Finite Group Databasebeta

← D11×#2331 #14912606

Subgroups — D11×#2331 #14912606

Order 2816.

2526 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13071365C211yesmaximal, characteristic, complemented
3#13071364C211yesmaximal, characteristic, complemented
4#13071363C212yesmaximal, complemented
5#13071362C211yesmaximal, characteristic, complemented
6#13071361C214yesmaximal, complemented
7#13071360C212yesmaximal, complemented
8#13071359C214yesmaximal, complemented
9D11×#391C214yesmaximal
10D11×#389C212yesmaximal
11D11×#387C214yesmaximal
12D11×#382C211yesmaximal, characteristic
13C4×C4⋊C4×D11C212yesmaximal
14D11×#376C211yesmaximal, characteristic
15C11×#2331C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66997C2212yes—
19D11×C4⋊Q8C4116yescomplemented
20C2×C4⋊C4×D11C2212yes—
21C2×C4⋊C4×D11C2214yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C4⋊C4×D11C2212yes—
24C2×#66941C2212yes—
25C2×#66941C2212yes—
26C2×C42×D11C2211yescharacteristic
27C2×C42×D11C2214yes—
28C2×C42×D11C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C2×#66922C2211yescharacteristic
31C11×#391C2214yes—
32C11×#389C2212yes—
33C11×#387C2214yes—
34C11×#382C2211yescharacteristic
35C4×C11×C4⋊C4C2212yes—
36C11×#376C2211yescharacteristic
37#10622843C2214yes—
38#10622598C2212yes—
39#10622594C2214yes—
40#10622591C2214yes—
41#10622590C2212yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44#10622587C2214yes—
45#10622586C2212yes—
46#10622585C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49#10622546C2214yes—
50#10622545C2211yescharacteristic
51#10622545C2211yescharacteristic
52#10622545C2211yescharacteristic
53C4×Dic11⋊C4C2214yes—
54#10622542C2214yes—
55#10622541C2212yes—
56D11×#95C2212yes—
57D11×#95C2212yes—
58D11×#95C2214yes—
59D11×#95C2212yes—
60D11×#95C2212yes—
61D11×#95C2214yes—
62#10622268C2214yes—
63#10622267C2214yes—
64#10622266C2214yes—
65#10622265C2214yes—
66#10622263C2212yes—
67#10622263C2212yes—
68#10622262C2214yes—
69#10622261C2212yes—
70#10622261C2212yes—
71#10622260C2214yes—
72#10622259C2214yes—
73#10622259C2214yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C2×Q8×D11—48no—
78C2×Q8×D11C2×C4116yes—
79C22×C4×D11C2312yes—
80C22×C4×D11C2314yes—
81C22×C4×D11C2314yes—
82C22×C4×D11C2311yescharacteristic
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2312yes—
85C22×C4×D11C2311yescharacteristic
86C22×Dic22C2312yes—
87C22×Dic22C2314yes—
88C11×C4⋊Q8C2×C418yescomplemented
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2314yes—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97#66997C2×C4116yescomplemented
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2311yescharacteristic
117C4⋊C4×D11—28no—
118C4⋊C4×D11—48no—
119C4⋊C4×D11C2×C4116yes—
120C4⋊C4×D11C2×C4116yes—
121#66941C2×C4116yescomplemented
122#66941C2×C4116yescomplemented
123C42×D11—24no—
124C42×D11—48no—
125C42×D11C2×C418yes—
126C42×D11Q818yescomplemented
127#66922C2×C418yescomplemented
128C11×#95C2312yes—
129C11×#95C2312yes—
130C11×#95C2314yes—
131C11×#95C2314yes—
132C11×#95C2312yes—
133C11×#95C2312yes—
134C11⋊#95C2312yes—
135C11⋊#95C2312yes—
136C11⋊#95C2312yes—
137C11⋊#95C2314yes—
138C11⋊#95C2312yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2312yes—
146C11⋊#95C2312yes—
147C11⋊#95C2312yes—
148C11⋊#95C2314yes—
149C11⋊#95C2312yes—
150C2×#2331—111nomaximal, Sylow
151C23×D11C2411yescharacteristic
152C2×Q8×C11—44no—
153C2×Q8×C11C22×C418yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2414yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11C2412yes—
162C22×Dic11C2414yes—
163C22×Dic11C2411yescharacteristic
164C22×Dic11C2411yescharacteristic
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C22×Dic11C2411yescharacteristic
168Q8×D11—432no—
169C2×C4×D11—24no—
170C2×C4×D11—28no—
171C2×C4×D11—24no—
172C2×C4×D11—28no—
173C2×C4×D11—28no—
174C2×C4×D11—24no—
175C2×C4×D11—28no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—28no—
181C2×C4×D11C22×C414yes—
182C2×C4×D11C22×C414yes—
183C2×C4×D11C22×C4116yes—
184C2×C4×D11C22×C414yes—
185C2×C4×D11C2×Q818yes—
186C2×C4×D11C2×Q814yes—
187C2×C4×D11#4114yes—
188C2×Dic22—44no—
189C2×Dic22—44no—
190C2×Dic22—44no—
191C2×Dic22C22×C418yes—
192C2×Dic22C22×C4116yes—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—44no—
195C11×C4⋊C4C22×C418yes—
196C11×C4⋊C4C22×C418yes—
197C42×C11—22no—
198C42×C11—44no—
199C42×C11C22×C414yes—
200C42×C11C2×Q814yescomplemented
201C4⋊Dic11—24no—
202C4⋊Dic11—44no—
203C4⋊Dic11C22×C418yes—
204C4⋊Dic11C22×C418yes—
205Dic11⋊C4—28no—
206Dic11⋊C4—44no—
207Dic11⋊C4—44no—
208Dic11⋊C4C22×C4116yes—
209Dic11⋊C4C22×C4116yes—
210C4×Dic11—24no—
211C4×Dic11—22no—
212C4×Dic11—44no—
213C4×Dic11—44no—
214C4×Dic11—44no—
215C4×Dic11C22×C414yes—
216C4×Dic11C22×C414yes—
217C4×Dic11C22×C414yes—
218C4×Dic11C2×Q818yescomplemented
219C4×Dic11C2×Q814yescomplemented
220C22×C4⋊Q8—111no—
221#2331—114no—
222#2331—112no—
223#2331—114no—
224#2331—111no—
225#2331—112no—
226#2331—111no—
227#2331—111no—
228#2331D1111yescharacteristic, direct product factor
229C2×#391—114no—
230C2×#389—112no—
231C2×#387—114no—
232C2×#382—111no—
233C2×C4×C4⋊C4—112no—
234C2×#376—111no—
235C23×C11C2511yescharacteristic
236C22×D11C23×C412yes—
237C22×D11C22×Q812yes—
238C22×D11C2×#4112yes—
239C22×D11H(5,𝔽2)14yes—
240C22×D112−1+414yes—
241Q8×C11—48no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11C23×C412yes—
255C2×C4×C11C23×C412yes—
256C2×C4×C11C23×C418yes—
257C2×C4×C11C23×C412yes—
258C2×C4×C11C22×Q814yes—
259C2×C4×C11C22×Q812yes—
260C2×C4×C11C2×#4112yes—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11C23×C412yes—
274C2×Dic11C23×C412yes—
275C2×Dic11C23×C418yes—
276C2×Dic11C23×C412yes—
277C2×Dic11C22×Q814yes—
278C2×Dic11C22×Q812yes—
279C2×Dic11C2×#4112yes—
280C4×D11—232no—
281C4×D11—28no—
282C4×D11—28no—
283C4×D11—216no—
284C4×D11—48no—
285C4×D11—416no—
286C4×D11C4×Q8116yes—
287Dic22—416no—
288Dic22—48no—
289C23×Q8—112no—
290C2×C4⋊Q8—112no—
291C2×C4⋊Q8—1116no—
292C2×C4⋊Q8—112no—
293C2×C4⋊Q8—112no—
294C2×C4⋊Q8—111no—
295C2×C4⋊Q8C2×D1111yescharacteristic
296C22×C4⋊C4—112no—
297C22×C4⋊C4—112no—
298C22×C4⋊C4—112no—
299C22×C4⋊C4—114no—
300C22×C42—111no—
301C22×C42—111no—
302C22×C42—111no—
303C22×C42—114no—
304#391—114no—
305#391—114no—
306#391—114no—
307#391—114no—
308#391—114no—
309#391—114no—
310#391—114no—
311#391C2×D1114yes—
312#389—114no—
313#389—112no—
314#389—112no—
315#389—112no—
316#389—114no—
317#389C2×D1112yes—
318#387—114no—
319#387—114no—
320#387—114no—
321#387—114no—
322#387—114no—
323#387—114no—
324#387—114no—
325#387C2×D1114yes—
326#382—112no—
327#382—111no—
328#382—112no—
329#382—112no—
330#382C2×D1111yescharacteristic
331C4×C4⋊C4—112no—
332C4×C4⋊C4—112no—
333C4×C4⋊C4—114no—
334C4×C4⋊C4—112no—
335C4×C4⋊C4—114no—
336C4×C4⋊C4C2×D1112yes—
337#376—111no—
338#376—111no—
339#376—111no—
340#376—112no—
341#376—112no—
342#376C2×D1111yescharacteristic
343C2×#95—112no—
344C2×#95—112no—
345C2×#95—114no—
346C2×#95—112no—
347C2×#95—112no—
348C2×#95—114no—
349C22×C11C24×C411yescharacteristic
350C22×C11C23×Q811yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C2×H(5,𝔽2)12yes—
353C22×C11C2×2−1+412yes—
354C2×D11C2×C4×Q814yes—
355C2×D11#51814yes—
356C2×D11#51914yes—
357C2×D11#54218yes—
358C2×D11#54418yes—
359C4×C11—22no—
360C4×C11—28no—
361C4×C11—22no—
362C4×C11—24no—
363C4×C11—42no—
364C4×C11—44no—
365C4×C11C2×C4×Q814yes—
366Dic11—22no—
367Dic11—28no—
368Dic11—22no—
369Dic11—24no—
370Dic11—42no—
371Dic11—44no—
372Dic11C2×C4×Q814yes—
373C22×Q8—1116no—
374C22×Q8—114no—
375C22×Q8—112no—
376C22×Q8—448no—
377C22×Q8C22×D1112yes—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—112no—
383C23×C4—112no—
384C23×C4—114no—
385C4⋊Q8—1116no—
386C4⋊Q8—1116no—
387C4⋊Q8—1116no—
388C4⋊Q8—118no—
389C4⋊Q8C4×D1118yescomplemented
390C2×C4⋊C4—114no—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—1116no—
395C2×C4⋊C4—1116no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—228no—
402C2×C4⋊C4—448no—
403C2×C4⋊C4C22×D1112yes—
404C2×C4⋊C4C22×D1114yes—
405C2×C4⋊C4C22×D1112yes—
406C2×C4⋊C4C22×D1112yes—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—112no—
411C2×C42—111no—
412C2×C42—118no—
413C2×C42—118no—
414C2×C42—112no—
415C2×C42—111no—
416C2×C42—114no—
417C2×C42—114no—
418C2×C42—114no—
419C2×C42—224no—
420C2×C42—448no—
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1114yes—
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425#95—112no—
426#95—112no—
427#95—112no—
428#95—112no—
429#95—112no—
430#95—112no—
431#95—114no—
432#95—114no—
433#95—114no—
434#95—114no—
435#95—112no—
436#95—114no—
437#95—112no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95C22×D1112yes—
442#95C22×D1112yes—
443#95C22×D1114yes—
444#95C22×D1112yes—
445#95C22×D1112yes—
446#95C22×D1114yes—
447C2×C11C22×C4×Q811yescharacteristic
448C2×C11C2×#51811yescharacteristic
449C2×C11C2×#51911yescharacteristic
450C2×C11C2×#54212yes—
451C2×C11C2×#54412yes—
452D11#233118yesdirect product factor
453C24—111no—
454C2×Q8—44no—
455C2×Q8—1116no—
456C2×Q8—118no—
457C2×Q8—444no—
458C2×Q8—444no—
459C2×Q8—444no—
460C2×Q8—4432no—
461C2×Q8C2×C4×D1118yes—
462C22×C4—111no—
463C22×C4—114no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—114no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—1116no—
473C22×C4—118no—
474C22×C4—112no—
475C22×C4—114no—
476C22×C4—224no—
477C22×C4—228no—
478C22×C4—228no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—228no—
488C22×C4C23×D1112yes—
489C22×C4C23×D1114yes—
490C22×C4C23×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492C22×C4C23×D1114yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1111yescharacteristic
495C4⋊C4—24no—
496C4⋊C4—44no—
497C4⋊C4—1116no—
498C4⋊C4—1116no—
499C4⋊C4—118no—
500C4⋊C4—118no—
501C4⋊C4—228no—
502C4⋊C4—224no—
503C4⋊C4—444no—
504C4⋊C4—444no—
505C4⋊C4—444no—
506C4⋊C4C2×C4×D1118yes—
507C4⋊C4C2×C4×D1118yes—
508C42—22no—
509C42—44no—
510C42—114no—
511C42—114no—
512C42—114no—
513C42—118no—
514C42—114no—
515C42—224no—
516C42—222no—
517C42—444no—
518C42—444no—
519C42—444no—
520C42C2×C4×D1114yes—
521C42Q8×D1114yescomplemented
522C11C2×#233111yescharacteristic, complemented, Sylow
523C23—112no—
524C23—112no—
525C23—112no—
526C23—114no—
527C23—114no—
528C23C24×D1111yescharacteristic
529Q8—48no—
530Q8—448no—
531Q8—4416no—
532C2×C4—22no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—1116no—
548C2×C4—112no—
549C2×C4—112no—
550C2×C4—118no—
551C2×C4—114no—
552C2×C4—228no—
553C2×C4—2232no—
554C2×C4—2216no—
555C2×C4—228no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—448no—
569C2×C4—4416no—
570C2×C4C22×C4×D1112yes—
571C2×C4C22×C4×D1112yes—
572C2×C4C22×C4×D1118yes—
573C2×C4C22×C4×D1112yes—
574C2×C4C2×Q8×D1114yes—
575C2×C4C2×Q8×D1112yes—
576C2×C4#41×D1112yes—
577C22—118no—
578C22—118no—
579C22—114no—
580C22—114no—
581C22—114no—
582C22C23×C4×D1111yescharacteristic
583C22C22×Q8×D1111yescharacteristic
584C22C2×#41×D1111yescharacteristic
585C22D11×H(5,𝔽2)12yes—
586C22D11×2−1+412yes—
587C4—24no—
588C4—22no—
589C4—28no—
590C4—22no—
591C4—42no—
592C4—44no—
593C4—114no—
594C4—224no—
595C4—222no—
596C4—228no—
597C4—222no—
598C4—442no—
599C4—444no—
600C4C4×Q8×D1114yes—
601C2—118no—
602C2C2×C4×Q8×D1111yescharacteristic
603C2D11×#51811yescharacteristic
604C2D11×#51911yescharacteristic
605C2D11×#54212yes—
606C2D11×#54412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2331C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2331D11
hypocenterC11C2×#2331
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2331

Complements

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

NH ≅ G/Ntype
2. #13071365C2semidirect
3. #13071364C2semidirect
4. #13071363C2semidirect
5. #13071362C2semidirect
6. #13071361C2semidirect
7. #13071360C2semidirect
8. #13071359C2semidirect
15. C11×#2331C2semidirect
19. D11×C4⋊Q8C4semidirect
88. C11×C4⋊Q8C2×C4semidirect
97. #66997C2×C4semidirect
121. #66941C2×C4semidirect
122. #66941C2×C4semidirect
126. C42×D11Q8semidirect
127. #66922C2×C4semidirect
200. C42×C11C2×Q8semidirect
218. C4×Dic11C2×Q8semidirect
219. C4×Dic11C2×Q8semidirect
228. #2331D11direct (N × H)
389. C4⋊Q8C4×D11semidirect
452. D11#2331direct (N × H)
521. C42Q8×D11semidirect
522. C11C2×#2331semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130713652
#130713642
#130713632
#130713622
#130713612
#130713602
#130713592
D11×#3912
D11×#3892
D11×#3872
D11×#3822
C4×C4⋊C4×D112
D11×#3762
C11×#23312
C2×#233111