Finite Group Databasebeta

← Dic11×#453 #14759648

Subgroups — Dic11×#453 #14759648

Order 2816.

1578 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1H(5,𝔽2)×Dic11C211yesmaximal, characteristic, complemented
2AGL(1,ℤ/8)×Dic11C212yesmaximal, complemented
3#127×Dic11C211yesmaximal, characteristic, complemented
4#13069015C211yesmaximal, characteristic, complemented
5#13068994C212yesmaximal, complemented
6#13068844C212yesmaximal, complemented
7#13068828C211yesmaximal, characteristic, complemented
8#13068570C211yesmaximal, characteristic, complemented
9#104×Dic11C212yesmaximal, complemented
10#100×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#453C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C2×C11×AGL(1,ℤ/8)C2212yes—
14C2×C11×#127C2211yescharacteristic
15#10623358—22no—
16#10623358C2212yes—
17#41×Dic11—22no—
18#41×Dic11C2212yes—
19#10623329—22no—
20#10623329—22no—
21#10623329C2211yescharacteristic
22C2×D4×Dic11—22no—
23C2×D4×Dic11—22no—
24C2×D4×Dic11—22no—
25C2×D4×Dic11C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic, complemented
27C11×#453C418yescomplemented
28C2×C11×#104C2212yes—
29C2×C11×#100C2211yescharacteristic
30C2×#66901C2212yes—
31#10622845C2212yes—
32#10622834—22no—
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic, complemented
35C2×#66897C2211yescharacteristic
36#10622828C2212yescomplemented
37#10622777—22no—
38SD16×Dic11—22no—
39#10622765—22no—
40D8×Dic11—22no—
41#10622734C2212yescomplemented
42M16×Dic11C2212yescomplemented
43#10622548C2211yescharacteristic, complemented
44C42×Dic11C2211yescharacteristic, complemented
45#10622193C2212yescomplemented
46#10622192C2212yescomplemented
47#10622161C2212yescomplemented
48C11×H(5,𝔽2)—24no—
49C11×H(5,𝔽2)—22no—
50C11×H(5,𝔽2)C2×C414yescomplemented
51C2×C11×#41—22no—
52C2×C11×#41C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11C2311yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×Dic11—22no—
59C23×Dic11—21no—
60C23×Dic11D412yes—
61C11×AGL(1,ℤ/8)—24no—
62C11×AGL(1,ℤ/8)C2×C418yescomplemented
63C2×C11×SD16—22no—
64C2×C11×D8—22no—
65C2×C11×M16C2312yes—
66C11×#127—22no—
67C11×#127C2×C414yescomplemented
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11D412yes—
76Q8×Dic11—22no—
77Q8×Dic11D412yescomplemented
78Q8×Dic11D412yescomplemented
79D4×Dic11—24no—
80D4×Dic11—24no—
81D4×Dic11—24no—
82D4×Dic11—24no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—24no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11—22no—
89D4×Dic11—22no—
90D4×Dic11—22no—
91D4×Dic11—22no—
92D4×Dic11—22no—
93D4×Dic11—48no—
94D4×Dic11D412yescomplemented
95D4×Dic11D412yescomplemented
96#66979—24no—
97#66979—22no—
98#66979—22no—
99#66979C2312yes—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4×Dic11—22no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×#4318C2312yes—
112C11×#104C2×C418yescomplemented
113C11×#100C2×C414yescomplemented
114#66901—24no—
115#66899—22no—
116#66897—22no—
117#66896—22no—
118#66896—22no—
119#66896—22no—
120#66882—22no—
121#66881—22no—
122#66879—22no—
123C8×Dic11—22no—
124C4×#453—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—21no—
127C24×C11C2×D412yes—
128C11×#41—28no—
129C11×#41—28no—
130C11×#41—22no—
131C11×#41—22no—
132C11×#41C22×C414yes—
133C11×#41#4114yes—
134C2×Q8×C11C2×D412yes—
135C2×D4×C11—24no—
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C2×D4×C11—28no—
139C2×D4×C11—22no—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
142C2×D4×C11—22no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—44no—
148C2×D4×C11—44no—
149C2×D4×C11C22×C412yes—
150C2×D4×C11C22×C412yescomplemented
151C2×D4×C11C2×D412yes—
152C2×D4×C11#4112yes—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—22no—
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—44no—
167C22×Dic11—44no—
168C22×Dic11—41no—
169C22×Dic11—41no—
170C22×Dic11—84no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D412yes—
173C22×Dic11C2×D411yescharacteristic
174C11×SD16—28no—
175C11×D8—28no—
176C11×M16—22no—
177C11×M16C22×C414yescomplemented
178C2×C8×C11—22no—
179C42×C11—21no—
180C42×C11C22×C412yescomplemented
181C22⋊Dic11—24no—
182C22⋊Dic11—24no—
183C22⋊Dic11—24no—
184C22⋊Dic11—22no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—44no—
188C22⋊Dic11—44no—
189C22⋊Dic11—42no—
190C4⋊Dic11—24no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—44no—
196C4⋊Dic11C2×D412yes—
197C4⋊Dic11C2×D412yes—
198C4×Dic11—24no—
199C4×Dic11—24no—
200C4×Dic11—22no—
201C4×Dic11—22no—
202C4×Dic11—22no—
203C4×Dic11—22no—
204C4×Dic11—42no—
205C4×Dic11C2×D412yes—
206C4×Dic11C2×D412yes—
207#4318—22no—
208#4318—22no—
209C2×C11⋊C8—22no—
210C4×H(5,𝔽2)—111no—
211C2×#453D1111yescharacteristic
212C4×AGL(1,ℤ/8)—112no—
213C4×#127—111no—
214#1887—111no—
215#1883—112no—
216#1859—112no—
217#1856—111no—
218#1792—111no—
219C4×#104—112no—
220C4×#100—111no—
221C23×C11—28no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—82no—
233C23×C11—82no—
234C23×C11C4×D414yes—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11C4×D414yescomplemented
238D4×C11—216no—
239D4×C11—24no—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—24no—
243D4×C11—22no—
244D4×C11—24no—
245D4×C11—416no—
246D4×C11—42no—
247D4×C11C4×D414yescomplemented
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—44no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—41no—
272C2×Dic11—82no—
273C2×Dic11—82no—
274C2×Dic11—82no—
275C2×Dic11—82no—
276C2×Dic11—84no—
277C2×Dic11—82no—
278C2×Dic11—82no—
279C2×Dic11#12012yes—
280C2×Dic11#12011yescharacteristic
281C2×Dic11#12011yescharacteristic
282C8×C11—24no—
283C11⋊C8—42no—
284C2×H(5,𝔽2)C2×D1111yescharacteristic
285C2×AGL(1,ℤ/8)C2×D1112yes—
286C2×#127C2×D1111yescharacteristic
287#520—112no—
288#520—222no—
289#518—111no—
290#518—222no—
291#518—222no—
292C4×#41—112no—
293C4×#41—222no—
294C2×C4×D4—111no—
295C2×C4×D4—111no—
296C2×C4×D4—222no—
297C2×C4×D4—222no—
298C2×C4×D4—222no—
299#453Dic1118yesdirect product factor
300#442—222no—
301#440—222no—
302C4×SD16—222no—
303C4×D8—222no—
304#428—112no—
305C2×#104—112no—
306C2×#104C2×D1112yes—
307#418—112no—
308#417—112no—
309C2×#100—111no—
310C2×#100C2×D1111yescharacteristic
311C4×M16—112no—
312#390—111no—
313#390—111no—
314#390—222no—
315#384—111no—
316C43—111no—
317#343—112no—
318#339—112no—
319#339—112no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—88no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11C2×#12011yescharacteristic
338C22×C11#52511yescharacteristic
339C4×C11—24no—
340C4×C11—24no—
341C4×C11C2×C4×D412yes—
342C4×C11#52512yes—
343Dic11—21no—
344Dic11—22no—
345Dic11—42no—
346Dic11—42no—
347Dic11—42no—
348Dic11—42no—
349Dic11—81no—
350Dic11#45312yesdirect product factor
351H(5,𝔽2)—24no—
352H(5,𝔽2)—22no—
353H(5,𝔽2)C2×Dic1114yescomplemented
354C2×#41—22no—
355C2×#41C22×D1112yes—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C22×D1111yescharacteristic
360C22×D4C22×D1111yescharacteristic
361C23×C4—112no—
362C23×C4—221no—
363C23×C4—222no—
364AGL(1,ℤ/8)—24no—
365AGL(1,ℤ/8)C2×Dic1118yescomplemented
366C2×SD16—22no—
367C2×D8—22no—
368C2×M16—112no—
369C2×M16C22×D1112yes—
370#127—22no—
371#127C2×Dic1114yescomplemented
372C4×Q8—112no—
373C4×Q8—112no—
374C4×Q8—222no—
375C4×D4—112no—
376C4×D4—112no—
377C4×D4—222no—
378C4×D4—222no—
379C4×D4—222no—
380C4×D4—222no—
381C4×D4—222no—
382C4×D4—222no—
383C4×D4—222no—
384C4×D4—224no—
385C4×D4—222no—
386C4×D4—224no—
387C4×D4—224no—
388C4×D4—224no—
389C4×D4—224no—
390C4×D4—222no—
391C4×D4—448no—
392#117—112no—
393#117—222no—
394#117—222no—
395#117—224no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—222no—
401C2×C22⋊C4—112no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—222no—
411C2×C42—221no—
412C2×C42—222no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#107—222no—
416#106—222no—
417#104—224no—
418#104C2×Dic1118yescomplemented
419#103—222no—
420#102—222no—
421#102—222no—
422#102—222no—
423#100—222no—
424#100C2×Dic1114yescomplemented
425#97—222no—
426C4×C8—222no—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11—44no—
430C2×C11—44no—
431C2×C11—82no—
432C2×C11C4×#12011yescharacteristic
433C2×C11C2×#45311yescharacteristic
434C2×C11#301811yescharacteristic
435C24—22no—
436C24—21no—
437C24D4×D1112yes—
438#41—28no—
439#41—28no—
440#41—22no—
441#41—22no—
442#41#434114yes—
443#41C22×Dic1114yes—
444C2×Q8D4×D1112yes—
445C2×D4—24no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—22no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4D4×D1112yes—
460C2×D4#434112yes—
461C2×D4C22×Dic1112yes—
462C2×D4C22×Dic1112yescomplemented
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—112no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—221no—
478C22×C4—441no—
479C22×C4—441no—
480C22×C4—444no—
481C22×C4—444no—
482C22×C4—884no—
483C22×C4C23×D1111yescharacteristic
484SD16—28no—
485D8—28no—
486M16—22no—
487M16—222no—
488M16—222no—
489M16C22×Dic1114yescomplemented
490C2×C8—22no—
491C2×C8—222no—
492C4⋊C4—112no—
493C4⋊C4—112no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C4⋊C4—224no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—444no—
500C22⋊C4—224no—
501C22⋊C4—222no—
502C22⋊C4—222no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C22⋊C4—222no—
506C22⋊C4—442no—
507C22⋊C4—444no—
508C22⋊C4—444no—
509C42—21no—
510C42—112no—
511C42—112no—
512C42—222no—
513C42—222no—
514C42—224no—
515C42—224no—
516C42—222no—
517C42—222no—
518C42—442no—
519C42C22×Dic1112yescomplemented
520C11C4×#45311yescharacteristic, complemented, Sylow
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—82no—
533C23—82no—
534C23D4×Dic1114yes—
535C23C2×D4×D1111yescharacteristic
536Q8—22no—
537Q8D4×Dic1114yescomplemented
538D4—216no—
539D4—24no—
540D4—24no—
541D4—24no—
542D4—24no—
543D4—22no—
544D4—24no—
545D4—416no—
546D4—42no—
547D4D4×Dic1114yescomplemented
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—28no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—111no—
556C2×C4—112no—
557C2×C4—111no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—444no—
564C2×C4—444no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—441no—
571C2×C4—882no—
572C2×C4—882no—
573C2×C4—882no—
574C2×C4—882no—
575C2×C4—884no—
576C2×C4—882no—
577C2×C4—882no—
578C2×C4C2×D4×D1112yes—
579C2×C4C2×#434112yes—
580C2×C4C2×#434111yescharacteristic
581C2×C4C23×Dic1111yescharacteristic
582C8—24no—
583C8—442no—
584C22—21no—
585C22—21no—
586C22—24no—
587C22—24no—
588C22—44no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—82no—
596C22—82no—
597C22—88no—
598C22—81no—
599C22—81no—
600C22#1062311711yescharacteristic
601C22D11×#12011yescharacteristic
602C22C2×D4×Dic1111yescharacteristic
603C4—24no—
604C4—24no—
605C4—112no—
606C4—221no—
607C4—222no—
608C4—442no—
609C4—442no—
610C4—442no—
611C4—442no—
612C4—881no—
613C4#1062311712yes—
614C4C2×D4×Dic1112yes—
615C2—21no—
616C2—21no—
617C2—44no—
618C2—44no—
619C2—82no—
620C2#120×Dic1111yescharacteristic
621C2D11×#45311yescharacteristic
622C2#1307796111yescharacteristic
subgroupG/H
centerC22D11×#120
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#453C2
socleC22×C11C2×#120
cosocleC22×C4×C11C24
hypercenterC2×#453D11
hypocenterC11C4×#453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#453

Complements

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

NH ≅ G/Ntype
1. H(5,𝔽2)×Dic11C2semidirect
2. AGL(1,ℤ/8)×Dic11C2semidirect
3. #127×Dic11C2semidirect
4. #13069015C2semidirect
5. #13068994C2semidirect
6. #13068844C2semidirect
7. #13068828C2semidirect
8. #13068570C2semidirect
9. #104×Dic11C2semidirect
10. #100×Dic11C2semidirect
26. C2×D4×Dic11C22semidirect
27. C11×#453C4semidirect
34. #10622834C22semidirect
36. #10622828C22semidirect
41. #10622734C22semidirect
42. M16×Dic11C22semidirect
43. #10622548C22semidirect
44. C42×Dic11C22semidirect
45. #10622193C22semidirect
46. #10622192C22semidirect
47. #10622161C22semidirect
50. C11×H(5,𝔽2)C2×C4semidirect
62. C11×AGL(1,ℤ/8)C2×C4semidirect
67. C11×#127C2×C4semidirect
77. Q8×Dic11D4semidirect
78. Q8×Dic11D4semidirect
94. D4×Dic11D4semidirect
95. D4×Dic11D4semidirect
112. C11×#104C2×C4semidirect
113. C11×#100C2×C4semidirect
150. C2×D4×C11C22×C4semidirect
177. C11×M16C22×C4semidirect
180. C42×C11C22×C4semidirect
237. Q8×C11C4×D4semidirect
247. D4×C11C4×D4semidirect
299. #453Dic11direct (N × H)
350. Dic11#453direct (N × H)
353. H(5,𝔽2)C2×Dic11semidirect
365. AGL(1,ℤ/8)C2×Dic11semidirect
371. #127C2×Dic11semidirect
418. #104C2×Dic11semidirect
424. #100C2×Dic11semidirect
462. C2×D4C22×Dic11semidirect
489. M16C22×Dic11semidirect
519. C42C22×Dic11semidirect
520. C11C4×#453semidirect
537. Q8D4×Dic11semidirect
547. D4D4×Dic11semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×Dic112
AGL(1,ℤ/8)×Dic112
#127×Dic112
#130690152
#130689942
#130688442
#130688282
#130685702
#104×Dic112
#100×Dic112
C2×C11×#4532
C4×#45311