Finite Group Databasebeta

← #29665119

Subgroups — #29665119

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456834C211yesmaximal, characteristic
2#21456195C211yesmaximal, characteristic, complemented
3#21454824C211yesmaximal, characteristic, complemented
4#21445389C211yesmaximal, characteristic, complemented
5#21445382C211yesmaximal, characteristic, complemented
6#21445361C211yesmaximal, characteristic, complemented
7#21445354C211yesmaximal, characteristic, complemented
8#21445265C211yesmaximal, characteristic, complemented
9#21445258C211yesmaximal, characteristic, complemented
10#21445237C211yesmaximal, characteristic, complemented
11#21445230C211yesmaximal, characteristic, complemented
12#21444584C211yesmaximal, characteristic, complemented
13#21444529C211yesmaximal, characteristic, complemented
14#21444488C211yesmaximal, characteristic, complemented
15C61×#3252C211yesmaximal, characteristic, complemented
16C2×#14519774C2211yescharacteristic
17#16840152—21no—
18#16840128—21no—
19#16840128—21no—
20#16840128—21no—
21#16840110C2211yescharacteristic
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840110C2211yescharacteristic
25#16839962C2211yescharacteristic
26#16839962C2211yescharacteristic
27#16839957C2211yescharacteristic
28#16839957C2211yescharacteristic
29#16839912—21no—
30#16839895—21no—
31#16839893C2211yescharacteristic, complemented
32Q8×#92418C2211yescharacteristic, complemented
33#16839840—21no—
34#16839840C2211yescharacteristic, complemented
35#16839834—21no—
36D4×#92418C2211yescharacteristic, complemented
37#16839823—21no—
38#16839819C2211yescharacteristic
39#16839815C2211yescharacteristic
40#16839766—21no—
41#16839766—21no—
42#16839718—21no—
43C4×#11758194C2211yescharacteristic
44#16839514C2211yescharacteristic, complemented
45#16839514C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839512C2211yescharacteristic, complemented
48#16839511C2211yescharacteristic, complemented
49#16839511C2211yescharacteristic, complemented
50#16839508C2211yescharacteristic, complemented
51#16839508C2211yescharacteristic, complemented
52#16839505C2211yescharacteristic
53#16839505C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#529C2211yescharacteristic
58C61×#479—21no—
59C61×#477C2211yescharacteristic, complemented
60C61×#476C2211yescharacteristic, complemented
61C61×#470—21no—
62C61×#468—21no—
63C61×#464—21no—
64C61×#462C2211yescharacteristic, complemented
65C61×#461C2211yescharacteristic, complemented
66C61×#423C2211yescharacteristic
67C22×D244—21no—
68C22×D244—21no—
69C22×D244—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758199—21no—
73C2×#11758199—21no—
74C2×#11758194—21no—
75C2×#11758194D411yescharacteristic
76C2×#11758194D411yescharacteristic
77C22×#92418—21no—
78#14519774—21no—
79#14519774—21no—
80#14519774—21no—
81#14519774C2311yescharacteristic
82#14519774C2311yescharacteristic
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85C4⋊#92418C2311yescharacteristic
86C4⋊#92418C2311yescharacteristic
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89#14519697—21no—
90#14519697—21no—
91#14519697—21no—
92#14519697—21no—
93#14519697—21no—
94#14519697—21no—
95#14519697—21no—
96#14519697—21no—
97#14519697—21no—
98#14519697—21no—
99#14519697—21no—
100#14519697—21no—
101C22⋊#92418—21no—
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105#14519688—21no—
106#14519688—21no—
107#14519688D411yescharacteristic
108#14519688D411yescharacteristic
109C4×#92418—21no—
110C4×#92418—21no—
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C2×Q16×C61—21no—
114C2×SD16×C61—21no—
115C2×M16×C61—21no—
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118#126×C61—21no—
119#125×C61—21no—
120#125×C61D411yescharacteristic
121#124×C61D411yescharacteristic
122#123×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61D411yescharacteristic
126#121×C61D411yescharacteristic
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#117×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142#103×C61—21no—
143#102×C61—21no—
144C23×D61—41no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61C2×D411yescharacteristic
150C22×C4×C61—21no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C2×D244—21no—
155C2×D244—21no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244—21no—
160C2×D244—42no—
161C2×D244—42no—
162C2×D244—41no—
163C2×D244—41no—
164C2×D244—41no—
165C2×D244—81no—
166C2×D244—81no—
167C2×D244—82no—
168Q16×C61—81no—
169SD16×C61—81no—
170M16×C61—81no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—41no—
182C4⋊C4×C61—41no—
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—21no—
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—41no—
191C42×C61—21no—
192C42×C61—41no—
193C42×C61C2×D411yescharacteristic
194C42×C61C2×D411yescharacteristic
195C42×C61#4111yescharacteristic
196C42×C61C2411yescharacteristic
197#11758201—81no—
198#11758201—81no—
199#11758199—81no—
200#11758199—81no—
201#11758194—41no—
202#11758194—41no—
203#11758194—42no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—42no—
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C2×#92418C2×D411yescharacteristic
213C23×C61—21no—
214C23×C61#12111yescharacteristic
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—82no—
218C22×D61—82no—
219C22×D61—82no—
220Q8×C61—21no—
221Q8×C61—21no—
222Q8×C61—41no—
223Q8×C61—41no—
224Q8×C61—81no—
225D4×C61—21no—
226D4×C61—21no—
227D4×C61—81no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250D244—41no—
251D244—41no—
252D244—41no—
253D244—41no—
254D244—81no—
255D244—81no—
256D244—82no—
257D244—82no—
258D244—82no—
259C8×C61—41no—
260C8×C61—41no—
261#92418—21no—
262#92418—21no—
263#92418—21no—
264#92418—21no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#19380—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61C2×#12111yescharacteristic
277C2×D61—81no—
278C2×D61—81no—
279C2×D61—81no—
280C2×D61—81no—
281C2×D61—81no—
282C2×D61—81no—
283C2×D61—164no—
284C4×C61—21no—
285C4×C61—21no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—41no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—81no—
292C4×C61—81no—
293C4×C61#57511yescharacteristic
294C4×C61#57511yescharacteristic
295C4×C61#57611yescharacteristic
296C4×C61#57711yescharacteristic
297#3252D6111yescharacteristic, complemented
298#3217—611no—
299#3138—611no—
300#2969—611no—
301#1702—611no—
302#1701—611no—
303#1698—611no—
304#1697—611no—
305#1682—611no—
306#1681—611no—
307#1678—611no—
308#1677—611no—
309#1569—611no—
310#1554—611no—
311#1545—611no—
312C2×C61—41no—
313C2×C61—81no—
314C2×C61#304011yescharacteristic
315C2×C61#306211yescharacteristic
316C2×C61#306811yescharacteristic
317D61—161no—
318D61—161no—
319#533C2×D6111yescharacteristic
320C2×#127—611no—
321#529C2×D6111yescharacteristic
322#496—1221no—
323#490—1221no—
324#490—1221no—
325#490—1221no—
326#486—611no—
327#486—611no—
328#486—611no—
329#486—611no—
330#479—21no—
331#477C2×D6111yescharacteristic, complemented
332#476C2×D6111yescharacteristic, complemented
333#470—21no—
334#468—21no—
335#464—21no—
336#462C2×D6111yescharacteristic, complemented
337#461C2×D6111yescharacteristic, complemented
338#460—611no—
339#460—611no—
340#459—611no—
341#459—611no—
342#450—1221no—
343#447—1221no—
344#446—611no—
345C8×Q8—611no—
346#436—611no—
347#436—1221no—
348#435—1221no—
349C8×D4—611no—
350#433—1221no—
351#432—611no—
352#431—611no—
353#423C2×D6111yescharacteristic
354#418—1221no—
355#418—1221no—
356#405—1221no—
357C4×M16—611no—
358#335—611no—
359#335—611no—
360#334—611no—
361#334—611no—
362#333—611no—
363#333—611no—
364#332—611no—
365#332—611no—
366#331—611no—
367#331—611no—
368#331—611no—
369#331—611no—
370C61#1938011yescharacteristic, complemented, Sylow
371C22×D4—1221no—
372C22×D4—1221no—
373C22×D4—1221no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—1221no—
377C2×SD16—1221no—
378C2×D8—1221no—
379C2×D8—1221no—
380C2×M16—21no—
381C2×M16—611no—
382C2×M16—611no—
383C2×M16—1221no—
384C22×C8—1221no—
385C4⋊Q8C22×D6111yescharacteristic
386C4⋊Q8C22×D6111yescharacteristic
387#127—611no—
388#127—611no—
389#127—1221no—
390#127—1221no—
391#127—1221no—
392#126—21no—
393#125—21no—
394#125C22⋊D6111yescharacteristic
395#124C22⋊D6111yescharacteristic
396#123—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8C22⋊D6111yescharacteristic
400#121C22⋊D6111yescharacteristic
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8C22×D6111yescharacteristic
404C4×D4—21no—
405C4×D4C22×D6111yescharacteristic
406#117—21no—
407#117—21no—
408C2×C42C22×D6111yescharacteristic
409#107—21no—
410#106—21no—
411C4⋊C8—21no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8C22×D6111yescharacteristic
419C4⋊C8C22×D6111yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431#102—1221no—
432#102—1221no—
433#102—1221no—
434#102—1221no—
435#102—1221no—
436C22⋊C8—1221no—
437C22⋊C8—1221no—
438C22⋊C8—1221no—
439C22⋊C8—1221no—
440#97—611no—
441#97—611no—
442#97—1221no—
443#97—1221no—
444C4×C8—611no—
445C4×C8—611no—
446C4×C8—1221no—
447C4×C8—1221no—
448C24—2441no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×C22⋊D6111yescharacteristic
452C2×D4—21no—
453C2×D4—1221no—
454C2×D4—1221no—
455C2×D4—1221no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—4881no—
460C2×D4—4881no—
461C2×D4—4882no—
462C2×D4—2442no—
463C2×D4—2442no—
464C2×D4—2441no—
465C2×D4—2441no—
466C2×D4—2441no—
467C2×D4C2×C22⋊D6111yescharacteristic
468C22×C4—21no—
469C22×C4D4×D6111yescharacteristic
470C22×C4#1175822411yescharacteristic
471C22×C4C2×C22⋊D6111yescharacteristic
472Q16—81no—
473SD16—81no—
474SD16—4881no—
475SD16—4881no—
476D8—4881no—
477D8—4881no—
478M16—81no—
479M16—2441no—
480M16—2441no—
481M16—2442no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—611no—
485C2×C8—611no—
486C2×C8—611no—
487C2×C8—611no—
488C2×C8—1221no—
489C2×C8—1221no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—2442no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×C22⋊D6111yescharacteristic
504C4⋊C4C2×C22⋊D6111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C42—21no—
512C42—41no—
513C42D4×D6111yescharacteristic
514C42#1175822411yescharacteristic
515C42C2×C22⋊D6111yescharacteristic
516C42C23×D6111yescharacteristic
517C23—21no—
518C23—4882no—
519C23—4882no—
520C23—4882no—
521C23—2441no—
522C23—2441no—
523C23#1451974911yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—81no—
532D4—4881no—
533D4—4881no—
534D4—4882no—
535D4—4882no—
536D4—4882no—
537D4—2441no—
538D4—2441no—
539D4—2441no—
540D4—2441no—
541D4—2441no—
542D4—2441no—
543D4—2441no—
544D4—2441no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4#1451974911yescharacteristic
558C2×C4#1451974911yescharacteristic
559C2×C4#1451974911yescharacteristic
560C2×C4C2×D4×D6111yescharacteristic
561C2×C4C22×C22⋊D6111yescharacteristic
562C2×C4C2×#1175822411yescharacteristic
563C8—41no—
564C8—41no—
565C8—1221no—
566C8—1221no—
567C8—1221no—
568C8—1221no—
569C8—2441no—
570C8—2441no—
571C8—2441no—
572C8—2441no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—9764no—
580C22—4881no—
581C22—4881no—
582C22—4881no—
583C22—4881no—
584C22—4881no—
585C22—4881no—
586C22C2×#1451974911yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#1684056111yescharacteristic
597C4#1684056111yescharacteristic
598C4#1684056511yescharacteristic
599C4#1684057011yescharacteristic
600C2—41no—
601C2—81no—
602C2—9761no—
603C2—9761no—
604C2#2145531511yescharacteristic
605C2#2145550111yescharacteristic
606C2#2145554911yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3252C2
socleC22×C61C2×#121
prime radical#21456834C2
hypercenter#3252D61
hypocenterC61#19380
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #21456195C2semidirect
3. #21454824C2semidirect
4. #21445389C2semidirect
5. #21445382C2semidirect
6. #21445361C2semidirect
7. #21445354C2semidirect
8. #21445265C2semidirect
9. #21445258C2semidirect
10. #21445237C2semidirect
11. #21445230C2semidirect
12. #21444584C2semidirect
13. #21444529C2semidirect
14. #21444488C2semidirect
15. C61×#3252C2semidirect
31. #16839893C22semidirect
32. Q8×#92418C22semidirect
34. #16839840C22semidirect
36. D4×#92418C22semidirect
44. #16839514C22semidirect
45. #16839514C22semidirect
46. #16839512C22semidirect
47. #16839512C22semidirect
48. #16839511C22semidirect
49. #16839511C22semidirect
50. #16839508C22semidirect
51. #16839508C22semidirect
59. C61×#477C22semidirect
60. C61×#476C22semidirect
64. C61×#462C22semidirect
65. C61×#461C22semidirect
297. #3252D61semidirect
331. #477C2×D61semidirect
332. #476C2×D61semidirect
336. #462C2×D61semidirect
337. #461C2×D61semidirect
370. C61#19380semidirect

Maximal subgroups

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

subgroupindex
#214568342
#214561952
#214548242
#214453892
#214453822
#214453612
#214453542
#214452652
#214452582
#214452372
#214452302
#214445842
#214445292
#214444882
C61×#32522
#1938061