Finite Group Databasebeta

← #29677053

Subgroups — #29677053

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#21458124C211yesmaximal, characteristic, complemented
2#21458055C211yesmaximal, characteristic, complemented
3#21457420C211yesmaximal, characteristic, complemented
4#21445421C211yesmaximal, characteristic, complemented
5#21445364C211yesmaximal, characteristic, complemented
6#21445354C211yesmaximal, characteristic, complemented
7#21445315C211yesmaximal, characteristic, complemented
8#21445284C211yesmaximal, characteristic, complemented
9#21445047C211yesmaximal, characteristic, complemented
10#21444997C211yesmaximal, characteristic, complemented
11#21444968C211yesmaximal, characteristic, complemented
12#21444908C211yesmaximal, characteristic, complemented
13#21444704C211yesmaximal, characteristic, complemented
14#21444702C211yesmaximal, characteristic, complemented
15C61×#3354C211yesmaximal, characteristic, complemented
16C2×#14519801—21no—
17#16840416C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840135C2211yescharacteristic
20#16840112C2211yescharacteristic, complemented
21#16840112C2211yescharacteristic, complemented
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840095—21no—
25#16840086—21no—
26#16840049C2211yescharacteristic
27#16840042C2211yescharacteristic, complemented
28#16840013—21no—
29#16840010—21no—
30#16840009—21no—
31#16839967C2211yescharacteristic
32#16839964C2211yescharacteristic
33#16839957C2211yescharacteristic
34#16839957C2211yescharacteristic
35#16839914—21no—
36#16839908—21no—
37#16839907—21no—
38#16839895—21no—
39C4×#11758199C2211yescharacteristic
40#16839841C2211yescharacteristic
41#16839840C2211yescharacteristic
42#16839840C2211yescharacteristic, complemented
43#16839766—21no—
44#16839763—21no—
45#16839515C2211yescharacteristic, complemented
46#16839514C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839509C2211yescharacteristic, complemented
49#16839508C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic, complemented
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56C61×#555C2211yescharacteristic
57C61×#547C2211yescharacteristic, complemented
58C61×#498C2211yescharacteristic, complemented
59C61×#482—21no—
60C61×#481—21no—
61C61×#476C2211yescharacteristic, complemented
62C61×#474C2211yescharacteristic
63C61×#469—21no—
64C4×D8×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic, complemented
66C61×#428—21no—
67C2×#11758224—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70#14519801—44no—
71C2×#11758190—21no—
72C2×#11758190—21no—
73C2×#11758200—21no—
74C2×#11758201—21no—
75C2×#11758199—21no—
76C2×#11758199—21no—
77C2×#11758199D411yescharacteristic
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758189—21no—
81#14519777C2311yescharacteristic
82#14519774C2311yescharacteristic
83#14519761—41no—
84#14519757—21no—
85#14519752—21no—
86#14519751—21no—
87#14519751—21no—
88#14519747—41no—
89C4×D244C2311yescharacteristic
90C2×C4⋊Dic61—21no—
91#14519710—21no—
92#14519710D411yescharacteristic
93#14519708—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—41no—
101#14519700—21no—
102#14519698—21no—
103#14519698D411yescharacteristic
104#14519697—21no—
105#14519697—21no—
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×D8×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#124×C61—41no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124#121×C61—21no—
125#121×C61—21no—
126#121×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61D411yescharacteristic
135#106×C61—21no—
136#106×C61—21no—
137#106×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139#102×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—81no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×D4×C61—41no—
151C2×D4×C61—41no—
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C22×Dic61—41no—
162#11758224—42no—
163#11758224—81no—
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—
175D8×C61—22no—
176M16×C61—42no—
177C2×C8×C61—21no—
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—41no—
185C4⋊C4×C61C2×D411yescharacteristic
186C4⋊C4×C61C2×D411yescharacteristic
187C4⋊C4×C61C2×D411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C22⋊C4×C61—41no—
192C22⋊C4×C61—41no—
193C22⋊C4×C61—41no—
194C42×C61—41no—
195C42×C61C2411yescharacteristic
196#11758201—81no—
197#11758200—42no—
198#11758199—41no—
199#11758199—42no—
200#11758199—81no—
201#11758198—21no—
202#11758198—41no—
203#11758198—41no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—41no—
207C4⋊Dic61C2×D411yescharacteristic
208#11758194—81no—
209#11758194—81no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418C2×D411yescharacteristic
215C2×#92418C2×D411yescharacteristic
216#11758190—42no—
217#11758190—81no—
218#11758189—42no—
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—81no—
230D4×C61—21no—
231D4×C61—21no—
232D4×C61—21no—
233D4×C61—21no—
234D4×C61—21no—
235D4×C61—21no—
236D4×C61—82no—
237D4×C61—161no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—41no—
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—82no—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C2×C4×C61H(5,𝔽2)11yescharacteristic
253C22⋊D61—82no—
254C22⋊D61—82no—
255C2×Dic61—21no—
256C2×Dic61—41no—
257C2×Dic61—82no—
258D244—21no—
259D244—21no—
260D244—41no—
261D244—41no—
262D244—41no—
263D244—41no—
264D244—81no—
265D244—82no—
266C4×D61—41no—
267C4×D61—41no—
268Dic122—41no—
269Dic122—41no—
270C8×C61—21no—
271C8×C61—41no—
272C8×C61AGL(1,ℤ/8)12yes—
273#92418—21no—
274#92418—21no—
275#92418—41no—
276#92418—41no—
277#92418—41no—
278#92418—41no—
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#3354D6111yescharacteristic, complemented
310#3330—611no—
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#555C2×D6111yescharacteristic
334#547—611no—
335#547C2×D6111yescharacteristic, complemented
336D42—611no—
337#498C2×D6111yescharacteristic, complemented
338#492—611no—
339#487—611no—
340#487—611no—
341#486—611no—
342#486—611no—
343#484—1221no—
344#482—21no—
345#482—1221no—
346#481—21no—
347#476—611no—
348#476C2×D6111yescharacteristic, complemented
349#474—611no—
350#474C2×D6111yescharacteristic
351#469—21no—
352#469—1221no—
353#468—1221no—
354#468—1221no—
355#461—611no—
356#461—611no—
357#459—611no—
358#459—611no—
359#450—1221no—
360#449—1221no—
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—21no—
370#418—1221no—
371#417—1221no—
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—1221no—
386C22×D4—1221no—
387C22×D4—1221no—
388AGL(1,ℤ/8)—2444no—
389C2×SD16—1221no—
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—41no—
406#123—41no—
407#123—2441no—
408C22⋊Q8—21no—
409C22⋊Q8—1221no—
410#121—21no—
411#121—21no—
412#121—21no—
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—21no—
422#117—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—1221no—
425#107—21no—
426#107—611no—
427#107—1221no—
428#107C22⋊D6111yescharacteristic
429#106—21no—
430#106—21no—
431#106—21no—
432#106—1221no—
433C4⋊C8—611no—
434C4⋊C8—611no—
435C4⋊C8—611no—
436C4⋊C8C22×D6111yescharacteristic
437#103—1221no—
438#103—1221no—
439#103—1221no—
440#103—1221no—
441#103—2441no—
442#102—21no—
443#102—21no—
444#102—611no—
445#102—611no—
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—81no—
465#41—4881no—
466#41—2442no—
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—1221no—
491C22×C4—2441no—
492SD16—4881no—
493SD16—4881no—
494SD16—2442no—
495SD16—2442no—
496D8—22no—
497D8—4881no—
498D8—2441no—
499D8—2442no—
500M16—42no—
501M16—4881no—
502M16—4881no—
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—611no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—2441no—
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—41no—
531C22⋊C4—1221no—
532C22⋊C4—2441no—
533C22⋊C4—2441no—
534C42—41no—
535C42C23×D6111yescharacteristic
536C23—21no—
537C23—21no—
538C23—21no—
539C23—1221no—
540C23—9761no—
541C23—4882no—
542C23—4882no—
543C23—2441no—
544Q8—41no—
545Q8—41no—
546Q8—81no—
547Q8—2441no—
548Q8—2441no—
549D4—21no—
550D4—21no—
551D4—21no—
552D4—21no—
553D4—21no—
554D4—21no—
555D4—82no—
556D4—161no—
557D4—1221no—
558D4—1221no—
559D4—4881no—
560D4—4882no—
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—1221no—
580C2×C4—4882no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4C2×D4×D6111yescharacteristic
585C2×C4C22×C22⋊D6111yescharacteristic
586C2×C4#1451982211yescharacteristic
587C8—21no—
588C8—41no—
589C8—1221no—
590C8—1221no—
591C8—2441no—
592C8—2441no—
593C8—2441no—
594C8—2441no—
595C8#1451980212yes—
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—
621C4C2×#1451980211yescharacteristic
622C4#1684055811yescharacteristic
623C4#1684056611yescharacteristic
624C4#1684057011yescharacteristic
625C2—81no—
626C2—81no—
627C2—81no—
628C2—9761no—
629C2—4881no—
630C2#2145741911yescharacteristic
631C2#2145742411yescharacteristic
632C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3354C2
socleC22×C61D42
hypercenter#3354D61
hypocenterC61#20301
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3354

Complements

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

NH ≅ G/Ntype
1. #21458124C2semidirect
2. #21458055C2semidirect
3. #21457420C2semidirect
4. #21445421C2semidirect
5. #21445364C2semidirect
6. #21445354C2semidirect
7. #21445315C2semidirect
8. #21445284C2semidirect
9. #21445047C2semidirect
10. #21444997C2semidirect
11. #21444968C2semidirect
12. #21444908C2semidirect
13. #21444704C2semidirect
14. #21444702C2semidirect
15. C61×#3354C2semidirect
20. #16840112C22semidirect
21. #16840112C22semidirect
27. #16840042C22semidirect
42. #16839840C22semidirect
45. #16839515C22semidirect
46. #16839514C22semidirect
47. #16839511C22semidirect
48. #16839509C22semidirect
49. #16839508C22semidirect
52. D4⋊#92418C22semidirect
53. D4⋊#92418C22semidirect
55. C8×#92418C22semidirect
57. C61×#547C22semidirect
58. C61×#498C22semidirect
61. C61×#476C22semidirect
65. C61×#436C22semidirect
309. #3354D61semidirect
335. #547C2×D61semidirect
337. #498C2×D61semidirect
348. #476C2×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
#214581242
#214580552
#214574202
#214454212
#214453642
#214453542
#214453152
#214452842
#214450472
#214449972
#214449682
#214449082
#214447042
#214447022
C61×#33542
#2030161