Finite Group Databasebeta

← #15640547

Subgroups — #15640547

Order 2816.

2136 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082396C211yesmaximal, characteristic, complemented
2#13080904C214yesmaximal, complemented
3#13080538C214yesmaximal, complemented
4D4×#4324C214yesmaximal, complemented
5#13080212C214yesmaximal, complemented
6#13079538C212yesmaximal, complemented
7#13079488C214yesmaximal, complemented
8#13078670C212yesmaximal, complemented
9#13077900C214yesmaximal, complemented
10#13077683C211yesmaximal, characteristic, complemented
11C11×#3549C211yesmaximal, characteristic, complemented
12C2×#67043C2212yescomplemented
13C11×H(3,𝔽4)—22no—
14C11×#555—21no—
15C11×#555C2214yes—
16D42×C11—21no—
17D42×C11C2214yes—
18C11×#535—24no—
19C11×#535C2214yes—
20C11×#532C2212yes—
21C11×#532C2211yescharacteristic
22#10623356C2212yescomplemented
23C22×#4324C2214yescomplemented
24C2×#66985C2214yescomplemented
25D11×C4⋊Q8—21no—
26#10623247—21no—
27#10623206—22no—
28#10623142—24no—
29#10623082C2214yescomplemented
30D4×Dic22C2214yescomplemented
31C4×#4339C2211yescharacteristic, complemented
32C2×#66922C2211yescharacteristic, complemented
33#10622847C2214yescomplemented
34#10622831C2218yescomplemented
35#10622706C2214yescomplemented
36#10622704C2212yescomplemented
37#10622697C2212yescomplemented
38#10622689C2214yes—
39#10622688C2212yes—
40#10622685C2212yes—
41#10622655C2218yescomplemented
42#10622654C2218yescomplemented
43#10622653C2218yescomplemented
44#10622653C2218yescomplemented
45#10622650C2214yescomplemented
46#10622650C2218yescomplemented
47#10622648C2214yescomplemented
48#10622632C2214yescomplemented
49#10622632C2214yescomplemented
50C4×#4324C2214yescomplemented
51C4×#4323C2214yescomplemented
52#10622625C2214yescomplemented
53D4×C11⋊C8C2214yescomplemented
54#10622617C2214yescomplemented
55#10622615C2214yescomplemented
56#10622609C2218yescomplemented
57#10622538C2212yescomplemented
58C2×C11×#41—22no—
59C2×C11×#41C2312yes—
60C22×D4×C11—24no—
61C22×D4×C11C2314yes—
62#67043—44no—
63#67043—44no—
64C2×Q8×D11—22no—
65C2×#4341—22no—
66C2×#4341—24no—
67C2×#4339C2311yescharacteristic
68C2×#4339C2314yes—
69C22×Dic22C2314yes—
70C22×Dic22C2312yes—
71C11×C4⋊Q8D411yescharacteristic
72C11×C4⋊Q8C2312yes—
73C11×#127—24no—
74C11×#127D411yescharacteristic
75C11×#127C2312yes—
76C11×#124—24no—
77C11×#124—28no—
78C11×#124—22no—
79C11×#124D412yes—
80C11×#121—24no—
81C11×#121—22no—
82C11×#121—24no—
83C11×#121D414yes—
84C11×#121C2314yes—
85C11×#121C2318yes—
86C11×#120—24no—
87C11×#120—24no—
88C11×#120—28no—
89C4×D4×C11—22no—
90C4×D4×C11C2314yes—
91C4×D4×C11C2314yes—
92C11×#117—24no—
93C11×#117C2314yes—
94C2×C42×C11C2311yescharacteristic
95#66997—22no—
96#66991—24no—
97#66989—22no—
98#66988—24no—
99D4×Dic11—24no—
100C2×#4324—48no—
101C2×#4324C2314yes—
102C2×#4324C2318yes—
103C2×#4324C2318yes—
104#66985—48no—
105C2×#4323C2314yes—
106C4×C22⋊D11—22no—
107#66979C2311yescharacteristic
108C2×C4⋊Dic11—22no—
109#66977C2318yes—
110C2×#4318C2314yes—
111C22×C11⋊C8C2314yes—
112C4⋊C4×D11—24no—
113#66941—24no—
114#66936—28no—
115#66931—28no—
116C4×D44C2312yes—
117#66925—21no—
118C42×D11—21no—
119#66922—21no—
120#66922—21no—
121#66922C2314yes—
122C4×Dic22C2312yes—
123#66896C2314yes—
124#66896C2314yes—
125C22⋊(C11⋊C8)C2314yes—
126C22⋊(C11⋊C8)C2318yes—
127#66874C2318yes—
128#66874C2318yes—
129#66874C2314yes—
130#66873C2314yes—
131#66872C2314yes—
132#66871C2314yes—
133C4⋊(C11⋊C8)C2312yes—
134C4⋊(C11⋊C8)C2312yes—
135C4×C11⋊C8C2314yes—
136#61664—111nomaximal, Sylow
137C24×C11—24no—
138C11×#41—42no—
139C11×#41—42no—
140C11×#41—84no—
141C2×Q8×C11—22no—
142C2×Q8×C11C2×D412yes—
143C2×D4×C11—28no—
144C2×D4×C11—24no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11—24no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11—88no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2×D414yes—
153C2×D4×C11C2×D412yes—
154C2×D4×C11C2414yes—
155C22×C4×C11—24no—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2414yes—
159C2×C22⋊D11—21no—
160C2×C22⋊D11—24no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163Q8×D11—48no—
164#4341—48no—
165#4341—416no—
166#4339—22no—
167#4339—28no—
168#4339—22no—
169#4339—44no—
170C2×D44C2411yescharacteristic
171C2×C4×D11—21no—
172C2×C4×D11—22no—
173C2×C4×D11—24no—
174C2×Dic22—28no—
175C2×Dic22—22no—
176C2×Dic22—24no—
177C2×Dic22—44no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22C2414yes—
181C2×Dic22C2411yescharacteristic
182C11×C4⋊C4—22no—
183C11×C4⋊C4C2×D414yes—
184C11×C4⋊C4C2414yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C11×C22⋊C4C2×D418yes—
190C42×C11—24no—
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2412yes—
194C22⋊Dic11—28no—
195C22⋊Dic11—21no—
196#4324—28no—
197#4324—48no—
198#4324—48no—
199#4323—28no—
200(C2×D11)⋊C4—22no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11C2412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—28no—
206C4×Dic11—22no—
207C4×Dic11—21no—
208#4318—44no—
209C2×C11⋊C8—44no—
210C2×C11⋊C8C2414yes—
211C2×C11⋊C8C2414yes—
212#3549D1111yescharacteristic, complemented
213#3499—111no—
214#3329—114no—
215#3303—114no—
216D4×SD16—114no—
217#3272—114no—
218#3206—112no—
219#3200—114no—
220#3106—112no—
221#3010—114no—
222#2979—111no—
223C23×C11—24no—
224C23×C11—84no—
225C23×C11—88no—
226C23×C11C22×D414yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—21no—
229Q8×C11—42no—
230Q8×C11—82no—
231D4×C11—28no—
232D4×C11—24no—
233D4×C11—24no—
234D4×C11—42no—
235D4×C11—44no—
236D4×C11—44no—
237D4×C11—84no—
238D4×C11—82no—
239D4×C11—88no—
240D4×C11—84no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—24no—
247C2×C4×C11—48no—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D414yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D412yes—
252C2×C4×C11C2511yescharacteristic
253C22⋊D11—24no—
254C22⋊D11—48no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—48no—
259C2×Dic11—44no—
260D44—21no—
261D44H(5,𝔽2)12yes—
262C4×D11—24no—
263C4×D11—48no—
264C4×D11—44no—
265Dic22—21no—
266Dic22—24no—
267Dic22—24no—
268Dic22—48no—
269Dic22—44no—
270Dic22H(5,𝔽2)12yes—
271C11⋊C8—24no—
272C11⋊C8—24no—
273C2×2−1+4—112no—
274C2×AGL(1,ℤ/8)—114no—
275C22×SD16—114no—
276H(3,𝔽4)—22no—
277#555—21no—
278#555C2×D1114yes—
279D4×Q8—114no—
280#547—114no—
281#547—224no—
282D42—21no—
283D42C2×D1114yes—
284#536—112no—
285#536—222no—
286#535—24no—
287#535C2×D1114yes—
288#532—221no—
289#532C2×D1112yes—
290#532C2×D1111yescharacteristic
291C2×C4⋊Q8—111no—
292C2×C4⋊Q8—221no—
293C4×#41—111no—
294#492—114no—
295#487—114no—
296#485—118no—
297#482—114no—
298#477—112no—
299#476—112no—
300#468—118no—
301#465—118no—
302#461—114no—
303#461—114no—
304#460—112no—
305#459—112no—
306#450—118no—
307#449—114no—
308#449—118no—
309#448—118no—
310#448—118no—
311C4×SD16—114no—
312C4×D8—114no—
313#436—114no—
314C8×D4—114no—
315#431—112no—
316#419—114no—
317#416—114no—
318#408—114no—
319C22×C11—21no—
320C22×C11—24no—
321C22×C11—22no—
322C22×C11—28no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—168no—
327C22×C11C23×D411yescharacteristic
328C2×D11—22no—
329C2×D11—42no—
330C4×C11—21no—
331C4×C11—24no—
332C4×C11—22no—
333C4×C11—44no—
334C4×C11#57714yes—
335C4×C11C2×H(5,𝔽2)11yescharacteristic
336C4×C11C2×H(5,𝔽2)11yescharacteristic
337Dic11—22no—
338Dic11—44no—
339Dic11—42no—
3402−1+4—444no—
3412−1+4—444no—
342C2×#41—22no—
343C2×#41—111no—
344C2×#41—114no—
345C2×#41—222no—
346C2×#41—224no—
347C2×#41C22×D1112yes—
348C22×Q8—114no—
349C22×Q8—112no—
350C22×Q8—222no—
351C22×D4—24no—
352C22×D4C22×D1114yes—
353AGL(1,ℤ/8)—448no—
354C2×SD16—114no—
355C2×SD16—118no—
356C2×SD16—118no—
357C2×SD16—448no—
358C2×D8—114no—
359C2×M16—114no—
360C22×C8—114no—
361C4⋊Q8—114no—
362C4⋊Q8—222no—
363C4⋊Q8—224no—
364C4⋊Q8—221no—
365C4⋊Q8—221no—
366C4⋊Q8C22⋊D1111yescharacteristic
367C4⋊Q8C22×D1112yes—
368#127—24no—
369#127C22⋊D1111yescharacteristic
370#127C22×D1112yes—
371#124—24no—
372#124—28no—
373#124—22no—
374#124—222no—
375#124C22⋊D1112yes—
376#123—224no—
377#123—228no—
378C22⋊Q8—118no—
379C22⋊Q8—228no—
380#121—24no—
381#121—22no—
382#121—24no—
383#121—224no—
384#121C22⋊D1114yes—
385#121C22×D1114yes—
386#121C22×D1118yes—
387#120—24no—
388#120—24no—
389#120—28no—
390C4×Q8—112no—
391C4×D4—22no—
392C4×D4—112no—
393C4×D4—224no—
394C4×D4—222no—
395C4×D4C22×D1114yes—
396C4×D4C22×D1114yes—
397#117—24no—
398#117—111no—
399#117—221no—
400#117C22×D1114yes—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—224no—
403C2×C42—221no—
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#106—114no—
407C4⋊C8—112no—
408C4⋊C8—112no—
409#103—118no—
410#103—114no—
411#103—118no—
412#102—114no—
413#102—114no—
414#102—114no—
415C22⋊C8—114no—
416C22⋊C8—118no—
417C4×C8—114no—
418C2×C11—41no—
419C2×C11—44no—
420C2×C11—84no—
421C2×C11#348411yescharacteristic
422C2×C11C2×#57712yes—
423D11—42no—
424C24—24no—
425#41—42no—
426#41—42no—
427#41—84no—
428#41—222no—
429#41—222no—
430#41—228no—
431#41—444no—
432#41—448no—
433#41—4416no—
434C2×Q8—22no—
435C2×Q8—111no—
436C2×Q8—114no—
437C2×Q8—228no—
438C2×Q8—224no—
439C2×Q8—222no—
440C2×Q8—444no—
441C2×Q8—442no—
442C2×Q8—442no—
443C2×Q8—448no—
444C2×Q8C2×C22⋊D1112yes—
445C2×D4—28no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—24no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—88no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—224no—
456C2×D4C2×C22⋊D1114yes—
457C2×D4C2×C22⋊D1112yes—
458C2×D4C2×C22⋊D1114yes—
459C2×D4C23×D1114yes—
460C22×C4—24no—
461C22×C4—221no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4C2×C22⋊D1112yes—
467C22×C4C23×D1111yescharacteristic
468C22×C4C23×D1114yes—
469SD16—228no—
470SD16—448no—
471SD16—448no—
472D8—228no—
473M16—444no—
474C2×C8—114no—
475C2×C8—114no—
476C2×C8—444no—
477C4⋊C4—22no—
478C4⋊C4—112no—
479C4⋊C4—224no—
480C4⋊C4—228no—
481C4⋊C4—224no—
482C4⋊C4—222no—
483C4⋊C4C2×C22⋊D1114yes—
484C4⋊C4C23×D1114yes—
485C22⋊C4—24no—
486C22⋊C4—28no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—221no—
490C22⋊C4—228no—
491C22⋊C4—222no—
492C22⋊C4C2×C22⋊D1118yes—
493C42—24no—
494C42—221no—
495C42—222no—
496C42C2×C22⋊D1111yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1112yes—
499C11#6166411yescharacteristic, complemented, Sylow
500C23—24no—
501C23—84no—
502C23—88no—
503C23—221no—
504C23C22×C22⋊D1114yes—
505C23C22×C22⋊D1111yescharacteristic
506Q8—42no—
507Q8—82no—
508Q8—112no—
509Q8—221no—
510Q8—224no—
511Q8—224no—
512Q8—448no—
513Q8—444no—
514D4—28no—
515D4—24no—
516D4—24no—
517D4—42no—
518D4—44no—
519D4—44no—
520D4—84no—
521D4—82no—
522D4—88no—
523D4—84no—
524D4—112no—
525D4—224no—
526D4—221no—
527D4—448no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—48no—
535C2×C4—224no—
536C2×C4—221no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—448no—
540C2×C4—448no—
541C2×C4—444no—
542C2×C4—444no—
543C2×C4C22×C22⋊D1114yes—
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1112yes—
546C2×C4C22×C22⋊D1112yes—
547C2×C4C24×D1111yescharacteristic
548C8—224no—
549C8—224no—
550C22—21no—
551C22—24no—
552C22—22no—
553C22—28no—
554C22—44no—
555C22—44no—
556C22—44no—
557C22—168no—
558C22—222no—
559C22—442no—
560C22C23×C22⋊D1111yescharacteristic
561C4—21no—
562C4—24no—
563C4—22no—
564C4—44no—
565C4—222no—
566C4—444no—
567C4—442no—
568C4#1062336714yes—
569C4D11×H(5,𝔽2)11yescharacteristic
570C4D11×H(5,𝔽2)11yescharacteristic
571C2—44no—
572C2—41no—
573C2—84no—
574C2—442no—
575C2#1308224711yescharacteristic
576C2C2×#1062336712yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3549C2
socleC22×C11C23×D4
hypercenter#3549D11
hypocenterC11#61664
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #532 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #13082396C2semidirect
2. #13080904C2semidirect
3. #13080538C2semidirect
4. D4×#4324C2semidirect
5. #13080212C2semidirect
6. #13079538C2semidirect
7. #13079488C2semidirect
8. #13078670C2semidirect
9. #13077900C2semidirect
10. #13077683C2semidirect
11. C11×#3549C2semidirect
12. C2×#67043C22semidirect
22. #10623356C22semidirect
23. C22×#4324C22semidirect
24. C2×#66985C22semidirect
29. #10623082C22semidirect
30. D4×Dic22C22semidirect
31. C4×#4339C22semidirect
32. C2×#66922C22semidirect
33. #10622847C22semidirect
34. #10622831C22semidirect
35. #10622706C22semidirect
36. #10622704C22semidirect
37. #10622697C22semidirect
41. #10622655C22semidirect
42. #10622654C22semidirect
43. #10622653C22semidirect
44. #10622653C22semidirect
45. #10622650C22semidirect
46. #10622650C22semidirect
47. #10622648C22semidirect
48. #10622632C22semidirect
49. #10622632C22semidirect
50. C4×#4324C22semidirect
51. C4×#4323C22semidirect
52. #10622625C22semidirect
53. D4×C11⋊C8C22semidirect
54. #10622617C22semidirect
55. #10622615C22semidirect
56. #10622609C22semidirect
57. #10622538C22semidirect
212. #3549D11semidirect
499. C11#61664semidirect

Maximal subgroups

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

subgroupindex
#130823962
#130809042
#130805382
D4×#43242
#130802122
#130795382
#130794882
#130786702
#130779002
#130776832
C11×#35492
#6166411