Finite Group Databasebeta

← Dic11×#469 #14760418

Subgroups — Dic11×#469 #14760418

Order 2816.

1170 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic11C211yesmaximal, characteristic, complemented
2C2×M16×Dic11C211yesmaximal, characteristic, complemented
3#121×Dic11C212yesmaximal, complemented
4#13069493C211yesmaximal, characteristic, complemented
5#13069360C211yesmaximal, characteristic, complemented
6#13069315C212yesmaximal, complemented
7#13069055C212yesmaximal, complemented
8#13068649C211yesmaximal, characteristic, complemented
9#106×Dic11C211yesmaximal, characteristic, complemented
10#102×Dic11C212yesmaximal, complemented
11C2×C11×#469C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×D4×Dic11—22no—
16C2×D4×Dic11C2212yes—
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C11×#469C418yescomplemented
20C2×C11×#106C2211yescharacteristic
21C2×C11×#102C2212yes—
22#10622834C2212yes—
23#10622833—22no—
24C2×#66896C2212yes—
25C2×#66896C2212yes—
26#10622825C2212yes—
27D8×Dic11—24no—
28M16×Dic11—24no—
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622598C2212yes—
36C4⋊C4×Dic11C2212yes—
37#10622564—22no—
38C22⋊C4×Dic11—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11—22no—
43C22×D4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—22no—
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
48C2×C11×D8—22no—
49C2×C11×D8—22no—
50C2×C11×D8C2×C414yescomplemented
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16C2×C414yescomplemented
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C11×#121—24no—
57C11×#121C2×C418yescomplemented
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64D4×Dic11—24no—
65D4×Dic11—24no—
66D4×Dic11—48no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2312yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318—22no—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C11×#106C2×C414yescomplemented
83C11×#102C2×C418yescomplemented
84#66896—24no—
85#66896—24no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66882—22no—
90#66881—22no—
91#66879—22no—
92#66879—22no—
93C8×Dic11—22no—
94C8×Dic11D414yescomplemented
95C4×#469—111nomaximal, Sylow
96C24×C11—22no—
97C24×C11C2×D411yescharacteristic
98C2×D4×C11—28no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—44no—
105C2×D4×C11—44no—
106C2×D4×C11C22×C414yes—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—24no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—42no—
122C22×Dic11—44no—
123C22×Dic11—44no—
124C22×Dic11—44no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C11×D8—28no—
130C11×M16—28no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C22×C412yes—
134C2×C8×C11C22×C412yes—
135C2×C8×C11C2×D412yes—
136C2×C8×C11#4112yes—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C22×C414yes—
139C11×C22⋊C4—28no—
140C22⋊Dic11—44no—
141C22⋊Dic11—44no—
142C22⋊Dic11—44no—
143C22⋊Dic11—44no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—44no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C4×Dic11—21no—
152C4×Dic11—21no—
153C4×Dic11—44no—
154C4×Dic11C2×D412yes—
155C4×Dic11#4112yes—
156#4318—28no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8C2×D412yes—
162C2×C11⋊C8#4112yes—
163C2×#469D1111yescharacteristic
164C2×C4×D8—111no—
165C2×C4×M16—111no—
166C4×#121—112no—
167#1972—111no—
168#1944—111no—
169#1936—112no—
170#1895—112no—
171#1809—111no—
172C4×#106—111no—
173C4×#102—112no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—24no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11C4×D412yes—
186C23×C11C22×D411yescharacteristic
187D4×C11—24no—
188D4×C11—24no—
189D4×C11—416no—
190D4×C11—42no—
191D4×C11—42no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11C4×D412yes—
202C2×C4×C11C23×C411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×Dic11—22no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—44no—
214C2×Dic11—44no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—88no—
222C2×Dic11#12112yes—
223C2×Dic11#12112yes—
224C2×Dic11AGL(1,ℤ/8)14yes—
225C8×C11—22no—
226C8×C11C4×D414yescomplemented
227C11⋊C8—22no—
228C11⋊C8—22no—
229C22×D8C2×D1111yescharacteristic
230C22×M16—111no—
231C22×M16C2×D1111yescharacteristic
232C2×#121C2×D1112yes—
233C2×C4×D4—112no—
234C2×C4×D4—222no—
235C22×C42—111no—
236#469Dic1118yesdirect product factor
237C4×D8—224no—
238C2×#107—111no—
239C2×#106—111no—
240C2×#106C2×D1111yescharacteristic
241C2×#102—112no—
242C2×#102—112no—
243C2×#102C2×D1112yes—
244C4×M16—224no—
245C2×#97—111no—
246C2×#97—111no—
247C2×C4×C8—111no—
248C2×C4×C8—111no—
249#390—112no—
250#389—112no—
251#388—222no—
252#386—222no—
253#380—112no—
254C4×C4⋊C4—112no—
255C4×C22⋊C4—222no—
256#340—112no—
257#340—112no—
258#340—112no—
259C22×C11—24no—
260C22×C11—22no—
261C22×C11—42no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11C2×C4×D411yescharacteristic
272C22×C11C2×#12111yescharacteristic
273C22×C11#53211yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)12yes—
275C22×C11#57512yes—
276C4×C11—22no—
277C4×C11—44no—
278C4×C11C2×C4×D411yescharacteristic
279C4×C11C4×#4111yescharacteristic
280C4×C11#52511yescharacteristic
281C4×C11#52911yescharacteristic
282Dic11—22no—
283Dic11—41no—
284Dic11—41no—
285Dic11—82no—
286Dic11—82no—
287Dic11#46914yesdirect product factor
288C22×D4—22no—
289C22×D4C22×D1112yes—
290C23×C4—111no—
291C23×C4—111no—
292C23×C4—222no—
293C23×C4C22×D1111yescharacteristic
294C2×D8—22no—
295C2×D8—22no—
296C2×D8C2×Dic1114yescomplemented
297C2×M16—22no—
298C2×M16—22no—
299C2×M16—222no—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16C2×Dic1114yescomplemented
303C22×C8—111no—
304C22×C8—111no—
305C22×C8C22×D1111yescharacteristic
306C22×C8C22×D1111yescharacteristic
307#121—24no—
308#121C2×Dic1118yescomplemented
309C4×D4—224no—
310C4×D4—224no—
311C4×D4—448no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—112no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4C22×D1112yes—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C42—111no—
322C2×C42—111no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—222no—
326C2×C42—222no—
327C2×C42—222no—
328#107—222no—
329#106—222no—
330#106C2×Dic1114yescomplemented
331#102—224no—
332#102—224no—
333#102C2×Dic1118yescomplemented
334#97—222no—
335#97—222no—
336C4×C8—114no—
337C4×C8—222no—
338#95—222no—
339#95—222no—
340#95—222no—
341C2×C11—42no—
342C2×C11—84no—
343C2×C11C4×#12111yescharacteristic
344C2×C11C4×AGL(1,ℤ/8)12yes—
345C2×C11C2×#46911yescharacteristic
346C2×C11#305411yescharacteristic
347C2×C11#317112yes—
348C24—22no—
349C24D4×D1111yescharacteristic
350C2×D4—28no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—22no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—44no—
357C2×D4—44no—
358C2×D4C22×Dic1114yes—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—222no—
369C22×C4—222no—
370C22×C4—224no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—444no—
374C22×C4—444no—
375C22×C4—444no—
376C22×C4—442no—
377C22×C4D4×D1111yescharacteristic
378C22×C4#434112yes—
379C22×C4C22×Dic1112yes—
380C22×C4C23×D1111yescharacteristic
381D8—28no—
382M16—28no—
383M16—228no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—112no—
387C2×C8—112no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8D4×D1112yes—
393C2×C8#434112yes—
394C2×C8C22×Dic1112yes—
395C2×C8C22×Dic1112yes—
396C4⋊C4—22no—
397C4⋊C4—222no—
398C4⋊C4—222no—
399C4⋊C4—222no—
400C4⋊C4—222no—
401C4⋊C4—444no—
402C4⋊C4C22×Dic1114yes—
403C22⋊C4—28no—
404C22⋊C4—444no—
405C22⋊C4—444no—
406C22⋊C4—444no—
407C22⋊C4—444no—
408C42—112no—
409C42—112no—
410C42—222no—
411C42—222no—
412C42—221no—
413C42—221no—
414C42—444no—
415C11C4×#46911yescharacteristic, complemented, Sylow
416C23—22no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—24no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23D4×Dic1112yes—
428C23C2×D4×D1111yescharacteristic
429D4—24no—
430D4—24no—
431D4—416no—
432D4—42no—
433D4—42no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—114no—
444C2×C4—112no—
445C2×C4—112no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—444no—
452C2×C4—444no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—888no—
460C2×C4D4×Dic1112yes—
461C2×C4C2×D4×D1111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C2×#434111yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C2×C4C23×Dic1111yescharacteristic
467C8—22no—
468C8—222no—
469C8—222no—
470C8D4×Dic1114yescomplemented
471C22—22no—
472C22—24no—
473C22—42no—
474C22—41no—
475C22—41no—
476C22—44no—
477C22—44no—
478C22—44no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—82no—
483C22#1062312711yescharacteristic
484C22D11×#12111yescharacteristic
485C22D11×AGL(1,ℤ/8)12yes—
486C22#1062330412yes—
487C22C2×D4×Dic1111yescharacteristic
488C4—22no—
489C4—44no—
490C4—114no—
491C4—222no—
492C4—441no—
493C4—441no—
494C4—882no—
495C4—882no—
496C4#1062313111yescharacteristic
497C4#1062313711yescharacteristic
498C4C2×D4×Dic1111yescharacteristic
499C4#41×Dic1111yescharacteristic
500C2—42no—
501C2—84no—
502C2#121×Dic1111yescharacteristic
503C2AGL(1,ℤ/8)×Dic1112yes—
504C2D11×#46911yescharacteristic
505C2#1307822311yescharacteristic
506C2#1307920612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#469C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#469D11
hypocenterC11C4×#469
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×D8×Dic11C2semidirect
2. C2×M16×Dic11C2semidirect
3. #121×Dic11C2semidirect
4. #13069493C2semidirect
5. #13069360C2semidirect
6. #13069315C2semidirect
7. #13069055C2semidirect
8. #13068649C2semidirect
9. #106×Dic11C2semidirect
10. #102×Dic11C2semidirect
19. C11×#469C4semidirect
50. C2×C11×D8C2×C4semidirect
53. C2×C11×M16C2×C4semidirect
57. C11×#121C2×C4semidirect
82. C11×#106C2×C4semidirect
83. C11×#102C2×C4semidirect
94. C8×Dic11D4semidirect
226. C8×C11C4×D4semidirect
236. #469Dic11direct (N × H)
287. Dic11#469direct (N × H)
296. C2×D8C2×Dic11semidirect
302. C2×M16C2×Dic11semidirect
308. #121C2×Dic11semidirect
330. #106C2×Dic11semidirect
333. #102C2×Dic11semidirect
415. C11C4×#469semidirect
470. C8D4×Dic11semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic112
C2×M16×Dic112
#121×Dic112
#130694932
#130693602
#130693152
#130690552
#130686492
#106×Dic112
#102×Dic112
C2×C11×#4692
C4×#46911