Finite Group Databasebeta

← D11×#3253 #15626633

Subgroups — D11×#3253 #15626633

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#532C212yesmaximal, complemented
2#13079997C211yesmaximal, characteristic, complemented
3#13079996C214yesmaximal, complemented
4#13079995C214yesmaximal, complemented
5#13079994C212yesmaximal, complemented
6#13079993C214yesmaximal, complemented
7D11×#476C214yesmaximal, complemented
8D11×#469C214yesmaximal, complemented
9D11×#459C214yesmaximal, complemented
10D11×#423C211yesmaximal, characteristic, complemented
11C11×#3253C211yesmaximal, characteristic, complemented
12C2×#41×D11—22no—
13C11×#532C2212yescomplemented
14#10623363—22no—
15C2×D8×D11C2214yes—
16C2×M16×D11C2212yes—
17#10623256C2212yescomplemented
18D11×C4⋊Q8C2212yes—
19#10623247C2212yescomplemented
20D11×#127C2212yes—
21D11×#124—22no—
22#10623199—22no—
23D11×#121—22no—
24D11×#121C2214yes—
25#10623127—22no—
26#10623127C2214yescomplemented
27#10623079—22no—
28#10623079C2214yescomplemented
29C4×D4×D11—22no—
30C4×D4×D11C2214yes—
31#10623008C2212yescomplemented
32C2×C42×D11C2211yescharacteristic
33C11×#476C2214yescomplemented
34C11×#469C2214yescomplemented
35C11×#459C2214yescomplemented
36C11×#423C2211yescharacteristic, complemented
37#10622772C2214yescomplemented
38#10622763C2218yescomplemented
39#10622748C2214yescomplemented
40#10622731C2212yescomplemented
41#10622697C2214yescomplemented
42#10622685C2214yescomplemented
43#10622652C2218yescomplemented
44#10622628C2214yescomplemented
45#10622621C2214yescomplemented
46#10622537C2211yescharacteristic, complemented
47#10622483C2218yescomplemented
48#10622478C2214yescomplemented
49D11×#106C2214yes—
50#10622456C2214yescomplemented
51#10622455C2214yescomplemented
52#10622450C2214yescomplemented
53D11×C4⋊C8C2214yes—
54#10622399C2218yescomplemented
55#10622395C2218yescomplemented
56D11×#102C2218yes—
57#10622374C2218yescomplemented
58C2×C11×#41—22no—
59#41×D11—416no—
60C2×#4343—22no—
61C2×Q8×D11—22no—
62C2×#4341—24no—
63C2×#4341—22no—
64C2×D4×D11—24no—
65C2×D4×D11—22no—
66C2×D4×D11—22no—
67C2×D4×D11C2314yes—
68C2×#4339—22no—
69C2×#4339—24no—
70C22×C4×D11—24no—
71C22×C4×D11D412yes—
72C22×C4×D11C2311yescharacteristic
73C2×C11×D8C2314yes—
74C2×C11×M16C2312yes—
75C11×C4⋊Q8C2312yes—
76C11×#127C2312yes—
77C11×#124—22no—
78C11×#121—22no—
79C11×#121C2314yes—
80C4×D4×C11—22no—
81C4×D4×C11C2314yes—
82C2×C42×C11C2311yescharacteristic
83#67000—22no—
84#66997—22no—
85#66993—22no—
86#66993—22no—
87#66993C2314yes—
88#66992—24no—
89#66992—24no—
90#66991—22no—
91#66991C2314yes—
92#66989—22no—
93D4×Dic11—22no—
94D4×Dic11C2314yes—
95C2×#4323C2318yes—
96#66983—22no—
97#66983C2314yes—
98C4×C22⋊D11—24no—
99C4×C22⋊D11—24no—
100C2×C4×Dic11D412yes—
101C2×C4×Dic11C2311yescharacteristic
102C2×#4318C2312yes—
103D8×D11—48no—
104M16×D11—44no—
105C2×D88C2314yes—
106C2×#4313C2314yes—
107C2×C8×D11C2314yes—
108#66948—22no—
109#66948C2314yes—
110#66946—22no—
111#66946C2314yes—
112C4⋊C4×D11—22no—
113C4⋊C4×D11C2314yes—
114#66941—22no—
115#66941C2314yes—
116#66938—24no—
117#66938—24no—
118#66937—24no—
119#66937—24no—
120(C22⋊D11)⋊C4—24no—
121(C22⋊D11)⋊C4—24no—
122C22⋊C4×D11—24no—
123C22⋊C4×D11—24no—
124#66928—22no—
125#66927C2312yes—
126C4×D44—22no—
127C4×D44C2314yes—
128C42×D11D411yescharacteristic
129C42×D11D411yescharacteristic
130C42×D11D411yescharacteristic
131C42×D11D411yescharacteristic
132C42×D11C2312yes—
133C42×D11C2312yes—
134#66922C2312yes—
135C11×#106C2314yes—
136C11×C4⋊C8C2314yes—
137C11×#102C2318yes—
138#66896C2318yes—
139#66885C2318yes—
140#66881C2314yes—
141Dic11⋊C8C2318yes—
142#66873C2318yes—
143#66872C2318yes—
144C4⋊(C11⋊C8)C2314yes—
145C2×#3253—111nomaximal, Sylow
146C23×D11—24no—
147C23×D11C2×D411yescharacteristic
148C11×#41—48no—
149C2×Q8×C11—22no—
150C2×D4×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11C2414yes—
154C22×C4×C11—24no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—24no—
161C2×C22⋊D11—24no—
162C22×Dic11—24no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D412yes—
165#4343—48no—
166Q8×D11—48no—
167#4341—48no—
168#4341—416no—
169D4×D11—28no—
170D4×D11—28no—
171D4×D11—416no—
172D4×D11—48no—
173D4×D11—48no—
174#4339—48no—
175#4339—416no—
176C2×D44—24no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44C2414yes—
180C2×C4×D11—28no—
181C2×C4×D11—22no—
182C2×C4×D11—22no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—416no—
187C2×C4×D11C2×D411yescharacteristic
188C2×C4×D11C2×D411yescharacteristic
189C2×C4×D11C2×D412yes—
190C2×C4×D11C2×D412yes—
191C2×C4×D11C2×D412yes—
192C2×C4×D11C2×D412yes—
193C2×C4×D11C2411yescharacteristic
194C2×C4×D11C2411yescharacteristic
195C2×Dic22—24no—
196C2×Dic22—22no—
197C11×D8—44no—
198C11×M16—42no—
199C2×C8×C11C2414yes—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C2414yes—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C42×C11C2×D411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2412yes—
207C22⋊Dic11—24no—
208C22⋊Dic11—24no—
209#4323—48no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—24no—
214C4⋊Dic11—22no—
215C4⋊Dic11C2414yes—
216Dic11⋊C4—24no—
217Dic11⋊C4—24no—
218C4×Dic11C2×D411yescharacteristic
219C4×Dic11C2×D411yescharacteristic
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2×D412yes—
224C4×Dic11C2412yes—
225#4318—42no—
226C2×C11⋊C8C2414yes—
227D88—44no—
228#4313—44no—
229C8×D11—28no—
230C2×#532—112no—
231#3253—114no—
232#3253—114no—
233#3253—114no—
234#3253—111no—
235#3253—112no—
236#3253D1111yescharacteristic, direct product factor
237C2×#476—114no—
238C2×#469—114no—
239C2×#459—114no—
240C2×#423—111no—
241C23×C11—24no—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11C22×D411yescharacteristic
250C22×D11C22×D411yescharacteristic
251Q8×C11—44no—
252D4×C11—24no—
253D4×C11—24no—
254D4×C11—44no—
255D4×C11—48no—
256D4×C11—44no—
257C2×C4×C11—24no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—24no—
261C2×C4×C11—48no—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D412yes—
264C2×C4×C11C22×D412yes—
265C2×C4×C11C2511yescharacteristic
266C22⋊D11—48no—
267C22⋊D11—48no—
268C22⋊D11—48no—
269C22⋊D11—48no—
270C22⋊D11—48no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—48no—
275C2×Dic11C22×D411yescharacteristic
276C2×Dic11C22×D412yes—
277C2×Dic11C22×D411yescharacteristic
278C2×Dic11C22×D412yes—
279D44—24no—
280D44—24no—
281D44—44no—
282D44—48no—
283D44—44no—
284C4×D11—22no—
285C4×D11—24no—
286C4×D11—24no—
287C4×D11—21no—
288C4×D11—21no—
289C4×D11—22no—
290C4×D11—24no—
291C4×D11—48no—
292C4×D11—48no—
293C4×D11—48no—
294C4×D11AGL(1,ℤ/8)18yes—
295C4×D11H(5,𝔽2)12yes—
296C4×D112−1+412yes—
297Dic22—48no—
298Dic22—44no—
299C8×C11—24no—
300C11⋊C8—24no—
301C22×#41—222no—
302C22×D8—114no—
303C22×M16—112no—
304#532—112no—
305#532—112no—
306#532—114no—
307#532—114no—
308#532—112no—
309#532—222no—
310#532—222no—
311#532—222no—
312#532—222no—
313#532C2×D1112yescomplemented
314C2×C4⋊Q8—112no—
315C2×#127—112no—
316C2×#124—222no—
317C2×#121—114no—
318C2×#121—222no—
319C2×C4×D4—114no—
320C2×C4×D4—222no—
321C22×C42—111no—
322#476—114no—
323#476—114no—
324#476—118no—
325#476—114no—
326#476—118no—
327#476C2×D1114yescomplemented
328#469—114no—
329#469—114no—
330#469—118no—
331#469—114no—
332#469—118no—
333#469C2×D1114yescomplemented
334#459—118no—
335#459—114no—
336#459—114no—
337#459—114no—
338#459—118no—
339#459C2×D1114yescomplemented
340C2×#106—114no—
341#423—112no—
342#423—111no—
343#423—114no—
344#423C2×D1111yescharacteristic, complemented
345C2×C4⋊C8—114no—
346C2×#102—118no—
347C22×C11—21no—
348C22×C11—22no—
349C22×C11—44no—
350C22×C11—44no—
351C22×C11—44no—
352C22×C11C23×D411yescharacteristic
353C2×D11—21no—
354C2×D11—22no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—816no—
360C2×D11#53712yes—
361C2×D11C2×AGL(1,ℤ/8)14yes—
362C4×C11—21no—
363C4×C11—22no—
364C4×C11—44no—
365C4×C11C2×AGL(1,ℤ/8)14yes—
366C4×C11C2×H(5,𝔽2)11yescharacteristic
367C4×C11C2×2−1+411yescharacteristic
368Dic11—21no—
369Dic11—22no—
370Dic11—44no—
371Dic11#53712yes—
372Dic11C2×AGL(1,ℤ/8)14yes—
373C2×#41—22no—
374C2×#41—224no—
375C2×#41—224no—
376C2×#41—222no—
377C2×#41—222no—
378C2×#41—222no—
379C2×#41—4416no—
380C22×Q8—222no—
381C22×D4—114no—
382C22×D4—222no—
383C22×D4—222no—
384C22×D4—224no—
385C23×C4—112no—
386C23×C4—111no—
387C23×C4—224no—
388C2×D8—118no—
389C2×D8—114no—
390C2×D8—448no—
391C2×D8C22×D1114yes—
392C2×M16—112no—
393C2×M16—114no—
394C2×M16—444no—
395C2×M16C22×D1112yes—
396C22×C8—114no—
397C4⋊Q8—114no—
398C4⋊Q8—112no—
399C4⋊Q8—222no—
400C4⋊Q8—222no—
401C4⋊Q8C22×D1112yes—
402#127—114no—
403#127—112no—
404#127—222no—
405#127—222no—
406#127C22×D1112yes—
407#124—22no—
408#124—224no—
409#124—224no—
410#124—222no—
411#124—222no—
412#124—222no—
413#121—22no—
414#121—114no—
415#121—114no—
416#121—114no—
417#121—224no—
418#121—224no—
419#121—222no—
420#121—224no—
421#121—222no—
422#121—224no—
423#121—222no—
424#121C22×D1114yes—
425C4×D4—22no—
426C4×D4—114no—
427C4×D4—114no—
428C4×D4—114no—
429C4×D4—224no—
430C4×D4—224no—
431C4×D4—222no—
432C4×D4—224no—
433C4×D4—224no—
434C4×D4—222no—
435C4×D4—222no—
436C4×D4C22×D1114yes—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—222no—
439C2×C22⋊C4—224no—
440C2×C22⋊C4—224no—
441C2×C42—112no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42C22×D1111yescharacteristic
450#106—114no—
451#106—118no—
452#106C22×D1114yes—
453C4⋊C8—118no—
454C4⋊C8—114no—
455C4⋊C8C22×D1114yes—
456#102—118no—
457#102—118no—
458#102—118no—
459#102C22×D1118yes—
460C2×C11—41no—
461C2×C11—84no—
462C2×C11C2×#53711yescharacteristic
463C2×C11C22×AGL(1,ℤ/8)12yes—
464D11—41no—
465D11—84no—
466D11#325314yesdirect product factor
467C24—111no—
468C24—224no—
469#41—48no—
470#41—448no—
471#41—4416no—
472#41—448no—
473#41—4416no—
474#41—448no—
475C2×Q8—22no—
476C2×Q8—224no—
477C2×Q8—222no—
478C2×Q8—448no—
479C2×D4—24no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—114no—
483C2×D4—224no—
484C2×D4—228no—
485C2×D4—228no—
486C2×D4—224no—
487C2×D4—224no—
488C2×D4—224no—
489C2×D4—224no—
490C2×D4—224no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—448no—
494C2×D4—448no—
495C2×D4—4416no—
496C2×D4C23×D1114yes—
497C22×C4—24no—
498C22×C4—112no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—112no—
502C22×C4—111no—
503C22×C4—112no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—222no—
509C22×C4—228no—
510C22×C4—222no—
511C22×C4—224no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—4416no—
516C22×C4D4×D1112yes—
517C22×C4C23×D1111yescharacteristic
518D8—44no—
519D8—444no—
520D8—448no—
521M16—42no—
522M16—444no—
523M16—442no—
524C2×C8—114no—
525C2×C8—228no—
526C2×C8C23×D1114yes—
527C4⋊C4—22no—
528C4⋊C4—114no—
529C4⋊C4—224no—
530C4⋊C4—224no—
531C4⋊C4—222no—
532C4⋊C4C23×D1114yes—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—224no—
536C22⋊C4—224no—
537C22⋊C4—224no—
538C22⋊C4—224no—
539C22⋊C4—224no—
540C22⋊C4—224no—
541C42—111no—
542C42—112no—
543C42—112no—
544C42—112no—
545C42—112no—
546C42—111no—
547C42—112no—
548C42D4×D1111yescharacteristic
549C42D4×D1111yescharacteristic
550C42C23×D1112yes—
551C11C2×#325311yescharacteristic, complemented, Sylow
552C23—24no—
553C23—111no—
554C23—111no—
555C23—224no—
556C23—222no—
557C23—224no—
558C23—448no—
559C23—448no—
560C23—448no—
561C23C2×D4×D1111yescharacteristic
562Q8—44no—
563Q8—444no—
564Q8—448no—
565D4—24no—
566D4—24no—
567D4—44no—
568D4—48no—
569D4—44no—
570D4—224no—
571D4—224no—
572D4—444no—
573D4—448no—
574D4—448no—
575D4—448no—
576D4—448no—
577D4—448no—
578D4—448no—
579D4—444no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—24no—
584C2×C4—48no—
585C2×C4—111no—
586C2×C4—112no—
587C2×C4—118no—
588C2×C4—112no—
589C2×C4—112no—
590C2×C4—111no—
591C2×C4—112no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—224no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—224no—
602C2×C4—448no—
603C2×C4—448no—
604C2×C4—448no—
605C2×C4—448no—
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×D4×D1112yes—
608C2×C4C2×D4×D1112yes—
609C2×C4C24×D1111yescharacteristic
610C8—24no—
611C8—224no—
612C22—21no—
613C22—22no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—112no—
618C22—114no—
619C22—221no—
620C22—222no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22—444no—
625C22—8816no—
626C22C22×D4×D1111yescharacteristic
627C4—21no—
628C4—22no—
629C4—44no—
630C4—112no—
631C4—114no—
632C4—221no—
633C4—222no—
634C4—444no—
635C4D11×AGL(1,ℤ/8)14yes—
636C4D11×H(5,𝔽2)11yescharacteristic
637C4D11×2−1+411yescharacteristic
638C2—41no—
639C2—84no—
640C2—114no—
641C2—441no—
642C2—884no—
643C2D11×#53711yescharacteristic
644C2C2×D11×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3253C2
socleC22×C11C23×D4
hypercenter#3253D11
hypocenterC11C2×#3253
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. D11×#532C2semidirect
2. #13079997C2semidirect
3. #13079996C2semidirect
4. #13079995C2semidirect
5. #13079994C2semidirect
6. #13079993C2semidirect
7. D11×#476C2semidirect
8. D11×#469C2semidirect
9. D11×#459C2semidirect
10. D11×#423C2semidirect
11. C11×#3253C2semidirect
13. C11×#532C22semidirect
17. #10623256C22semidirect
19. #10623247C22semidirect
26. #10623127C22semidirect
28. #10623079C22semidirect
31. #10623008C22semidirect
33. C11×#476C22semidirect
34. C11×#469C22semidirect
35. C11×#459C22semidirect
36. C11×#423C22semidirect
37. #10622772C22semidirect
38. #10622763C22semidirect
39. #10622748C22semidirect
40. #10622731C22semidirect
41. #10622697C22semidirect
42. #10622685C22semidirect
43. #10622652C22semidirect
44. #10622628C22semidirect
45. #10622621C22semidirect
46. #10622537C22semidirect
47. #10622483C22semidirect
48. #10622478C22semidirect
50. #10622456C22semidirect
51. #10622455C22semidirect
52. #10622450C22semidirect
54. #10622399C22semidirect
55. #10622395C22semidirect
57. #10622374C22semidirect
236. #3253D11direct (N × H)
313. #532C2×D11semidirect
327. #476C2×D11semidirect
333. #469C2×D11semidirect
339. #459C2×D11semidirect
344. #423C2×D11semidirect
466. D11#3253direct (N × H)
551. C11C2×#3253semidirect

Maximal subgroups

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

subgroupindex
D11×#5322
#130799972
#130799962
#130799952
#130799942
#130799932
D11×#4762
D11×#4692
D11×#4592
D11×#4232
C11×#32532
C2×#325311