Finite Group Databasebeta

← #14737467

Subgroups — #14737467

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079588C211yesmaximal, characteristic, complemented
2#13079350C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068175C211yesmaximal, characteristic, complemented
5#13068151C211yesmaximal, characteristic, complemented
6#13068124C211yesmaximal, characteristic, complemented
7#13068098C211yesmaximal, characteristic, complemented
8#13068058C211yesmaximal, characteristic, complemented
9#13068034C211yesmaximal, characteristic, complemented
10#13067993C211yesmaximal, characteristic, complemented
11#13067969C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067278C211yesmaximal, characteristic, complemented
14#13067266C211yesmaximal, characteristic, complemented
15C11×#3247C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#478—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#466—21no—
23C11×#465—21no—
24C11×#463—21no—
25C11×#460C2211yescharacteristic
26C11×#459C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622692C2211yescharacteristic
30#10622686C2211yescharacteristic
31#10622683C2211yescharacteristic
32#10622681—21no—
33#10622672—21no—
34#10622660—21no—
35#10622652—21no—
36#10622652—21no—
37#10622650—21no—
38#10622644C2211yescharacteristic
39#10622640C2211yescharacteristic
40#10622637C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622627—21no—
45#10622627—21no—
46#10622625—21no—
47#10622625C2211yescharacteristic
48#10622624—21no—
49D4×C11⋊C8C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53#10622538C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339—21no—
69C2×C11×SD16—21no—
70C2×C11×D8—21no—
71C22×C8×C11—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124—21no—
77C11×#124D411yescharacteristic
78C11×#123—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121—21no—
81C11×#121—21no—
82C11×#121D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4324—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95C2×#4323—21no—
96#66983—21no—
97#66983—21no—
98C2×#4318—21no—
99C2×#4318D411yescharacteristic
100C2×#4318D411yescharacteristic
101C22×C11⋊C8—21no—
102#66928—21no—
103#66927C2311yescharacteristic
104C4×D44—21no—
105C4×D44—21no—
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#106—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#102—21no—
114C11×#102—21no—
115C11×#102—21no—
116#66896—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66873—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66872—21no—
129#66872—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19248—111nomaximal, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C2×D4×C11C2×D411yescharacteristic
154C22×C4×C11—21no—
155C22×C4×C11—41no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C2×C22⋊D11—41no—
160#4339—81no—
161#4339—81no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×C4×D11—41no—
166C2×Dic22—21no—
167C11×SD16—81no—
168C11×D8—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—81no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C42×C11—21no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4326—81no—
193#4325—81no—
194#4324—81no—
195#4323—42no—
196#4323—42no—
197#4323—81no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202#4318—22no—
203#4318—41no—
204#4318—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#3247D1111yescharacteristic, complemented
215#3212—111no—
216#3184—111no—
217#2969—111no—
218#1701—111no—
219#1697—111no—
220#1692—111no—
221#1688—111no—
222#1682—111no—
223#1678—111no—
224#1671—111no—
225#1667—111no—
226#1565—111no—
227#1543—111no—
228#1540—111no—
229C23×C11—21no—
230C23×C11—41no—
231C23×C11#12111yescharacteristic
232C22×D11—41no—
233Q8×C11—21no—
234Q8×C11—21no—
235Q8×C11—81no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—81no—
243D4×C11—81no—
244D4×C11—82no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—82no—
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C22⋊D11—82no—
264C2×Dic11—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—81no—
270C4×D11—82no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8#13512yes—
283#532—111no—
284#532C2×D1111yescharacteristic
285#529C2×D1111yescharacteristic
286#498—111no—
287#495—221no—
288#493—111no—
289#488—221no—
290#486—111no—
291#486—111no—
292#478—21no—
293#477C2×D1111yescharacteristic
294#476C2×D1111yescharacteristic
295#469—221no—
296#469—221no—
297#466—21no—
298#465—21no—
299#463—21no—
300#462—111no—
301#461—111no—
302#460—111no—
303#460C2×D1111yescharacteristic
304#459—111no—
305#459C2×D1111yescharacteristic
306#452—221no—
307#449—221no—
308#446—111no—
309C8×Q8—111no—
310#442—221no—
311#442—221no—
312#436—111no—
313#436—221no—
314#435—221no—
315C8×D4—111no—
316#433—221no—
317#431—111no—
318#431—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320#405—221no—
321C4×M16—111no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326#333—111no—
327#333—111no—
328#332—111no—
329#332—111no—
330#331—111no—
331#331—111no—
332#331—111no—
333#331—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11C2×#12111yescharacteristic
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—81no—
355C4×C11C2×#13511yescharacteristic
356C4×C11#57511yescharacteristic
357C4×C11#57611yescharacteristic
358C4×C11#57711yescharacteristic
359Dic11—81no—
360C2×#41—21no—
361C2×#41—221no—
362C2×Q16—221no—
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×D8—21no—
367C2×D8—221no—
368C2×D8—221no—
369C2×D8—221no—
370C2×M16—111no—
371C2×M16—111no—
372C2×M16—221no—
373C22×C8—21no—
374C22×C8—221no—
375C4⋊Q8—111no—
376C4⋊Q8C22×D1111yescharacteristic
377#127—111no—
378#127C22×D1111yescharacteristic
379#126—21no—
380#125C22⋊D1111yescharacteristic
381#124—21no—
382#124—221no—
383#124C22⋊D1111yescharacteristic
384#123—21no—
385C22⋊Q8C22⋊D1111yescharacteristic
386#121—21no—
387#121—21no—
388#121—221no—
389#121—221no—
390#121C22⋊D1111yescharacteristic
391C4×Q8C22×D1111yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4C22×D1111yescharacteristic
398#117—21no—
399C2×C42C22×D1111yescharacteristic
400#107—21no—
401#106—21no—
402#106—221no—
403#106—221no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—21no—
414#103—221no—
415#103—221no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424#102—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429#97—111no—
430#97—111no—
431#97—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8—221no—
436C4×C8—221no—
437C2×C11—41no—
438C2×C11—81no—
439C2×C11—161no—
440C2×C11#303511yescharacteristic
441C2×C11#306211yescharacteristic
442C2×C11#306811yescharacteristic
443D11—161no—
444#41—82no—
445#41—881no—
446#41—881no—
447C2×Q8—21no—
448C2×Q8—221no—
449C2×Q8C2×C22⋊D1111yescharacteristic
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—441no—
459C2×D4C2×C22⋊D1111yescharacteristic
460C22×C4—21no—
461C22×C4—41no—
462C22×C4—441no—
463C22×C4D4×D1111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466Q16—881no—
467SD16—81no—
468SD16—881no—
469SD16—881no—
470D8—81no—
471D8—442no—
472D8—442no—
473D8—881no—
474M16—222no—
475M16—441no—
476M16—442no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—81no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—442no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4C2×C22⋊D1111yescharacteristic
498C4⋊C4C2×C22⋊D1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—21no—
509C42D4×D1111yescharacteristic
510C42#434111yescharacteristic
511C42C2×C22⋊D1111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1924811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—41no—
516C23—441no—
517C23#6699211yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—81no—
521Q8—441no—
522Q8—441no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—81no—
530D4—81no—
531D4—82no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—881no—
537D4—882no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—82no—
550C2×C4—441no—
551C2×C4—882no—
552C2×C4#6699211yescharacteristic
553C2×C4#6699211yescharacteristic
554C2×C4#6699211yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×#434111yescharacteristic
557C2×C4C22×C22⋊D1111yescharacteristic
558C8—41no—
559C8—41no—
560C8—112no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—441no—
565C8—441no—
566C8—441no—
567C8—441no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22C2×#6699211yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—881no—
590C4D11×#13511yescharacteristic
591C4#1062329911yescharacteristic
592C4#1062336611yescharacteristic
593C4#1062336811yescharacteristic
594C2—41no—
595C2—81no—
596C2—161no—
597C2—1761no—
598C2#1307806711yescharacteristic
599C2#1307829811yescharacteristic
600C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3247C2
socleC22×C11C2×#121
hypercenter#3247D11
hypocenterC11#19248
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3247

Complements

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

NH ≅ G/Ntype
1. #13079588C2semidirect
2. #13079350C2semidirect
3. #13077621C2semidirect
4. #13068175C2semidirect
5. #13068151C2semidirect
6. #13068124C2semidirect
7. #13068098C2semidirect
8. #13068058C2semidirect
9. #13068034C2semidirect
10. #13067993C2semidirect
11. #13067969C2semidirect
12. #13067366C2semidirect
13. #13067278C2semidirect
14. #13067266C2semidirect
15. C11×#3247C2semidirect
214. #3247D11semidirect
513. C11#19248semidirect

Maximal subgroups

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

subgroupindex
#130795882
#130793502
#130776212
#130681752
#130681512
#130681242
#130680982
#130680582
#130680342
#130679932
#130679692
#130673662
#130672782
#130672662
C11×#32472
#1924811