Finite Group Databasebeta

← #29671396

Subgroups — #29671396

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458490C211yesmaximal, characteristic, complemented
2#21457637C211yesmaximal, characteristic, complemented
3#21457440C211yesmaximal, characteristic
4#21445412C211yesmaximal, characteristic, complemented
5#21445339C211yesmaximal, characteristic, complemented
6#21445303C211yesmaximal, characteristic, complemented
7#21445237C211yesmaximal, characteristic, complemented
8#21445230C211yesmaximal, characteristic, complemented
9#21444944C211yesmaximal, characteristic, complemented
10#21444934C211yesmaximal, characteristic, complemented
11#21444897C211yesmaximal, characteristic, complemented
12#21444891C211yesmaximal, characteristic, complemented
13#21444709C211yesmaximal, characteristic, complemented
14SD16×#92418C211yesmaximal, characteristic, complemented
15C61×#3385C211yesmaximal, characteristic, complemented
16C2×#14519804—21no—
17#16840434C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840139C2211yescharacteristic
20#16840136C2211yescharacteristic
21#16840136C2211yescharacteristic, complemented
22#16840110—21no—
23#16840110C2211yescharacteristic
24#16840110C2211yescharacteristic, complemented
25#16840080—21no—
26#16840049—21no—
27#16840049C2211yescharacteristic
28#16840049C2211yescharacteristic
29#16840016—21no—
30#16839993—21no—
31#16839962—21no—
32#16839962C2211yescharacteristic
33#16839962C2211yescharacteristic
34#16839962C2211yescharacteristic, complemented
35#16839957C2211yescharacteristic
36#16839912—21no—
37#16839910—21no—
38#16839897—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758201—21no—
41C4×#11758201C2211yescharacteristic
42#16839841C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44C2×#14519697—21no—
45#16839513C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839511C2211yescharacteristic, complemented
48#16839511C2211yescharacteristic, complemented
49#16839505C2211yescharacteristic
50#16839505C2211yescharacteristic, complemented
51Q8⋊#92418C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic, complemented
56Q82×C61C2211yescharacteristic, complemented
57C61×#554C2211yescharacteristic
58C61×#501—21no—
59C61×#500C2211yescharacteristic, complemented
60C61×#479—21no—
61C61×#477C2211yescharacteristic, complemented
62C61×#476C2211yescharacteristic
63C61×#474—21no—
64C61×#446C2211yescharacteristic, complemented
65C61×#440—21no—
66C4×SD16×C61C2211yescharacteristic
67C2×#11758226—21no—
68C22×D244—21no—
69C2×D4×D61—21no—
70#14519804—44no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758201—41no—
75C2×#11758201—41no—
76C2×#11758201D411yescharacteristic
77C2×D488—21no—
78C2×D488—21no—
79C2×#11758199—21no—
80C2×#11758189—21no—
81C22×#92418—21no—
82#14519774—21no—
83#14519774C2311yescharacteristic
84#14519774C2311yescharacteristic
85#14519752—21no—
86#14519752—21no—
87#14519752—41no—
88#14519751—21no—
89#14519747—41no—
90C4×D244—21no—
91C4×D244C2311yescharacteristic
92#14519708—21no—
93#14519708—21no—
94#14519708D411yescharacteristic
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701D411yescharacteristic
100#14519697—21no—
101#14519697—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107#14519697—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×SD16×C61D411yescharacteristic
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61—21no—
119C4⋊Q8×C61—41no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—21no—
130C4×D4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134#107×C61—21no—
135#106×C61—21no—
136#106×C61D411yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#97×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154C2×C22⋊D61—41no—
155#11758226—42no—
156#11758226—81no—
157D4×D61—42no—
158D4×D61—81no—
159C2×D244—21no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—42no—
166C2×D244—41no—
167C2×D244—41no—
168C2×D244—41no—
169C2×D244—81no—
170C2×D244C2×D411yescharacteristic
171C2×C4×D61—21no—
172C2×C4×D61—41no—
173SD16×C61SD1614yescomplemented
174C2×C8×C61—21no—
175C2×C8×C61C2×D411yescharacteristic
176C2×C8×C61C2×D411yescharacteristic
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—41no—
184C4⋊C4×C61—41no—
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—41no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—41no—
195C42×C61C2411yescharacteristic
196#11758201—41no—
197#11758201—42no—
198#11758201—42no—
199#11758201—82no—
200#11758201—82no—
201#11758201—81no—
202#11758199—42no—
203#11758198—21no—
204#11758198—41no—
205#11758198—41no—
206C4⋊Dic61C2×D411yescharacteristic
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—81no—
212C2×#92418C2×D411yescharacteristic
213C2×#92418C2×D411yescharacteristic
214D488—42no—
215D488—81no—
216#11758189—42no—
217C23×C61—21no—
218C22×D61—21no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—82no—
222C22×D61—82no—
223C22×D61—161no—
224Q8×C61—21no—
225Q8×C61—21no—
226Q8×C61—21no—
227Q8×C61—81no—
228Q8×C61—81no—
229Q8×C61—161no—
230Q8×C61C2×SD1612yes—
231D4×C61—21no—
232D4×C61C2×SD1612yes—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—161no—
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61H(5,𝔽2)11yescharacteristic
246C22⋊D61—82no—
247C2×Dic61—21no—
248D244—21no—
249D244—21no—
250D244—41no—
251D244—41no—
252D244—41no—
253D244—41no—
254D244—41no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—82no—
259D244—81no—
260D244—81no—
261D244—82no—
262D244—161no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—82no—
266C8×C61—21no—
267C8×C61—41no—
268C8×C61C2×SD1612yes—
269#92418—22no—
270#92418—21no—
271#92418—21no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#19893—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61D4211yescharacteristic
280C2×D61—41no—
281C2×D61—41no—
282C2×D61—41no—
283C2×D61—81no—
284C2×D61—81no—
285C2×D61—81no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—164no—
290C4×C61—22no—
291C4×C61—21no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—81no—
297C4×C61—81no—
298C4×C61C22×SD1611yescharacteristic
299C4×C61#57511yescharacteristic
300C4×C61#57711yescharacteristic
301C4×C61#57711yescharacteristic
302Dic61—41no—
303#3385D6111yescharacteristic, complemented
304#3362—611no—
305#3295—611no—
306#3274—611no—
307#1706—611no—
308#1695—611no—
309#1688—611no—
310#1678—611no—
311#1677—611no—
312#1631—611no—
313#1629—611no—
314#1623—611no—
315#1622—611no—
316#1590—611no—
317C8×SD16—611no—
318C2×C61—42no—
319C2×C61#327511yescharacteristic
320C2×C61D4×SD1611yescharacteristic
321C2×C61#329211yescharacteristic
322D61—81no—
323D61—161no—
324D61—161no—
325C2×AGL(1,ℤ/8)—1221no—
326Q82C2×D6111yescharacteristic, complemented
327#554C2×D6111yescharacteristic
328#550—611no—
329D42—611no—
330#501—21no—
331#500C2×D6111yescharacteristic, complemented
332#493—611no—
333#492—611no—
334#492—611no—
335#486—611no—
336#486—611no—
337#486—1221no—
338#481—1221no—
339#479—21no—
340#477C2×D6111yescharacteristic, complemented
341#476—611no—
342#476—611no—
343#476—1221no—
344#476C2×D6111yescharacteristic
345#474—21no—
346#469—1221no—
347#465—1221no—
348#460—611no—
349#460—611no—
350#460—611no—
351#460—1221no—
352#459—611no—
353#450—1221no—
354#449—1221no—
355#447—1221no—
356#446C2×D6111yescharacteristic, complemented
357C8×Q8—611no—
358#440—21no—
359C4×SD16—611no—
360C4×SD16—1221no—
361C4×SD16C2×D6111yescharacteristic
362#436—611no—
363C8×D4—611no—
364C2×#102—1221no—
365#334—611no—
366#334—611no—
367#333—611no—
368#333—611no—
369#331—611no—
370#331—611no—
371Q8⋊C8—611no—
372Q8⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375C82—611no—
376C61#1989311yescharacteristic, complemented, Sylow
377C2×#41—1221no—
378C22×D4—1221no—
379C22×D4—1221no—
380AGL(1,ℤ/8)—2444no—
381C2×SD16—611no—
382C2×SD16—1221no—
383C2×SD16—1221no—
384C2×SD16—1221no—
385C2×SD16—2441no—
386C2×SD16—2441no—
387C2×SD16C22⋊D6111yescharacteristic
388C2×D8—1221no—
389C2×D8—1221no—
390C2×D8—1221no—
391C2×M16—1221no—
392C22×C8—1221no—
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—41no—
396C4⋊Q8C22×D6111yescharacteristic
397C4⋊Q8C22×D6111yescharacteristic
398#127—611no—
399#127—611no—
400#127—1221no—
401#125—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404#121—1221no—
405#121—1221no—
406#121—1221no—
407#121—2441no—
408#120—2441no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8C22×D6111yescharacteristic
412C4×Q8C22×D6111yescharacteristic
413C4×D4—21no—
414C4×D4—611no—
415C4×D4—1221no—
416C4×D4C22×D6111yescharacteristic
417C2×C4⋊C4—21no—
418#107—21no—
419#107—21no—
420#107—21no—
421#106—21no—
422#106—611no—
423#106—1221no—
424#106—1221no—
425#106C22⋊D6111yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—611no—
428C4⋊C8—611no—
429C4⋊C8—611no—
430C4⋊C8—1221no—
431C4⋊C8C22×D6111yescharacteristic
432#103—21no—
433#103—611no—
434#103C22⋊D6111yescharacteristic
435#102—21no—
436#102—611no—
437#102—1221no—
438#102—1221no—
439#102—1221no—
440#102—1221no—
441#102—1221no—
442#102—1221no—
443#102—1221no—
444#102—1221no—
445#102—1221no—
446#102—1221no—
447#102C22⋊D6111yescharacteristic
448C22⋊C8—1221no—
449C22⋊C8—1221no—
450#97—21no—
451C4×C8—611no—
452C4×C8—611no—
453C4×C8—1221no—
454C4×C8C22×D6111yescharacteristic
455C24—2441no—
456#41—4881no—
457#41—2442no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—41no—
461C2×Q8D4×D6111yescharacteristic
462C2×Q8C2×C22⋊D6111yescharacteristic
463C2×D4—611no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—1221no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—4881no—
471C2×D4—4881no—
472C2×D4—2441no—
473C2×D4—2441no—
474C2×D4—2441no—
475C2×D4—2442no—
476C2×D4—2441no—
477C2×D4—2442no—
478C2×D4C2×C22⋊D6111yescharacteristic
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—1221no—
482C22×C4—2441no—
483SD16—4882no—
484SD16—4882no—
485SD16—4881no—
486SD16—2441no—
487SD16—2442no—
488SD16—2442no—
489SD16#1175820114yescomplemented
490D8—4881no—
491D8—2442no—
492D8—2442no—
493M16—2442no—
494C2×C8—21no—
495C2×C8—611no—
496C2×C8—611no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—4881no—
502C2×C8C2×C22⋊D6111yescharacteristic
503C2×C8C2×C22⋊D6111yescharacteristic
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—611no—
515C4⋊C4D4×D6111yescharacteristic
516C4⋊C4C2×C22⋊D6111yescharacteristic
517C4⋊C4C2×C22⋊D6111yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—1221no—
521C22⋊C4—2441no—
522C22⋊C4—2441no—
523C42—21no—
524C42—21no—
525C42—41no—
526C42C23×D6111yescharacteristic
527C23—21no—
528C23—1221no—
529C23—9761no—
530C23—4882no—
531C23—4882no—
532C23—2441no—
533C23—2441no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—81no—
538Q8—81no—
539Q8—161no—
540Q8C2×#1175820112yes—
541D4—21no—
542D4—1221no—
543D4—1221no—
544D4—9761no—
545D4—4881no—
546D4—4881no—
547D4—4882no—
548D4—4882no—
549D4—4882no—
550D4—2441no—
551D4—2441no—
552D4—2441no—
553D4—2441no—
554D4—2441no—
555D4—2441no—
556D4—2441no—
557D4—2441no—
558D4C2×#1175820112yes—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—161no—
569C2×C4—1221no—
570C2×C4—4882no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4C2×D4×D6111yescharacteristic
574C2×C4C22×C22⋊D6111yescharacteristic
575C2×C4#1451982211yescharacteristic
576C8—21no—
577C8—41no—
578C8—1222no—
579C8—1221no—
580C8—1221no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C8C2×#1175820112yes—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—9764no—
589C22—4881no—
590C22—4881no—
591C22—4881no—
592C22—4881no—
593C22—4881no—
594C22—4881no—
595C22—2441no—
596C22—2441no—
597C22—2441no—
598C22D4×C22⋊D6111yescharacteristic
599C4—22no—
600C4—21no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—2441no—
608C4C22×#1175820111yescharacteristic
609C4#1684056111yescharacteristic
610C4#1684057011yescharacteristic
611C4#1684057111yescharacteristic
612C2—42no—
613C2—9761no—
614C2—9761no—
615C2—4881no—
616C2#2145744411yescharacteristic
617C2D4×#1175820111yescharacteristic
618C2#2145761611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3385C2
socleC22×C61D42
prime radical#21457440C2
hypercenter#3385D61
hypocenterC61#19893
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
1. #21458490C2semidirect
2. #21457637C2semidirect
4. #21445412C2semidirect
5. #21445339C2semidirect
6. #21445303C2semidirect
7. #21445237C2semidirect
8. #21445230C2semidirect
9. #21444944C2semidirect
10. #21444934C2semidirect
11. #21444897C2semidirect
12. #21444891C2semidirect
13. #21444709C2semidirect
14. SD16×#92418C2semidirect
15. C61×#3385C2semidirect
21. #16840136C22semidirect
24. #16840110C22semidirect
34. #16839962C22semidirect
39. Q8×#92418C22semidirect
45. #16839513C22semidirect
46. #16839512C22semidirect
47. #16839511C22semidirect
48. #16839511C22semidirect
50. #16839505C22semidirect
51. Q8⋊#92418C22semidirect
52. Q8⋊#92418C22semidirect
55. C8×#92418C22semidirect
56. Q82×C61C22semidirect
59. C61×#500C22semidirect
61. C61×#477C22semidirect
64. C61×#446C22semidirect
173. SD16×C61SD16semidirect
303. #3385D61semidirect
326. Q82C2×D61semidirect
331. #500C2×D61semidirect
340. #477C2×D61semidirect
356. #446C2×D61semidirect
376. C61#19893semidirect
489. SD16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214584902
#214576372
#214574402
#214454122
#214453392
#214453032
#214452372
#214452302
#214449442
#214449342
#214448972
#214448912
#214447092
SD16×#924182
C61×#33852
#1989361