Finite Group Databasebeta

← #29662755

Subgroups — #29662755

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456394C211yesmaximal, characteristic, complemented
2#21455879C211yesmaximal, characteristic, complemented
3#21454786C211yesmaximal, characteristic, complemented
4#21445361C211yesmaximal, characteristic, complemented
5#21445357C211yesmaximal, characteristic, complemented
6#21445354C211yesmaximal, characteristic, complemented
7#21445350C211yesmaximal, characteristic, complemented
8#21445345C211yesmaximal, characteristic, complemented
9#21445340C211yesmaximal, characteristic, complemented
10#21445301C211yesmaximal, characteristic, complemented
11#21445296C211yesmaximal, characteristic, complemented
12#21444565C211yesmaximal, characteristic, complemented
13#21444481C211yesmaximal, characteristic, complemented
14#21444479C211yesmaximal, characteristic, complemented
15C61×#3106C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840165C2211yescharacteristic
18#16840138C2211yescharacteristic
19#16840110C2211yescharacteristic
20#16840108C2211yescharacteristic
21#16840086—21no—
22#16840057C2211yescharacteristic
23#16840052C2211yescharacteristic
24#16839996—21no—
25#16839996—21no—
26#16839962C2211yescharacteristic
27#16839957C2211yescharacteristic
28#16839907—21no—
29#16839893C2211yescharacteristic
30#16839893C2211yescharacteristic
31C4×#11758201—21no—
32C4×#11758199—21no—
33C4×#11758199—21no—
34C4×#11758199—21no—
35#16839840C2211yescharacteristic
36#16839840C2211yescharacteristic
37#16839834—21no—
38#16839834—21no—
39#16839815—21no—
40#16839815C2211yescharacteristic
41#16839815C2211yescharacteristic
42C4×#11758194—21no—
43C2×C4×#92418C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839510C2211yescharacteristic
51#16839510C2211yescharacteristic
52#16839506C2211yescharacteristic
53#16839506C2211yescharacteristic
54#16839505C2211yescharacteristic
55#16839505C2211yescharacteristic
56C61×#532C2211yescharacteristic
57C4×#41×C61C2211yescharacteristic
58C61×#482—21no—
59C61×#477C2211yescharacteristic
60C61×#476C2211yescharacteristic
61C61×#460C2211yescharacteristic
62C61×#459C2211yescharacteristic
63C61×#449—21no—
64C4×SD16×C61—21no—
65C4×D8×C61—21no—
66C61×#431C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758201—21no—
69C2×#11758199—21no—
70C2×#11758199—21no—
71C2×#11758199—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C22×#92418D411yescharacteristic
75C22×#92418D411yescharacteristic
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519765—21no—
79#14519751—21no—
80#14519751—21no—
81C4×D244—21no—
82C4×D244—21no—
83#14519710—21no—
84#14519710—21no—
85#14519710—21no—
86#14519708—21no—
87C4⋊#92418—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93#14519701—21no—
94#14519698—21no—
95#14519698—21no—
96#14519698—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—
107C4×#92418—21no—
108C4×#92418—21no—
109C4×#92418D411yescharacteristic
110C4×#92418D411yescharacteristic
111C4×#92418C2311yescharacteristic
112C4×#92418C2311yescharacteristic
113C2×#41×C61—21no—
114C2×#41×C61D411yescharacteristic
115C2×SD16×C61—21no—
116C2×D8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118#127×C61C2311yescharacteristic
119#124×C61—21no—
120#121×C61—21no—
121#121×C61—21no—
122C4×Q8×C61D411yescharacteristic
123C4×Q8×C61C2311yescharacteristic
124C4×D4×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61—21no—
128C4×D4×C61D411yescharacteristic
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131#117×C61D411yescharacteristic
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#107×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142C22⋊C8×C61—21no—
143C4×C8×C61—21no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—82no—
147C2×Q8×C61—21no—
148C2×Q8×C61C2×D411yescharacteristic
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—41no—
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C2×C22⋊D61—41no—
163#11758222—82no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×C4×D61—41no—
168C2×Dic122—21no—
169SD16×C61—42no—
170D8×C61—42no—
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×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61#4111yescharacteristic
190C42×C61C2411yescharacteristic
191#11758201—42no—
192#11758199—42no—
193#11758199—42no—
194#11758199—42no—
195#11758198—41no—
196#11758198—41no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199#11758194—42no—
200#11758194—42no—
201C2×#92418—22no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—41no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209C2×#92418C2×D411yescharacteristic
210C2×#92418C2×D411yescharacteristic
211C23×C61—21no—
212C23×C61—41no—
213C23×C61#12111yescharacteristic
214C22×D61—41no—
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—81no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—42no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—41no—
224D4×C61—41no—
225D4×C61—81no—
226D4×C61—82no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—22no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—42no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61—41no—
240C2×C4×C61—82no—
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C22⋊D61—82no—
248C2×Dic61—41no—
249D244—41no—
250D244—41no—
251D244—41no—
252D244—41no—
253D244—81no—
254C4×D61—82no—
255Dic122—81no—
256C8×C61—41no—
257C8×C61—41no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#92418#13512yes—
266#19160—611nomaximal, Sylow
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—81no—
274C22×C61—81no—
275C22×C61—81no—
276C22×C61C2×#12111yescharacteristic
277C2×D61—81no—
278C2×D61—81no—
279C2×D61—81no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—21no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—41no—
286C4×C61—81no—
287C4×C61#47212yes—
288C4×C61C2×#13511yescharacteristic
289C4×C61#57511yescharacteristic
290C4×C61#57511yescharacteristic
291C4×C61#57511yescharacteristic
292Dic61—81no—
293#3169—611no—
294#3106—611no—
295#3106D6111yescharacteristic, complemented
296#2965—611no—
297#1698—611no—
298#1698—611no—
299#1697—611no—
300#1697—611no—
301#1696—611no—
302#1695—611no—
303#1688—611no—
304#1687—611no—
305#1564—611no—
306#1543—611no—
307#1543—611no—
308C2×C61—41no—
309C2×C61—81no—
310C2×C61—161no—
311C2×C61#303511yescharacteristic
312C2×C61#305411yescharacteristic
313C2×C61C2×#47211yescharacteristic
314D61—161no—
315#532—611no—
316#532C2×D6111yescharacteristic
317C4×#41C2×D6111yescharacteristic
318#500—611no—
319#493—611no—
320#486—611no—
321#486—611no—
322#482—21no—
323#482—1221no—
324#477—611no—
325#477C2×D6111yescharacteristic
326#476—611no—
327#476C2×D6111yescharacteristic
328#466—1221no—
329#466—1221no—
330#460—611no—
331#460C2×D6111yescharacteristic
332#459—611no—
333#459C2×D6111yescharacteristic
334#449—21no—
335#449—1221no—
336#446—611no—
337#446—611no—
338C4×SD16—21no—
339C4×SD16—1221no—
340C4×D8—21no—
341C4×D8—1221no—
342C4×D8—1221no—
343C4×D8—1221no—
344#436—611no—
345#436—611no—
346#435—1221no—
347#435—1221no—
348#431—611no—
349#431—611no—
350#431—1221no—
351#431C2×D6111yescharacteristic
352C4×M16—1221no—
353C2×C4×C8—611no—
354#335—611no—
355#335—611no—
356#334—611no—
357#334—611no—
358#333—611no—
359#333—611no—
360#333—611no—
361#333—611no—
362#331—611no—
363#331—611no—
364#331—611no—
365#331—611no—
366C61#1916011yescharacteristic, complemented, Sylow
367C2×#41—21no—
368C2×#41—1221no—
369C2×#41C22⋊D6111yescharacteristic
370C2×SD16—21no—
371C2×SD16—1221no—
372C2×D8—21no—
373C2×D8—1221no—
374C2×D8—1221no—
375C2×D8—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C22×C8—611no—
379C22×C8—611no—
380C4⋊Q8—611no—
381C4⋊Q8C22×D6111yescharacteristic
382#127—611no—
383#127C22×D6111yescharacteristic
384#124—21no—
385#124—1221no—
386#121—21no—
387#121—21no—
388#121—1221no—
389#121—1221no—
390C4×Q8C22⋊D6111yescharacteristic
391C4×Q8C22×D6111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—1221no—
397C4×D4—1221no—
398C4×D4C22⋊D6111yescharacteristic
399C4×D4C22×D6111yescharacteristic
400#117—21no—
401#117C22⋊D6111yescharacteristic
402C2×C42—21no—
403C2×C42C22×D6111yescharacteristic
404#107—21no—
405#107—1221no—
406#107—1221no—
407#107—1221no—
408#106—21no—
409#106—1221no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—1221no—
415C4⋊C8—1221no—
416C4⋊C8C22×D6111yescharacteristic
417C4⋊C8C22×D6111yescharacteristic
418#103—21no—
419#103—1221no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426#102—1221no—
427#102—1221no—
428#102—1221no—
429#102—1221no—
430C22⋊C8—21no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—1221no—
436#97—1221no—
437C4×C8—21no—
438C4×C8—611no—
439C4×C8—611no—
440C4×C8—611no—
441C4×C8—611no—
442C4×C8—1221no—
443C4×C8—1221no—
444#41—41no—
445#41—41no—
446#41—82no—
447#41—4882no—
448C2×Q8—21no—
449C2×Q8—1221no—
450C2×Q8C2×C22⋊D6111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—2441no—
460C2×D4C2×C22⋊D6111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—2441no—
466C22×C4D4×D6111yescharacteristic
467C22×C4#1175822411yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469SD16—42no—
470SD16—2442no—
471D8—42no—
472D8—2442no—
473D8—2442no—
474D8—2442no—
475M16—2442no—
476M16—2442no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—611no—
480C2×C8—611no—
481C2×C8—611no—
482C2×C8—611no—
483C2×C8—1222no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—2441no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—1221no—
494C4⋊C4—1221no—
495C4⋊C4C2×C22⋊D6111yescharacteristic
496C4⋊C4C2×C22⋊D6111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—2441no—
503C22⋊C4—2441no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42D4×D6111yescharacteristic
508C42#1175822411yescharacteristic
509C42C2×C22⋊D6111yescharacteristic
510C42C23×D6111yescharacteristic
511C23—21no—
512C23—41no—
513C23—2441no—
514C23#1451974911yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—81no—
518Q8—4881no—
519D4—21no—
520D4—21no—
521D4—42no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—81no—
527D4—82no—
528D4—4881no—
529D4—4882no—
530D4—2441no—
531D4—2441no—
532D4—2441no—
533D4—2441no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—4882no—
549C2×C4—2441no—
550C2×C4#1451974911yescharacteristic
551C2×C4#1451974911yescharacteristic
552C2×C4#1451974911yescharacteristic
553C2×C4C2×D4×D6111yescharacteristic
554C2×C4C22×C22⋊D6111yescharacteristic
555C2×C4C2×#1175822411yescharacteristic
556C8—41no—
557C8—41no—
558C8—612no—
559C8—1221no—
560C8—1221no—
561C8—1221no—
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8—2441no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—4881no—
576C22—4881no—
577C22—4881no—
578C22C2×#1451974911yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—4881no—
587C4#1684003012yes—
588C4#135×D6111yescharacteristic
589C4#1684055911yescharacteristic
590C4#1684056011yescharacteristic
591C4#1684056011yescharacteristic
592C2—41no—
593C2—81no—
594C2—161no—
595C2—9761no—
596C2#2145527011yescharacteristic
597C2#2145542511yescharacteristic
598C2C2×#1684003011yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3106C2
socleC22×C61C2×#121
hypercenter#3106D61
hypocenterC61#19160
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #21456394C2semidirect
2. #21455879C2semidirect
3. #21454786C2semidirect
4. #21445361C2semidirect
5. #21445357C2semidirect
6. #21445354C2semidirect
7. #21445350C2semidirect
8. #21445345C2semidirect
9. #21445340C2semidirect
10. #21445301C2semidirect
11. #21445296C2semidirect
12. #21444565C2semidirect
13. #21444481C2semidirect
14. #21444479C2semidirect
15. C61×#3106C2semidirect
295. #3106D61semidirect
366. C61#19160semidirect

Maximal subgroups

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

subgroupindex
#214563942
#214558792
#214547862
#214453612
#214453572
#214453542
#214453502
#214453452
#214453402
#214453012
#214452962
#214445652
#214444812
#214444792
C61×#31062
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