Finite Group Databasebeta

← #14724410

Subgroups — #14724410

Order 2816.

622 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#13079209C211yesmaximal, characteristic
2#13077760C211yesmaximal, characteristic, complemented
3#13077693C211yesmaximal, characteristic, complemented
4#13067528C211yesmaximal, characteristic, complemented
5#13067518C211yesmaximal, characteristic, complemented
6#13067508C211yesmaximal, characteristic, complemented
7#13067440C211yesmaximal, characteristic, complemented
8#13067427C211yesmaximal, characteristic, complemented
9#13067419C211yesmaximal, characteristic, complemented
10#13067408C211yesmaximal, characteristic, complemented
11#13067382C211yesmaximal, characteristic, complemented
12#13067073C211yesmaximal, characteristic, complemented
13#13067065C211yesmaximal, characteristic, complemented
14C8×#4313C211yesmaximal, characteristic, complemented
15C11×#1589C211yesmaximal, characteristic, complemented
16#10623088C2211yescharacteristic
17#10623079C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622772C411yescharacteristic
22#10622767C411yescharacteristic
23#10622742—21no—
24#10622741—21no—
25#10622740—21no—
26#10622732—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29D4×C11⋊C8C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622499C411yescharacteristic
32#10622489C411yescharacteristic
33#10622450C2211yescharacteristic
34#10622448C2211yescharacteristic
35#10622447C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622395C411yescharacteristic
38#10622393C411yescharacteristic
39#10622378C411yescharacteristic
40#10622377C411yescharacteristic
41#10622343—21no—
42#10622343—21no—
43#10622340—21no—
44#10622333—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48#10622298C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×D8C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C4×D4×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66993C2×C411yescharacteristic
74#66991C2×C411yescharacteristic
75#66991C2×C411yescharacteristic
76#66989C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81#66979—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C2×#4314C2×C411yescharacteristic
85C2×#4313—21no—
86C2×#4313—21no—
87C2×#4313C2×C411yescharacteristic
88C2×#4313C2×C411yescharacteristic
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91#66950C2×C411yescharacteristic
92#66948C2×C411yescharacteristic
93#66943C2×C411yescharacteristic
94#66941C2×C411yescharacteristic
95#66938—21no—
96#66937—21no—
97#66936—21no—
98#66932—21no—
99C4×D44C2311yescharacteristic
100C42×D11C2311yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#107C2×C411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8D411yescharacteristic
121(C2×D11)⋊C8D411yescharacteristic
122#66881C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66879—21no—
125#66879—21no—
126#66879C2×C411yescharacteristic
127#66879C2×C411yescharacteristic
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8D411yescharacteristic
132Dic11⋊C8D411yescharacteristic
133C8×Dic11—21no—
134C8×Dic11—21no—
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17968—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153#4339—81no—
154#4339—81no—
155C2×D44—21no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11C22×C411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×C4×D11#4111yescharacteristic
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C11×D8—22no—
164C11×M16—81no—
165C11×M16—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179C22⋊Dic11—21no—
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182#4324—22no—
183#4323—22no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11#4111yescharacteristic
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#4314—22no—
208#4313—22no—
209#4313—22no—
210#4313—81no—
211#4313—81no—
212C8×D11—42no—
213C8×D11—81no—
214#3171—111no—
215#2993—111no—
216#2981—111no—
217#1594—111no—
218#1592—111no—
219#1590—111no—
220#1589D1111yescharacteristic, complemented
221#1580—111no—
222SD16⋊C8—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1569—111no—
226#1494—111no—
227#1492—111no—
228C8×M16—111no—
229C23×C11—21no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—81no—
247C22⋊D11—81no—
248C22⋊D11—81no—
249C22⋊D11—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11C4×D411yescharacteristic
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256D44—21no—
257D44—21no—
258D44—81no—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266Dic22—21no—
267Dic22—21no—
268Dic22—81no—
269C8×C11—22no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11#13112yes—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8#13112yes—
283#532—111no—
284#529—111no—
285#501—111no—
286#496—111no—
287#490—111no—
288#489—111no—
289#469—111no—
290#469—111no—
291#468—111no—
292#468—111no—
293#446—111no—
294C8×Q8—111no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×D8—111no—
298C4×D8C2×D1111yescharacteristic
299#436—111no—
300#436—221no—
301#436C2×D1111yescharacteristic
302#436C2×D1111yescharacteristic
303#435—221no—
304#435—221no—
305#435—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—111no—
309#433—221no—
310#432—111no—
311#431—111no—
312#424—221no—
313#423—111no—
314#408—221no—
315#408—221no—
316C4×M16—111no—
317C2×C4×C8—111no—
318#335—111no—
319#335C2×D1111yescharacteristic
320#334—111no—
321#334—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329D4⋊C8C2×D1111yescharacteristic
330#322—111no—
331#322—111no—
332C82—111no—
333C82C2×D1111yescharacteristic
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×C4×D411yescharacteristic
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11C2×#13111yescharacteristic
351C4×C11C2×#13111yescharacteristic
352C4×C11#57611yescharacteristic
353C4×C11#57711yescharacteristic
354Dic11—21no—
355Dic11—21no—
356Dic11—21no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360C2×#41—221no—
361C2×SD16—111no—
362C2×SD16—111no—
363C2×D8—111no—
364C2×D8C4×D1111yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—111no—
368C2×M16—111no—
369C2×M16—221no—
370C2×M16—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—111no—
376#127—111no—
377#126—221no—
378#125—111no—
379#124—111no—
380#124—221no—
381#123—221no—
382C22⋊Q8—111no—
383#121—111no—
384#121—111no—
385#121—111no—
386#121—221no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4C22×D1111yescharacteristic
392C4×D4C22×D1111yescharacteristic
393#117—221no—
394C2×C42—111no—
395#107—111no—
396#107C4×D1111yescharacteristic
397#106—111no—
398#106—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—111no—
409#103—111no—
410#102—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102C4×D1111yescharacteristic
415#102C4×D1111yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—111no—
419C22⋊C8—111no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#97—111no—
426#97—111no—
427#97—221no—
428#97—221no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—221no—
433C4×C8—221no—
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C2×C11—81no—
438C2×C11—81no—
439C2×C11#293111yescharacteristic
440C2×C11#294611yescharacteristic
441C2×C11#295611yescharacteristic
442D11—41no—
443D11—81no—
444#41—881no—
445#41—881no—
446C2×Q8—111no—
447C2×Q8—221no—
448C2×D4—111no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4C2×C4×D1111yescharacteristic
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—221no—
462SD16—222no—
463SD16—222no—
464D8—22no—
465D8—222no—
466M16—81no—
467M16—81no—
468M16—222no—
469M16—222no—
470M16—881no—
471M16—881no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—442no—
483C2×C8—881no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8C2×C4×D1111yescharacteristic
487C2×C8C2×C4×D1111yescharacteristic
488C2×C8D4×D1111yescharacteristic
489C2×C8D4×D1111yescharacteristic
490C4⋊C4—111no—
491C4⋊C4—111no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4C2×C4×D1111yescharacteristic
498C4⋊C4C2×C4×D1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C42—111no—
509C42—111no—
510C42—111no—
511C42—221no—
512C42C23×D1111yescharacteristic
513C11#1796811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—111no—
517C23—221no—
518Q8—221no—
519Q8—221no—
520Q8—881no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—221no—
526D4—221no—
527D4—881no—
528D4—881no—
529D4—881no—
530D4—881no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4C22×C4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—112no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—441no—
565C8—441no—
566C8—441no—
567C8#6696012yes—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—221no—
575C22—221no—
576C22—221no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22C4×D4×D1111yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—221no—
585C4—221no—
586C4—221no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4C2×#6696011yescharacteristic
591C4D11×#13111yescharacteristic
592C4#1062328811yescharacteristic
593C4#1062330111yescharacteristic
594C2—81no—
595C2—81no—
596C2—441no—
597C2—881no—
598C2#1307732511yescharacteristic
599C2#1307744111yescharacteristic
600C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1589C2
socleC22×C11C2×C4×D4
prime radical#13079209C2
cosocleC42×C11C24
hypercenter#1589D11
hypocenterC11#17968
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1589

Complements

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

NH ≅ G/Ntype
2. #13077760C2semidirect
3. #13077693C2semidirect
4. #13067528C2semidirect
5. #13067518C2semidirect
6. #13067508C2semidirect
7. #13067440C2semidirect
8. #13067427C2semidirect
9. #13067419C2semidirect
10. #13067408C2semidirect
11. #13067382C2semidirect
12. #13067073C2semidirect
13. #13067065C2semidirect
14. C8×#4313C2semidirect
15. C11×#1589C2semidirect
220. #1589D11semidirect
513. C11#17968semidirect

Maximal subgroups

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

subgroupindex
#130792092
#130777602
#130776932
#130675282
#130675182
#130675082
#130674402
#130674272
#130674192
#130674082
#130673822
#130670732
#130670652
C8×#43132
C11×#15892
#1796811