Finite Group Databasebeta

← #29669855

Subgroups — #29669855

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#21458524C211yesmaximal, characteristic, complemented
2#21457643C211yesmaximal, characteristic, complemented
3#21457545C211yesmaximal, characteristic, complemented
4#21445459C211yesmaximal, characteristic, complemented
5#21445384C211yesmaximal, characteristic, complemented
6#21445228C211yesmaximal, characteristic, complemented
7#21445226C211yesmaximal, characteristic, complemented
8#21445162C211yesmaximal, characteristic, complemented
9#21445032C211yesmaximal, characteristic, complemented
10#21444970C211yesmaximal, characteristic, complemented
11#21444883C211yesmaximal, characteristic, complemented
12#21444873C211yesmaximal, characteristic, complemented
13#21444655C211yesmaximal, characteristic, complemented
14#21444643C211yesmaximal, characteristic, complemented
15C61×#3294C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840469C2211yescharacteristic
18#16840433C2211yescharacteristic, complemented
19#16840138C2211yescharacteristic
20#16840136C2211yescharacteristic, complemented
21#16840125—21no—
22#16840114C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic, complemented
24#16840108C2211yescharacteristic
25#16840078—21no—
26#16840065—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16839993—21no—
30#16839989—21no—
31#16839969C2211yescharacteristic, complemented
32#16839959C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839955—21no—
36#16839922—21no—
37#16839913—21no—
38#16839907—21no—
39#16839892C2211yescharacteristic, complemented
40#16839871—21no—
41C4×#11758200C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43D4×#92418C2211yescharacteristic, complemented
44C2×#14519698—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
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—
67C2×#11758222—21no—
68#14519797—44no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C2×#11758200D411yescharacteristic
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758199—21no—
76C2×#11758199—41no—
77C22×#92418—21no—
78C22×#92418—21no—
79#14519777C2311yescharacteristic
80#14519774C2311yescharacteristic
81#14519773—21no—
82#14519768—21no—
83#14519756—21no—
84#14519754—41no—
85#14519751—21no—
86#14519750—41no—
87C4×Dic122C2311yescharacteristic
88D4×Dic61—21no—
89#14519739—21no—
90C2×C4⋊Dic61—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708D411yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519701—21no—
99#14519700—41no—
100#14519700D411yescharacteristic
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519698D411yescharacteristic
109#14519697—21no—
110#14519697—21no—
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—
166C2×C22⋊D61—41no—
167C2×C22⋊D61—41no—
168C22×Dic61—41no—
169#11758222—42no—
170#11758222—81no—
171C2×D244—21no—
172C2×D244—21no—
173C2×D244—21no—
174C2×C4×D61—41no—
175C2×Dic122—21no—
176C2×Dic122C2×D411yescharacteristic
177D8×C61—22no—
178D8×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—41no—
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C4⋊C4×C61C2×D411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C42×C61C2411yescharacteristic
195C22⋊Dic61—41no—
196#11758202—42no—
197#11758201—42no—
198#11758201—81no—
199#11758200—22no—
200#11758200—81no—
201#11758199—42no—
202#11758199—42no—
203#11758199—82no—
204#11758198—41no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61—41no—
208C4⋊Dic61C2×D411yescharacteristic
209#11758196—21no—
210#11758196—41no—
211C4×Dic61—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—42no—
217C2×#92418—81no—
218C2×#92418C2×D411yescharacteristic
219C2×#92418C2×D411yescharacteristic
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—41no—
224C23×C61—82no—
225C23×C61—82no—
226C23×C61—161no—
227C22×D61—41no—
228Q8×C61—41no—
229Q8×C61—41no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—41no—
237D4×C61—41no—
238D4×C61—81no—
239D4×C61—82no—
240D4×C61—82no—
241D4×C61—82no—
242D4×C61#13512yescomplemented
243D4×C61AGL(1,ℤ/8)12yes—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—82no—
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C22⋊D61—82no—
259C22⋊D61—161no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—41no—
263C2×Dic61—161no—
264D244—41no—
265D244—41no—
266D244—41no—
267D244—41no—
268D244—81no—
269C4×D61—82no—
270Dic122—21no—
271Dic122—21no—
272Dic122—81no—
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—41no—
290C22×C61—41no—
291C22×C61—41no—
292C22×C61—81no—
293C22×C61—81no—
294C22×C61—81no—
295C22×C61—164no—
296C22×C61D4211yescharacteristic
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C4×C61—21no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—81no—
305C4×C61C2×#13511yescharacteristic
306C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
307C4×C61#57611yescharacteristic
308C4×C61#57711yescharacteristic
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312#3366—611no—
313#3295—611no—
314#3294D6111yescharacteristic, complemented
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—81no—
330C2×C61—161no—
331C2×C61#326411yescharacteristic
332C2×C61#328211yescharacteristic
333C2×C61#328811yescharacteristic
334D61—161no—
335C2×#135—1221no—
336#554—611no—
337#550—611no—
338#547C2×D6111yescharacteristic
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—1221no—
348#480—21no—
349#478—1221no—
350#476—611no—
351#476—611no—
352#474C2×D6111yescharacteristic
353#466—21no—
354#465—1221no—
355#465—1221no—
356#462—611no—
357#460—611no—
358#459—611no—
359#459—611no—
360#459—1221no—
361#459C2×D6111yescharacteristic
362#452—1221no—
363#450—1221no—
364#449—1221no—
365#447—21no—
366#446—611no—
367#442—1221no—
368C4×SD16—611no—
369C4×D8C2×D6111yescharacteristic
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—21no—
388C2×#41—1221no—
389C22×D4—21no—
390C22×D4—21no—
391#135—2444no—
392C2×Q16—1221no—
393C2×SD16—611no—
394C2×SD16—1221no—
395C2×SD16—1221no—
396C2×SD16—1221no—
397C2×D8—21no—
398C2×D8—1221no—
399C2×D8—1221no—
400C2×D8—2441no—
401C2×D8C22⋊D6111yescharacteristic
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—1221no—
411#123—41no—
412C22⋊Q8—21no—
413C22⋊Q8—1221no—
414C22⋊Q8—2441no—
415#121—21no—
416#121—21no—
417#121—21no—
418#121—1221no—
419#121—2441no—
420#120—41no—
421C4×Q8—611no—
422C4×D4—1221no—
423C4×D4—1221no—
424C4×D4C22×D6111yescharacteristic
425C4×D4C22×D6111yescharacteristic
426C4×D4C22×D6111yescharacteristic
427C2×C4⋊C4—21no—
428C2×C4⋊C4—1221no—
429#107—21no—
430#107C22⋊D6111yescharacteristic
431#106—611no—
432#106—1221no—
433#106—1221no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8—611no—
437C4⋊C8—1221no—
438C4⋊C8C22×D6111yescharacteristic
439#103—611no—
440#103—1221no—
441#103—2441no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—611no—
447#102—1221no—
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#102C22⋊D6111yescharacteristic
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—42no—
467#41—81no—
468#41—4881no—
469#41—2442no—
470C2×Q8—21no—
471C2×Q8—611no—
472C2×Q8—1221no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—41no—
481C2×D4—81no—
482C2×D4—81no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—2441no—
487C2×D4—2441no—
488C2×D4D4×D6111yescharacteristic
489C2×D4C2×C22⋊D6111yescharacteristic
490C2×D4C2×C22⋊D6111yescharacteristic
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—2441no—
496C22×C4—2441no—
497Q16—2442no—
498SD16—1222no—
499SD16—4881no—
500SD16—4881no—
501SD16—2442no—
502D8—22no—
503D8—81no—
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—41no—
522C4⋊C4—611no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—2441no—
527C4⋊C4—2441no—
528C4⋊C4D4×D6111yescharacteristic
529C4⋊C4C2×C22⋊D6111yescharacteristic
530C4⋊C4C2×C22⋊D6111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—2441no—
537C22⋊C4—2441no—
538C42—1221no—
539C42C23×D6111yescharacteristic
540C23—21no—
541C23—21no—
542C23—21no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—161no—
547C23—2441no—
548Q8—41no—
549Q8—41no—
550Q8—1221no—
551Q8—1221no—
552Q8—4881no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—21no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—81no—
562D4—82no—
563D4—82no—
564D4—82no—
565D4—9761no—
566D4—4881no—
567D4—4882no—
568D4—2441no—
569D4—2441no—
570D4—2441no—
571D4—2441no—
572D4#1451979712yescomplemented
573D4#1451980112yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—82no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—9761no—
588C2×C4—4882no—
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—41no—
609C22—41no—
610C22—41no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—164no—
615C22—4881no—
616C22—4881no—
617C22—4881no—
618C22D4×C22⋊D6111yescharacteristic
619C4—21no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—4881no—
625C4—2441no—
626C4—2441no—
627C4C2×#1451979711yescharacteristic
628C4C2×#1451980111yescharacteristic
629C4#1684056311yescharacteristic
630C4#1684057311yescharacteristic
631C2—42no—
632C2—42no—
633C2—81no—
634C2—161no—
635C2—9761no—
636C2#2145729911yescharacteristic
637C2#2145752211yescharacteristic
638C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3294C2
socleC22×C61D42
hypercenter#3294D61
hypocenterC61#19788
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. #21458524C2semidirect
2. #21457643C2semidirect
3. #21457545C2semidirect
4. #21445459C2semidirect
5. #21445384C2semidirect
6. #21445228C2semidirect
7. #21445226C2semidirect
8. #21445162C2semidirect
9. #21445032C2semidirect
10. #21444970C2semidirect
11. #21444883C2semidirect
12. #21444873C2semidirect
13. #21444655C2semidirect
14. #21444643C2semidirect
15. C61×#3294C2semidirect
18. #16840433C22semidirect
20. #16840136C22semidirect
22. #16840114C22semidirect
23. #16840109C22semidirect
28. #16840052C22semidirect
31. #16839969C22semidirect
39. #16839892C22semidirect
43. D4×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
50. #16839505C22semidirect
51. #16839492C22semidirect
54. D4⋊#92418C22semidirect
55. #16839483C22semidirect
242. D4×C61#135semidirect
314. #3294D61semidirect
386. C61#19788semidirect
572. D4#14519797semidirect

Maximal subgroups

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

subgroupindex
#214585242
#214576432
#214575452
#214454592
#214453842
#214452282
#214452262
#214451622
#214450322
#214449702
#214448832
#214448732
#214446552
#214446432
C61×#32942
#1978861