Finite Group Databasebeta

← Dic11×#540 #14912883

Subgroups — Dic11×#540 #14912883

Order 2816.

2518 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#13071410C214yesmaximal, complemented
2#13071383C214yesmaximal, complemented
3#13071358C211yesmaximal, characteristic, complemented
4#13071342C211yesmaximal, characteristic, complemented
5#13071311C212yesmaximal, complemented
6#13071259C212yesmaximal, complemented
7#13071225C211yesmaximal, characteristic, complemented
8#127×Dic11C211yesmaximal, characteristic, complemented
9#125×Dic11C211yesmaximal, characteristic, complemented
10#123×Dic11C214yesmaximal, complemented
11#121×Dic11C212yesmaximal, complemented
12#121×Dic11C214yesmaximal, complemented
13C4×D4×Dic11C212yesmaximal, complemented
14#117×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#540C211yesmaximal, characteristic
16C11×#540C4116yescomplemented
17C2×C11×#127C2211yescharacteristic
18C2×C11×#125C2211yescharacteristic
19C2×C11×#123C2214yes—
20C2×C11×#121C2214yes—
21C2×C11×#121C2212yes—
22C2×C4×D4×C11C2212yes—
23C2×C11×#117C2211yescharacteristic
24C2×D4×Dic11C2212yes—
25C2×D4×Dic11C2212yes—
26C2×D4×Dic11C2214yes—
27C2×D4×Dic11C2214yes—
28C2×#66979C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2214yes—
31#10622834C2214yes—
32#10622834C2214yes—
33#10622834C2212yes—
34#10622834C2212yes—
35#10622833C2214yes—
36#10622833C2214yes—
37#10622833C2214yes—
38#10622833C2214yes—
39#10622825C2214yes—
40#10622825C2212yes—
41#10622824C2214yes—
42C4×C22⋊Dic11C2214yes—
43#10622598C2214yes—
44#10622598C2212yes—
45#10622598C2212yes—
46#10622594C2214yes—
47#10622594C2214yes—
48#10622594C2214yes—
49C4⋊C4×Dic11C2214yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54#10622564C2214yes—
55#10622564C2214yes—
56#10622564C2214yes—
57#10622564C2214yes—
58#10622564C2214yes—
59#10622563C2214yes—
60C22⋊C4×Dic11C2212yes—
61C22⋊C4×Dic11C2214yes—
62C22⋊C4×Dic11C2212yes—
63C22⋊C4×Dic11C2214yes—
64C22⋊C4×Dic11C2214yes—
65#10622549C2211yescharacteristic
66#10622548C2211yescharacteristic
67C4×C4⋊Dic11C2212yes—
68#10622545C2211yescharacteristic
69#10622545C2211yescharacteristic
70C42×Dic11C2211yescharacteristic
71C42×Dic11C2211yescharacteristic
72C22×D4×C11C2312yes—
73C22×D4×C11C2314yes—
74C22×D4×C11C2314yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2314yes—
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2314yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2314yes—
81C11×#127C2×C418yescomplemented
82C11×#125C2×C418yescomplemented
83C11×#123C2×C4132yescomplemented
84C11×#121C2×C4132yescomplemented
85C11×#121C2×C4116yescomplemented
86C4×D4×C11C2×C4116yescomplemented
87C11×#117C2×C418yescomplemented
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2314yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C22⋊Dic11C2312yes—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2314yes—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2314yes—
101C2×C22⋊Dic11C2314yes—
102C2×C22⋊Dic11C2314yes—
103C2×C22⋊Dic11C2314yes—
104D4×Dic11—28no—
105D4×Dic11—28no—
106D4×Dic11—48no—
107D4×Dic11—48no—
108#66979—24no—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2314yes—
115C2×C4×Dic11—24no—
116C2×C4×Dic11—48no—
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2312yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C11⋊#95C2312yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C4×#540—111nomaximal, Sylow
142C24×C11C2411yescharacteristic
143C24×C11C2414yes—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11—44no—
150C2×D4×C11C22×C418yes—
151C2×D4×C11C22×C4116yes—
152C2×D4×C11C22×C4116yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—44no—
156C22×C4×C11—44no—
157C22×C4×C11C22×C414yes—
158C22×C4×C11C22×C4116yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2411yescharacteristic
162C22×C4×C11C2414yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—28no—
167C22×Dic11—28no—
168C22×Dic11—28no—
169C22×Dic11—24no—
170C22×Dic11—28no—
171C22×Dic11—44no—
172C22×Dic11—42no—
173C22×Dic11—44no—
174C22×Dic11C2411yescharacteristic
175C22×Dic11C2414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2411yescharacteristic
178C22×Dic11C2414yes—
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2412yes—
181C22×Dic11C2411yescharacteristic
182C11×C4⋊C4C22×C418yes—
183C11×C4⋊C4C22×C418yes—
184C11×C4⋊C4C22×C4116yes—
185C11×C22⋊C4C22×C418yes—
186C11×C22⋊C4C22×C4116yes—
187C11×C22⋊C4C22×C4116yes—
188C42×C11C22×C414yes—
189C42×C11C22×C414yes—
190C22⋊Dic11—24no—
191C22⋊Dic11—28no—
192C22⋊Dic11—28no—
193C22⋊Dic11—44no—
194C22⋊Dic11—44no—
195C22⋊Dic11—44no—
196C22⋊Dic11—44no—
197C22⋊Dic11—44no—
198C4⋊Dic11—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—44no—
202C4⋊Dic11—44no—
203C4⋊Dic11—44no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—24no—
207C4×Dic11—28no—
208C4×Dic11—24no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211C4×Dic11—44no—
212C4×Dic11—44no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11#4114yes—
216C4×Dic11#4114yes—
217C2×#540D1111yescharacteristic
218#2335—114no—
219#2333—114no—
220#2330—111no—
221#2328—111no—
222#2324—112no—
223#2319—112no—
224#2314—111no—
225C4×#127—111no—
226C4×#125—111no—
227C4×#123—114no—
228C4×#121—112no—
229C4×#121—114no—
230C42×D4—112no—
231C4×#117—111no—
232C23×C11—21no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—21no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—24no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—22no—
242C23×C11C23×C412yes—
243C23×C11C23×C418yes—
244C23×C11C2511yescharacteristic
245D4×C11—216no—
246D4×C11—416no—
247D4×C11—416no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—28no—
257C2×C4×C11—416no—
258C2×C4×C11C23×C414yes—
259C2×C4×C11C23×C414yes—
260C2×C4×C11C23×C412yes—
261C2×C4×C11C23×C418yes—
262C2×C4×C11C23×C412yes—
263C2×C4×C11C2×#4112yes—
264C2×C4×C11C2×#4112yes—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—44no—
282C2×Dic11—416no—
283C2×Dic11—44no—
284C2×Dic11—416no—
285C2×Dic11C2×#4112yes—
286C2×Dic11C2×#4114yes—
287C2×Dic11C2×#4112yes—
288C2×Dic11H(5,𝔽2)14yes—
289#540Dic11116yesdirect product factor
290C2×#127C2×D1111yescharacteristic
291C2×#125C2×D1111yescharacteristic
292C2×#123C2×D1114yes—
293C2×#121C2×D1112yes—
294C2×#121C2×D1114yes—
295C2×C4×D4—112no—
296C2×C4×D4—112no—
297C2×C4×D4—114no—
298C2×C4×D4—114no—
299C2×C4×D4C2×D1112yes—
300C2×#117—111no—
301C2×#117C2×D1111yescharacteristic
302C22×C42—111no—
303C22×C42—114no—
304#390—112no—
305#390—114no—
306#390—112no—
307#390—114no—
308#389—112no—
309#389—112no—
310#389—114no—
311#388—114no—
312#388—114no—
313#388—114no—
314#388—114no—
315#388—114no—
316#387—114no—
317#387—114no—
318#387—114no—
319#386—114no—
320#386—114no—
321#386—114no—
322#386—114no—
323#385—114no—
324#384—111no—
325#382—111no—
326#381—114no—
327#380—112no—
328#380—114no—
329C4×C4⋊C4—112no—
330C4×C4⋊C4—114no—
331C4×C4⋊C4—112no—
332C4×C4⋊C4—112no—
333C4×C4⋊C4—112no—
334C4×C4⋊C4—112no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—112no—
337C4×C22⋊C4—114no—
338C4×C22⋊C4—112no—
339C4×C22⋊C4—114no—
340C4×C22⋊C4—114no—
341#376—111no—
342#376—111no—
343C43—111no—
344C43—111no—
345C22×C11—22no—
346C22×C11—28no—
347C22×C11—28no—
348C22×C11—24no—
349C22×C11—28no—
350C22×C11—44no—
351C22×C11—41no—
352C22×C11—44no—
353C22×C11—41no—
354C22×C11—42no—
355C22×C11—44no—
356C22×C11—44no—
357C22×C11C24×C411yescharacteristic
358C22×C11C22×#4111yescharacteristic
359C22×C11C22×#4111yescharacteristic
360C22×C11C2×H(5,𝔽2)12yes—
361C22×C11#58512yes—
362C4×C11—22no—
363C4×C11—24no—
364C4×C11—28no—
365C4×C11—24no—
366C4×C11C4×#4114yes—
367Dic11—22no—
368Dic11—24no—
369Dic11—41no—
370Dic11—44no—
371Dic11—41no—
372Dic11—42no—
373Dic11—44no—
374Dic11#54014yesdirect product factor
375C22×D4C22×D1112yes—
376C22×D4C22×D1114yes—
377C22×D4C22×D1114yes—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—114no—
381C23×C4—111no—
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1114yes—
384#127C2×Dic1118yescomplemented
385#125C2×Dic1118yescomplemented
386#123C2×Dic11132yescomplemented
387#121C2×Dic11132yescomplemented
388#121C2×Dic11116yescomplemented
389C4×D4—228no—
390C4×D4—228no—
391C4×D4—448no—
392C4×D4—448no—
393C4×D4C2×Dic11116yescomplemented
394#117—224no—
395#117C2×Dic1118yescomplemented
396C2×C4⋊C4—112no—
397C2×C4⋊C4—112no—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—114no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1112yes—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—112no—
406C2×C22⋊C4—114no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—114no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4C22×D1112yes—
414C2×C22⋊C4C22×D1114yes—
415C2×C22⋊C4C22×D1114yes—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—112no—
420C2×C42—114no—
421C2×C42—112no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—112no—
426C2×C42—112no—
427C2×C42—114no—
428C2×C42—114no—
429C2×C42—224no—
430C2×C42—448no—
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#95—112no—
434#95—112no—
435#95—112no—
436#95—112no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—114no—
441#95—114no—
442#95—114no—
443#95—114no—
444C2×C11—42no—
445C2×C11—48no—
446C2×C11C2×C4×#4111yescharacteristic
447C2×C11C4×H(5,𝔽2)12yes—
448C2×C11C2×#54011yescharacteristic
449C2×C11#345511yescharacteristic
450C2×C11#346012yes—
451C24C23×D1111yescharacteristic
452C24C23×D1114yes—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4C22×Dic1118yes—
460C2×D4C22×Dic11116yes—
461C2×D4C22×Dic11116yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—112no—
469C22×C4—111no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—111no—
473C22×C4—114no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—228no—
477C22×C4—228no—
478C22×C4—228no—
479C22×C4—224no—
480C22×C4—228no—
481C22×C4—444no—
482C22×C4—442no—
483C22×C4—444no—
484C22×C4C22×Dic1114yes—
485C22×C4C22×Dic11116yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C22×C4C23×D1111yescharacteristic
489C22×C4C23×D1114yes—
490C22×C4C23×D1111yescharacteristic
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4—224no—
494C4⋊C4—444no—
495C4⋊C4—444no—
496C4⋊C4—444no—
497C4⋊C4C22×Dic1118yes—
498C4⋊C4C22×Dic1118yes—
499C4⋊C4C22×Dic11116yes—
500C22⋊C4—224no—
501C22⋊C4—228no—
502C22⋊C4—228no—
503C22⋊C4—444no—
504C22⋊C4—444no—
505C22⋊C4—444no—
506C22⋊C4—444no—
507C22⋊C4—444no—
508C22⋊C4C22×Dic1118yes—
509C22⋊C4C22×Dic11116yes—
510C22⋊C4C22×Dic11116yes—
511C42—114no—
512C42—114no—
513C42—222no—
514C42—222no—
515C42—224no—
516C42—228no—
517C42—224no—
518C42—222no—
519C42—222no—
520C42—444no—
521C42—444no—
522C42—442no—
523C42—442no—
524C42C22×Dic1114yes—
525C42C22×Dic1114yes—
526C11C4×#54011yescharacteristic, complemented, Sylow
527C23—21no—
528C23—24no—
529C23—24no—
530C23—21no—
531C23—24no—
532C23—22no—
533C23—24no—
534C23—24no—
535C23—22no—
536C23—24no—
537C23C23×Dic1112yes—
538C23C23×Dic1118yes—
539C23C24×D1111yescharacteristic
540D4—216no—
541D4—416no—
542D4—416no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—28no—
552C2×C4—416no—
553C2×C4—112no—
554C2×C4—114no—
555C2×C4—112no—
556C2×C4—114no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—444no—
574C2×C4—4416no—
575C2×C4—444no—
576C2×C4—4416no—
577C2×C4#41×D1112yes—
578C2×C4#41×D1112yes—
579C2×C4C23×Dic1114yes—
580C2×C4C23×Dic1114yes—
581C2×C4C23×Dic1112yes—
582C2×C4C23×Dic1118yes—
583C2×C4C23×Dic1112yes—
584C22—22no—
585C22—28no—
586C22—28no—
587C22—24no—
588C22—28no—
589C22—44no—
590C22—41no—
591C22—41no—
592C22—44no—
593C22—44no—
594C22—42no—
595C22—44no—
596C22C2×#41×D1111yescharacteristic
597C22C2×#41×D1111yescharacteristic
598C22D11×H(5,𝔽2)12yes—
599C22#1062345512yes—
600C22C24×Dic1111yescharacteristic
601C4—22no—
602C4—24no—
603C4—28no—
604C4—24no—
605C4—114no—
606C4—222no—
607C4—224no—
608C4—441no—
609C4—444no—
610C4—441no—
611C4—444no—
612C4—442no—
613C4#41×Dic1114yes—
614C2—42no—
615C2—48no—
616C2C2×#41×Dic1111yescharacteristic
617C2H(5,𝔽2)×Dic1112yes—
618C2D11×#54011yescharacteristic
619C2#1308200011yescharacteristic
620C2#1308203112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#540C2
socle, cosocleC23×C11C25
hypercenterC2×#540D11
hypocenterC11C4×#540
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #13071410C2semidirect
2. #13071383C2semidirect
3. #13071358C2semidirect
4. #13071342C2semidirect
5. #13071311C2semidirect
6. #13071259C2semidirect
7. #13071225C2semidirect
8. #127×Dic11C2semidirect
9. #125×Dic11C2semidirect
10. #123×Dic11C2semidirect
11. #121×Dic11C2semidirect
12. #121×Dic11C2semidirect
13. C4×D4×Dic11C2semidirect
14. #117×Dic11C2semidirect
16. C11×#540C4semidirect
81. C11×#127C2×C4semidirect
82. C11×#125C2×C4semidirect
83. C11×#123C2×C4semidirect
84. C11×#121C2×C4semidirect
85. C11×#121C2×C4semidirect
86. C4×D4×C11C2×C4semidirect
87. C11×#117C2×C4semidirect
289. #540Dic11direct (N × H)
374. Dic11#540direct (N × H)
384. #127C2×Dic11semidirect
385. #125C2×Dic11semidirect
386. #123C2×Dic11semidirect
387. #121C2×Dic11semidirect
388. #121C2×Dic11semidirect
393. C4×D4C2×Dic11semidirect
395. #117C2×Dic11semidirect
526. C11C4×#540semidirect

Maximal subgroups

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

subgroupindex
#130714102
#130713832
#130713582
#130713422
#130713112
#130712592
#130712252
#127×Dic112
#125×Dic112
#123×Dic112
#121×Dic112
C4×D4×Dic112
#117×Dic112
C2×C11×#5402
C4×#54011