Finite Group Databasebeta

← #15640512

Subgroups — #15640512

Order 2816.

2272 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083021C211yesmaximal, characteristic, complemented
2#13080858C214yesmaximal, complemented
3#13080566C214yesmaximal, complemented
4D4×#4323C214yesmaximal, complemented
5#13080236C214yesmaximal, complemented
6#13079534C212yesmaximal, complemented
7#13079477C214yesmaximal, complemented
8#13078676C212yesmaximal, complemented
9#13077884C214yesmaximal, complemented
10#13077683C211yesmaximal, characteristic, complemented
11C11×#3498C211yesmaximal, characteristic, complemented
12C2×C11×H(5,𝔽2)C2212yescomplemented
13C11×#550C2214yescomplemented
14D42×C11—24no—
15D42×C11C2214yescomplemented
16C11×#535—22no—
17C11×#535C2212yescomplemented
18C11×#532—21no—
19C11×#532C2211yescharacteristic
20C2×C11×#127—21no—
21C2×C11×#127C2211yescharacteristic, complemented
22C4×C11×#41C2211yescharacteristic, complemented
23#10623361C2214yescomplemented
24C2×#67002C2214yescomplemented
25C22×#4323C2214yescomplemented
26#10623265—21no—
27#10623248—21no—
28#10623214—22no—
29#10623138—24no—
30#10623094C2214yescomplemented
31D4×D44C2214yescomplemented
32#10623008C2212yescomplemented
33#10622851C2214yescomplemented
34#10622851C2218yescomplemented
35#10622847C2214yescomplemented
36#10622846C2214yescomplemented
37#10622830C2218yescomplemented
38#10622830C2218yescomplemented
39#10622828C2214yescomplemented
40#10622686C2214yescomplemented
41#10622685C2214yescomplemented
42#10622685C2214yescomplemented
43#10622683C2214yescomplemented
44#10622652C2218yescomplemented
45#10622651C2218yescomplemented
46#10622649C2218yescomplemented
47#10622648C2218yescomplemented
48#10622640C2212yescomplemented
49C4×#4325C2214yescomplemented
50#10622634C2212yescomplemented
51#10622628C2212yescomplemented
52C4×#4323C2214yescomplemented
53#10622625C2214yescomplemented
54D4×C11⋊C8C2214yescomplemented
55#10622621C2212yescomplemented
56#10622616C2214yescomplemented
57#10622538C2212yescomplemented
58C11×H(5,𝔽2)—44no—
59C11×H(5,𝔽2)—44no—
60C2×C11×#41—22no—
61C2×C11×#41C2311yescharacteristic
62C2×C11×#41C2314yes—
63C2×C11×#41C2312yes—
64C22×D4×C11—22no—
65C22×D4×C11—24no—
66C22×D4×C11—24no—
67C22×D4×C11—22no—
68C22×D4×C11C2314yes—
69C22×D4×C11C2312yes—
70C2×D4×D11—24no—
71C2×#4339—22no—
72C22×D44C2314yes—
73C11×C4⋊Q8D411yescharacteristic
74C11×#127—22no—
75C11×#127—24no—
76C11×#127—21no—
77C11×#127—21no—
78C11×#127D411yescharacteristic
79C11×#127C2314yes—
80C11×#124—22no—
81C11×#124D412yes—
82C11×#121—24no—
83C11×#121—28no—
84C11×#121D414yes—
85C11×#121C2318yes—
86C11×#120—24no—
87C11×#120—28no—
88C4×Q8×C11C2312yes—
89C4×D4×C11—22no—
90C4×D4×C11—24no—
91C4×D4×C11C2312yes—
92C4×D4×C11C2314yes—
93C11×#117—21no—
94C11×#117C2311yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97#67002—48no—
98#67000—24no—
99C2×#4325C2314yes—
100#66993—24no—
101#66991—24no—
102#66990—24no—
103#66990—24no—
104C2×#4323—48no—
105C2×#4323C2314yes—
106C2×#4323C2318yes—
107C2×#4323C2318yes—
108#66983—22no—
109#66983C2314yes—
110#66983C2318yes—
111#66979C2314yes—
112C2×#4318C2314yes—
113C22×C11⋊C8C2314yes—
114#66948—24no—
115#66945—24no—
116#66938—28no—
117#66935—28no—
118#66928—22no—
119#66927C2312yes—
120C4×D44—22no—
121C4×D44C2314yes—
122#66922C2312yes—
123#66899C2314yes—
124#66896C2314yes—
125#66896C2318yes—
126#66896C2318yes—
127C22⋊(C11⋊C8)C2314yes—
128C22⋊(C11⋊C8)C2318yes—
129#66873C2314yes—
130#66873C2314yes—
131#66872C2314yes—
132#66871C2314yes—
133C4⋊(C11⋊C8)C2312yes—
134C4⋊(C11⋊C8)C2312yes—
135C4×C11⋊C8C2314yes—
136#61661—111nomaximal, Sylow
137C24×C11—24no—
138C24×C11—22no—
139C23×D11—24no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41—28no—
143C11×#41—42no—
144C11×#41—42no—
145C11×#41—44no—
146C11×#41—48no—
147C2×Q8×C11C2×D412yes—
148C2×Q8×C11C2411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—28no—
151C2×D4×C11—24no—
152C2×D4×C11—28no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—22no—
156C2×D4×C11—24no—
157C2×D4×C11—44no—
158C2×D4×C11—42no—
159C2×D4×C11—42no—
160C2×D4×C11—48no—
161C2×D4×C11—416no—
162C2×D4×C11—84no—
163C2×D4×C11—88no—
164C2×D4×C11C2×D414yes—
165C2×D4×C11C2×D412yes—
166C2×D4×C11C2×D414yes—
167C2×D4×C11C2414yes—
168C2×D4×C11C2411yescharacteristic
169C22×C4×C11—21no—
170C22×C4×C11—22no—
171C22×C4×C11—24no—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2414yes—
175C2×C22⋊D11—28no—
176C2×C22⋊D11—24no—
177D4×D11—88no—
178#4339—84no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—24no—
182C2×D44—44no—
183C2×D44—44no—
184C2×D44C2414yes—
185C2×C4×D11—24no—
186C2×Dic22—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4C2×D414yes—
189C11×C4⋊C4C2412yes—
190C11×C22⋊C4—21no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—28no—
193C11×C22⋊C4C2×D418yes—
194C42×C11—21no—
195C42×C11—22no—
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2412yes—
199C22⋊Dic11—24no—
200#4325—28no—
201#4323—28no—
202#4323—48no—
203#4323—48no—
204(C2×D11)⋊C4—24no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—28no—
207C4⋊Dic11—22no—
208C4⋊Dic11C2414yes—
209C4×Dic11—24no—
210#4318—44no—
211C2×C11⋊C8—44no—
212C2×C11⋊C8C2414yes—
213C2×C11⋊C8C2414yes—
214#3549—111no—
215#3498D1111yescharacteristic, complemented
216#3325—114no—
217#3305—114no—
218D4×D8—114no—
219#3274—114no—
220#3205—112no—
221#3199—114no—
222#3106—112no—
223#3008—114no—
224#2979—111no—
225C23×C11—21no—
226C23×C11—24no—
227C23×C11—48no—
228C23×C11—44no—
229C23×C11—84no—
230C23×C11—88no—
231C23×C11C22×D414yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—24no—
234C22×D11—84no—
235C22×D11—88no—
236Q8×C11—21no—
237Q8×C11—42no—
238Q8×C11H(5,𝔽2)12yes—
239D4×C11—24no—
240D4×C11—28no—
241D4×C11—21no—
242D4×C11—24no—
243D4×C11—24no—
244D4×C11—42no—
245D4×C11—44no—
246D4×C11—48no—
247D4×C11—48no—
248D4×C11—44no—
249D4×C11—48no—
250D4×C11—84no—
251D4×C11—88no—
252D4×C11H(5,𝔽2)12yes—
253C2×C4×C11—24no—
254C2×C4×C11—21no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—48no—
262C2×C4×C11—44no—
263C2×C4×C11C22×D414yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D412yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C2511yescharacteristic
268C22⋊D11—84no—
269C22⋊D11—88no—
270C2×Dic11—24no—
271D44—24no—
272D44—24no—
273D44—44no—
274D44—84no—
275D44—82no—
276C4×D11—48no—
277Dic22—82no—
278C11⋊C8—24no—
279C11⋊C8—24no—
280C2×H(5,𝔽2)C2×D1112yescomplemented
281C2×AGL(1,ℤ/8)—114no—
282C22×D8—114no—
283H(3,𝔽4)—222no—
284#555—114no—
285#555—221no—
286#550C2×D1114yescomplemented
287D42—24no—
288D42—114no—
289D42—221no—
290D42C2×D1114yescomplemented
291#535—22no—
292#535—114no—
293#535—224no—
294#535C2×D1112yescomplemented
295#532—21no—
296#532—112no—
297#532C2×D1111yescharacteristic
298C2×#127—21no—
299C2×#127C2×D1111yescharacteristic, complemented
300C4×#41C2×D1111yescharacteristic, complemented
301#493—114no—
302#486—114no—
303#482—118no—
304#482—114no—
305#477—112no—
306#476—112no—
307#469—118no—
308#466—118no—
309#460—112no—
310#459—114no—
311#459—114no—
312#459—112no—
313#449—114no—
314#449—118no—
315#447—118no—
316#447—118no—
317#447—118no—
318C4×SD16—114no—
319C4×D8—114no—
320#436—114no—
321C8×D4—114no—
322#431—112no—
323#418—114no—
324#416—114no—
325#408—114no—
326C22×C11—21no—
327C22×C11—22no—
328C22×C11—24no—
329C22×C11—22no—
330C22×C11—28no—
331C22×C11—42no—
332C22×C11—44no—
333C22×C11—48no—
334C22×C11—168no—
335C22×C11—164no—
336C22×C11C23×D411yescharacteristic
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—168no—
341C4×C11—21no—
342C4×C11—22no—
343C4×C11—24no—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11#57614yes—
347C4×C11C2×H(5,𝔽2)11yescharacteristic
348C4×C11C2×H(5,𝔽2)11yescharacteristic
349Dic11—44no—
350H(5,𝔽2)—44no—
351H(5,𝔽2)—44no—
352C2×#41—22no—
353C2×#41—222no—
354C2×#41C22×D1111yescharacteristic
355C2×#41C22×D1114yes—
356C2×#41C22×D1112yes—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—114no—
362C22×D4—224no—
363C22×D4C22×D1114yes—
364C22×D4C22×D1112yes—
365AGL(1,ℤ/8)—448no—
366C2×SD16—114no—
367C2×D8—114no—
368C2×D8—118no—
369C2×D8—118no—
370C2×D8—448no—
371C2×M16—114no—
372C22×C8—114no—
373C4⋊Q8—112no—
374C4⋊Q8C22⋊D1111yescharacteristic
375#127—22no—
376#127—24no—
377#127—21no—
378#127—21no—
379#127—112no—
380#127—224no—
381#127C22⋊D1111yescharacteristic
382#127C22×D1114yes—
383#124—22no—
384#124—224no—
385#124—228no—
386#124—222no—
387#124C22⋊D1112yes—
388#121—24no—
389#121—28no—
390#121—114no—
391#121—118no—
392#121—224no—
393#121—222no—
394#121—224no—
395#121C22⋊D1114yes—
396#121C22×D1118yes—
397#120—24no—
398#120—28no—
399#120—224no—
400#120—224no—
401#120—228no—
402C4×Q8C22×D1112yes—
403C4×D4—22no—
404C4×D4—24no—
405C4×D4—114no—
406C4×D4—222no—
407C4×D4C22×D1112yes—
408C4×D4C22×D1114yes—
409#117—21no—
410#117—114no—
411#117—224no—
412#117C22×D1111yescharacteristic
413C2×C42—21no—
414C2×C42C22×D1111yescharacteristic
415#107—114no—
416#106—114no—
417C4⋊C8—112no—
418C4⋊C8—112no—
419#103—114no—
420#102—118no—
421#102—114no—
422#102—118no—
423#102—114no—
424#102—114no—
425C22⋊C8—114no—
426C22⋊C8—118no—
427C4×C8—114no—
428C2×C11—44no—
429C2×C11—41no—
430C2×C11—42no—
431C2×C11—84no—
432C2×C11#348411yescharacteristic
433C2×C11C2×#57612yes—
434D11—84no—
435C24—24no—
436C24—22no—
437C24—224no—
438#41—22no—
439#41—22no—
440#41—28no—
441#41—42no—
442#41—42no—
443#41—44no—
444#41—48no—
445#41—884no—
446C2×Q8—222no—
447C2×Q8C2×C22⋊D1112yes—
448C2×Q8C23×D1111yescharacteristic
449C2×D4—21no—
450C2×D4—28no—
451C2×D4—24no—
452C2×D4—28no—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—44no—
458C2×D4—42no—
459C2×D4—42no—
460C2×D4—48no—
461C2×D4—416no—
462C2×D4—84no—
463C2×D4—88no—
464C2×D4—114no—
465C2×D4—228no—
466C2×D4—224no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—224no—
470C2×D4—444no—
471C2×D4—444no—
472C2×D4—888no—
473C2×D4C2×C22⋊D1114yes—
474C2×D4C2×C22⋊D1114yes—
475C2×D4C2×C22⋊D1112yes—
476C2×D4C23×D1114yes—
477C2×D4C23×D1111yescharacteristic
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—224no—
482C22×C4C2×C22⋊D1112yes—
483C22×C4C23×D1111yescharacteristic
484C22×C4C23×D1114yes—
485SD16—228no—
486D8—228no—
487D8—448no—
488D8—448no—
489M16—444no—
490C2×C8—114no—
491C2×C8—114no—
492C2×C8—444no—
493C4⋊C4—22no—
494C4⋊C4—114no—
495C4⋊C4—222no—
496C4⋊C4C2×C22⋊D1114yes—
497C4⋊C4C23×D1112yes—
498C22⋊C4—21no—
499C22⋊C4—22no—
500C22⋊C4—28no—
501C22⋊C4—224no—
502C22⋊C4—228no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4C2×C22⋊D1118yes—
506C42—21no—
507C42—22no—
508C42—224no—
509C42C2×C22⋊D1111yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C23×D1112yes—
512C11#6166111yescharacteristic, complemented, Sylow
513C23—21no—
514C23—24no—
515C23—48no—
516C23—44no—
517C23—84no—
518C23—88no—
519C23—224no—
520C23—884no—
521C23—888no—
522C23C22×C22⋊D1111yescharacteristic
523C23C22×C22⋊D1114yes—
524Q8—21no—
525Q8—42no—
526Q8—882no—
527Q8#6703712yes—
528D4—24no—
529D4—28no—
530D4—21no—
531D4—24no—
532D4—24no—
533D4—42no—
534D4—44no—
535D4—48no—
536D4—48no—
537D4—44no—
538D4—48no—
539D4—84no—
540D4—88no—
541D4—224no—
542D4—224no—
543D4—444no—
544D4—884no—
545D4—882no—
546D4—888no—
547D4—884no—
548D4#6703712yes—
549C2×C4—24no—
550C2×C4—21no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—48no—
558C2×C4—44no—
559C2×C4—224no—
560C2×C4—448no—
561C2×C4C22×C22⋊D1111yescharacteristic
562C2×C4C22×C22⋊D1114yes—
563C2×C4C22×C22⋊D1112yes—
564C2×C4C22×C22⋊D1112yes—
565C2×C4C24×D1111yescharacteristic
566C8—224no—
567C8—224no—
568C22—21no—
569C22—22no—
570C22—24no—
571C22—22no—
572C22—28no—
573C22—42no—
574C22—44no—
575C22—48no—
576C22—168no—
577C22—164no—
578C22—444no—
579C22—444no—
580C22—444no—
581C22—1768no—
582C22C23×C22⋊D1111yescharacteristic
583C4—21no—
584C4—22no—
585C4—24no—
586C4—22no—
587C4—42no—
588C4—444no—
589C4#1062336614yes—
590C4C2×#6703711yescharacteristic
591C4C2×#6703711yescharacteristic
592C2—41no—
593C2—44no—
594C2—42no—
595C2—84no—
596C2—884no—
597C2#1308225111yescharacteristic
598C2C2×#1062336612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3498C2
socleC22×C11C23×D4
hypercenter#3498D11
hypocenterC11#61661
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #532 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #13083021C2semidirect
2. #13080858C2semidirect
3. #13080566C2semidirect
4. D4×#4323C2semidirect
5. #13080236C2semidirect
6. #13079534C2semidirect
7. #13079477C2semidirect
8. #13078676C2semidirect
9. #13077884C2semidirect
10. #13077683C2semidirect
11. C11×#3498C2semidirect
12. C2×C11×H(5,𝔽2)C22semidirect
13. C11×#550C22semidirect
15. D42×C11C22semidirect
17. C11×#535C22semidirect
21. C2×C11×#127C22semidirect
22. C4×C11×#41C22semidirect
23. #10623361C22semidirect
24. C2×#67002C22semidirect
25. C22×#4323C22semidirect
30. #10623094C22semidirect
31. D4×D44C22semidirect
32. #10623008C22semidirect
33. #10622851C22semidirect
34. #10622851C22semidirect
35. #10622847C22semidirect
36. #10622846C22semidirect
37. #10622830C22semidirect
38. #10622830C22semidirect
39. #10622828C22semidirect
40. #10622686C22semidirect
41. #10622685C22semidirect
42. #10622685C22semidirect
43. #10622683C22semidirect
44. #10622652C22semidirect
45. #10622651C22semidirect
46. #10622649C22semidirect
47. #10622648C22semidirect
48. #10622640C22semidirect
49. C4×#4325C22semidirect
50. #10622634C22semidirect
51. #10622628C22semidirect
52. C4×#4323C22semidirect
53. #10622625C22semidirect
54. D4×C11⋊C8C22semidirect
55. #10622621C22semidirect
56. #10622616C22semidirect
57. #10622538C22semidirect
215. #3498D11semidirect
280. C2×H(5,𝔽2)C2×D11semidirect
286. #550C2×D11semidirect
290. D42C2×D11semidirect
294. #535C2×D11semidirect
299. C2×#127C2×D11semidirect
300. C4×#41C2×D11semidirect
512. C11#61661semidirect

Maximal subgroups

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

subgroupindex
#130830212
#130808582
#130805662
D4×#43232
#130802362
#130795342
#130794772
#130786762
#130778842
#130776832
C11×#34982
#6166111