Finite Group Databasebeta

← #15640553

Subgroups — #15640553

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#13083021C211yesmaximal, characteristic, complemented
2#13080910C214yesmaximal, complemented
3#13080544C214yesmaximal, complemented
4D4×#4325C214yesmaximal, complemented
5#13080216C214yesmaximal, complemented
6#13079541C212yesmaximal, complemented
7#13079483C214yesmaximal, complemented
8#13078676C212yesmaximal, complemented
9#13077902C214yesmaximal, complemented
10#13077683C211yesmaximal, characteristic, complemented
11C11×#3499C211yesmaximal, characteristic, complemented
12C2×C11×2−1+4C2212yescomplemented
13D4×Q8×C11C2214yescomplemented
14C11×#547—24no—
15C11×#547C2214yescomplemented
16C11×#536—22no—
17C11×#536C2212yescomplemented
18C11×#532—21no—
19C11×#532C2211yescharacteristic
20C2×C11×C4⋊Q8—21no—
21C2×C11×C4⋊Q8C2211yescharacteristic, complemented
22C4×C11×#41C2211yescharacteristic, complemented
23#10623361C2214yes—
24C2×#67002C2214yescomplemented
25C22×#4325C2214yescomplemented
26#10623265—21no—
27#10623248—21no—
28#10623214—22no—
29#10623138—24no—
30#10623094C2214yes—
31D4×D44C2214yes—
32#10623008C2212yes—
33#10622851C2214yescomplemented
34#10622851C2218yescomplemented
35#10622847C2214yescomplemented
36#10622846C2214yescomplemented
37#10622840C2218yescomplemented
38#10622840C2218yescomplemented
39#10622838C2214yescomplemented
40#10622698C2214yes—
41#10622696C2214yescomplemented
42#10622696C2214yescomplemented
43#10622694C2214yescomplemented
44#10622662C2218yescomplemented
45#10622661C2218yescomplemented
46#10622659C2218yescomplemented
47#10622658C2218yescomplemented
48#10622640C2212yes—
49C4×#4325C2214yescomplemented
50#10622634C2212yescomplemented
51#10622628C2212yes—
52C4×#4323C2214yescomplemented
53#10622625C2214yescomplemented
54D4×C11⋊C8C2214yescomplemented
55#10622621C2212yescomplemented
56#10622616C2214yescomplemented
57#10622538C2212yescomplemented
58C11×2−1+4—44no—
59C11×2−1+4—44no—
60C2×C11×#41—22no—
61C2×C11×#41—24no—
62C2×C11×#41C2311yescharacteristic
63C2×C11×#41C2314yes—
64C2×C11×#41C2312yes—
65C22×Q8×C11—22no—
66C22×Q8×C11C2314yes—
67C22×Q8×C11C2312yes—
68C2×D4×D11—24no—
69C2×#4339—22no—
70C22×D44C2314yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8—24no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8—21no—
75C11×C4⋊Q8D411yescharacteristic
76C11×C4⋊Q8C2314yes—
77C11×#127D411yescharacteristic
78C11×#124—22no—
79C11×#124D412yes—
80C11×#123—24no—
81C11×#123—28no—
82C11×C22⋊Q8—28no—
83C11×C22⋊Q8C2318yes—
84C11×#121—24no—
85C11×#121D414yes—
86C4×Q8×C11C2312yes—
87C4×D4×C11—24no—
88C4×D4×C11—22no—
89C4×D4×C11C2312yes—
90C4×D4×C11C2314yes—
91C11×#117—21no—
92C11×#117C2311yescharacteristic
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—24no—
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97#67002—48no—
98#67000—24no—
99C2×#4325—48no—
100C2×#4325C2314yes—
101C2×#4325C2318yes—
102C2×#4325C2318yes—
103#66993—24no—
104#66991—24no—
105#66990—24no—
106#66990—24no—
107C2×#4323C2314yes—
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#66899C2318yes—
125#66899C2318yes—
126#66896C2314yes—
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#61664—111nomaximal, Sylow
137C23×D11—24no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—28no—
141C11×#41—42no—
142C11×#41—42no—
143C11×#41—44no—
144C11×#41—48no—
145C11×#41—416no—
146C2×Q8×C11—24no—
147C2×Q8×C11—22no—
148C2×Q8×C11—28no—
149C2×Q8×C11—44no—
150C2×Q8×C11—42no—
151C2×Q8×C11—42no—
152C2×Q8×C11—48no—
153C2×Q8×C11C2×D412yes—
154C2×Q8×C11C2414yes—
155C2×Q8×C11C2411yescharacteristic
156C2×D4×C11—21no—
157C2×D4×C11—24no—
158C2×D4×C11C2×D414yes—
159C2×D4×C11C2×D412yes—
160C2×D4×C11C2×D414yes—
161C2×D4×C11C2411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—24no—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2414yes—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—24no—
172D4×D11—88no—
173#4339—84no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—24no—
177C2×D44—44no—
178C2×D44—44no—
179C2×D44C2414yes—
180C2×C4×D11—24no—
181C2×Dic22—22no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—28no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2×D414yes—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4C2×D418yes—
192C42×C11—21no—
193C42×C11—22no—
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2412yes—
197C22⋊Dic11—24no—
198#4325—28no—
199#4325—48no—
200#4325—48no—
201#4323—28no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—28no—
205C4⋊Dic11—22no—
206C4⋊Dic11C2414yes—
207C4×Dic11—24no—
208#4318—44no—
209C2×C11⋊C8—44no—
210C2×C11⋊C8C2414yes—
211C2×C11⋊C8C2414yes—
212#3549—111no—
213#3499D1111yescharacteristic, complemented
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—21no—
224C23×C11C22×D414yes—
225C23×C11C22×D411yescharacteristic
226C22×D11—24no—
227C22×D11—84no—
228C22×D11—88no—
229Q8×C11—21no—
230Q8×C11—24no—
231Q8×C11—24no—
232Q8×C11—42no—
233Q8×C11—48no—
234Q8×C11—44no—
235Q8×C11H(5,𝔽2)12yes—
236D4×C11—24no—
237D4×C11—28no—
238D4×C11—21no—
239D4×C11—42no—
240D4×C11—44no—
241D4×C11—48no—
242D4×C11H(5,𝔽2)12yes—
243C2×C4×C11—24no—
244C2×C4×C11—21no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—48no—
253C2×C4×C11—48no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11C22×D414yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D412yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—84no—
262C22⋊D11—88no—
263C2×Dic11—24no—
264D44—24no—
265D44—24no—
266D44—44no—
267D44—84no—
268D44—82no—
269C4×D11—48no—
270Dic22—82no—
271C11⋊C8—24no—
272C11⋊C8—24no—
273C2×2−1+4C2×D1112yescomplemented
274C2×AGL(1,ℤ/8)—114no—
275C22×SD16—114no—
276H(3,𝔽4)—222no—
277#555—114no—
278#555—221no—
279D4×Q8C2×D1114yescomplemented
280#547—24no—
281#547C2×D1114yescomplemented
282D42—114no—
283D42—221no—
284#536—22no—
285#536C2×D1112yescomplemented
286#535—114no—
287#535—224no—
288#532—21no—
289#532—112no—
290#532C2×D1111yescharacteristic
291C2×C4⋊Q8—21no—
292C2×C4⋊Q8C2×D1111yescharacteristic, complemented
293C4×#41C2×D1111yescharacteristic, complemented
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—22no—
321C22×C11—24no—
322C22×C11—22no—
323C22×C11—28no—
324C22×C11—42no—
325C22×C11C23×D411yescharacteristic
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—168no—
330C4×C11—21no—
331C4×C11—22no—
332C4×C11—24no—
333C4×C11—22no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11#57714yes—
337C4×C11C2×H(5,𝔽2)11yescharacteristic
338C4×C11C2×H(5,𝔽2)11yescharacteristic
339Dic11—44no—
3402−1+4—44no—
3412−1+4—44no—
342C2×#41—22no—
343C2×#41—24no—
344C2×#41—222no—
345C2×#41C22×D1111yescharacteristic
346C2×#41C22×D1114yes—
347C2×#41C22×D1112yes—
348C22×Q8—22no—
349C22×Q8C22×D1114yes—
350C22×Q8C22×D1112yes—
351C22×D4—114no—
352C22×D4—224no—
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—22no—
362C4⋊Q8—24no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—112no—
366C4⋊Q8C22⋊D1111yescharacteristic
367C4⋊Q8C22×D1114yes—
368#127—112no—
369#127—224no—
370#127C22⋊D1111yescharacteristic
371#124—22no—
372#124—224no—
373#124—228no—
374#124—222no—
375#124C22⋊D1112yes—
376#123—24no—
377#123—28no—
378C22⋊Q8—28no—
379C22⋊Q8C22×D1118yes—
380#121—24no—
381#121—114no—
382#121—118no—
383#121—224no—
384#121—222no—
385#121—224no—
386#121C22⋊D1114yes—
387#120—224no—
388#120—224no—
389#120—228no—
390C4×Q8C22×D1112yes—
391C4×D4—24no—
392C4×D4—22no—
393C4×D4—114no—
394C4×D4—222no—
395C4×D4C22×D1112yes—
396C4×D4C22×D1114yes—
397#117—21no—
398#117—114no—
399#117—224no—
400#117C22×D1111yescharacteristic
401C2×C4⋊C4—22no—
402C2×C4⋊C4—24no—
403C2×C42—21no—
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—44no—
419C2×C11—41no—
420C2×C11—42no—
421C2×C11#348411yescharacteristic
422C2×C11C2×#57712yes—
423D11—84no—
424C24—224no—
425#41—22no—
426#41—22no—
427#41—28no—
428#41—42no—
429#41—42no—
430#41—44no—
431#41—48no—
432#41—416no—
433#41—884no—
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—28no—
437C2×Q8—44no—
438C2×Q8—42no—
439C2×Q8—42no—
440C2×Q8—48no—
441C2×Q8—222no—
442C2×Q8C2×C22⋊D1112yes—
443C2×Q8C23×D1114yes—
444C2×Q8C23×D1111yescharacteristic
445C2×D4—21no—
446C2×D4—24no—
447C2×D4—114no—
448C2×D4—228no—
449C2×D4—224no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—224no—
453C2×D4—444no—
454C2×D4—444no—
455C2×D4—888no—
456C2×D4C2×C22⋊D1114yes—
457C2×D4C2×C22⋊D1112yes—
458C2×D4C2×C22⋊D1114yes—
459C2×D4C23×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
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—24no—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—22no—
481C4⋊C4—114no—
482C4⋊C4—222no—
483C4⋊C4C2×C22⋊D1114yes—
484C4⋊C4C23×D1112yes—
485C22⋊C4—21no—
486C22⋊C4—28no—
487C22⋊C4—22no—
488C22⋊C4—224no—
489C22⋊C4—228no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4C2×C22⋊D1118yes—
493C42—21no—
494C42—22no—
495C42—224no—
496C42C2×C22⋊D1111yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C23×D1112yes—
499C11#6166411yescharacteristic, complemented, Sylow
500C23—21no—
501C23—224no—
502C23—884no—
503C23—888no—
504C23C22×C22⋊D1114yes—
505C23C22×C22⋊D1111yescharacteristic
506Q8—21no—
507Q8—24no—
508Q8—24no—
509Q8—42no—
510Q8—48no—
511Q8—44no—
512Q8—882no—
513Q8#6703712yes—
514D4—24no—
515D4—28no—
516D4—21no—
517D4—42no—
518D4—44no—
519D4—48no—
520D4—224no—
521D4—224no—
522D4—444no—
523D4—884no—
524D4—882no—
525D4—888no—
526D4—884no—
527D4#6703712yes—
528C2×C4—24no—
529C2×C4—21no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—48no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—224no—
542C2×C4—448no—
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C22×C22⋊D1114yes—
545C2×C4C22×C22⋊D1112yes—
546C2×C4C22×C22⋊D1112yes—
547C2×C4C24×D1111yescharacteristic
548C8—224no—
549C8—224no—
550C22—21no—
551C22—22no—
552C22—24no—
553C22—22no—
554C22—28no—
555C22—42no—
556C22—444no—
557C22—444no—
558C22—444no—
559C22—1768no—
560C22C23×C22⋊D1111yescharacteristic
561C4—21no—
562C4—22no—
563C4—24no—
564C4—22no—
565C4—44no—
566C4—42no—
567C4—444no—
568C4#1062336814yes—
569C4C2×#6703711yescharacteristic
570C4C2×#6703711yescharacteristic
571C2—44no—
572C2—41no—
573C2—42no—
574C2—884no—
575C2#1308225111yescharacteristic
576C2C2×#1062336812yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3499C2
socleC22×C11C23×D4
hypercenter#3499D11
hypocenterC11#61664
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #532 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13083021C2semidirect
2. #13080910C2semidirect
3. #13080544C2semidirect
4. D4×#4325C2semidirect
5. #13080216C2semidirect
6. #13079541C2semidirect
7. #13079483C2semidirect
8. #13078676C2semidirect
9. #13077902C2semidirect
10. #13077683C2semidirect
11. C11×#3499C2semidirect
12. C2×C11×2−1+4C22semidirect
13. D4×Q8×C11C22semidirect
15. C11×#547C22semidirect
17. C11×#536C22semidirect
21. C2×C11×C4⋊Q8C22semidirect
22. C4×C11×#41C22semidirect
24. C2×#67002C22semidirect
25. C22×#4325C22semidirect
33. #10622851C22semidirect
34. #10622851C22semidirect
35. #10622847C22semidirect
36. #10622846C22semidirect
37. #10622840C22semidirect
38. #10622840C22semidirect
39. #10622838C22semidirect
41. #10622696C22semidirect
42. #10622696C22semidirect
43. #10622694C22semidirect
44. #10622662C22semidirect
45. #10622661C22semidirect
46. #10622659C22semidirect
47. #10622658C22semidirect
49. C4×#4325C22semidirect
50. #10622634C22semidirect
52. C4×#4323C22semidirect
53. #10622625C22semidirect
54. D4×C11⋊C8C22semidirect
55. #10622621C22semidirect
56. #10622616C22semidirect
57. #10622538C22semidirect
213. #3499D11semidirect
273. C2×2−1+4C2×D11semidirect
279. D4×Q8C2×D11semidirect
281. #547C2×D11semidirect
285. #536C2×D11semidirect
292. C2×C4⋊Q8C2×D11semidirect
293. C4×#41C2×D11semidirect
499. C11#61664semidirect

Maximal subgroups

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

subgroupindex
#130830212
#130809102
#130805442
D4×#43252
#130802162
#130795412
#130794832
#130786762
#130779022
#130776832
C11×#34992
#6166411