Finite Group Databasebeta

← #29663011

Subgroups — #29663011

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455884C211yesmaximal, characteristic, complemented
2#21455268C211yesmaximal, characteristic
3#21454837C211yesmaximal, characteristic, complemented
4#21445377C211yesmaximal, characteristic, complemented
5#21445363C211yesmaximal, characteristic, complemented
6#21445329C211yesmaximal, characteristic, complemented
7#21445281C211yesmaximal, characteristic, complemented
8#21445260C211yesmaximal, characteristic, complemented
9#21445246C211yesmaximal, characteristic, complemented
10#21445210C211yesmaximal, characteristic, complemented
11#21445164C211yesmaximal, characteristic, complemented
12#21444571C211yesmaximal, characteristic, complemented
13#21444524C211yesmaximal, characteristic, complemented
14#21444519C211yesmaximal, characteristic, complemented
15C61×#3182C211yesmaximal, characteristic, complemented
16C2×#14519797—21no—
17C4×#11758222C2211yescharacteristic
18#16840100—21no—
19#16840044C2211yescharacteristic
20#16840039C2211yescharacteristic
21#16839981—21no—
22#16839974—21no—
23#16839969C2211yescharacteristic
24#16839969C2211yescharacteristic
25#16839964C2211yescharacteristic
26#16839964C2211yescharacteristic
27#16839959C2211yescharacteristic
28#16839954C2211yescharacteristic
29#16839922—21no—
30C8×Dic122C2211yescharacteristic
31C8×Dic122C2211yescharacteristic
32C4×#11758202—21no—
33C4×#11758201—21no—
34#16839841C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839838—21no—
37#16839838—21no—
38#16839819C2211yescharacteristic
39#16839817—21no—
40#16839815C2211yescharacteristic
41C2×C4⋊#92418C2211yescharacteristic
42#16839758—21no—
43#16839714—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#532C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#492C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#468—21no—
63C61×#468—21no—
64C61×#440—21no—
65C61×#440—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68#14519797—44no—
69C2×#11758202—21no—
70C2×#11758202—21no—
71C2×#11758200—21no—
72C2×#11758201—21no—
73C2×#11758201—21no—
74C2×#11758199—21no—
75C2×#11758189—21no—
76C2×#11758189—21no—
77C22×#92418—21no—
78C4×Dic122D411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×D244D411yescharacteristic
81C4×D244C2311yescharacteristic
82C4×C22⋊D61—21no—
83C4×C22⋊D61—21no—
84#14519736D411yescharacteristic
85#14519734—21no—
86C42×D61—21no—
87#14519710—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519706—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519700—21no—
103#14519698—21no—
104#14519698—21no—
105#14519697—21no—
106C22⋊#92418—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111C4×#92418—21no—
112C8×Dic61—21no—
113C8×Dic61—21no—
114C2×#41×C61—21no—
115C2×SD16×C61—21no—
116C2×SD16×C61—21no—
117C2×M16×C61D411yescharacteristic
118C2×M16×C61D411yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#125×C61—21no—
124#124×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127#121×C61—21no—
128#121×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131C4×D4×C61—21no—
132C4×D4×C61—21no—
133#117×C61—21no—
134C2×C42×C61C2311yescharacteristic
135#107×C61—21no—
136#107×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#97×C61D411yescharacteristic
142#97×C61D411yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C4×C8×C61C2311yescharacteristic
145#41×C61—42no—
146#41×C61—42no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C22×C4×C61—41no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C2×C22⋊D61—21no—
159#11758222—22no—
160#11758222—41no—
161C2×D244C2×D411yescharacteristic
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×Dic122C2×D411yescharacteristic
166SD16×C61—42no—
167SD16×C61—42no—
168M16×C61—22no—
169M16×C61—41no—
170C2×C8×C61C2×D411yescharacteristic
171C2×C8×C61C2×D411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
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—41no—
181C4⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61—41no—
184C22⋊C4×C61—41no—
185C42×C61—41no—
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61#4111yescharacteristic
189C42×C61C2411yescharacteristic
190C22⋊Dic61—21no—
191#11758202—42no—
192#11758202—42no—
193#11758201—42no—
194#11758201—42no—
195#11758200—42no—
196#11758199—42no—
197#11758198—21no—
198#11758198—21no—
199C4⋊Dic61C2×D411yescharacteristic
200C4⋊Dic61C2×D411yescharacteristic
201#11758196—21no—
202#11758196—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—42no—
213#11758189—42no—
214#11758189—42no—
215C23×C61—41no—
216C23×C61#12111yescharacteristic
217C22×D61—21no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—41no—
221Q8×C61—41no—
222Q8×C61—41no—
223Q8×C61—41no—
224D4×C61—41no—
225D4×C61—41no—
226D4×C61—41no—
227D4×C61—41no—
228D4×C61—81no—
229D4×C61—82no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—82no—
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C22⋊D61—42no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249D244—21no—
250D244—21no—
251C4×D61—42no—
252C4×D61—41no—
253C4×D61—41no—
254C4×D61—81no—
255Dic122—21no—
256Dic122AGL(1,ℤ/8)12yes—
257C8×C61—21no—
258C8×C61—21no—
259C8×C61—21no—
260C8×C61#13512yescomplemented
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#19182—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—81no—
272C22×C61—81no—
273C22×C61—81no—
274C22×C61C2×#12111yescharacteristic
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—21no—
281C4×C61—21no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61C2×#13511yescharacteristic
286C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
287C4×C61#57511yescharacteristic
288C4×C61#57511yescharacteristic
289Dic61—22no—
290Dic61—41no—
291Dic61—41no—
292#3182D6111yescharacteristic, complemented
293#3107—611no—
294#3035—611no—
295#2971—611no—
296#1701—611no—
297#1699—611no—
298#1693—611no—
299#1685—611no—
300#1682—611no—
301#1680—611no—
302#1674—611no—
303#1666—611no—
304#1565—611no—
305#1553—611no—
306#1552—611no—
307C2×C61—41no—
308C2×C61—161no—
309C2×C61#303511yescharacteristic
310C2×C61#305511yescharacteristic
311C2×C61#306911yescharacteristic
312D61—81no—
313C2×#135—1221no—
314#533C2×D6111yescharacteristic
315#532C2×D6111yescharacteristic
316C4×#41—611no—
317#500C2×D6111yescharacteristic
318#492C2×D6111yescharacteristic
319#487C2×D6111yescharacteristic
320#486C2×D6111yescharacteristic
321#485—1221no—
322#475—611no—
323#474—611no—
324#468—21no—
325#468—21no—
326#464—1221no—
327#463—1221no—
328#462—611no—
329#462—611no—
330#461—611no—
331#461—611no—
332#460—611no—
333#459—611no—
334#452—1221no—
335C8×Q8—611no—
336C8×Q8—611no—
337#440—21no—
338#440—21no—
339C4×Q16—1221no—
340C4×SD16—1221no—
341#436—611no—
342#436—611no—
343#436—1221no—
344#436—1221no—
345#432—611no—
346#432—1221no—
347#431—611no—
348C2×C4⋊C8—611no—
349#416—1221no—
350C4×M16—1221no—
351C4×M16C2×D6111yescharacteristic
352#335—611no—
353#335—611no—
354#334—611no—
355#334—611no—
356#332—611no—
357#332—611no—
358#332—611no—
359#332—611no—
360#332—611no—
361#332—611no—
362#331—611no—
363#331—611no—
364C61#1918211yescharacteristic, complemented, Sylow
365C2×#41—21no—
366C2×#41—611no—
367#135—2444no—
368C2×Q16—1221no—
369C2×Q16—1221no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—1221no—
373C2×SD16—1221no—
374C2×SD16—1221no—
375C2×D8—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16C22⋊D6111yescharacteristic
379C2×M16C22⋊D6111yescharacteristic
380C22×C8—1221no—
381C4⋊Q8C22×D6111yescharacteristic
382C4⋊Q8C22×D6111yescharacteristic
383C4⋊Q8C22×D6111yescharacteristic
384#127C22×D6111yescharacteristic
385#125—21no—
386#124—21no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389#121—21no—
390#121—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8—611no—
394C4×Q8—611no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—611no—
398C4×D4—611no—
399C4×D4—1221no—
400C4×D4—1221no—
401#117—21no—
402#117—611no—
403#117—1221no—
404C2×C42—1221no—
405C2×C42C22×D6111yescharacteristic
406#107—21no—
407#107—21no—
408#107—1221no—
409#106—1221no—
410C4⋊C8—611no—
411C4⋊C8—611no—
412C4⋊C8—611no—
413C4⋊C8—611no—
414C4⋊C8—611no—
415C4⋊C8—611no—
416C4⋊C8—1221no—
417C4⋊C8—1221no—
418C4⋊C8—1221no—
419#103—21no—
420#103—21no—
421#103—1221no—
422#103—1221no—
423#103—1221no—
424#103—1221no—
425#103—1221no—
426#102—21no—
427#102—21no—
428#102—1221no—
429#102—1221no—
430#102—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1221no—
434C22⋊C8—1221no—
435#97—1221no—
436#97C22⋊D6111yescharacteristic
437#97C22⋊D6111yescharacteristic
438C4×C8—1221no—
439C4×C8—1221no—
440C4×C8—1221no—
441C4×C8C22×D6111yescharacteristic
442C4×C8C22×D6111yescharacteristic
443#41—42no—
444#41—42no—
445#41—1222no—
446#41—2441no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—611no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—611no—
456C2×D4—1221no—
457C22×C4—41no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4D4×D6111yescharacteristic
462C22×C4#1175822411yescharacteristic
463C22×C4C2×C22⋊D6111yescharacteristic
464Q16—2442no—
465Q16—2442no—
466SD16—42no—
467SD16—42no—
468SD16—2442no—
469SD16—2442no—
470SD16—2442no—
471D8—2442no—
472M16—22no—
473M16—41no—
474M16—2442no—
475M16—2442no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—2442no—
483C2×C8C2×C22⋊D6111yescharacteristic
484C2×C8C2×C22⋊D6111yescharacteristic
485C2×C8C2×C22⋊D6111yescharacteristic
486C2×C8C2×C22⋊D6111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—611no—
496C4⋊C4—611no—
497C4⋊C4—1221no—
498C4⋊C4—1221no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—1221no—
503C22⋊C4—1221no—
504C22⋊C4—1221no—
505C42—41no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42D4×D6111yescharacteristic
510C42#1175822411yescharacteristic
511C42C2×C22⋊D6111yescharacteristic
512C42C23×D6111yescharacteristic
513C23—41no—
514C23—1221no—
515C23#1451974811yescharacteristic
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—612no—
523Q8—1221no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—1221no—
531D4—1221no—
532D4—2442no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—4881no—
546C2×C4—2442no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4#1451974811yescharacteristic
550C2×C4#1451974811yescharacteristic
551C2×C4#1451974811yescharacteristic
552C2×C4C2×D4×D6111yescharacteristic
553C2×C4C22×C22⋊D6111yescharacteristic
554C2×C4C2×#1175822411yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—2441no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C8—2441no—
563C8—2441no—
564C8#1451979712yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—2441no—
572C22—2441no—
573C22—2441no—
574C22C2×#1451974811yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—1222no—
583C4—2441no—
584C4—2441no—
585C4C2×#1451979711yescharacteristic
586C4AGL(1,ℤ/8)×D6111yescharacteristic
587C4#1684055811yescharacteristic
588C4#1684056011yescharacteristic
589C2—41no—
590C2—161no—
591C2—4881no—
592C2#2145526811yescharacteristic
593C2#2145543211yescharacteristic
594C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3182C2
socleC22×C61C2×#121
prime radical#21455268C2
hypercenter#3182D61
hypocenterC61#19182
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #21455884C2semidirect
3. #21454837C2semidirect
4. #21445377C2semidirect
5. #21445363C2semidirect
6. #21445329C2semidirect
7. #21445281C2semidirect
8. #21445260C2semidirect
9. #21445246C2semidirect
10. #21445210C2semidirect
11. #21445164C2semidirect
12. #21444571C2semidirect
13. #21444524C2semidirect
14. #21444519C2semidirect
15. C61×#3182C2semidirect
260. C8×C61#135semidirect
292. #3182D61semidirect
364. C61#19182semidirect
564. C8#14519797semidirect

Maximal subgroups

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

subgroupindex
#214558842
#214552682
#214548372
#214453772
#214453632
#214453292
#214452812
#214452602
#214452462
#214452102
#214451642
#214445712
#214445242
#214445192
C61×#31822
#1918261