Finite Group Databasebeta

← #14739215

Subgroups — #14739215

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079549C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068072C211yesmaximal, characteristic, complemented
5#13068065C211yesmaximal, characteristic, complemented
6#13068030C211yesmaximal, characteristic, complemented
7#13068023C211yesmaximal, characteristic, complemented
8#13067974C211yesmaximal, characteristic, complemented
9#13067969C211yesmaximal, characteristic, complemented
10#13067966C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic, complemented
13#13067312C211yesmaximal, characteristic, complemented
14#13067265C211yesmaximal, characteristic, complemented
15C11×#3115C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#482—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#449—21no—
25C11×#442—21no—
26C11×#440—21no—
27C11×#432C2211yescharacteristic
28#10622851—21no—
29#10622851—21no—
30#10622851—21no—
31#10622698C2211yescharacteristic
32#10622694C2211yescharacteristic
33#10622686C2211yescharacteristic
34#10622683C2211yescharacteristic
35#10622670—21no—
36#10622670—21no—
37#10622640C2211yescharacteristic
38C4×#4325—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622616—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×#4339—21no—
70C2×C11×SD16—21no—
71C2×C11×D8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#124—21no—
75C11×#121—21no—
76C11×#121—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11C2311yescharacteristic
85C11×#117—21no—
86C11×#117D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4323—21no—
93C2×#4323—21no—
94C2×#4323—21no—
95#66983—21no—
96#66983—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100#66928—21no—
101#66927C2311yescharacteristic
102C4×D44—21no—
103C4×D44—21no—
104#66922C2311yescharacteristic
105C11×#107—21no—
106C11×#106—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#102—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C11×#97—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)D411yescharacteristic
125C22⋊(C11⋊C8)D411yescharacteristic
126#66873—21no—
127#66873—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)D411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19412—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—81no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—41no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C2×C22⋊D11—41no—
165#4339—82no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×C4×D11—41no—
170C2×Dic22—21no—
171C11×SD16—42no—
172C11×D8—42no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11#4111yescharacteristic
192C42×C11C2411yescharacteristic
193#4325—42no—
194#4325—81no—
195#4325—81no—
196#4323—42no—
197#4323—81no—
198#4323—81no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8—81no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214#3207—111no—
215#3115D1111yescharacteristic, complemented
216#3106—111no—
217#2988—111no—
218#1684—111no—
219#1683—111no—
220#1678—111no—
221#1677—111no—
222#1668—111no—
223#1667—111no—
224#1666—111no—
225#1665—111no—
226#1572—111no—
227#1551—111no—
228#1540—111no—
229C23×C11—21no—
230C23×C11—41no—
231C23×C11#12111yescharacteristic
232C22×D11—41no—
233Q8×C11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11#13512yes—
237D4×C11—24no—
238D4×C11—21no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—81no—
244D4×C11—82no—
245D4×C11#13512yes—
246C2×C4×C11—24no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—81no—
259C2×C4×C11—82no—
260C2×C4×C11#12111yescharacteristic
261C2×C4×C11#12111yescharacteristic
262C2×C4×C11#12111yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C22⋊D11—82no—
267C2×Dic11—41no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—41no—
272D44—81no—
273C4×D11—82no—
274Dic22—81no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#532—111no—
286#532C2×D1111yescharacteristic
287C4×#41C2×D1111yescharacteristic
288#493—111no—
289#492—111no—
290#487—111no—
291#486—111no—
292#482—21no—
293#482—221no—
294#477—111no—
295#476—111no—
296#475C2×D1111yescharacteristic
297#474C2×D1111yescharacteristic
298#463—221no—
299#463—221no—
300#460—111no—
301#460C2×D1111yescharacteristic
302#459—111no—
303#459C2×D1111yescharacteristic
304#449—21no—
305#449—221no—
306#449—221no—
307#449—221no—
308C8×Q8—111no—
309C8×Q8—111no—
310#442—21no—
311#440—21no—
312C4×SD16—221no—
313C4×D8—221no—
314C8×D4—111no—
315C8×D4—111no—
316C8×D4—221no—
317C8×D4—221no—
318#432C2×D1111yescharacteristic
319#431—111no—
320#431—111no—
321#431—221no—
322C2×C4⋊C8—111no—
323C2×C4⋊C8—221no—
324#335—111no—
325#335—111no—
326#334—111no—
327#334—111no—
328#333—111no—
329#333—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334#331—111no—
335#331—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—21no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11C2×#12111yescharacteristic
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11C2×#13511yescharacteristic
358C4×C11C2×#13511yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361Dic11—81no—
362C2×#41—21no—
363C2×#41—221no—
364C2×#41C22⋊D1111yescharacteristic
365C2×SD16—21no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×SD16—221no—
369C2×D8—21no—
370C2×D8—221no—
371C2×D8—221no—
372C2×D8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C4⋊Q8—111no—
377C4⋊Q8C22×D1111yescharacteristic
378#127—111no—
379#127C22×D1111yescharacteristic
380#124—21no—
381#124—221no—
382#121—21no—
383#121—21no—
384#121—221no—
385#121—221no—
386C4×Q8C22⋊D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4C22⋊D1111yescharacteristic
395C4×D4C22×D1111yescharacteristic
396#117—21no—
397#117C22⋊D1111yescharacteristic
398C2×C42—21no—
399C2×C42C22×D1111yescharacteristic
400#107—21no—
401#107—221no—
402#106—21no—
403#106—221no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—111no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8—221no—
413C4⋊C8C22×D1111yescharacteristic
414C4⋊C8C22×D1111yescharacteristic
415#103—21no—
416#103—221no—
417#103—221no—
418#103—221no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—221no—
423#102—221no—
424#102—221no—
425#102—221no—
426#102—221no—
427C22⋊C8—21no—
428C22⋊C8—111no—
429C22⋊C8—111no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C22⋊C8—221no—
433#97—21no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8—221no—
438C4×C8—221no—
439C2×C11—41no—
440C2×C11—42no—
441C2×C11—161no—
442C2×C11#304511yescharacteristic
443C2×C11#305011yescharacteristic
444C2×C11#306811yescharacteristic
445D11—161no—
446#41—22no—
447#41—22no—
448#41—81no—
449#41—81no—
450#41—882no—
451C2×Q8—21no—
452C2×Q8—221no—
453C2×Q8C2×C22⋊D1111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—441no—
463C2×D4C2×C22⋊D1111yescharacteristic
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—441no—
469C22×C4D4×D1111yescharacteristic
470C22×C4#434111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472SD16—42no—
473SD16—442no—
474SD16—881no—
475SD16—881no—
476D8—42no—
477D8—442no—
478D8—881no—
479D8—881no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—881no—
491C2×C8—881no—
492C2×C8—881no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4C2×C22⋊D1111yescharacteristic
500C4⋊C4C2×C22⋊D1111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—441no—
507C22⋊C4—441no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42D4×D1111yescharacteristic
512C42#434111yescharacteristic
513C42C2×C22⋊D1111yescharacteristic
514C42C23×D1111yescharacteristic
515C11#1941211yescharacteristic, complemented, Sylow
516C23—21no—
517C23—41no—
518C23—441no—
519C23#6699211yescharacteristic
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—881no—
524Q8#6700312yes—
525D4—24no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—82no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—881no—
538D4—882no—
539D4#6700312yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—82no—
554C2×C4—441no—
555C2×C4—882no—
556C2×C4#6699211yescharacteristic
557C2×C4#6699211yescharacteristic
558C2×C4#6699211yescharacteristic
559C2×C4C2×D4×D1111yescharacteristic
560C2×C4C2×#434111yescharacteristic
561C2×C4C22×C22⋊D1111yescharacteristic
562C8—41no—
563C8—41no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—441no—
569C8—441no—
570C8—441no—
571C8—441no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22C2×#6699211yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—22no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—881no—
594C4#1062330511yescharacteristic
595C4#1062330611yescharacteristic
596C4C2×#6700311yescharacteristic
597C4C2×#6700311yescharacteristic
598C2—41no—
599C2—42no—
600C2—161no—
601C2—1761no—
602C2#1307815911yescharacteristic
603C2#1307819411yescharacteristic
604C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3115C2
socleC22×C11C2×#121
hypercenter#3115D11
hypocenterC11#19412
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3115

Complements

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

NH ≅ G/Ntype
1. #13079549C2semidirect
2. #13078676C2semidirect
3. #13077727C2semidirect
4. #13068072C2semidirect
5. #13068065C2semidirect
6. #13068030C2semidirect
7. #13068023C2semidirect
8. #13067974C2semidirect
9. #13067969C2semidirect
10. #13067966C2semidirect
11. #13067959C2semidirect
12. #13067397C2semidirect
13. #13067312C2semidirect
14. #13067265C2semidirect
15. C11×#3115C2semidirect
215. #3115D11semidirect
515. C11#19412semidirect

Maximal subgroups

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

subgroupindex
#130795492
#130786762
#130777272
#130680722
#130680652
#130680302
#130680232
#130679742
#130679692
#130679662
#130679592
#130673972
#130673122
#130672652
C11×#31152
#1941211