Finite Group Databasebeta

← #14910358

Subgroups — #14910358

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622760C211yesmaximal, characteristic, complemented
2C2×#10622806C211yesmaximal, characteristic, complemented
3#13080303C211yesmaximal, characteristic, complemented
4#13070875C211yesmaximal, characteristic, complemented
5#13070731C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070668C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070554C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070527C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070448C211yesmaximal, characteristic, complemented
15C11×#3280C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic, complemented
18C11×#546—21no—
19C2×#66957C2211yescharacteristic
20C22×D88C2211yescharacteristic, complemented
21#10623081—21no—
22C11×#495C2211yescharacteristic, complemented
23C11×#467C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25C11×#463—21no—
26C11×#450—21no—
27C11×#449—21no—
28C4×C11×D8C2211yescharacteristic, complemented
29C8×D4×C11C2211yescharacteristic
30#10622806—24no—
31C2×#66893C2211yescharacteristic, complemented
32C2×#66892C2211yescharacteristic, complemented
33C2×#66892C2211yescharacteristic, complemented
34C2×#66891C2211yescharacteristic, complemented
35C2×#66891C2211yescharacteristic, complemented
36#10622760—24no—
37C2×#66890C2211yescharacteristic
38C2×#66890C2211yescharacteristic
39C2×#66890C2211yescharacteristic
40C2×#66890C2211yescharacteristic
41#10622729C2211yescharacteristic, complemented
42#10622728C2211yescharacteristic
43C2×#66876C2211yescharacteristic, complemented
44C2×#66876C2211yescharacteristic, complemented
45#10622457—21no—
46#10622347—21no—
47#10622344—21no—
48#10622309C2211yescharacteristic, complemented
49C4×D88C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C4⋊(C11⋊C16)C2211yescharacteristic, complemented
60C4×C11⋊C16C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C22×D4×C11—21no—
63C2×#4339—21no—
64C22×D44—21no—
65C11×#135—22no—
66C11×#135—41no—
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×D8—22no—
71C2×C11×D8—21no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#124—21no—
78C11×#123—41no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—41no—
82C11×#120—41no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C2×C11×C22⋊C4—41no—
86#66990—41no—
87#66983—21no—
88#66977—21no—
89C2×Dic44C2311yescharacteristic
90#66957—22no—
91#66957—41no—
92C2×D88—22no—
93C2×D88—21no—
94C2×D88—41no—
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C2×#4314—21no—
99#66947—41no—
100#66937—41no—
101C22⋊C4×D11—41no—
102#66928—21no—
103C4×D44—21no—
104C11×#107C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66893—41no—
113#66892—22no—
114#66892—22no—
115#66891—22no—
116#66891—22no—
117#66890—22no—
118#66890—22no—
119#66890—41no—
120#66890D414yescomplemented
121#66885—21no—
122#66885—21no—
123#66882C2311yescharacteristic
124#66880—21no—
125#66876—22no—
126#66876—22no—
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#33839—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C11×#41—42no—
135C11×#41—81no—
136C2×Q8×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—42no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—81no—
144C2×D4×C11D811yescharacteristic
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151#4339—42no—
152#4339—81no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—42no—
156C2×D44—41no—
157C2×D44—81no—
158C2×C4×D11—41no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×SD16—42no—
164C11×SD16—81no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—42no—
169C11×D8C2×D412yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2411yescharacteristic
178C11×C4⋊C4—21no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4D811yescharacteristic
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4D811yescharacteristic
187C11×C22⋊C4D811yescharacteristic
188C42×C11C2×D411yescharacteristic
189C22⋊Dic11—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193(C2×D11)⋊C4—41no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic44—21no—
197Dic44—21no—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—42no—
202D88C2×D412yes—
203#4314—42no—
204#4314—81no—
205C11⋊C16—21no—
206C11⋊C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#509—111no—
210C2×#509—111no—
211#3280—111no—
212#3280D1111yescharacteristic, complemented
213#2249—111no—
214#2220—111no—
215#2220—111no—
216#2210—111no—
217#2210—111no—
218#2189—111no—
219#2189—111no—
220#2184—111no—
221#2184—111no—
222C4×D16—111no—
223#2169—111no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—82no—
227C23×C11—82no—
228C23×C11—161no—
229C23×C11C2×D811yescharacteristic
230C23×C11C2×D811yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—161no—
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—82no—
244D4×C11—82no—
245D4×C11—161no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—82no—
253C2×C4×C11—161no—
254C2×C4×C11C2×D811yescharacteristic
255C2×C4×C11C2×D811yescharacteristic
256C2×C4×C11C2×D811yescharacteristic
257C2×C4×C11C2×D811yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C22⋊D11—82no—
260C22⋊D11—161no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263D44—22no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—82no—
268C4×D11—82no—
269C4×D11—161no—
270Dic22—41no—
271Dic22—41no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11C22×D411yescharacteristic
276C8×C11H(5,𝔽2)11yescharacteristic
277C2×#135—111no—
278C2×#135C2×D1111yescharacteristic
279C22×D8—111no—
280C22×D8C2×D1111yescharacteristic, complemented
281#546—21no—
282#546—221no—
283#509—224no—
284#509—224no—
285C2×Q32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×D16—111no—
291C2×D16—111no—
292C2×D16—111no—
293C2×D16—111no—
294C2×M32—111no—
295C2×M32—111no—
296#495—111no—
297#495C2×D1111yescharacteristic, complemented
298#467—111no—
299#467C2×D1111yescharacteristic, complemented
300#466—111no—
301#466C2×D1111yescharacteristic
302#463—21no—
303#463—221no—
304#450—21no—
305#450—221no—
306#449—21no—
307#449—221no—
308C4×D8—111no—
309C4×D8C2×D1111yescharacteristic, complemented
310C8×D4C2×D1111yescharacteristic
311#366—111no—
312C4⋊C16—111no—
313#358—111no—
314#358—111no—
315#357—111no—
316#357—111no—
317#357—111no—
318#357—111no—
319C22⋊C16—111no—
320C22⋊C16—111no—
321C4×C16—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—164no—
335C22×C11C22×D811yescharacteristic
336C2×D11—42no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—164no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11D4211yescharacteristic
350C4×C11#57611yescharacteristic
351Dic11—81no—
352Dic11—81no—
353C2×#41—21no—
354C2×#41—221no—
355C22×D4—21no—
356C22×D4—221no—
357#135—22no—
358#135—41no—
359#135—222no—
360#135—441no—
361C2×Q16—111no—
362C2×Q16C22×D1111yescharacteristic
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×D8—22no—
368C2×D8—21no—
369C2×D8—41no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—222no—
373C2×D8—221no—
374C2×D8—441no—
375C2×D8C22×D1111yescharacteristic
376C2×D8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378C22×C8C22×D1111yescharacteristic
379#124—21no—
380#124—221no—
381#123—41no—
382#123—441no—
383C22⋊Q8—21no—
384C22⋊Q8—221no—
385#121—21no—
386#121—41no—
387#121—221no—
388#121—441no—
389#120—41no—
390#120—441no—
391C4×D4—21no—
392C4×D4—221no—
393C4×D4C22⋊D1111yescharacteristic
394C2×C22⋊C4—41no—
395C2×C22⋊C4—441no—
396Q32—441no—
397SD32—222no—
398SD32—222no—
399SD32—222no—
400SD32—222no—
401D16—114no—
402D16—222no—
403D16—222no—
404D16—441no—
405M32—222no—
406M32—222no—
407C2×C16—111no—
408C2×C16—111no—
409C2×C16—111no—
410C2×C16—111no—
411#107—111no—
412#107C22×D1111yescharacteristic
413C4⋊C8C22⋊D1111yescharacteristic
414#103—21no—
415#103—221no—
416#102—21no—
417#102—21no—
418#102—221no—
419#102—221no—
420C22⋊C8C22⋊D1111yescharacteristic
421C22⋊C8C22⋊D1111yescharacteristic
422C4×C8C22×D1111yescharacteristic
423C2×C11—41no—
424C2×C11—41no—
425C2×C11—82no—
426C2×C11—161no—
427C2×C11D4×D811yescharacteristic
428C2×C11#341411yescharacteristic
429C2×C11#341511yescharacteristic
430D11—82no—
431D11—161no—
432C24—41no—
433C24—441no—
434#41—42no—
435#41—81no—
436#41—442no—
437#41—881no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—81no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—442no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—881no—
454C2×D4#432311yescharacteristic
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461Q16—21no—
462Q16—21no—
463Q16—221no—
464Q16—221no—
465SD16—42no—
466SD16—81no—
467SD16—442no—
468SD16—881no—
469D8—21no—
470D8—21no—
471D8—21no—
472D8—42no—
473D8—112no—
474D8—221no—
475D8—221no—
476D8—221no—
477D8—442no—
478D8D4×D1112yes—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8C2×C22⋊D1111yescharacteristic
484C2×C8C2×C22⋊D1111yescharacteristic
485C2×C8C2×C22⋊D1111yescharacteristic
486C2×C8C23×D1111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—221no—
490C4⋊C4—441no—
491C4⋊C4#432311yescharacteristic
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4#432311yescharacteristic
503C22⋊C4#432311yescharacteristic
504C42C2×C22⋊D1111yescharacteristic
505C16—112no—
506C16—221no—
507C16—221no—
508C16—221no—
509C11#3383911yescharacteristic, complemented, Sylow
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—441no—
516C23—441no—
517C23—882no—
518C23—882no—
519C23—1761no—
520C23C2×#432311yescharacteristic
521C23C2×#432311yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—82no—
533D4—161no—
534D4—222no—
535D4—441no—
536D4—441no—
537D4—441no—
538D4—882no—
539D4—882no—
540D4—1761no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—82no—
548C2×C4—161no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—882no—
552C2×C4—1761no—
553C2×C4C2×#432311yescharacteristic
554C2×C4C2×#432311yescharacteristic
555C2×C4C2×#432311yescharacteristic
556C2×C4C2×#432311yescharacteristic
557C2×C4C22×C22⋊D1111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8C2×D4×D1111yescharacteristic
562C8#6703711yescharacteristic
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—164no—
576C22—442no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—1764no—
583C22C22×#432311yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—81no—
589C4—81no—
590C4—881no—
591C4—881no—
592C4D4×C22⋊D1111yescharacteristic
593C4#1062336611yescharacteristic
594C2—41no—
595C2—41no—
596C2—82no—
597C2—161no—
598C2—882no—
599C2—1761no—
600C2D4×#432311yescharacteristic
601C2#1308175011yescharacteristic
602C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3280C2
socleC22×C11C22×D8
hypercenter#3280D11
hypocenterC11#33839
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. C2×#10622806C2semidirect
3. #13080303C2semidirect
4. #13070875C2semidirect
5. #13070731C2semidirect
6. #13070727C2semidirect
7. #13070671C2semidirect
8. #13070668C2semidirect
9. #13070556C2semidirect
10. #13070554C2semidirect
11. #13070528C2semidirect
12. #13070527C2semidirect
13. C4×#66890C2semidirect
14. #13070448C2semidirect
15. C11×#3280C2semidirect
17. C22×C11×D8C22semidirect
20. C22×D88C22semidirect
22. C11×#495C22semidirect
23. C11×#467C22semidirect
28. C4×C11×D8C22semidirect
31. C2×#66893C22semidirect
32. C2×#66892C22semidirect
33. C2×#66892C22semidirect
34. C2×#66891C22semidirect
35. C2×#66891C22semidirect
41. #10622729C22semidirect
43. C2×#66876C22semidirect
44. C2×#66876C22semidirect
48. #10622309C22semidirect
49. C4×D88C22semidirect
50. #10622202C22semidirect
51. #10622200C22semidirect
52. #10622200C22semidirect
53. C22⋊(C11⋊C16)C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622129C22semidirect
58. #10622127C22semidirect
59. C4⋊(C11⋊C16)C22semidirect
60. C4×C11⋊C16C22semidirect
120. #66890D4semidirect
212. #3280D11semidirect
280. C22×D8C2×D11semidirect
297. #495C2×D11semidirect
299. #467C2×D11semidirect
309. C4×D8C2×D11semidirect
509. C11#33839semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
C2×#106228062
#130803032
#130708752
#130707312
#130707272
#130706712
#130706682
#130705562
#130705542
#130705282
#130705272
C4×#668902
#130704482
C11×#32802
#3383911