Finite Group Databasebeta

← Dic11×#534 #14912790

Subgroups — Dic11×#534 #14912790

Order 2816.

3770 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C212yesmaximal, complemented
2#13071321C214yesmaximal, complemented
3#13071288C214yesmaximal, complemented
4#13071277C214yesmaximal, complemented
5#13071230C211yesmaximal, characteristic, complemented
6#13071194C212yesmaximal, complemented
7#123×Dic11C214yesmaximal, complemented
8#121×Dic11C214yesmaximal, complemented
9#120×Dic11C214yesmaximal, complemented
10C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#534C211yesmaximal, characteristic
12C23×D4×C11C2212yes—
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2212yescomplemented
15C11×#534C4116yescomplemented
16C2×C11×#123C2214yes—
17C2×C11×#121C2214yes—
18C2×C11×#120C2214yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yescomplemented
23C2×D4×Dic11—216no—
24C2×D4×Dic11C2214yes—
25C2×D4×Dic11C2214yes—
26C2×D4×Dic11C2214yescomplemented
27C2×D4×Dic11C2214yescomplemented
28C2×D4×Dic11C2214yescomplemented
29C22×C4⋊Dic11C2212yescomplemented
30C22×C4×Dic11C2212yescomplemented
31C22×C4×Dic11C2212yescomplemented
32#10622860C2214yescomplemented
33#10622834C2214yescomplemented
34#10622833C2214yes—
35#10622833C2214yes—
36#10622833C2218yescomplemented
37#10622833C2218yescomplemented
38#10622825C2214yescomplemented
39#10622824C2214yescomplemented
40C2×C11⋊#95C2212yescomplemented
41#10622598C2214yescomplemented
42#10622594C2218yescomplemented
43C4⋊C4×Dic11C2214yescomplemented
44#10622564C2218yescomplemented
45#10622564C2218yescomplemented
46#10622563C2214yescomplemented
47#10622563C2218yescomplemented
48#10622563C2214yescomplemented
49C22⋊C4×Dic11C2218yescomplemented
50C22⋊C4×Dic11C2214yescomplemented
51C22⋊C4×Dic11C2214yescomplemented
52C25×C11C2312yes—
53C25×C11C2311yescharacteristic
54C22×D4×C11—28no—
55C22×D4×C11—28no—
56C22×D4×C11C2×C4116yescomplemented
57C22×D4×C11C2314yes—
58C22×D4×C11C2314yes—
59C22×D4×C11C2314yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2312yes—
62C23×Dic11—28no—
63C23×Dic11—44no—
64C23×Dic11—48no—
65C23×Dic11D418yescomplemented
66C23×Dic11C2314yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2314yes—
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C11×#123C2×C4132yescomplemented
76C11×#121C2×C4132yescomplemented
77C11×#120C2×C4132yescomplemented
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4C2×C418yescomplemented
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—28no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92D4×Dic11—216no—
93D4×Dic11—216no—
94D4×Dic11—216no—
95D4×Dic11—216no—
96D4×Dic11—48no—
97C2×C4⋊Dic11—28no—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2314yes—
101C2×C4⋊Dic11C2314yes—
102C2×C4×Dic11—28no—
103C2×C4×Dic11—44no—
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C4×#534—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—42no—
116C24×C11—44no—
117C24×C11—42no—
118C24×C11—44no—
119C24×C11C22×C414yes—
120C24×C11C22×C418yescomplemented
121C24×C11C2×D414yes—
122C24×C11#4114yes—
123C24×C11C2414yes—
124C24×C11C2412yes—
125C24×C11C2411yescharacteristic
126C2×D4×C11—264no—
127C2×D4×C11—28no—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11C22×C4116yes—
134C2×D4×C11C22×C4116yescomplemented
135C2×D4×C11C22×C4116yescomplemented
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11C22×C418yescomplemented
141C22×C4×C11C22×C418yescomplemented
142C22×C4×C11C2414yes—
143C22×C4×C11C2414yes—
144C22×Dic11—24no—
145C22×Dic11—28no—
146C22×Dic11—28no—
147C22×Dic11—28no—
148C22×Dic11—216no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—44no—
155C22×Dic11—44no—
156C22×Dic11—48no—
157C22×Dic11—42no—
158C22×Dic11—44no—
159C22×Dic11—416no—
160C22×Dic11—432no—
161C22×Dic11C2×D418yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D418yes—
164C22×Dic11C2×D414yes—
165C22×Dic11C2414yes—
166C22×Dic11C2414yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2411yescharacteristic
170C22×Dic11C2411yescharacteristic
171C11×C4⋊C4C22×C4116yescomplemented
172C11×C22⋊C4C22×C4116yescomplemented
173C11×C22⋊C4C22×C4132yescomplemented
174C22⋊Dic11—28no—
175C22⋊Dic11—28no—
176C22⋊Dic11—28no—
177C22⋊Dic11—28no—
178C22⋊Dic11—28no—
179C22⋊Dic11—48no—
180C22⋊Dic11—48no—
181C4⋊Dic11—28no—
182C4⋊Dic11—28no—
183C4⋊Dic11—44no—
184C4⋊Dic11—44no—
185C4×Dic11—28no—
186C4×Dic11—28no—
187C4×Dic11—28no—
188C4×Dic11—44no—
189C2×#534D1111yescharacteristic
190C22×C4×D4—112no—
191#2325—114no—
192#2322—114no—
193#2321—114no—
194#2315—111no—
195#2308—112no—
196C4×#123—114no—
197C4×#121—114no—
198C4×#120—114no—
199C2×C4×C22⋊C4—111no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—216no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11—416no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—416no—
217C23×C11C4×D4116yescomplemented
218C23×C11C23×C418yes—
219C23×C11C23×C414yes—
220C23×C11C23×C412yes—
221C23×C11C22×D412yes—
222C23×C11C22×D414yes—
223C23×C11C2×#4114yes—
224C23×C11C2×#4112yes—
225C23×C11C2511yescharacteristic
226D4×C11—232no—
227D4×C11—232no—
228D4×C11—416no—
229C2×C4×C11—216no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—48no—
235C2×C4×C11C23×C418yes—
236C2×C4×C11C23×C418yes—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—216no—
240C2×Dic11—28no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—28no—
246C2×Dic11—28no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11—416no—
251C2×Dic11—48no—
252C2×Dic11—48no—
253C2×Dic11—48no—
254C2×Dic11—416no—
255C2×Dic11C22×D414yes—
256C2×Dic11C22×D412yes—
257C2×Dic11C22×D412yes—
258C2×Dic11H(5,𝔽2)14yes—
259C23×D4C2×D1112yes—
260C24×C4—111no—
261C24×C4—112no—
262#534Dic11116yesdirect product factor
263C2×#123C2×D1114yes—
264C2×#121C2×D1114yes—
265C2×#120C2×D1114yes—
266C2×C4×D4—114no—
267C2×C4×D4—114no—
268C2×C4×D4—114no—
269C2×C4×D4—114no—
270C2×C4×D4—114no—
271C2×C4×D4—2216no—
272C22×C4⋊C4—112no—
273C22×C22⋊C4—111no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4C2×D1111yescharacteristic
277C22×C42—112no—
278C22×C42—112no—
279#390—114no—
280#389—114no—
281#388—118no—
282#388—118no—
283#387—118no—
284#386—114no—
285#386—114no—
286#386—118no—
287#386—118no—
288#385—114no—
289#385—114no—
290#385—118no—
291#381—114no—
292#380—114no—
293#379—114no—
294C4×C4⋊C4—114no—
295C4×C22⋊C4—114no—
296C4×C22⋊C4—114no—
297C4×C22⋊C4—118no—
298C2×#95—112no—
299C22×C11—24no—
300C22×C11—28no—
301C22×C11—24no—
302C22×C11—22no—
303C22×C11—24no—
304C22×C11—22no—
305C22×C11—28no—
306C22×C11—24no—
307C22×C11—28no—
308C22×C11—216no—
309C22×C11—416no—
310C22×C11—432no—
311C22×C11—44no—
312C22×C11—44no—
313C22×C11—48no—
314C22×C11C2×C4×D418yes—
315C22×C11C2×C4×D414yes—
316C22×C11C24×C411yescharacteristic
317C22×C11C23×D411yescharacteristic
318C22×C11C22×#4111yescharacteristic
319C22×C11C2×H(5,𝔽2)12yes—
320C22×C11#58512yes—
321C4×C11—28no—
322C4×C11—28no—
323Dic11—24no—
324Dic11—22no—
325Dic11—44no—
326Dic11—44no—
327Dic11—44no—
328Dic11#53414yesdirect product factor
329C25C22×D1112yes—
330C25C22×D1111yescharacteristic
331C22×D4—28no—
332C22×D4—28no—
333C22×D4C2×Dic11116yescomplemented
334C22×D4C22×D1114yes—
335C22×D4C22×D1114yes—
336C22×D4C22×D1114yes—
337C23×C4—111no—
338C23×C4—112no—
339C23×C4—118no—
340C23×C4—112no—
341C23×C4—111no—
342C23×C4—114no—
343C23×C4—112no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4—114no—
347C23×C4—228no—
348C23×C4—444no—
349C23×C4—448no—
350C23×C4C22×D1112yes—
351C23×C4C22×D1112yes—
352#123C2×Dic11132yescomplemented
353#121C2×Dic11132yescomplemented
354#120C2×Dic11132yescomplemented
355C4×D4—2216no—
356C4×D4—2216no—
357C4×D4—2216no—
358C4×D4—2216no—
359C4×D4—448no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4C22×D1114yes—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4C2×Dic1118yescomplemented
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1118yes—
379C2×C42—114no—
380C2×C42—114no—
381C2×C42—114no—
382C2×C42—114no—
383C2×C42—228no—
384C2×C42—444no—
385#95—118no—
386#95—118no—
387#95—118no—
388#95—118no—
389C2×C11—28no—
390C2×C11—24no—
391C2×C11—48no—
392C2×C11C22×C4×D411yescharacteristic
393C2×C11C4×H(5,𝔽2)12yes—
394C2×C11C2×#53411yescharacteristic
395C2×C11#344911yescharacteristic
396C2×C11#345912yes—
397C24—24no—
398C24—24no—
399C24—42no—
400C24—44no—
401C24—42no—
402C24—44no—
403C24D4×D1114yes—
404C24#434114yes—
405C24C22×Dic1114yes—
406C24C22×Dic1118yescomplemented
407C24C23×D1114yes—
408C24C23×D1112yes—
409C24C23×D1111yescharacteristic
410C2×D4—264no—
411C2×D4—28no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—44no—
416C2×D4—44no—
417C2×D4C22×Dic11116yes—
418C2×D4C22×Dic11116yescomplemented
419C2×D4C22×Dic11116yescomplemented
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—111no—
425C22×C4—118no—
426C22×C4—114no—
427C22×C4—112no—
428C22×C4—111no—
429C22×C4—118no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—224no—
435C22×C4—228no—
436C22×C4—228no—
437C22×C4—228no—
438C22×C4—2216no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—4416no—
443C22×C4—442no—
444C22×C4—444no—
445C22×C4—442no—
446C22×C4—448no—
447C22×C4—444no—
448C22×C4—442no—
449C22×C4—444no—
450C22×C4—4432no—
451C22×C4C22×Dic1118yescomplemented
452C22×C4C22×Dic1118yescomplemented
453C22×C4C23×D1114yes—
454C22×C4C23×D1114yes—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—444no—
458C4⋊C4—444no—
459C4⋊C4C22×Dic11116yescomplemented
460C22⋊C4—228no—
461C22⋊C4—228no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—448no—
466C22⋊C4—448no—
467C22⋊C4C22×Dic11116yescomplemented
468C22⋊C4C22×Dic11132yescomplemented
469C42—228no—
470C42—228no—
471C42—228no—
472C42—444no—
473C11C4×#53411yescharacteristic, complemented, Sylow
474C23—22no—
475C23—24no—
476C23—22no—
477C23—24no—
478C23—216no—
479C23—24no—
480C23—24no—
481C23—28no—
482C23—28no—
483C23—44no—
484C23—44no—
485C23—48no—
486C23—48no—
487C23—416no—
488C23—48no—
489C23—48no—
490C23—416no—
491C23D4×Dic11116yescomplemented
492C23C2×D4×D1112yes—
493C23C2×D4×D1114yes—
494C23C2×#434114yes—
495C23C2×#434112yes—
496C23C23×Dic1118yes—
497C23C23×Dic1114yes—
498C23C23×Dic1112yes—
499C23C24×D1111yescharacteristic
500D4—232no—
501D4—232no—
502D4—416no—
503C2×C4—216no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—48no—
509C2×C4—112no—
510C2×C4—114no—
511C2×C4—114no—
512C2×C4—112no—
513C2×C4—2216no—
514C2×C4—228no—
515C2×C4—222no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—228no—
522C2×C4—224no—
523C2×C4—228no—
524C2×C4—4416no—
525C2×C4—444no—
526C2×C4—448no—
527C2×C4—4416no—
528C2×C4—448no—
529C2×C4—448no—
530C2×C4—448no—
531C2×C4C23×Dic1118yes—
532C2×C4C23×Dic1118yes—
533C22—24no—
534C22—22no—
535C22—24no—
536C22—22no—
537C22—24no—
538C22—28no—
539C22—24no—
540C22—28no—
541C22—28no—
542C22—216no—
543C22—416no—
544C22—432no—
545C22—44no—
546C22—44no—
547C22—48no—
548C22C2×D4×Dic1118yes—
549C22C2×D4×Dic1114yes—
550C22C22×D4×D1111yescharacteristic
551C22C22×#434111yescharacteristic
552C22D11×H(5,𝔽2)12yes—
553C22#1062345512yes—
554C22C24×Dic1111yescharacteristic
555C4—28no—
556C4—28no—
557C4—114no—
558C4—224no—
559C4—222no—
560C4—444no—
561C4—444no—
562C4—444no—
563C2—28no—
564C2—24no—
565C2—48no—
566C2C22×D4×Dic1111yescharacteristic
567C2H(5,𝔽2)×Dic1112yes—
568C2D11×#53411yescharacteristic
569C2#1308194211yescharacteristic
570C2#1308202212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#534C2
socle, cosocleC23×C11C25
hypercenterC2×#534D11
hypocenterC11C4×#534
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. #13071321C2semidirect
3. #13071288C2semidirect
4. #13071277C2semidirect
5. #13071230C2semidirect
6. #13071194C2semidirect
7. #123×Dic11C2semidirect
8. #121×Dic11C2semidirect
9. #120×Dic11C2semidirect
10. C2×C22⋊C4×Dic11C2semidirect
14. C24×Dic11C22semidirect
15. C11×#534C4semidirect
22. C22×C22⋊Dic11C22semidirect
26. C2×D4×Dic11C22semidirect
27. C2×D4×Dic11C22semidirect
28. C2×D4×Dic11C22semidirect
29. C22×C4⋊Dic11C22semidirect
30. C22×C4×Dic11C22semidirect
31. C22×C4×Dic11C22semidirect
32. #10622860C22semidirect
33. #10622834C22semidirect
36. #10622833C22semidirect
37. #10622833C22semidirect
38. #10622825C22semidirect
39. #10622824C22semidirect
40. C2×C11⋊#95C22semidirect
41. #10622598C22semidirect
42. #10622594C22semidirect
43. C4⋊C4×Dic11C22semidirect
44. #10622564C22semidirect
45. #10622564C22semidirect
46. #10622563C22semidirect
47. #10622563C22semidirect
48. #10622563C22semidirect
49. C22⋊C4×Dic11C22semidirect
50. C22⋊C4×Dic11C22semidirect
51. C22⋊C4×Dic11C22semidirect
56. C22×D4×C11C2×C4semidirect
65. C23×Dic11D4semidirect
75. C11×#123C2×C4semidirect
76. C11×#121C2×C4semidirect
77. C11×#120C2×C4semidirect
79. C2×C11×C22⋊C4C2×C4semidirect
120. C24×C11C22×C4semidirect
134. C2×D4×C11C22×C4semidirect
135. C2×D4×C11C22×C4semidirect
140. C22×C4×C11C22×C4semidirect
141. C22×C4×C11C22×C4semidirect
171. C11×C4⋊C4C22×C4semidirect
172. C11×C22⋊C4C22×C4semidirect
173. C11×C22⋊C4C22×C4semidirect
217. C23×C11C4×D4semidirect
262. #534Dic11direct (N × H)
328. Dic11#534direct (N × H)
333. C22×D4C2×Dic11semidirect
352. #123C2×Dic11semidirect
353. #121C2×Dic11semidirect
354. #120C2×Dic11semidirect
376. C2×C22⋊C4C2×Dic11semidirect
406. C24C22×Dic11semidirect
418. C2×D4C22×Dic11semidirect
419. C2×D4C22×Dic11semidirect
451. C22×C4C22×Dic11semidirect
452. C22×C4C22×Dic11semidirect
459. C4⋊C4C22×Dic11semidirect
467. C22⋊C4C22×Dic11semidirect
468. C22⋊C4C22×Dic11semidirect
473. C11C4×#534semidirect
491. C23D4×Dic11semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
#130713212
#130712882
#130712772
#130712302
#130711942
#123×Dic112
#121×Dic112
#120×Dic112
C2×C22⋊C4×Dic112
C2×C11×#5342
C4×#53411