Finite Group Databasebeta

← #29669864

Subgroups — #29669864

Order 15616.

680 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#21458475C211yesmaximal, characteristic, complemented
2#21457645C211yesmaximal, characteristic, complemented
3D4×#11758201C211yesmaximal, characteristic, complemented
4#21445459C211yesmaximal, characteristic, complemented
5#21445359C211yesmaximal, characteristic, complemented
6#21445253C211yesmaximal, characteristic, complemented
7#21445226C211yesmaximal, characteristic, complemented
8#21445169C211yesmaximal, characteristic, complemented
9#21445025C211yesmaximal, characteristic, complemented
10#21444984C211yesmaximal, characteristic, complemented
11#21444878C211yesmaximal, characteristic, complemented
12#21444872C211yesmaximal, characteristic
13#21444653C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3373C211yesmaximal, characteristic, complemented
16C22×#11758201—21no—
17#16840472C2211yescharacteristic
18D4×D244C2211yescharacteristic
19#16840138C2211yescharacteristic
20#16840136C2211yescharacteristic
21#16840116—21no—
22#16840114C2211yescharacteristic, complemented
23#16840109C2211yescharacteristic
24#16840108C2211yescharacteristic, complemented
25#16840082—21no—
26#16840062—21no—
27#16840057C2211yescharacteristic, complemented
28#16840052C2211yescharacteristic
29#16839994—21no—
30#16839993—21no—
31#16839974—21no—
32#16839964C2211yescharacteristic
33#16839962C2211yescharacteristic
34#16839962C2211yescharacteristic
35#16839954C2211yescharacteristic
36#16839912—21no—
37#16839911—21no—
38#16839901—21no—
39Q8×#92418C2211yescharacteristic, complemented
40C4×#11758201C2211yescharacteristic
41C4×#11758199—21no—
42C8×D244C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44#102×D61—21no—
45#16839515C2211yescharacteristic, complemented
46#16839512C2211yescharacteristic, complemented
47#16839510C2211yescharacteristic, complemented
48#16839508C2211yescharacteristic, complemented
49#16839506C2211yescharacteristic, complemented
50#16839505C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic, complemented
52Q8⋊#92418C2211yescharacteristic, complemented
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic, complemented
56C61×#559C2211yescharacteristic, complemented
57D4×Q8×C61C2211yescharacteristic
58C61×#489—21no—
59C61×#486C2211yescharacteristic, complemented
60C61×#476—21no—
61C61×#475C2211yescharacteristic, complemented
62C61×#463—21no—
63C61×#459C2211yescharacteristic
64C61×#446C2211yescharacteristic, complemented
65C61×#442—21no—
66C4×SD16×C61C2211yescharacteristic
67C22×D244—21no—
68C2×D4×D61—21no—
69C2×#11758201—21no—
70C2×#11758201—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758201—44no—
75C2×#11758201D411yescharacteristic
76C2×#11758199—21no—
77C2×#11758199—41no—
78C22×#92418—21no—
79C2×C8×D61—21no—
80#14519777C2311yescharacteristic
81#14519774C2311yescharacteristic
82#14519769—21no—
83#14519755—41no—
84#14519753—21no—
85#14519752—21no—
86#14519751—21no—
87#14519747—41no—
88C4×D244—21no—
89C4×D244C2311yescharacteristic
90C4⋊C4×D61—21no—
91#14519710—21no—
92#14519708—21no—
93#14519708D411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519701—21no—
99#14519701—21no—
100#14519701D411yescharacteristic
101#14519700—41no—
102#14519699—21no—
103#14519699—21no—
104#14519698—21no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519697—21no—
109#14519697—21no—
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C22×Q8×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×D8×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#124×C61—21no—
123#124×C61—21no—
124#123×C61—41no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61C2311yescharacteristic
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61—21no—
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61C2311yescharacteristic
133#106×C61—21no—
134#106×C61D411yescharacteristic
135C4⋊C8×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137#103×C61—21no—
138#103×C61D411yescharacteristic
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142#102×C61D411yescharacteristic
143#97×C61—21no—
144C4×C8×C61C2311yescharacteristic
145C23×D61—41no—
146C2×Q8×C61—21no—
147C2×Q8×C61—41no—
148C2×Q8×C61—42no—
149C2×Q8×C61—81no—
150C2×Q8×C61C2×D411yescharacteristic
151C2×Q8×C61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61C2×D411yescharacteristic
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159C2×C22⋊D61—41no—
160D4×D61—42no—
161D4×D61—81no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—42no—
166C2×D244—41no—
167C2×D244—81no—
168C2×D244C2×D411yescharacteristic
169C2×C4×D61—21no—
170C2×C4×D61—41no—
171C2×Dic122—21no—
172SD16×C61—22no—
173D8×C61—42no—
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—41no—
182C4⋊C4×C61C2×D411yescharacteristic
183C4⋊C4×C61C2×D411yescharacteristic
184C4⋊C4×C61C2×D411yescharacteristic
185C22⋊C4×C61—21no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61—41no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61C2411yescharacteristic
193#11758201—22no—
194#11758201—42no—
195#11758201—42no—
196#11758201—42no—
197#11758201—81no—
198#11758201—81no—
199#11758199—42no—
200#11758199—82no—
201#11758198—21no—
202#11758198—41no—
203#11758198—41no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61C2×D411yescharacteristic
207#11758196—41no—
208#11758196—41no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—42no—
214C2×#92418C2×D411yescharacteristic
215C2×#92418C2×D411yescharacteristic
216C8×D61—81no—
217C23×C61—21no—
218C23×C61—41no—
219C22×D61—21no—
220C22×D61—41no—
221C22×D61—82no—
222C22×D61—82no—
223C22×D61—161no—
224Q8×C61—21no—
225Q8×C61—21no—
226Q8×C61—21no—
227Q8×C61—21no—
228Q8×C61—41no—
229Q8×C61—41no—
230Q8×C61—82no—
231D4×C61—21no—
232D4×C61—41no—
233D4×C61—41no—
234D4×C61—41no—
235D4×C61—41no—
236D4×C61—81no—
237D4×C61#13512yes—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—82no—
247C2×C4×C61—161no—
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×C4×C61H(5,𝔽2)11yescharacteristic
251C22⋊D61—82no—
252C2×Dic61—21no—
253C2×Dic61—41no—
254D244—21no—
255D244—41no—
256D244—41no—
257D244—41no—
258D244—41no—
259D244—81no—
260D244—82no—
261D244AGL(1,ℤ/8)12yes—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—161no—
265Dic122—81no—
266C8×C61—21no—
267C8×C61—21no—
268C8×C61—41no—
269#92418—21no—
270#92418—21no—
271#92418—41no—
272#92418—41no—
273#92418—41no—
274#92418—41no—
275#19789—611nomaximal, Sylow
276C22×C61—22no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—81no—
282C22×C61D4211yescharacteristic
283C2×D61—22no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61—81no—
287C2×D61—81no—
288C2×D61—81no—
289C2×D61—164no—
290C4×C61—21no—
291C4×C61—41no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—81no—
297C4×C61C2×#13511yescharacteristic
298C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C61#57711yescharacteristic
300C4×C61#57711yescharacteristic
301Dic61—41no—
302Dic61—81no—
303#3373D6111yescharacteristic, complemented
304#3361—611no—
305#3295—611no—
306D4×SD16—611no—
307#1717—611no—
308#1698—611no—
309#1681—611no—
310#1677—611no—
311#1666—611no—
312#1643—611no—
313#1637—611no—
314#1620—611no—
315#1619—611no—
316#1582—611no—
317SD16⋊C8—611no—
318C2×C61—42no—
319C2×C61—161no—
320C2×C61#326511yescharacteristic
321C2×C61#328211yescharacteristic
322C2×C61#328811yescharacteristic
323D61—42no—
324D61—161no—
325C22×SD16—1221no—
326#559C2×D6111yescharacteristic, complemented
327#554—611no—
328D4×Q8C2×D6111yescharacteristic
329D42—611no—
330#493—611no—
331#492—611no—
332#489—21no—
333#488—1221no—
334#487—611no—
335#486—611no—
336#486—611no—
337#486C2×D6111yescharacteristic, complemented
338#481—1221no—
339#478—1221no—
340#477—611no—
341#476—21no—
342#476—611no—
343#475C2×D6111yescharacteristic, complemented
344#465—1221no—
345#465—1221no—
346#463—21no—
347#463—1221no—
348#461—611no—
349#460—611no—
350#460—611no—
351#459—611no—
352#459C2×D6111yescharacteristic
353#450—1221no—
354#450—1221no—
355#448—1221no—
356#446C2×D6111yescharacteristic, complemented
357C8×Q8—611no—
358#442—21no—
359C4×SD16—611no—
360C4×SD16C2×D6111yescharacteristic
361C4×D8—1221no—
362C8×D4—611no—
363C8×D4—611no—
364C2×#102—1221no—
365#335—611no—
366#334—611no—
367#333—611no—
368#332—611no—
369#331—611no—
370#331—611no—
371Q8⋊C8—611no—
372Q8⋊C8—611no—
373D4⋊C8—611no—
374D4⋊C8—611no—
375#322—611no—
376C61#1978911yescharacteristic, complemented, Sylow
377C22×Q8—21no—
378C22×D4—1221no—
379C22×D4—1221no—
380C2×SD16—611no—
381C2×SD16—1221no—
382C2×SD16—1221no—
383C2×SD16—1221no—
384C2×SD16—1221no—
385C2×SD16—1221no—
386C2×SD16—2444no—
387C2×SD16C22⋊D6111yescharacteristic
388C2×D8—21no—
389C2×D8—1221no—
390C2×D8—2441no—
391C22×C8—1221no—
392C22×C8—1221no—
393C4⋊Q8—21no—
394C4⋊Q8—611no—
395C4⋊Q8C22×D6111yescharacteristic
396#127—611no—
397#127C22×D6111yescharacteristic
398#125—1221no—
399#124—21no—
400#124—21no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404C22⋊Q8—1221no—
405C22⋊Q8—2441no—
406#121—1221no—
407#121—1221no—
408#120—2441no—
409C4×Q8C22×D6111yescharacteristic
410C4×Q8C22×D6111yescharacteristic
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—611no—
415C4×D4—1221no—
416C4×D4C22×D6111yescharacteristic
417C2×C4⋊C4—1221no—
418#107—1221no—
419#106—21no—
420#106—611no—
421#106—1221no—
422#106C22⋊D6111yescharacteristic
423C4⋊C8—21no—
424C4⋊C8—611no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—1221no—
428C4⋊C8C22×D6111yescharacteristic
429#103—21no—
430#103—611no—
431#103—1221no—
432#103—1221no—
433#103—2441no—
434#103C22⋊D6111yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—611no—
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—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—42no—
459C2×Q8—81no—
460C2×Q8—1221no—
461C2×Q8D4×D6111yescharacteristic
462C2×Q8C2×C22⋊D6111yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—611no—
467C2×D4—1221no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—4881no—
471C2×D4—4881no—
472C2×D4—2441no—
473C2×D4—2442no—
474C2×D4—2441no—
475C2×D4—2442no—
476C2×D4C2×C22⋊D6111yescharacteristic
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—1221no—
481C22×C4—2441no—
482SD16—22no—
483SD16—1222no—
484SD16—4881no—
485SD16—4881no—
486SD16—2442no—
487SD16—2442no—
488SD16—2442no—
489D8—42no—
490D8—4882no—
491D8—2442no—
492C2×C8—21no—
493C2×C8—611no—
494C2×C8—611no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—4881no—
500C2×C8—2442no—
501C2×C8C2×C22⋊D6111yescharacteristic
502C2×C8C2×C22⋊D6111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—611no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—2441no—
512C4⋊C4—2441no—
513C4⋊C4D4×D6111yescharacteristic
514C4⋊C4C2×C22⋊D6111yescharacteristic
515C4⋊C4C2×C22⋊D6111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—1221no—
522C22⋊C4—2441no—
523C22⋊C4—2441no—
524C42—21no—
525C42—21no—
526C42C23×D6111yescharacteristic
527C23—21no—
528C23—41no—
529C23—1221no—
530C23—9761no—
531C23—4882no—
532C23—4882no—
533C23—2441no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—82no—
541Q8—4881no—
542D4—21no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—612no—
549D4—1221no—
550D4—4881no—
551D4—4882no—
552D4—4882no—
553D4—2441no—
554D4—2441no—
555D4—2441no—
556D4—2441no—
557D4#1451979712yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—82no—
567C2×C4—161no—
568C2×C4—1221no—
569C2×C4—9761no—
570C2×C4—2441no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4C2×D4×D6111yescharacteristic
574C2×C4C22×C22⋊D6111yescharacteristic
575C2×C4#1451982211yescharacteristic
576C8—21no—
577C8—21no—
578C8—41no—
579C8—1221no—
580C8—1221no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C8—2441no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—1222no—
592C22—9764no—
593C22—4881no—
594C22—4881no—
595C22—4881no—
596C22—2441no—
597C22—2441no—
598C22D4×C22⋊D6111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—4881no—
607C4—2441no—
608C4C2×#1451979711yescharacteristic
609C4AGL(1,ℤ/8)×D6111yescharacteristic
610C4#1684057011yescharacteristic
611C4#1684057211yescharacteristic
612C2—42no—
613C2—161no—
614C2—9761no—
615C2—2442no—
616C2#2145730811yescharacteristic
617C2#2145752711yescharacteristic
618C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3373C2
socleC22×C61D42
prime radical#21444872C2
hypercenter#3373D61
hypocenterC61#19789
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3373

Complements

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

NH ≅ G/Ntype
1. #21458475C2semidirect
2. #21457645C2semidirect
3. D4×#11758201C2semidirect
4. #21445459C2semidirect
5. #21445359C2semidirect
6. #21445253C2semidirect
7. #21445226C2semidirect
8. #21445169C2semidirect
9. #21445025C2semidirect
10. #21444984C2semidirect
11. #21444878C2semidirect
13. #21444653C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3373C2semidirect
22. #16840114C22semidirect
24. #16840108C22semidirect
27. #16840057C22semidirect
39. Q8×#92418C22semidirect
45. #16839515C22semidirect
46. #16839512C22semidirect
47. #16839510C22semidirect
48. #16839508C22semidirect
49. #16839506C22semidirect
51. Q8⋊#92418C22semidirect
52. Q8⋊#92418C22semidirect
55. #16839483C22semidirect
56. C61×#559C22semidirect
59. C61×#486C22semidirect
61. C61×#475C22semidirect
64. C61×#446C22semidirect
303. #3373D61semidirect
326. #559C2×D61semidirect
337. #486C2×D61semidirect
343. #475C2×D61semidirect
356. #446C2×D61semidirect
376. C61#19789semidirect

Maximal subgroups

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

subgroupindex
#214584752
#214576452
D4×#117582012
#214454592
#214453592
#214452532
#214452262
#214451692
#214450252
#214449842
#214448782
#214448722
#214446532
SD16⋊#924182
C61×#33732
#1978961