Finite Group Databasebeta

← D11×#2643 #14920220

Subgroups — D11×#2643 #14920220

Order 2816.

2546 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074574C211yesmaximal, characteristic, complemented
2#13074573C211yesmaximal, characteristic, complemented
3#13074572C213yesmaximal, complemented
4#13074571C213yesmaximal, complemented
5#13074570C213yesmaximal, complemented
6#13074569C211yesmaximal, characteristic, complemented
7#13074568C213yesmaximal, complemented
8D11×#401C211yesmaximal, characteristic, complemented
9D11×#400C213yesmaximal, complemented
10D11×#397C213yesmaximal, complemented
11D11×#396C211yesmaximal, characteristic, complemented
12D11×#386C213yesmaximal
13D11×#385C213yesmaximal, complemented
14C2×D11×#95C211yesmaximal, characteristic, complemented
15C11×#2643C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C23×C4×D11C2213yes—
18C2×C4⋊C4×D11C2213yes—
19C2×C4⋊C4×D11C2213yes—
20C2×C22⋊C4×D11C2213yes—
21C2×C22⋊C4×D11C2213yes—
22C2×C22⋊C4×D11C2213yes—
23C11×#401C2211yescharacteristic, complemented
24C11×#400C2213yescomplemented
25C11×#397C2213yescomplemented
26C11×#396C2211yescharacteristic, complemented
27C11×#386C2213yes—
28C11×#385C2213yescomplemented
29C2×C11×#95C2211yescharacteristic, complemented
30#10622833C2213yes—
31#10622826C2213yes—
32#10622823C2213yescomplemented
33C2×C11⋊#95C2213yescomplemented
34#10622607C2213yescomplemented
35#10622606C2213yescomplemented
36#10622602C2213yescomplemented
37#10622602C2213yescomplemented
38#10622599C2213yescomplemented
39#10622595C2213yescomplemented
40#10622571C2213yes—
41#10622569C2213yes—
42#10622569C2213yes—
43#10622566C2213yescomplemented
44#10622565C2213yescomplemented
45#10622565C2213yescomplemented
46#10622563C2213yescomplemented
47#10622561C2213yescomplemented
48#10622559C2213yescomplemented
49#10622289C2211yescharacteristic, complemented
50#10622288C2213yescomplemented
51#10622288C2213yescomplemented
52#10622287C2213yescomplemented
53#10622281C2213yescomplemented
54#10622281C2213yescomplemented
55#10622278C2213yes—
56#10622278C2213yes—
57D11×#95C2211yescharacteristic
58D11×#95C2213yes—
59D11×#95C2213yes—
60D11×#95C2213yes—
61D11×#95C2213yes—
62D11×#95C2213yes—
63D11×#95C2213yescomplemented
64D11×#95C2211yescharacteristic, complemented
65C11⋊#401C2213yescomplemented
66C11⋊#401C2211yescharacteristic, complemented
67C11⋊#401C2213yescomplemented
68#10622273C2213yescomplemented
69#10622273C2213yescomplemented
70#10622272C2213yescomplemented
71#10622271C2213yescomplemented
72#10622271C2213yescomplemented
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11C2313yes—
77C22×C22⋊D11C2311yescharacteristic
78C22×C22⋊D11C2311yescharacteristic
79C23×Dic11C2313yes—
80C2×D4×D11—212no—
81C22×D44C2311yescharacteristic
82C22×C4×D11—212no—
83C22×C4×D11—46no—
84C22×C4×D11—46no—
85C22×C4×D11C2313yes—
86C22×C4×D11C2313yes—
87C22×C4×D11C2313yes—
88C22×C4×D11C2313yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2313yes—
91C22×C4×D11C2313yes—
92C2×C11×C4⋊C4C2313yes—
93C2×C11×C4⋊C4C2313yes—
94C2×C11×C22⋊C4C2313yes—
95C2×C11×C22⋊C4C2313yes—
96C2×C11×C22⋊C4C2313yes—
97C2×C22⋊Dic11C2313yes—
98C2×C22⋊Dic11C2313yes—
99C2×C22⋊Dic11C2313yes—
100C2×(C2×D11)⋊C4C2313yes—
101C2×(C2×D11)⋊C4C2313yes—
102C2×(C2×D11)⋊C4C2313yes—
103C2×(C2×D11)⋊C4C2313yes—
104C2×(C2×D11)⋊C4C2313yes—
105C2×(C2×D11)⋊C4C2313yes—
106C2×C4⋊Dic11C2313yes—
107C2×C4⋊Dic11C2313yes—
108C2×Dic11⋊C4C2313yes—
109C2×Dic11⋊C4C2313yes—
110C2×Dic11⋊C4C2313yes—
111C2×Dic11⋊C4C2313yes—
112C4⋊C4×D11—46no—
113C4⋊C4×D11—46no—
114C22⋊C4×D11—212no—
115C22⋊C4×D11—46no—
116C22⋊C4×D11—46no—
117C11×#95C2313yes—
118C11×#95C2313yes—
119C11×#95C2313yes—
120C11×#95C2313yes—
121C11×#95C2311yescharacteristic
122C11×#95C2313yes—
123C11⋊#95C2313yes—
124C11⋊#95C2313yes—
125C11⋊#95C2313yes—
126C11⋊#95C2313yes—
127C11⋊#95C2313yes—
128C11⋊#95C2313yes—
129C11⋊#95C2313yes—
130C11⋊#95C2313yes—
131C11⋊#95C2313yes—
132C11⋊#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2313yes—
136C11⋊#95C2313yes—
137C11⋊#95C2313yes—
138C11⋊#95C2313yes—
139C2×#2643—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
141C24×C11C2411yescharacteristic
142C23×D11—26no—
143C23×D11—22no—
144C23×D11—26no—
145C23×D11—26no—
146C23×D11—22no—
147C23×D11#41112yes—
148C23×D11C2411yescharacteristic
149C23×D11C2411yescharacteristic
150C23×D11C2411yescharacteristic
151C2×D4×C11—26no—
152C22×C4×C11—26no—
153C22×C4×C11—43no—
154C22×C4×C11—43no—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2413yes—
157C22×C4×C11C2413yes—
158C22×C4×C11C2413yes—
159C22×C4×C11C2413yes—
160C2×C22⋊D11—26no—
161C2×C22⋊D11—26no—
162C22×Dic11—26no—
163C22×Dic11—43no—
164C22×Dic11—43no—
165C22×Dic11C2411yescharacteristic
166C22×Dic11C2413yes—
167C22×Dic11C2413yes—
168C22×Dic11C2413yes—
169C22×Dic11C2413yes—
170D4×D11—416no—
171C2×D44—26no—
172C2×C4×D11—26no—
173C2×C4×D11—26no—
174C2×C4×D11—26no—
175C2×C4×D11—26no—
176C2×C4×D11—26no—
177C2×C4×D11—26no—
178C2×C4×D11—26no—
179C2×C4×D11—26no—
180C2×C4×D11—26no—
181C2×C4×D11—26no—
182C2×C4×D11—26no—
183C2×C4×D11—26no—
184C2×C4×D11—26no—
185C2×C4×D11—26no—
186C2×C4×D11—26no—
187C2×C4×D11—43no—
188C2×C4×D11—43no—
189C2×C4×D11—43no—
190C2×C4×D11—43no—
191C2×C4×D11—448no—
192C11×C4⋊C4—43no—
193C11×C4⋊C4—43no—
194C11×C22⋊C4—26no—
195C11×C22⋊C4—43no—
196C11×C22⋊C4—43no—
197C22⋊Dic11—26no—
198C22⋊Dic11—43no—
199C22⋊Dic11—43no—
200(C2×D11)⋊C4—26no—
201(C2×D11)⋊C4—26no—
202(C2×D11)⋊C4—43no—
203(C2×D11)⋊C4—43no—
204(C2×D11)⋊C4—43no—
205(C2×D11)⋊C4—43no—
206C4⋊Dic11—43no—
207C4⋊Dic11—43no—
208Dic11⋊C4—43no—
209Dic11⋊C4—43no—
210Dic11⋊C4—43no—
211Dic11⋊C4—43no—
212#2643—111no—
213#2643—113no—
214#2643—113no—
215#2643—111no—
216#2643—113no—
217#2643—113no—
218#2643—111no—
219#2643D1111yescharacteristic, direct product factor
220C2×#401—111no—
221C2×#400—113no—
222C2×#397—113no—
223C2×#396—111no—
224C2×#386—113no—
225C2×#385—113no—
226C22×#95—111no—
227C23×C11—23no—
228C23×C11—21no—
229C23×C11—23no—
230C23×C11—23no—
231C23×C11—21no—
232C23×C11C2×#4116yes—
233C23×C11C2511yescharacteristic
234C22×D11—23no—
235C22×D11—21no—
236C22×D11—224no—
237C22×D11—224no—
238C22×D11—23no—
239C22×D11—23no—
240C22×D11—21no—
241C22×D11—44no—
242C22×D11—412no—
243C22×D11—412no—
244C22×D11#126116yes—
245C22×D11C2×#4116yes—
246C22×D11C2×#4116yes—
247C22×D11H(5,𝔽2)16yes—
248C22×D112−1+412yes—
249D4×C11—44no—
250C2×C4×C11—23no—
251C2×C4×C11—23no—
252C2×C4×C11—23no—
253C2×C4×C11—23no—
254C2×C4×C11—23no—
255C2×C4×C11—23no—
256C2×C4×C11—23no—
257C2×C4×C11—23no—
258C2×C4×C11—23no—
259C2×C4×C11—23no—
260C2×C4×C11—23no—
261C2×C4×C11—23no—
262C2×C4×C11—23no—
263C2×C4×C11—412no—
264C22⋊D11—44no—
265C22⋊D11—44no—
266C2×Dic11—23no—
267C2×Dic11—23no—
268C2×Dic11—23no—
269C2×Dic11—23no—
270C2×Dic11—23no—
271C2×Dic11—23no—
272C2×Dic11—23no—
273C2×Dic11—23no—
274C2×Dic11—23no—
275C2×Dic11—23no—
276C2×Dic11—23no—
277C2×Dic11—23no—
278C2×Dic11—23no—
279C2×Dic11—412no—
280D44—44no—
281C4×D11—412no—
282C4×D11—412no—
283C4×D11—44no—
284C4×D11—412no—
285C4×D11—412no—
286C4×D11—412no—
287C4×D11—412no—
288C23×D4—111no—
289C24×C4—113no—
290C22×C4⋊C4—113no—
291C22×C4⋊C4—113no—
292C22×C22⋊C4—113no—
293C22×C22⋊C4—113no—
294C22×C22⋊C4—113no—
295#401—113no—
296#401—113no—
297#401—111no—
298#401C2×D1111yescharacteristic, complemented
299#400—113no—
300#400—113no—
301#400—113no—
302#400—113no—
303#400—113no—
304#400—113no—
305#400—113no—
306#400C2×D1113yescomplemented
307#397—113no—
308#397—113no—
309#397—113no—
310#397—113no—
311#397—113no—
312#397—113no—
313#397—113no—
314#397C2×D1113yescomplemented
315#396—113no—
316#396—113no—
317#396—111no—
318#396C2×D1111yescharacteristic, complemented
319#386—113no—
320#386—113no—
321#386—113no—
322#386—113no—
323#386—113no—
324#386—113no—
325#386—113no—
326#386C2×D1113yes—
327#385—113no—
328#385—113no—
329#385—113no—
330#385—113no—
331#385—113no—
332#385—113no—
333#385—113no—
334#385C2×D1113yescomplemented
335C2×#95—113no—
336C2×#95—111no—
337C2×#95—113no—
338C2×#95—113no—
339C2×#95—113no—
340C2×#95—113no—
341C2×#95—113no—
342C2×#95—113no—
343C2×#95—111no—
344C2×#95C2×D1111yescharacteristic, complemented
345C22×C11—26no—
346C22×C11—26no—
347C22×C11—41no—
348C22×C11—43no—
349C22×C11—43no—
350C22×C11C2×#12614yes—
351C22×C11C22×#4113yes—
352C22×C11C2×H(5,𝔽2)13yes—
353C22×C11C2×2−1+411yescharacteristic
354C2×D11—26no—
355C2×D11—26no—
356C2×D11—232no—
357C2×D11—41no—
358C2×D11—43no—
359C2×D11—43no—
360C2×D11—88no—
361C2×D11C2×#12614yes—
362C2×D11C2×#12614yes—
363C2×D11#538112yes—
364C2×D11#539112yes—
365C4×C11—41no—
366C4×C11—43no—
367C4×C11—43no—
368C4×C11—43no—
369C4×C11—43no—
370Dic11—41no—
371Dic11—43no—
372Dic11—43no—
373Dic11—43no—
374Dic11—43no—
375C25—111no—
376C25—111no—
377C22×D4—111no—
378C22×D4—111no—
379C22×D4—111no—
380C22×D4—2212no—
381C22×D4C22×D1111yescharacteristic
382C23×C4—113no—
383C23×C4—113no—
384C23×C4—113no—
385C23×C4—113no—
386C23×C4—113no—
387C23×C4—111no—
388C23×C4—113no—
389C23×C4—113no—
390C23×C4—2212no—
391C23×C4—446no—
392C23×C4—446no—
393C23×C4C22×D1113yes—
394C2×C4⋊C4—113no—
395C2×C4⋊C4—113no—
396C2×C4⋊C4—113no—
397C2×C4⋊C4—113no—
398C2×C4⋊C4—113no—
399C2×C4⋊C4—113no—
400C2×C4⋊C4—446no—
401C2×C4⋊C4—446no—
402C2×C4⋊C4C22×D1113yes—
403C2×C4⋊C4C22×D1113yes—
404C2×C22⋊C4—113no—
405C2×C22⋊C4—113no—
406C2×C22⋊C4—113no—
407C2×C22⋊C4—113no—
408C2×C22⋊C4—113no—
409C2×C22⋊C4—113no—
410C2×C22⋊C4—113no—
411C2×C22⋊C4—113no—
412C2×C22⋊C4—113no—
413C2×C22⋊C4—2212no—
414C2×C22⋊C4—446no—
415C2×C22⋊C4—446no—
416C2×C22⋊C4C22×D1113yes—
417C2×C22⋊C4C22×D1113yes—
418C2×C22⋊C4C22×D1113yes—
419#95—113no—
420#95—113no—
421#95—113no—
422#95—113no—
423#95—113no—
424#95—113no—
425#95—113no—
426#95—113no—
427#95—113no—
428#95—113no—
429#95—113no—
430#95—113no—
431#95—113no—
432#95—113no—
433#95—113no—
434#95—113no—
435#95C22×D1111yescharacteristic
436#95C22×D1113yes—
437#95C22×D1113yes—
438#95C22×D1113yes—
439#95C22×D1113yes—
440#95C22×D1113yes—
441C2×C11—24no—
442C2×C11—81no—
443C2×C11C22×#12611yescharacteristic
444C2×C11C2×#53813yes—
445C2×C11C2×#53913yes—
446D11—24no—
447D11—81no—
448D11#264318yesdirect product factor
449C24—111no—
450C24—1112no—
451C24—111no—
452C24—111no—
453C24—226no—
454C24—222no—
455C24—226no—
456C24—226no—
457C24—222no—
458C24C23×D1111yescharacteristic
459C24C23×D1111yescharacteristic
460C2×D4—26no—
461C2×D4—226no—
462C2×D4—226no—
463C2×D4—226no—
464C2×D4—4416no—
465C22×C4—26no—
466C22×C4—43no—
467C22×C4—43no—
468C22×C4—111no—
469C22×C4—113no—
470C22×C4—113no—
471C22×C4—113no—
472C22×C4—113no—
473C22×C4—226no—
474C22×C4—226no—
475C22×C4—226no—
476C22×C4—226no—
477C22×C4—226no—
478C22×C4—226no—
479C22×C4—226no—
480C22×C4—226no—
481C22×C4—226no—
482C22×C4—226no—
483C22×C4—226no—
484C22×C4—226no—
485C22×C4—226no—
486C22×C4—226no—
487C22×C4—226no—
488C22×C4—226no—
489C22×C4—443no—
490C22×C4—443no—
491C22×C4—443no—
492C22×C4—443no—
493C22×C4—4448no—
494C22×C4—443no—
495C22×C4—443no—
496C22×C4C23×D1111yescharacteristic
497C22×C4C23×D1113yes—
498C22×C4C23×D1113yes—
499C22×C4C23×D1113yes—
500C22×C4C23×D1113yes—
501C4⋊C4—43no—
502C4⋊C4—43no—
503C4⋊C4—443no—
504C4⋊C4—443no—
505C4⋊C4—443no—
506C4⋊C4—443no—
507C4⋊C4—443no—
508C4⋊C4—443no—
509C22⋊C4—26no—
510C22⋊C4—43no—
511C22⋊C4—43no—
512C22⋊C4—226no—
513C22⋊C4—226no—
514C22⋊C4—226no—
515C22⋊C4—443no—
516C22⋊C4—443no—
517C22⋊C4—443no—
518C22⋊C4—443no—
519C22⋊C4—443no—
520C22⋊C4—443no—
521C11C2×#264311yescharacteristic, complemented, Sylow
522C23—23no—
523C23—21no—
524C23—23no—
525C23—23no—
526C23—21no—
527C23—116no—
528C23—116no—
529C23—112no—
530C23—1116no—
531C23—116no—
532C23—2224no—
533C23—2224no—
534C23—223no—
535C23—221no—
536C23—223no—
537C23—223no—
538C23—221no—
539C23—444no—
540C23—4412no—
541C23—4412no—
542C23#41×D1116yes—
543C23C24×D1111yescharacteristic
544D4—44no—
545D4—444no—
546D4—444no—
547D4—444no—
548C2×C4—23no—
549C2×C4—23no—
550C2×C4—23no—
551C2×C4—23no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—23no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—412no—
562C2×C4—223no—
563C2×C4—223no—
564C2×C4—223no—
565C2×C4—223no—
566C2×C4—223no—
567C2×C4—223no—
568C2×C4—223no—
569C2×C4—223no—
570C2×C4—223no—
571C2×C4—223no—
572C2×C4—223no—
573C2×C4—223no—
574C2×C4—223no—
575C2×C4—4412no—
576C2×C4—4412no—
577C2×C4—444no—
578C2×C4—4412no—
579C2×C4—4412no—
580C2×C4—4412no—
581C2×C4—4412no—
582C2×C4—4412no—
583C22—26no—
584C22—26no—
585C22—41no—
586C22—43no—
587C22—43no—
588C22—114no—
589C22—1112no—
590C22—1112no—
591C22—114no—
592C22—2232no—
593C22—226no—
594C22—226no—
595C22—441no—
596C22—443no—
597C22—443no—
598C22—888no—
599C22D11×#12614yes—
600C22C2×#41×D1113yes—
601C22D11×H(5,𝔽2)13yes—
602C22D11×2−1+411yescharacteristic
603C4—41no—
604C4—43no—
605C4—43no—
606C4—43no—
607C4—43no—
608C4—441no—
609C4—443no—
610C4—443no—
611C4—443no—
612C4—443no—
613C2—24no—
614C2—81no—
615C2—118no—
616C2—224no—
617C2—881no—
618C2C2×D11×#12611yescharacteristic
619C2D11×#53813yes—
620C2D11×#53913yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2643C2
prime radicalC22×D4×D11C22
hypercenter#2643D11
hypocenterC11C2×#2643
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2643

Complements

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

NH ≅ G/Ntype
1. #13074574C2semidirect
2. #13074573C2semidirect
3. #13074572C2semidirect
4. #13074571C2semidirect
5. #13074570C2semidirect
6. #13074569C2semidirect
7. #13074568C2semidirect
8. D11×#401C2semidirect
9. D11×#400C2semidirect
10. D11×#397C2semidirect
11. D11×#396C2semidirect
13. D11×#385C2semidirect
14. C2×D11×#95C2semidirect
15. C11×#2643C2semidirect
23. C11×#401C22semidirect
24. C11×#400C22semidirect
25. C11×#397C22semidirect
26. C11×#396C22semidirect
28. C11×#385C22semidirect
29. C2×C11×#95C22semidirect
32. #10622823C22semidirect
33. C2×C11⋊#95C22semidirect
34. #10622607C22semidirect
35. #10622606C22semidirect
36. #10622602C22semidirect
37. #10622602C22semidirect
38. #10622599C22semidirect
39. #10622595C22semidirect
43. #10622566C22semidirect
44. #10622565C22semidirect
45. #10622565C22semidirect
46. #10622563C22semidirect
47. #10622561C22semidirect
48. #10622559C22semidirect
49. #10622289C22semidirect
50. #10622288C22semidirect
51. #10622288C22semidirect
52. #10622287C22semidirect
53. #10622281C22semidirect
54. #10622281C22semidirect
63. D11×#95C22semidirect
64. D11×#95C22semidirect
65. C11⋊#401C22semidirect
66. C11⋊#401C22semidirect
67. C11⋊#401C22semidirect
68. #10622273C22semidirect
69. #10622273C22semidirect
70. #10622272C22semidirect
71. #10622271C22semidirect
72. #10622271C22semidirect
219. #2643D11direct (N × H)
298. #401C2×D11semidirect
306. #400C2×D11semidirect
314. #397C2×D11semidirect
318. #396C2×D11semidirect
334. #385C2×D11semidirect
344. C2×#95C2×D11semidirect
448. D11#2643direct (N × H)
521. C11C2×#2643semidirect

Maximal subgroups

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

subgroupindex
#130745742
#130745732
#130745722
#130745712
#130745702
#130745692
#130745682
D11×#4012
D11×#4002
D11×#3972
D11×#3962
D11×#3862
D11×#3852
C2×D11×#952
C11×#26432
C2×#264311