Finite Group Databasebeta

← #29669851

Subgroups — #29669851

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458526C211yesmaximal, characteristic, complemented
2#21457632C211yesmaximal, characteristic, complemented
3#21457550C211yesmaximal, characteristic, complemented
4#21445460C211yesmaximal, characteristic, complemented
5#21445385C211yesmaximal, characteristic, complemented
6#21445230C211yesmaximal, characteristic, complemented
7#21445225C211yesmaximal, characteristic, complemented
8#21445160C211yesmaximal, characteristic, complemented
9#21445033C211yesmaximal, characteristic, complemented
10#21444968C211yesmaximal, characteristic, complemented
11#21444882C211yesmaximal, characteristic, complemented
12#21444873C211yesmaximal, characteristic, complemented
13#21444656C211yesmaximal, characteristic, complemented
14#21444641C211yesmaximal, characteristic, complemented
15C61×#3295C211yesmaximal, characteristic, complemented
16C2×#14519798—21no—
17#16840434C2211yescharacteristic, complemented
18#16840416C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840135C2211yescharacteristic, complemented
21#16840128—21no—
22#16840112C2211yescharacteristic, complemented
23#16840110C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic
25#16840073—21no—
26#16840059—21no—
27#16840049C2211yescharacteristic, complemented
28#16840042C2211yescharacteristic
29#16839996—21no—
30#16839992—21no—
31#16839972C2211yescharacteristic, complemented
32#16839957—21no—
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839954C2211yescharacteristic
36#16839927—21no—
37#16839908—21no—
38#16839896—21no—
39#16839893C2211yescharacteristic, complemented
40#16839872—21no—
41C4×#11758199C2211yescharacteristic
42C8×D244C2211yescharacteristic, complemented
43D4×#92418C2211yescharacteristic
44C2×#14519698—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839509C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic, complemented
55#16839484C2211yescharacteristic, complemented
56C61×#554C2211yescharacteristic
57D42×C61C2211yescharacteristic
58C61×#486C2211yescharacteristic
59C61×#481—21no—
60C61×#476C2211yescharacteristic
61C61×#465—21no—
62C61×#460C2211yescharacteristic
63C61×#450—21no—
64C4×SD16×C61C2211yescharacteristic
65C8×D4×C61C2211yescharacteristic
66C2×#102×C61—21no—
67C2×#11758226—21no—
68C2×#11758224—21no—
69#14519798—44no—
70C2×#11758202—21no—
71C2×#11758190—21no—
72C2×#11758190—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—41no—
77C2×#11758199D411yescharacteristic
78C22×#92418—21no—
79C2×C8×D61—21no—
80#14519777C2311yescharacteristic
81#14519774—21no—
82#14519774C2311yescharacteristic
83#14519761—41no—
84#14519757—21no—
85#14519752—21no—
86#14519752—41no—
87#14519751—21no—
88C4×D244—21no—
89C4×D244C2311yescharacteristic
90C2×C4⋊Dic61—21no—
91#14519710—21no—
92#14519710D411yescharacteristic
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—41no—
99#14519700—21no—
100#14519698—21no—
101#14519698—21no—
102#14519698—21no—
103#14519698—21no—
104#14519698D411yescharacteristic
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113#14519688—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×D4×C61—21no—
117C22×D4×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61D411yescharacteristic
120C22×C8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#125×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—41no—
126#121×C61—21no—
127#121×C61—21no—
128#120×C61—41no—
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—21no—
134#106×C61—21no—
135#106×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C24×C61—41no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—41no—
152C2×D4×C61—41no—
153C2×D4×C61—42no—
154C2×D4×C61—42no—
155C2×D4×C61—81no—
156C2×D4×C61—81no—
157C2×D4×C61C2×D411yescharacteristic
158C2×D4×C61C2×D411yescharacteristic
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—41no—
162C2×C22⋊D61—41no—
163C22×Dic61—41no—
164#11758226—42no—
165#11758226—81no—
166#11758224—42no—
167#11758224—81no—
168C2×D244—21no—
169C2×D244—21no—
170C2×D244—21no—
171C2×D244—41no—
172C2×D244—41no—
173C2×D244C2×D411yescharacteristic
174C2×C4×D61—21no—
175C2×C4×D61—41no—
176C2×Dic122—21no—
177SD16×C61—22no—
178SD16×C61—81no—
179C2×C8×C61—21no—
180C2×C8×C61—81no—
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—41no—
187C4⋊C4×C61—41no—
188C4⋊C4×C61C2×D411yescharacteristic
189C4⋊C4×C61C2×D411yescharacteristic
190C4⋊C4×C61C2×D411yescharacteristic
191C22⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C42×C61—21no—
196C42×C61C2411yescharacteristic
197#11758202—42no—
198#11758199—22no—
199#11758199—42no—
200#11758199—42no—
201#11758199—81no—
202#11758199—82no—
203#11758198—21no—
204#11758198—41no—
205#11758198—41no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—41no—
209C4⋊Dic61C2×D411yescharacteristic
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—81no—
215C2×#92418C2×D411yescharacteristic
216C2×#92418C2×D411yescharacteristic
217#11758190—42no—
218#11758190—81no—
219C8×D61—42no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—41no—
223C23×C61—82no—
224C23×C61—82no—
225C23×C61—161no—
226C22×D61—21no—
227C22×D61—41no—
228Q8×C61—21no—
229Q8×C61—21no—
230Q8×C61—81no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—81no—
238D4×C61—82no—
239D4×C61—82no—
240D4×C61#13512yescomplemented
241D4×C61AGL(1,ℤ/8)12yes—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—161no—
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C22⋊D61—82no—
256C2×Dic61—21no—
257C2×Dic61—41no—
258C2×Dic61—82no—
259D244—21no—
260D244—21no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—41no—
265D244—81no—
266D244—82no—
267D244—161no—
268C4×D61—41no—
269C4×D61—41no—
270C4×D61—82no—
271Dic122—41no—
272Dic122—41no—
273C8×C61—21no—
274C8×C61—21no—
275C8×C61—41no—
276#92418—21no—
277#92418—21no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#19788—611nomaximal, Sylow
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61—81no—
290C22×C61—81no—
291C22×C61—81no—
292C22×C61—164no—
293C22×C61D4211yescharacteristic
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C4×C61—21no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61C2×#13511yescharacteristic
307C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C61#57611yescharacteristic
309C4×C61#57711yescharacteristic
310Dic61—41no—
311Dic61—81no—
312#3366—611no—
313#3295D6111yescharacteristic, complemented
314#3294—611no—
315#3284—611no—
316#1717—611no—
317#1702—611no—
318#1677—611no—
319#1677—611no—
320#1665—611no—
321#1644—611no—
322#1635—611no—
323#1621—611no—
324#1619—611no—
325#1582—611no—
326#1580—611no—
327C2×C61—42no—
328C2×C61—42no—
329C2×C61—161no—
330C2×C61#326411yescharacteristic
331C2×C61#328211yescharacteristic
332C2×C61#328811yescharacteristic
333D61—81no—
334D61—161no—
335C2×#135—1221no—
336#554C2×D6111yescharacteristic
337#550—611no—
338#547—611no—
339D42C2×D6111yescharacteristic
340#493—611no—
341#492—611no—
342#490—1221no—
343#487—611no—
344#486—611no—
345#486—611no—
346#486C2×D6111yescharacteristic
347#481—21no—
348#480—1221no—
349#478—1221no—
350#476—611no—
351#476C2×D6111yescharacteristic
352#474—611no—
353#466—1221no—
354#465—21no—
355#465—1221no—
356#462—611no—
357#460C2×D6111yescharacteristic
358#459—611no—
359#459—611no—
360#459—611no—
361#459—1221no—
362#452—1221no—
363#450—21no—
364#449—1221no—
365#447—1221no—
366#446—611no—
367#442—1221no—
368C4×SD16C2×D6111yescharacteristic
369C4×D8—611no—
370C8×D4—611no—
371C8×D4—611no—
372C8×D4C2×D6111yescharacteristic
373C2×#102—21no—
374C2×#102—1221no—
375#334—611no—
376#334—611no—
377#333—611no—
378#332—611no—
379#331—611no—
380#331—611no—
381Q8⋊C8—611no—
382D4⋊C8—611no—
383D4⋊C8—611no—
384D4⋊C8—611no—
385#322—611no—
386C61#1978811yescharacteristic, complemented, Sylow
387C2×#41—1221no—
388C2×#41—1221no—
389C22×D4—21no—
390C22×D4—21no—
391#135—2444no—
392C2×Q16—1221no—
393C2×SD16—21no—
394C2×SD16—1221no—
395C2×SD16—1221no—
396C2×SD16C22⋊D6111yescharacteristic
397C2×D8—611no—
398C2×D8—1221no—
399C2×D8—1221no—
400C2×D8—1221no—
401C2×D8—2441no—
402C22×C8—21no—
403C22×C8—1221no—
404C22×C8—1221no—
405C4⋊Q8—611no—
406C4⋊Q8C22×D6111yescharacteristic
407#127—611no—
408#127—1221no—
409#127C22×D6111yescharacteristic
410#125—21no—
411#123—2441no—
412C22⋊Q8—21no—
413C22⋊Q8—41no—
414C22⋊Q8—1221no—
415#121—21no—
416#121—21no—
417#121—1221no—
418#121—1221no—
419#121—2441no—
420#120—41no—
421C4×Q8C22×D6111yescharacteristic
422C4×D4—21no—
423C4×D4—611no—
424C4×D4—1221no—
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427C2×C4⋊C4—21no—
428C2×C4⋊C4—1221no—
429#107—611no—
430#107—1221no—
431#106—21no—
432#106—1221no—
433#106C22⋊D6111yescharacteristic
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—1221no—
438C4⋊C8C22×D6111yescharacteristic
439#103—1221no—
440#103—2441no—
441#103C22⋊D6111yescharacteristic
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—611no—
447#102—611no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—1221no—
453#102—1221no—
454#102—1221no—
455#102—1221no—
456#102—1221no—
457#102C22⋊D6111yescharacteristic
458C22⋊C8—21no—
459C22⋊C8—1221no—
460C22⋊C8—1221no—
461#97—1221no—
462C4×C8—611no—
463C4×C8—611no—
464C4×C8C22×D6111yescharacteristic
465C24—41no—
466#41—4881no—
467#41—4881no—
468#41—2442no—
469#41—2442no—
470C2×Q8—21no—
471C2×Q8—1221no—
472C2×Q8C2×C22⋊D6111yescharacteristic
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4—611no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—2441no—
487C2×D4—2441no—
488C2×D4—2441no—
489C2×D4D4×D6111yescharacteristic
490C2×D4C2×C22⋊D6111yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—41no—
494C22×C4—1221no—
495C22×C4—2441no—
496C22×C4—2441no—
497Q16—2442no—
498SD16—22no—
499SD16—81no—
500SD16—4881no—
501SD16—2442no—
502D8—1222no—
503D8—4881no—
504D8—4882no—
505D8—2442no—
506D8—2442no—
507C2×C8—21no—
508C2×C8—81no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—4881no—
516C2×C8—2442no—
517C2×C8C2×C22⋊D6111yescharacteristic
518C2×C8C2×C22⋊D6111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—611no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—2441no—
528C4⋊C4D4×D6111yescharacteristic
529C4⋊C4C2×C22⋊D6111yescharacteristic
530C4⋊C4C2×C22⋊D6111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—1221no—
536C22⋊C4—2441no—
537C22⋊C4—2441no—
538C42—21no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—21no—
542C23—41no—
543C23—82no—
544C23—82no—
545C23—161no—
546C23—1221no—
547C23—2441no—
548Q8—21no—
549Q8—21no—
550Q8—81no—
551Q8—2441no—
552Q8—2441no—
553D4—21no—
554D4—21no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—82no—
561D4—82no—
562D4—1221no—
563D4—1221no—
564D4—9761no—
565D4—4881no—
566D4—4882no—
567D4—4882no—
568D4—2441no—
569D4—2441no—
570D4—2441no—
571D4—2441no—
572D4#1451979812yescomplemented
573D4#1451980212yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—161no—
584C2×C4—1221no—
585C2×C4—4882no—
586C2×C4—4882no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4C2×D4×D6111yescharacteristic
591C2×C4C22×C22⋊D6111yescharacteristic
592C2×C4#1451982211yescharacteristic
593C8—21no—
594C8—21no—
595C8—41no—
596C8—1221no—
597C8—1221no—
598C8—2441no—
599C8—2441no—
600C8—2441no—
601C8—2441no—
602C22—22no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—164no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—2441no—
616C22—2441no—
617C22—2441no—
618C22D4×C22⋊D6111yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—4881no—
626C4—2441no—
627C4C2×#1451979811yescharacteristic
628C4C2×#1451980211yescharacteristic
629C4#1684056511yescharacteristic
630C4#1684056811yescharacteristic
631C2—42no—
632C2—42no—
633C2—161no—
634C2—9761no—
635C2—4881no—
636C2#2145730011yescharacteristic
637C2#2145752611yescharacteristic
638C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3295C2
socleC22×C61D42
hypercenter#3295D61
hypocenterC61#19788
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3295

Complements

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

NH ≅ G/Ntype
1. #21458526C2semidirect
2. #21457632C2semidirect
3. #21457550C2semidirect
4. #21445460C2semidirect
5. #21445385C2semidirect
6. #21445230C2semidirect
7. #21445225C2semidirect
8. #21445160C2semidirect
9. #21445033C2semidirect
10. #21444968C2semidirect
11. #21444882C2semidirect
12. #21444873C2semidirect
13. #21444656C2semidirect
14. #21444641C2semidirect
15. C61×#3295C2semidirect
17. #16840434C22semidirect
20. #16840135C22semidirect
22. #16840112C22semidirect
23. #16840110C22semidirect
27. #16840049C22semidirect
31. #16839972C22semidirect
39. #16839893C22semidirect
42. C8×D244C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839509C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
54. #16839489C22semidirect
55. #16839484C22semidirect
240. D4×C61#135semidirect
313. #3295D61semidirect
386. C61#19788semidirect
572. D4#14519798semidirect

Maximal subgroups

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

subgroupindex
#214585262
#214576322
#214575502
#214454602
#214453852
#214452302
#214452252
#214451602
#214450332
#214449682
#214448822
#214448732
#214446562
#214446412
C61×#32952
#1978861