Finite Group Databasebeta

← #29677046

Subgroups — #29677046

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458414C211yesmaximal, characteristic, complemented
2#21458063C211yesmaximal, characteristic, complemented
3#21457419C211yesmaximal, characteristic, complemented
4#21445422C211yesmaximal, characteristic, complemented
5#21445363C211yesmaximal, characteristic, complemented
6#21445352C211yesmaximal, characteristic, complemented
7#21445316C211yesmaximal, characteristic, complemented
8#21445286C211yesmaximal, characteristic, complemented
9#21445046C211yesmaximal, characteristic, complemented
10#21444996C211yesmaximal, characteristic, complemented
11#21444970C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444704C211yesmaximal, characteristic, complemented
14#21444702C211yesmaximal, characteristic, complemented
15C61×#3330C211yesmaximal, characteristic, complemented
16C2×#14519802—21no—
17#16840477C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840158C2211yescharacteristic, complemented
20#16840136C2211yescharacteristic
21#16840114C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic
23#16840109C2211yescharacteristic
24#16840089—21no—
25#16840083—21no—
26#16840080—21no—
27#16840052C2211yescharacteristic
28#16840052C2211yescharacteristic, complemented
29#16840039C2211yescharacteristic
30#16840014—21no—
31#16840013—21no—
32#16840010—21no—
33#16839964C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839957C2211yescharacteristic
36#16839912—21no—
37#16839907—21no—
38#16839894—21no—
39C4×#11758199C2211yescharacteristic
40#16839841C2211yescharacteristic
41#16839840C2211yescharacteristic
42#16839840C2211yescharacteristic, complemented
43#16839802—21no—
44#16839765—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839508C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56C61×#547C2211yescharacteristic
57C61×#547C2211yescharacteristic, complemented
58C61×#487C2211yescharacteristic, complemented
59C61×#484—21no—
60C61×#474C2211yescharacteristic, complemented
61C61×#468—21no—
62C61×#461C2211yescharacteristic
63C61×#449—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic, complemented
66C61×#417—21no—
67C22×D244—21no—
68C2×D4×D61—21no—
69#14519802—44no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758199—21no—
74C2×#11758199—21no—
75C2×#11758199D411yescharacteristic
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758189—21no—
79#14519777C2311yescharacteristic
80#14519774C2311yescharacteristic
81#14519763—41no—
82#14519752—21no—
83#14519751—21no—
84#14519751—21no—
85#14519748—21no—
86#14519747—41no—
87C4×D244C2311yescharacteristic
88#14519736—21no—
89#14519735—21no—
90#14519710—21no—
91#14519710D411yescharacteristic
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519700—41no—
101#14519699—21no—
102#14519699—21no—
103#14519698—21no—
104#14519698—21no—
105#14519698D411yescharacteristic
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—41no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112C22⋊#92418—21no—
113#14519689—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×SD16×C61—21no—
119C2×D8×C61D411yescharacteristic
120C2×M16×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122C4⋊Q8×C61C2311yescharacteristic
123#123×C61—41no—
124#123×C61—41no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131C4×D4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134#107×C61—21no—
135#107×C61D411yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146#41×C61—42no—
147#41×C61—42no—
148#41×C61—81no—
149#41×C61—81no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×D4×C61—41no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C2×D4×C61C2×D411yescharacteristic
156C2×D4×C61C2×D411yescharacteristic
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C2×C22⋊D61—41no—
163C2×C22⋊D61—41no—
164D4×D61—42no—
165D4×D61—81no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244—42no—
170C2×D244—41no—
171C2×D244—81no—
172C2×D244C2×D411yescharacteristic
173C2×C4×D61—21no—
174C2×Dic122—21no—
175SD16×C61—81no—
176D8×C61—41no—
177M16×C61—81no—
178C2×C8×C61—21no—
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—41no—
186C4⋊C4×C61—41no—
187C4⋊C4×C61C2×D411yescharacteristic
188C4⋊C4×C61C2×D411yescharacteristic
189C4⋊C4×C61C2×D411yescharacteristic
190C22⋊C4×C61—21no—
191C22⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C22⋊C4×C61—41no—
194C22⋊C4×C61—41no—
195C42×C61C2411yescharacteristic
196C22⋊Dic61—41no—
197#11758201—42no—
198#11758201—42no—
199#11758201—81no—
200#11758199—22no—
201#11758199—42no—
202#11758199—81no—
203#11758198—21no—
204#11758198—41no—
205#11758198—41no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61C2×D411yescharacteristic
209C4×Dic61—41no—
210#11758194—42no—
211#11758194—42no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418C2×D411yescharacteristic
217C2×#92418C2×D411yescharacteristic
218#11758189—81no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C22×D61—21no—
223C22×D61—41no—
224C22×D61—82no—
225C22×D61—82no—
226C22×D61—161no—
227Q8×C61—41no—
228Q8×C61—41no—
229Q8×C61—41no—
230Q8×C61—41no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—21no—
237D4×C61—82no—
238D4×C61—82no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—82no—
251C2×C4×C61—82no—
252C2×C4×C61C22×D411yescharacteristic
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C22⋊D61—82no—
256C22⋊D61—161no—
257C2×Dic61—21no—
258C2×Dic61—41no—
259D244—21no—
260D244—21no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—41no—
265D244—81no—
266D244—82no—
267C4×D61—41no—
268C4×D61—41no—
269Dic122—81no—
270C8×C61—21no—
271C8×C61—21no—
272C8×C61—41no—
273#92418—21no—
274#92418—41no—
275#92418—41no—
276#92418—41no—
277#92418—41no—
278#92418AGL(1,ℤ/8)12yes—
279#20301—611nomaximal, Sylow
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—41no—
288C22×C61—41no—
289C22×C61D4211yescharacteristic
290C2×D61—41no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—164no—
297C4×C61—21no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—41no—
301C4×C61—81no—
302C4×C61—81no—
303C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C61#57511yescharacteristic
305C4×C61#57611yescharacteristic
306C4×C61#57711yescharacteristic
307Dic61—41no—
308Dic61—81no—
309#3354—611no—
310#3330D6111yescharacteristic, complemented
311#3325—611no—
312#3272—611no—
313#1708—611no—
314#1699—611no—
315#1697—611no—
316#1691—611no—
317#1685—611no—
318#1646—611no—
319#1639—611no—
320#1635—611no—
321#1625—611no—
322#1589—611no—
323#1589—611no—
324C2×C61—81no—
325C2×C61—81no—
326C2×C61—81no—
327C2×C61#327211yescharacteristic
328C2×C61#327311yescharacteristic
329C2×C61#329011yescharacteristic
330D61—81no—
331D61—161no—
332C2×AGL(1,ℤ/8)—1221no—
333#555—611no—
334#547C2×D6111yescharacteristic
335#547C2×D6111yescharacteristic, complemented
336D42—611no—
337#498—611no—
338#492—611no—
339#487—611no—
340#487C2×D6111yescharacteristic, complemented
341#486—611no—
342#486—611no—
343#484—21no—
344#482—1221no—
345#482—1221no—
346#481—1221no—
347#476—611no—
348#476—611no—
349#474—611no—
350#474C2×D6111yescharacteristic, complemented
351#469—1221no—
352#469—1221no—
353#468—21no—
354#468—1221no—
355#461—611no—
356#461C2×D6111yescharacteristic
357#459—611no—
358#459—611no—
359#450—1221no—
360#449—21no—
361#449—1221no—
362#447—1221no—
363C4×D8—611no—
364C4×D8C2×D6111yescharacteristic
365#436—611no—
366#436—611no—
367#436—611no—
368#436C2×D6111yescharacteristic, complemented
369#428—1221no—
370#418—1221no—
371#417—21no—
372#335—611no—
373#335—611no—
374#333—611no—
375#332—611no—
376#332—611no—
377#331—611no—
378D4⋊C8—611no—
379D4⋊C8—611no—
380D4⋊C8—611no—
381D4⋊C8—611no—
382C82—611no—
383C61#2030111yescharacteristic, complemented, Sylow
384C2×#41—21no—
385C2×#41—21no—
386C22×D4—1221no—
387C22×D4—1221no—
388AGL(1,ℤ/8)—2444no—
389C2×SD16—21no—
390C2×SD16—1221no—
391C2×SD16—1221no—
392C2×SD16—1221no—
393C2×D8—611no—
394C2×D8—1221no—
395C2×D8—1221no—
396C2×D8C22⋊D6111yescharacteristic
397C2×M16—21no—
398C2×M16—1221no—
399C2×M16—1221no—
400C2×M16—1221no—
401C4⋊Q8—611no—
402C4⋊Q8C22×D6111yescharacteristic
403C4⋊Q8C22×D6111yescharacteristic
404#127—611no—
405#124—2441no—
406#123—41no—
407#123—41no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410#121—21no—
411#121—21no—
412#121—1221no—
413#121—1221no—
414#121—1221no—
415#121—1221no—
416#120—2441no—
417C4×D4—611no—
418C4×D4C22×D6111yescharacteristic
419C4×D4C22×D6111yescharacteristic
420C4×D4C22×D6111yescharacteristic
421#117—1221no—
422#117—1221no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425#107—21no—
426#107—611no—
427#107—1221no—
428#107C22⋊D6111yescharacteristic
429#106—1221no—
430#106—1221no—
431#106—1221no—
432#106—1221no—
433C4⋊C8—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8C22×D6111yescharacteristic
437#103—21no—
438#103—21no—
439#103—21no—
440#103—1221no—
441#103—2441no—
442#102—21no—
443#102—611no—
444#102—611no—
445#102—1221no—
446#102—1221no—
447#102—1221no—
448#102—1221no—
449#102—1221no—
450#102—1221no—
451#102—1221no—
452#102—2441no—
453#102C22⋊D6111yescharacteristic
454#102C22⋊D6111yescharacteristic
455C22⋊C8—21no—
456C22⋊C8—1221no—
457C22⋊C8—1221no—
458C22⋊C8—1221no—
459C4×C8—611no—
460C4×C8—611no—
461C4×C8C22×D6111yescharacteristic
462C24—2441no—
463#41—42no—
464#41—42no—
465#41—81no—
466#41—81no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—1221no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—611no—
473C2×D4—1221no—
474C2×D4—1221no—
475C2×D4—1221no—
476C2×D4—4881no—
477C2×D4—4881no—
478C2×D4—2441no—
479C2×D4—2442no—
480C2×D4—2441no—
481C2×D4—2442no—
482C2×D4—2441no—
483C2×D4D4×D6111yescharacteristic
484C2×D4C2×C22⋊D6111yescharacteristic
485C2×D4C2×C22⋊D6111yescharacteristic
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—1221no—
492SD16—81no—
493SD16—4881no—
494SD16—2442no—
495SD16—2442no—
496D8—41no—
497D8—1222no—
498D8—4881no—
499D8—2442no—
500M16—81no—
501M16—4881no—
502M16—2442no—
503M16—2442no—
504C2×C8—21no—
505C2×C8—611no—
506C2×C8—611no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8C2×C22⋊D6111yescharacteristic
512C2×C8C2×C22⋊D6111yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—611no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4D4×D6111yescharacteristic
523C4⋊C4C2×C22⋊D6111yescharacteristic
524C4⋊C4C2×C22⋊D6111yescharacteristic
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—1221no—
531C22⋊C4—2441no—
532C22⋊C4—2441no—
533C22⋊C4—2441no—
534C42—2441no—
535C42C23×D6111yescharacteristic
536C23—21no—
537C23—21no—
538C23—21no—
539C23—1221no—
540C23—9761no—
541C23—4882no—
542C23—4882no—
543C23—2441no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—4881no—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—82no—
556D4—82no—
557D4—1221no—
558D4—1221no—
559D4—9761no—
560D4—4881no—
561D4—4882no—
562D4—4882no—
563D4—2441no—
564D4—2441no—
565D4—2441no—
566D4—2441no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—1221no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4C22×C22⋊D6111yescharacteristic
586C2×C4#1451982211yescharacteristic
587C8—21no—
588C8—21no—
589C8—41no—
590C8—612no—
591C8—1221no—
592C8—2441no—
593C8—2441no—
594C8—2441no—
595C8—2441no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—9764no—
606C22—4881no—
607C22—4881no—
608C22—4881no—
609C22—2441no—
610C22—2441no—
611C22—2441no—
612C22D4×C22⋊D6111yescharacteristic
613C4—21no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—81no—
618C4—81no—
619C4—4881no—
620C4—2441no—
621C4AGL(1,ℤ/8)×D6111yescharacteristic
622C4#1684056011yescharacteristic
623C4#1684056511yescharacteristic
624C4#1684057211yescharacteristic
625C2—81no—
626C2—81no—
627C2—81no—
628C2—9761no—
629C2—4881no—
630C2#2145741311yescharacteristic
631C2#2145742611yescharacteristic
632C2#2145760511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3330C2
socleC22×C61D42
hypercenter#3330D61
hypocenterC61#20301
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3330

Complements

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

NH ≅ G/Ntype
1. #21458414C2semidirect
2. #21458063C2semidirect
3. #21457419C2semidirect
4. #21445422C2semidirect
5. #21445363C2semidirect
6. #21445352C2semidirect
7. #21445316C2semidirect
8. #21445286C2semidirect
9. #21445046C2semidirect
10. #21444996C2semidirect
11. #21444970C2semidirect
12. #21444908C2semidirect
13. #21444704C2semidirect
14. #21444702C2semidirect
15. C61×#3330C2semidirect
19. #16840158C22semidirect
21. #16840114C22semidirect
28. #16840052C22semidirect
42. #16839840C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839508C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
57. C61×#547C22semidirect
58. C61×#487C22semidirect
60. C61×#474C22semidirect
65. C61×#436C22semidirect
310. #3330D61semidirect
335. #547C2×D61semidirect
340. #487C2×D61semidirect
350. #474C2×D61semidirect
368. #436C2×D61semidirect
383. C61#20301semidirect

Maximal subgroups

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

subgroupindex
#214584142
#214580632
#214574192
#214454222
#214453632
#214453522
#214453162
#214452862
#214450462
#214449962
#214449702
#214449082
#214447042
#214447022
C61×#33302
#2030161