Finite Group Databasebeta

← #29670929

Subgroups — #29670929

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458464C211yesmaximal, characteristic, complemented
2#21458178C211yesmaximal, characteristic, complemented
3#21457537C211yesmaximal, characteristic
4#21445497C211yesmaximal, characteristic, complemented
5#21445318C211yesmaximal, characteristic, complemented
6#21445268C211yesmaximal, characteristic, complemented
7#21445205C211yesmaximal, characteristic, complemented
8#21445187C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445053C211yesmaximal, characteristic, complemented
11#21445025C211yesmaximal, characteristic, complemented
12#21444970C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3353C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17#16840472C2211yescharacteristic
18#16840417C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840160C2211yescharacteristic
21#16840141C2211yescharacteristic
22#16840116—21no—
23#16840114C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840091—21no—
26#16840079—21no—
27#16840069—21no—
28#16840052C2211yescharacteristic
29#16840052C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840001—21no—
32#16839988—21no—
33#16839974—21no—
34#16839967C2211yescharacteristic
35#16839964C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839924—21no—
38#16839922—21no—
39Q8×#92418C2211yescharacteristic
40C4×#11758201—21no—
41C4×#11758199C2211yescharacteristic
42C8×D244C2211yescharacteristic
43D4×#92418C2211yescharacteristic
44#106×D61—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52D4⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#547C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#484—21no—
60C61×#482—21no—
61C61×#475C2211yescharacteristic
62C61×#474C2211yescharacteristic
63C61×#468—21no—
64C4×SD16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#428—21no—
67C2×#11758222—21no—
68#14519797—44no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758199D411yescharacteristic
75C22×#92418—21no—
76C2×C8×D61—21no—
77#14519777C2311yescharacteristic
78#14519777C2311yescharacteristic
79#14519769—21no—
80#14519759—41no—
81#14519756—21no—
82#14519755—41no—
83#14519753—21no—
84#14519748—21no—
85C4×D244—21no—
86C4×D244C2311yescharacteristic
87C4⋊C4×D61—21no—
88C4⋊C4×D61—21no—
89#14519710—41no—
90#14519710D411yescharacteristic
91#14519709—21no—
92#14519709—21no—
93#14519708—21no—
94#14519708—21no—
95#14519708—21no—
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99C4⋊#92418C2311yescharacteristic
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701—21no—
105#14519700—21no—
106#14519700—41no—
107#14519698—21no—
108#14519698—21no—
109#14519698D411yescharacteristic
110#14519697D411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113C4×#92418—21no—
114C4×#92418C2311yescharacteristic
115C4×#92418C2311yescharacteristic
116C2×#41×C61—21no—
117C2×SD16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#126×C61—41no—
122#124×C61—21no—
123#123×C61—41no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126#121×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×D4×C61C2311yescharacteristic
130C4×D4×C61C2311yescharacteristic
131#117×C61—21no—
132C2×C4⋊C4×C61—21no—
133#107×C61—21no—
134#107×C61—21no—
135#107×C61—21no—
136#106×C61—21no—
137#106×C61D411yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#102×C61D411yescharacteristic
143C22⋊C8×C61—21no—
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—81no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×D4×C61—41no—
151C2×D4×C61C2×D411yescharacteristic
152C2×D4×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—41no—
156C2×C22⋊D61—41no—
157#11758222—42no—
158#11758222—81no—
159C2×D244C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—41no—
162C2×C4×D61—41no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165SD16×C61—22no—
166M16×C61—42no—
167C2×C8×C61—21no—
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C4⋊C4×C61C2×D411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C42×C61—21no—
186C42×C61—41no—
187C42×C61C2411yescharacteristic
188C22⋊Dic61—41no—
189#11758202—42no—
190#11758202—81no—
191#11758201—42no—
192#11758201—42no—
193#11758200—42no—
194#11758199—22no—
195#11758198—21no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61C2×D411yescharacteristic
202#11758196—41no—
203#11758196—41no—
204#11758196—41no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—42no—
210C2×#92418C2×D411yescharacteristic
211C2×#92418C2×D411yescharacteristic
212C8×D61—42no—
213C23×C61—21no—
214C23×C61—21no—
215C22×D61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222D4×C61—21no—
223D4×C61—21no—
224D4×C61—21no—
225D4×C61—21no—
226D4×C61—82no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—82no—
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C22⋊D61—82no—
242C2×Dic61—21no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245D244—21no—
246D244AGL(1,ℤ/8)12yes—
247C4×D61—41no—
248C4×D61—41no—
249C4×D61—82no—
250C4×D61—161no—
251Dic122—41no—
252Dic122—41no—
253Dic122—81no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61#13512yescomplemented
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#92418—41no—
262#92418—41no—
263#19860—611nomaximal, Sylow
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61D4211yescharacteristic
271C2×D61—22no—
272C2×D61—41no—
273C2×D61—41no—
274C4×C61—21no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61C2×#13511yescharacteristic
282C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
283C4×C61#57711yescharacteristic
284C4×C61#57811yescharacteristic
285Dic61—41no—
286Dic61—81no—
287Dic61—81no—
288#3360—611no—
289#3353D6111yescharacteristic, complemented
290#3335—611no—
291#3283—611no—
292#1723—611no—
293#1691—611no—
294#1683—611no—
295#1673—611no—
296#1670—611no—
297#1650—611no—
298#1647—611no—
299#1643—611no—
300#1635—611no—
301#1581—611no—
302SD16⋊C8—611no—
303C2×C61—81no—
304C2×C61—81no—
305C2×C61#326511yescharacteristic
306C2×C61#328311yescharacteristic
307C2×C61#328911yescharacteristic
308D61—42no—
309C2×#135—1221no—
310#556C2×D6111yescharacteristic
311#554—611no—
312#547—611no—
313#547C2×D6111yescharacteristic
314#500—611no—
315#500C2×D6111yescharacteristic
316#498—611no—
317#494—611no—
318#488—1221no—
319#487—611no—
320#487—611no—
321#484—21no—
322#483—1221no—
323#482—21no—
324#481—1221no—
325#479—1221no—
326#476—611no—
327#476—611no—
328#475—611no—
329#475C2×D6111yescharacteristic
330#474C2×D6111yescharacteristic
331#468—21no—
332#467—1221no—
333#465—1221no—
334#463—1221no—
335#461—611no—
336#461—611no—
337#461—611no—
338#452—1221no—
339#452—1221no—
340C8×Q8—611no—
341C4×SD16—1221no—
342C4×SD16C2×D6111yescharacteristic
343C4×D8—611no—
344#436C2×D6111yescharacteristic
345C8×D4—611no—
346C8×D4—611no—
347#428—21no—
348C2×#106—1221no—
349#335—611no—
350#335—611no—
351#333—611no—
352#332—611no—
353#332—611no—
354#332—611no—
355Q8⋊C8—611no—
356D4⋊C8—611no—
357D4⋊C8—611no—
358D4⋊C8—611no—
359#322—611no—
360C61#1986011yescharacteristic, complemented, Sylow
361C2×#41—21no—
362C2×#41—1221no—
363#135—2444no—
364C2×Q16—1221no—
365C2×Q16—1221no—
366C2×SD16—1221no—
367C2×SD16—1221no—
368C2×SD16—1221no—
369C2×SD16C22⋊D6111yescharacteristic
370C2×D8—611no—
371C2×M16—21no—
372C22×C8—1221no—
373C22×C8—1221no—
374C4⋊Q8—611no—
375C4⋊Q8—611no—
376C4⋊Q8C22×D6111yescharacteristic
377C4⋊Q8C22×D6111yescharacteristic
378#126—41no—
379#125—1221no—
380#124—21no—
381#123—41no—
382#123—2441no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—2441no—
388#121—21no—
389#121—1221no—
390C4×Q8—21no—
391C4×Q8C22×D6111yescharacteristic
392C4×D4—611no—
393C4×D4—1221no—
394C4×D4C22×D6111yescharacteristic
395C4×D4C22×D6111yescharacteristic
396#117—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—611no—
404#107—2441no—
405#106—21no—
406#106—1221no—
407#106—1221no—
408#106—1221no—
409#106—1221no—
410#106—1221no—
411#106C22⋊D6111yescharacteristic
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417#103—21no—
418#103—1221no—
419#103—1221no—
420#103—1221no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103—2441no—
425#103C22⋊D6111yescharacteristic
426#102—21no—
427#102—611no—
428#102—611no—
429#102—1221no—
430#102—1221no—
431#102C22⋊D6111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435C4×C8—611no—
436C4×C8—611no—
437C4×C8—1221no—
438C4×C8C22×D6111yescharacteristic
439#41—42no—
440#41—81no—
441#41—4881no—
442#41—2442no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—1221no—
446C2×Q8—1221no—
447C2×Q8C2×C22⋊D6111yescharacteristic
448C2×D4—41no—
449C2×D4—611no—
450C2×D4—2441no—
451C2×D4D4×D6111yescharacteristic
452C2×D4C2×C22⋊D6111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—41no—
456C22×C4—1221no—
457C22×C4—2441no—
458C22×C4—2441no—
459Q16—4881no—
460Q16—2442no—
461SD16—22no—
462SD16—2442no—
463SD16—2442no—
464SD16—2442no—
465D8—1222no—
466M16—42no—
467C2×C8—21no—
468C2×C8—611no—
469C2×C8—611no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—2442no—
475C2×C8—2442no—
476C2×C8C2×C22⋊D6111yescharacteristic
477C2×C8C2×C22⋊D6111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—611no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4D4×D6111yescharacteristic
494C4⋊C4C2×C22⋊D6111yescharacteristic
495C4⋊C4C2×C22⋊D6111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—1221no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—21no—
505C42—41no—
506C42C23×D6111yescharacteristic
507C23—21no—
508C23—21no—
509C23—1221no—
510Q8—21no—
511Q8—21no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—4881no—
517Q8—2441no—
518Q8—2441no—
519D4—21no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—82no—
524D4—612no—
525D4—1221no—
526D4—4882no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—82no—
538C2×C4—1221no—
539C2×C4—9761no—
540C2×C4—4882no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4C2×D4×D6111yescharacteristic
546C2×C4C22×C22⋊D6111yescharacteristic
547C2×C4#1451982211yescharacteristic
548C8—21no—
549C8—41no—
550C8—1221no—
551C8—1221no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8#1451979712yescomplemented
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—1222no—
564C22—2441no—
565C22—2441no—
566C22D4×C22⋊D6111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—4881no—
575C4—4881no—
576C4—2441no—
577C4C2×#1451979711yescharacteristic
578C4AGL(1,ℤ/8)×D6111yescharacteristic
579C4#1684057211yescharacteristic
580C4#1684057711yescharacteristic
581C2—81no—
582C2—81no—
583C2—2442no—
584C2#2145730811yescharacteristic
585C2#2145753711yescharacteristic
586C2#2145759011yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3353C2
socleC22×C61D42
prime radical#21457537C2
hypercenter#3353D61
hypocenterC61#19860
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3353

Complements

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

NH ≅ G/Ntype
1. #21458464C2semidirect
2. #21458178C2semidirect
4. #21445497C2semidirect
5. #21445318C2semidirect
6. #21445268C2semidirect
7. #21445205C2semidirect
8. #21445187C2semidirect
9. #21445075C2semidirect
10. #21445053C2semidirect
11. #21445025C2semidirect
12. #21444970C2semidirect
13. #21444646C2semidirect
14. SD16⋊#92418C2semidirect
15. C61×#3353C2semidirect
256. C8×C61#135semidirect
289. #3353D61semidirect
360. C61#19860semidirect
556. C8#14519797semidirect

Maximal subgroups

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

subgroupindex
#214584642
#214581782
#214575372
#214454972
#214453182
#214452682
#214452052
#214451872
#214450752
#214450532
#214450252
#214449702
#214446462
SD16⋊#924182
C61×#33532
#1986061