Finite Group Databasebeta

← D11×#2537 #14925508

Subgroups — D11×#2537 #14925508

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C214yesmaximal, complemented
2C2×C4×D4×D11C212yesmaximal, complemented
3#13073532C211yesmaximal, characteristic, complemented
4#13073531C214yesmaximal, complemented
5#13073530C214yesmaximal, complemented
6#13073529C212yesmaximal, complemented
7#13073528C214yesmaximal, complemented
8D11×#394C214yesmaximal, complemented
9D11×#384C211yesmaximal, characteristic, complemented
10D11×#380C214yesmaximal, complemented
11C11×#2537C211yesmaximal, characteristic, complemented
12C22×D4×D11C2214yes—
13C22×D4×D11C2212yes—
14C23×C4×D11C2214yes—
15C2×C11×#121C2214yescomplemented
16C2×C4×D4×C11C2212yescomplemented
17C2×#66992C2218yescomplemented
18C2×#66991C2214yescomplemented
19C2×D4×Dic11C2212yescomplemented
20C2×#66983C2214yescomplemented
21C2×C4×C22⋊D11C2214yescomplemented
22D11×#121—232no—
23C4×D4×D11—216no—
24C2×#66948C2214yescomplemented
25C2×#66946C2212yescomplemented
26C2×C4⋊C4×D11C2212yes—
27C2×C4⋊C4×D11C2214yes—
28C2×C4⋊C4×D11C2212yes—
29C2×#66937C2218yescomplemented
30C2×(C22⋊D11)⋊C4C2214yescomplemented
31C2×C22⋊C4×D11C2218yes—
32C2×C22⋊C4×D11C2214yes—
33C2×C4×D44C2212yescomplemented
34C2×C42×D11C2211yescharacteristic
35C11×#394C2214yescomplemented
36C11×#384C2211yescharacteristic, complemented
37C11×#380C2214yescomplemented
38#10622835C2214yescomplemented
39#10622825C2214yescomplemented
40#10622604C2214yescomplemented
41#10622600C2214yescomplemented
42#10622600C2214yescomplemented
43#10622589C2212yescomplemented
44#10622589C2214yescomplemented
45#10622574C2218yescomplemented
46#10622572C2218yescomplemented
47#10622555C2218yescomplemented
48#10622548C2211yescharacteristic, complemented
49#10622285C2214yescomplemented
50#10622280C2218yescomplemented
51D11×#95C2214yes—
52C24×D11C2314yes—
53C22×D4×C11C2314yes—
54C22×D4×C11C2312yes—
55C23×C4×C11C2314yes—
56C22×C22⋊D11C2318yes—
57C22×C22⋊D11C2314yes—
58C23×Dic11C2314yes—
59C2×D4×D11—232no—
60C2×D4×D11—28no—
61C2×D4×D11—28no—
62C2×D4×D11—48no—
63C2×D4×D11D4116yescomplemented
64C22×D44C2314yes—
65C22×D44C2312yes—
66C22×C4×D11—216no—
67C22×C4×D11—216no—
68C22×C4×D11—216no—
69C22×C4×D11C2314yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2312yes—
75C11×#121—216no—
76C4×D4×C11—28no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2318yes—
85#66992—232no—
86#66991—216no—
87D4×Dic11—28no—
88#66983—216no—
89C4×C22⋊D11—216no—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2318yes—
99C2×Dic11⋊C4C2314yes—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2312yes—
102#66948—216no—
103#66946—28no—
104C4⋊C4×D11—28no—
105C4⋊C4×D11—216no—
106C4⋊C4×D11—44no—
107#66937—232no—
108(C22⋊D11)⋊C4—216no—
109C22⋊C4×D11—232no—
110C22⋊C4×D11—216no—
111C4×D44—28no—
112C42×D11D418yescomplemented
113C11×#95C2314yes—
114C11⋊#95C2318yes—
115C11⋊#95C2314yes—
116C2×#2537—111nomaximal, Sylow
117C24×C11C2414yes—
118C23×D11—28no—
119C23×D11—28no—
120C23×D11—28no—
121C23×D11—28no—
122C23×D11—28no—
123C23×D11—28no—
124C23×D11C2×D4116yes—
125C23×D11C2414yes—
126C23×D11C2411yescharacteristic
127C2×D4×C11—216no—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—44no—
131C2×D4×C11C2×D418yescomplemented
132C22×C4×C11—28no—
133C22×C4×C11—28no—
134C22×C4×C11—28no—
135C22×C4×C11C2414yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2411yescharacteristic
138C22×C4×C11C2412yes—
139C2×C22⋊D11—28no—
140C2×C22⋊D11—28no—
141C2×C22⋊D11—216no—
142C2×C22⋊D11—216no—
143C2×C22⋊D11—48no—
144C2×C22⋊D11C2×D4116yescomplemented
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11—28no—
148C22×Dic11C2414yes—
149C22×Dic11C2414yes—
150C22×Dic11C2411yescharacteristic
151C22×Dic11C2412yes—
152D4×D11—264no—
153D4×D11—464no—
154C2×D44—216no—
155C2×D44—24no—
156C2×D44—24no—
157C2×D44—44no—
158C2×D44C2×D418yescomplemented
159C2×C4×D11—28no—
160C2×C4×D11—28no—
161C2×C4×D11—28no—
162C2×C4×D11—28no—
163C2×C4×D11—28no—
164C2×C4×D11—216no—
165C2×C4×D11—28no—
166C2×C4×D11—22no—
167C2×C4×D11—28no—
168C2×C4×D11—22no—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—464no—
173C2×C4×D11C2×D414yes—
174C2×C4×D11C2×D418yes—
175C2×C4×D11C2×D418yes—
176C2×C4×D11#4118yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—28no—
179C11×C4⋊C4—42no—
180C11×C22⋊C4—216no—
181C11×C22⋊C4—28no—
182C42×C11C2×D414yescomplemented
183C22⋊Dic11—28no—
184C22⋊Dic11—216no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—216no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11—28no—
191C4⋊Dic11—42no—
192Dic11⋊C4—28no—
193Dic11⋊C4—216no—
194Dic11⋊C4—44no—
195C4×Dic11C2×D414yescomplemented
196C4×Dic11C2×D418yescomplemented
197C22×#121—114no—
198C22×C4×D4—112no—
199#2537—114no—
200#2537—111no—
201#2537—114no—
202#2537—114no—
203#2537—112no—
204#2537D1111yescharacteristic, direct product factor
205C2×#394—114no—
206C2×#384—111no—
207C2×#380—114no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11C22×D418yes—
215C23×C11C2511yescharacteristic
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—232no—
223C22×D11—232no—
224C22×D11—232no—
225C22×D11—416no—
226C22×D11—416no—
227C22×D11—416no—
228C22×D11—416no—
229C22×D11C22×D418yes—
230C22×D11C22×D412yes—
231C22×D11C22×D414yes—
232C22×D11C2×#4114yes—
233C22×D11H(5,𝔽2)12yes—
234C22×D112−1+412yes—
235D4×C11—216no—
236D4×C11—416no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—24no—
240C2×C4×C11—28no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—416no—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D414yes—
247C2×C4×C11C22×D414yes—
248C2×C4×C11C2×#4114yes—
249C22⋊D11—232no—
250C22⋊D11—432no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—24no—
254C2×Dic11—28no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—416no—
259C2×Dic11C22×D412yes—
260C2×Dic11C22×D414yes—
261C2×Dic11C22×D414yes—
262C2×Dic11C2×#4114yes—
263D44—216no—
264D44—416no—
265C4×D11—28no—
266C4×D11—416no—
267C4×D11—416no—
268C4×D11—416no—
269C4×D11—416no—
270C4×D11#121132yescomplemented
271C23×D4—112no—
272C23×D4—114no—
273C24×C4—114no—
274C2×#121—114no—
275C2×#121—118no—
276C2×#121—114no—
277C2×#121—114no—
278C2×#121—118no—
279C2×#121—2232no—
280C2×#121C2×D1114yescomplemented
281C2×C4×D4—112no—
282C2×C4×D4—114no—
283C2×C4×D4—112no—
284C2×C4×D4—114no—
285C2×C4×D4—112no—
286C2×C4×D4—2216no—
287C2×C4×D4C2×D1112yescomplemented
288C22×C4⋊C4—112no—
289C22×C4⋊C4—114no—
290C22×C4⋊C4—112no—
291C22×C22⋊C4—114no—
292C22×C22⋊C4—118no—
293C22×C42—111no—
294#394—114no—
295#394—114no—
296#394—118no—
297#394—118no—
298#394—114no—
299#394C2×D1114yescomplemented
300#384—112no—
301#384—114no—
302#384—111no—
303#384C2×D1111yescharacteristic, complemented
304#380—114no—
305#380—114no—
306#380—114no—
307#380—118no—
308#380—118no—
309#380C2×D1114yescomplemented
310C2×#95—114no—
311C22×C11—28no—
312C22×C11—28no—
313C22×C11—28no—
314C22×C11—44no—
315C22×C11—44no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11C23×D411yescharacteristic
319C22×C11C23×D412yes—
320C22×C11C22×#4112yes—
321C22×C11C2×H(5,𝔽2)11yescharacteristic
322C22×C11C2×2−1+411yescharacteristic
323C2×D11—28no—
324C2×D11—28no—
325C2×D11—28no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—464no—
331C2×D11C2×#12118yes—
332C2×D11#53714yes—
333C2×D11D4214yes—
334C2×D11#54718yes—
335C2×D11#55514yes—
336C4×C11—22no—
337C4×C11—44no—
338C4×C11—44no—
339C4×C11C2×#12118yescomplemented
340Dic11—22no—
341Dic11—44no—
342Dic11—44no—
343Dic11C2×#12118yescomplemented
344C25—114no—
345C22×D4—114no—
346C22×D4—1116no—
347C22×D4—118no—
348C22×D4—112no—
349C22×D4—114no—
350C22×D4—228no—
351C22×D4—228no—
352C22×D4—2232no—
353C22×D4—448no—
354C22×D4C22×D1114yes—
355C22×D4C22×D1112yes—
356C23×C4—112no—
357C23×C4—111no—
358C23×C4—114no—
359C23×C4—114no—
360C23×C4—114no—
361C23×C4—114no—
362C23×C4—114no—
363C23×C4—2216no—
364C23×C4—2216no—
365C23×C4—2216no—
366C23×C4C22×D1114yes—
367#121—216no—
368#121—2232no—
369#121—2216no—
370#121—2216no—
371#121—2232no—
372#121—2216no—
373C4×D4—28no—
374C4×D4—2216no—
375C4×D4—228no—
376C4×D4—2216no—
377C4×D4—228no—
378C4×D4—228no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—228no—
386C2×C4⋊C4—2216no—
387C2×C4⋊C4—444no—
388C2×C4⋊C4C22×D1112yes—
389C2×C4⋊C4C22×D1114yes—
390C2×C4⋊C4C22×D1112yes—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—2216no—
398C2×C22⋊C4—2232no—
399C2×C22⋊C4C22×D1114yes—
400C2×C22⋊C4C22×D1118yes—
401C2×C42—111no—
402C2×C42—112no—
403C2×C42—118no—
404C2×C42C22×D1111yescharacteristic
405#95—114no—
406#95—118no—
407#95C22×D1114yes—
408C2×C11—48no—
409C2×C11C22×#12112yes—
410C2×C11C2×#53711yescharacteristic
411C2×C11C2×D4211yescharacteristic
412C2×C11C2×#54712yes—
413C2×C11C2×#55511yescharacteristic
414D11—48no—
415D11#253718yesdirect product factor
416C24—111no—
417C24—1116no—
418C24—114no—
419C24—228no—
420C24—228no—
421C24—228no—
422C24—228no—
423C24—228no—
424C24—228no—
425C24C23×D1114yes—
426C2×D4—216no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—44no—
430C2×D4—1116no—
431C2×D4—118no—
432C2×D4—2216no—
433C2×D4—2264no—
434C2×D4—228no—
435C2×D4—228no—
436C2×D4—2216no—
437C2×D4—2216no—
438C2×D4—224no—
439C2×D4—224no—
440C2×D4—444no—
441C2×D4—448no—
442C2×D4—4464no—
443C2×D4D4×D1118yescomplemented
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—112no—
448C22×C4—118no—
449C22×C4—118no—
450C22×C4—118no—
451C22×C4—111no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—228no—
456C22×C4—228no—
457C22×C4—228no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—228no—
461C22×C4—228no—
462C22×C4—2216no—
463C22×C4—228no—
464C22×C4—228no—
465C22×C4—228no—
466C22×C4—228no—
467C22×C4—228no—
468C22×C4—228no—
469C22×C4—228no—
470C22×C4—228no—
471C22×C4—4464no—
472C22×C4C23×D1114yes—
473C22×C4C23×D1114yes—
474C22×C4C23×D1111yescharacteristic
475C22×C4C23×D1112yes—
476C4⋊C4—24no—
477C4⋊C4—28no—
478C4⋊C4—42no—
479C4⋊C4—228no—
480C4⋊C4—2216no—
481C4⋊C4—224no—
482C4⋊C4—228no—
483C4⋊C4—444no—
484C4⋊C4—442no—
485C22⋊C4—216no—
486C22⋊C4—28no—
487C22⋊C4—228no—
488C22⋊C4—2216no—
489C22⋊C4—2216no—
490C22⋊C4—228no—
491C22⋊C4—2216no—
492C22⋊C4—228no—
493C42—114no—
494C42—118no—
495C42D4×D1114yescomplemented
496C11C2×#253711yescharacteristic, complemented, Sylow
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—112no—
504C23—114no—
505C23—114no—
506C23—112no—
507C23—112no—
508C23—118no—
509C23—2232no—
510C23—2232no—
511C23—2232no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—4416no—
519C23—4416no—
520C23—4416no—
521C23—4416no—
522C23C2×D4×D1118yes—
523C23C24×D1111yescharacteristic
524D4—216no—
525D4—416no—
526D4—2232no—
527D4—2216no—
528D4—4416no—
529D4—4432no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—28no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—416no—
538C2×C4—114no—
539C2×C4—114no—
540C2×C4—114no—
541C2×C4—1132no—
542C2×C4—112no—
543C2×C4—228no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—228no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—4416no—
552C2×C4—4416no—
553C2×C4—4416no—
554C2×C4—4416no—
555C2×C4—4416no—
556C2×C4C2×D4×D1112yes—
557C2×C4C2×D4×D1114yes—
558C2×C4C2×D4×D1114yes—
559C2×C4#41×D1114yes—
560C22—28no—
561C22—28no—
562C22—28no—
563C22—44no—
564C22—44no—
565C22—44no—
566C22—44no—
567C22—114no—
568C22—114no—
569C22—114no—
570C22—118no—
571C22—118no—
572C22—228no—
573C22—228no—
574C22—228no—
575C22—4464no—
576C22—444no—
577C22—444no—
578C22—444no—
579C22—444no—
580C22C22×D4×D1111yescharacteristic
581C22C22×D4×D1112yes—
582C22C2×#41×D1112yes—
583C22D11×H(5,𝔽2)11yescharacteristic
584C22D11×2−1+411yescharacteristic
585C4—22no—
586C4—44no—
587C4—44no—
588C4—118no—
589C4—222no—
590C4—444no—
591C4—444no—
592C4D11×#12118yescomplemented
593C2—48no—
594C2—118no—
595C2—448no—
596C2C2×D11×#12112yes—
597C2D11×#53711yescharacteristic
598C2D42×D1111yescharacteristic
599C2D11×#54712yes—
600C2D11×#55511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2537C2
hypercenter#2537D11
hypocenterC11C2×#2537
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×D11×#121C2semidirect
2. C2×C4×D4×D11C2semidirect
3. #13073532C2semidirect
4. #13073531C2semidirect
5. #13073530C2semidirect
6. #13073529C2semidirect
7. #13073528C2semidirect
8. D11×#394C2semidirect
9. D11×#384C2semidirect
10. D11×#380C2semidirect
11. C11×#2537C2semidirect
15. C2×C11×#121C22semidirect
16. C2×C4×D4×C11C22semidirect
17. C2×#66992C22semidirect
18. C2×#66991C22semidirect
19. C2×D4×Dic11C22semidirect
20. C2×#66983C22semidirect
21. C2×C4×C22⋊D11C22semidirect
24. C2×#66948C22semidirect
25. C2×#66946C22semidirect
29. C2×#66937C22semidirect
30. C2×(C22⋊D11)⋊C4C22semidirect
33. C2×C4×D44C22semidirect
35. C11×#394C22semidirect
36. C11×#384C22semidirect
37. C11×#380C22semidirect
38. #10622835C22semidirect
39. #10622825C22semidirect
40. #10622604C22semidirect
41. #10622600C22semidirect
42. #10622600C22semidirect
43. #10622589C22semidirect
44. #10622589C22semidirect
45. #10622574C22semidirect
46. #10622572C22semidirect
47. #10622555C22semidirect
48. #10622548C22semidirect
49. #10622285C22semidirect
50. #10622280C22semidirect
63. C2×D4×D11D4semidirect
112. C42×D11D4semidirect
131. C2×D4×C11C2×D4semidirect
144. C2×C22⋊D11C2×D4semidirect
158. C2×D44C2×D4semidirect
182. C42×C11C2×D4semidirect
195. C4×Dic11C2×D4semidirect
196. C4×Dic11C2×D4semidirect
204. #2537D11direct (N × H)
270. C4×D11#121semidirect
280. C2×#121C2×D11semidirect
287. C2×C4×D4C2×D11semidirect
299. #394C2×D11semidirect
303. #384C2×D11semidirect
309. #380C2×D11semidirect
339. C4×C11C2×#121semidirect
343. Dic11C2×#121semidirect
415. D11#2537direct (N × H)
443. C2×D4D4×D11semidirect
495. C42D4×D11semidirect
496. C11C2×#2537semidirect
592. C4D11×#121semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×C4×D4×D112
#130735322
#130735312
#130735302
#130735292
#130735282
D11×#3942
D11×#3842
D11×#3802
C11×#25372
C2×#253711