211yescharacteristic
39C8×Dic122C2211yescharacteristic
40C4×#11758202—21no—
41C4×#11758202C2211yescharacteristic
42#16839854—21no—
43D4×#92418C2211yescharacteristic
44#16839758—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839507C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#557C2211yescharacteristic
57C61×#550C2211yescharacteristic
58C61×#490—21no—
59C61×#486C2211yescharacteristic
60C61×#478—21no—
61C61×#474C2211yescharacteristic
62C61×#460—21no—
63C61×#460C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758202—21no—
72C2×#11758202D411yescharacteristic
73C2×#11758200—21no—
74C22×#92418—21no—
75#14519777—21no—
76#14519777C2311yescharacteristic
77#14519777C2311yescharacteristic
78#14519770—41no—
79#14519768—21no—
80#14519768—41no—
81#14519764—21no—
82#14519756—21no—
83Q8×Dic61—21no—
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519736—21no—
88#14519710—21no—
89#14519710D411yescharacteristic
90#14519708—21no—
91#14519708—41no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701D411yescharacteristic
102#14519700—21no—
103#14519700—21no—
104#14519700D411yescharacteristic
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519698—41no—
110C22⋊#92418—21no—
111C4×#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×#41×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120#127×C61—21no—
121#127×C61C2311yescharacteristic
122#125×C61—21no—
123#125×C61—41no—
124#121×C61—21no—
125#121×C61—41no—
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#107×C61—21no—
133#106×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61D411yescharacteristic
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144#41×C61—42no—
145#41×C61—81no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—41no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122C2×D411yescharacteristic
160SD16×C61—22no—
161SD16×C61—42no—
162C2×C8×C61—21no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C4⋊C4×C61C2×D411yescharacteristic
175C22⋊C4×C61—21no—
176C22⋊C4×C61—41no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—41no—
180C42×C61C2411yescharacteristic
181C22⋊Dic61—41no—
182C22⋊Dic61—41no—
183#11758202—41no—
184#11758202—42no—
185#11758202—42no—
186#11758202—81no—
187#11758202—81no—
188#11758202—81no—
189#11758200—81no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—41no—
195C4⋊Dic61—41no—
196C4⋊Dic61C2×D411yescharacteristic
197#11758196—21no—
198#11758196—41no—
199#11758196—41no—
200C4×Dic61—21no—
201C4×Dic61—41no—
202C4×Dic61—41no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—81no—
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C23×C61—21no—
211C23×C61—41no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61#13512yes—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—81no—
225D4×C61—82no—
226D4×C61—161no—
227C2×C4×C61—21no—
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—82no—
236C2×C4×C61C22×D411yescharacteristic
237C2×C4×C61C22×D411yescharacteristic
238C2×C4×C61H(5,𝔽2)11yescharacteristic
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243Dic122—21no—
244Dic122—21no—
245Dic122—41no—
246Dic122—41no—
247Dic122—41no—
248Dic122—41no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#19847—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61D4211yescharacteristic
266C4×C61—22no—
267C4×C61—21no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61C2×#13511yescharacteristic
274C4×C61#57511yescharacteristic
275C4×C61#57611yescharacteristic
276C4×C61#57811yescharacteristic
277Dic61—41no—
278Dic61—41no—
279Dic61—81no—
280Dic61—81no—
281#3395—611no—
282#3368D6111yescharacteristic
283#3364—611no—
284#3304—611no—
285#1720—611no—
286#1700—611no—
287#1682—611no—
288#1682—611no—
289#1669—611no—
290#1653—611no—
291#1652—611no—
292#1641—611no—
293#1626—611no—
294#1584—611no—
295SD16⋊C8—611no—
296C2×C61—81no—
297C2×C61—161no—
298C2×C61#326811yescharacteristic
299C2×C61#328511yescharacteristic
300C2×C61#328911yescharacteristic
301#557—611no—
302#557C2×D6111yescharacteristic
303#556—611no—
304#550C2×D6111yescharacteristic
305#498—611no—
306#494—611no—
307#494—1221no—
308#490—21no—
309#488—1221no—
310#487—611no—
311#486—611no—
312#486—611no—
313#486C2×D6111yescharacteristic
314#482—1221no—
315#479—1221no—
316#478—21no—
317#475—611no—
318#474—611no—
319#474C2×D6111yescharacteristic
320#465—1221no—
321#464—1221no—
322#462—611no—
323#462—611no—
324#462—611no—
325#462—1221no—
326#462—1221no—
327#460—21no—
328#460—611no—
329#460C2×D6111yescharacteristic
330#452—1221no—
331#446C2×D6111yescharacteristic
332C8×Q8—611no—
333C8×Q8—611no—
334#440—21no—
335C4×Q16—611no—
336C4×Q16—1221no—
337C4×Q16—1221no—
338C4×SD16C2×D6111yescharacteristic
339C8×D4—611no—
340#416—1221no—
341#335—611no—
342#335—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#331—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349Q8⋊C8—611no—
350D4⋊C8—611no—
351#322—611no—
352C61#1984711yescharacteristic, complemented, Sylow
353C2×#41—21no—
354C2×Q16—611no—
355C2×Q16—1221no—
356C2×Q16—1221no—
357C2×Q16—1221no—
358C2×Q16—1221no—
359C2×Q16—1221no—
360C2×SD16—21no—
361C2×SD16—1221no—
362C2×SD16C22⋊D6111yescharacteristic
363C22×C8—1221no—
364C4⋊Q8—21no—
365C4⋊Q8—611no—
366C4⋊Q8—611no—
367C4⋊Q8—1221no—
368C4⋊Q8C22×D6111yescharacteristic
369#127—21no—
370#127C22×D6111yescharacteristic
371#126—2441no—
372#125—21no—
373#125—41no—
374#125—1221no—
375#125—2441no—
376#124—1221no—
377C22⋊Q8—1221no—
378#121—21no—
379#121—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—611no—
383C4×Q8—1221no—
384C4×Q8—1221no—
385C4×Q8—1221no—
386C4×Q8C22×D6111yescharacteristic
387C4×Q8C22×D6111yescharacteristic
388C4×D4—21no—
389C4×D4C22×D6111yescharacteristic
390#117—1221no—
391#107—21no—
392#107—611no—
393#107—1221no—
394#106—1221no—
395#106—2441no—
396#106C22⋊D6111yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8C22×D6111yescharacteristic
404#103—611no—
405#103—611no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103C22⋊D6111yescharacteristic
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—1221no—
418#102—1221no—
419#102—1221no—
420#102—1221no—
421#102—2441no—
422#102C22⋊D6111yescharacteristic
423C22⋊C8—1221no—
424#97—21no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C4×C8—1221no—
429C4×C8C22×D6111yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—611no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8D4×D6111yescharacteristic
437C2×Q8C2×C22⋊D6111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4C2×C22⋊D6111yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446Q16—4881no—
447Q16—4881no—
448Q16—4881no—
449Q16—2441no—
450Q16—2442no—
451Q16—2442no—
452SD16—22no—
453SD16—42no—
454SD16—4881no—
455C2×C8—21no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—4881no—
463C2×C8C2×C22⋊D6111yescharacteristic
464C2×C8C2×C22⋊D6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—611no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C4⋊C4—2441no—
482C4⋊C4D4×D6111yescharacteristic
483C4⋊C4C2×C22⋊D6111yescharacteristic
484C4⋊C4C2×C22⋊D6111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—2441no—
488C22⋊C4—2441no—
489C42—21no—
490C42—21no—
491C42—41no—
492C42—1221no—
493C42—2441no—
494C42—2441no—
495C42C23×D6111yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—1221no—
504Q8—1221no—
505Q8—2441no—
506Q8—2441no—
507Q8—2441no—
508Q8—2441no—
509Q8#1451979712yes—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—81no—
517D4—82no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C22×C22⋊D6111yescharacteristic
534C2×C4#1451982211yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—1221no—
539C8—1221no—
540C8—2441no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D4×C22⋊D6111yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—4881no—
559C4—4881no—
560C4—2441no—
561C4—2441no—
562C4C2×#1451979711yescharacteristic
563C4#1684055811yescharacteristic
564C4#1684056611yescharacteristic
565C4#1684057711yescharacteristic
566C2—81no—
567C2—161no—
568C2#2145735311yescharacteristic
569C2#2145755611yescharacteristic
570C2#2145759211yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3368C2
socleC22×C61D42
prime radicalC61×#550C22
hypercenter#3368D61
hypocenterC61#19847
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3368

Complements

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

NH ≅ G/Ntype
1. #21458822C2semidirect
2. #21458502C2semidirect
4. #21445480C2semidirect
5. #21445373C2semidirect
6. #21445261C2semidirect
7. #21445260C2semidirect
8. #21445182C2semidirect
9. #21445096C2semidirect
10. #21445088C2semidirect
12. #21444914C2semidirect
13. #21444667C2semidirect
14. SD16⋊#92418C2semidirect
352. C61#19847semidirect

Maximal subgroups

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

subgroupindex
#214588222
#214585022
#214577582
#214454802
#214453732
#214452612
#214452602
#214451822
#214450962
#214450882
#214450122
#214449142
#214446672
SD16⋊#924182
C61×#33682
#1984761