Finite Group Databasebeta

← D11×#2043 #14781451

Subgroups — D11×#2043 #14781451

Order 2816.

1542 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×D11×#103C212yesmaximal
3C2×D11×#103C212yesmaximal
4D11×#389C211yesmaximal, characteristic
5#13069863C211yesmaximal, characteristic, complemented
6#13069862C211yesmaximal, characteristic, complemented
7#13069861C212yesmaximal, complemented
8#13069860C212yesmaximal, complemented
9#13069859C211yesmaximal, characteristic, complemented
10D11×#336C211yesmaximal, characteristic
11C11×#2043C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66997C2212yes—
15C22×C8×D11C2212yes—
16D11×C4⋊Q8—28no—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66941—21no—
23C2×#66941—21no—
24C2×C42×D11C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#103C2212yes—
28C11×#389C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33#10622598C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622585—21no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38#10622541C2211yescharacteristic
39D11×#103—28no—
40D11×#103—28no—
41D11×#95—21no—
42#10622260—21no—
43C11×#336C2211yescharacteristic
44#10622188C2212yes—
45#10622162C2211yescharacteristic
46C22×Q8×C11C2312yes—
47C2×Q8×D11—24no—
48C2×Q8×D11—24no—
49C2×Q8×D11—24no—
50C2×Q8×D11—24no—
51C2×Q8×D11—24no—
52C2×Q8×D11D418yes—
53C22×C4×D11—22no—
54C22×C4×D11—21no—
55C22×C4×D11—21no—
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22—22no—
60C22×Dic22C2312yes—
61C22×C8×C11C2312yes—
62C11×C4⋊Q8—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69#66997—24no—
70#66997—24no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C2×C8×D11—24no—
87C2×C8×D11—24no—
88C2×C8×D11—24no—
89C4⋊C4×D11—28no—
90C4⋊C4×D11—28no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11—24no—
93C4⋊C4×D11—44no—
94C4⋊C4×D11D414yes—
95#66941—28no—
96#66941—28no—
97C42×D11—24no—
98#66922—24no—
99C11×#103—24no—
100C11×#103—24no—
101C11×#95—21no—
102#66899—24no—
103#66899—24no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107#66880—24no—
108#66880—24no—
109#66874—24no—
110#66874—24no—
111C2×#2043—111nomaximal, Sylow
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11C2×D414yes—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C22×Dic11—21no—
126C22×Dic11—22no—
127C22×Dic11—21no—
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131Q8×D11—216no—
132Q8×D11—216no—
133Q8×D11—48no—
134Q8×D11—48no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—28no—
138C2×C4×D11—24no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—42no—
142C2×C4×D11—44no—
143C2×C4×D11—44no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C2×C4×D11SD1614yes—
149C2×C4×D11Q1614yes—
150C2×C4×D11C2×D414yes—
151C2×C4×D11C2×D412yes—
152C2×C4×D11#4112yes—
153C2×C4×D11#4114yes—
154C2×Dic22—28no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22—44no—
161C2×Dic22—44no—
162C2×Dic22C2×D414yes—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C2×D412yes—
172C42×C11—22no—
173C4⋊Dic11—24no—
174C4⋊Dic11—24no—
175C4⋊Dic11—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11—42no—
178C4⋊Dic11C2×D412yes—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—24no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C8×D11—48no—
192C22×C4⋊Q8—111no—
193C22×#103—112no—
194C22×#103—112no—
195C2×#389—111no—
196#2043—112no—
197#2043—112no—
198#2043—111no—
199#2043—111no—
200#2043—111no—
201#2043D1111yescharacteristic, direct product factor
202C2×#336—111no—
203C23×C11C22×D411yescharacteristic
204C22×D11#12012yes—
205C22×D11#12112yes—
206C22×D11#12412yes—
207C22×D11C2×SD1612yes—
208C22×D11C2×Q1612yes—
209C22×D11#13712yes—
210C22×D11#13712yes—
211Q8×C11—24no—
212Q8×C11—24no—
213Q8×C11—42no—
214Q8×C11—42no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11C2×SD1612yes—
229C2×C4×C11C2×Q1612yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C11C2×#4111yescharacteristic
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11#12012yes—
248C2×Dic11#12112yes—
249C2×Dic11#12412yes—
250C2×Dic11C2×SD1612yes—
251C2×Dic11C2×Q1612yes—
252C4×D11—28no—
253C4×D11—28no—
254C4×D11—416no—
255C4×D11—48no—
256C4×D11—84no—
257C4×D11#12118yes—
258C4×D11#12318yes—
259Dic22—24no—
260Dic22—24no—
261Dic22—42no—
262Dic22—42no—
263Dic22—416no—
264C8×C11—42no—
265C11⋊C8—42no—
266C23×Q8—112no—
267C23×C8—112no—
268C2×C4⋊Q8—112no—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8—221no—
271C2×C4⋊Q8—221no—
272C2×C4⋊Q8—228no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4—221no—
277C22×C4⋊C4—221no—
278C22×C4⋊C4—221no—
279C22×C42—111no—
280C2×#103—112no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#103—228no—
287C2×#103—228no—
288C2×#103C2×D1112yes—
289C2×#103C2×D1112yes—
290#389—111no—
291#389—111no—
292#389—111no—
293#389—221no—
294#389—221no—
295#389C2×D1111yescharacteristic
296C2×#95—221no—
297#336—112no—
298#336—111no—
299#336C2×D1111yescharacteristic
300C22×C11C2×#12011yescharacteristic
301C22×C11C2×#12111yescharacteristic
302C22×C11C2×#12411yescharacteristic
303C22×C11C22×SD1611yescharacteristic
304C22×C11C22×Q1611yescharacteristic
305C22×C11C2×#13711yescharacteristic
306C22×C11C2×#13711yescharacteristic
307C2×D11#39414yes—
308C2×D11#44814yes—
309C2×D11#45114yes—
310C2×D11#46114yes—
311C2×D11#46214yes—
312C2×D11#48714yes—
313C2×D11#49114yes—
314C4×C11—22no—
315C4×C11—22no—
316C4×C11—44no—
317C4×C11—42no—
318C4×C11—81no—
319C4×C11C2×#12112yes—
320C4×C11C2×#12312yes—
321Dic11—22no—
322Dic11—22no—
323Dic11—44no—
324Dic11—42no—
325Dic11—81no—
326Dic11#39414yes—
327C22×Q8—118no—
328C22×Q8—112no—
329C22×Q8—222no—
330C22×Q8—224no—
331C22×Q8—224no—
332C22×Q8—224no—
333C22×Q8—224no—
334C22×Q8—224no—
335C22×Q8C22×D1112yes—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—221no—
340C23×C4—222no—
341C23×C4—221no—
342C22×C8—112no—
343C22×C8—224no—
344C22×C8—224no—
345C22×C8—224no—
346C22×C8C22×D1112yes—
347C4⋊Q8—24no—
348C4⋊Q8—224no—
349C4⋊Q8—228no—
350C4⋊Q8—228no—
351C4⋊Q8—224no—
352C4⋊Q8—224no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—444no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—224no—
379C2×C42C22×D1111yescharacteristic
380#103—24no—
381#103—24no—
382#103—224no—
383#103—224no—
384#103—224no—
385#103—224no—
386#103—224no—
387#103—224no—
388#95—21no—
389#95—221no—
390#95—221no—
391#95—221no—
392C2×C11C2×#39411yescharacteristic
393C2×C11C2×#44811yescharacteristic
394C2×C11C2×#45111yescharacteristic
395C2×C11C2×#46111yescharacteristic
396C2×C11C2×#46211yescharacteristic
397C2×C11C2×#48711yescharacteristic
398C2×C11C2×#49111yescharacteristic
399D11#204318yesdirect product factor
400C24—111no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—114no—
407C2×Q8—228no—
408C2×Q8—2216no—
409C2×Q8—2216no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—444no—
416C2×Q8—444no—
417C2×Q8—448no—
418C2×Q8—448no—
419C2×Q8D4×D1114yes—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—111no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—228no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—221no—
441C22×C4—442no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—448no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—42no—
463C4⋊C4—112no—
464C4⋊C4—224no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4D4×D1112yes—
476C42—22no—
477C42—222no—
478C42—222no—
479C42—222no—
480C11C2×#204311yescharacteristic, complemented, Sylow
481C23—112no—
482C23—112no—
483C23—112no—
484C23—112no—
485C23—112no—
486C23—112no—
487C23—112no—
488C23C2×D4×D1111yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—42no—
492Q8—42no—
493Q8—224no—
494Q8—224no—
495Q8—4416no—
496Q8—442no—
497Q8—442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—112no—
512C2×C4—112no—
513C2×C4—112no—
514C2×C4—118no—
515C2×C4—118no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—228no—
519C2×C4—228no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—4416no—
527C2×C4—448no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—884no—
536C2×C4SD16×D1112yes—
537C2×C4Q16×D1112yes—
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×D4×D1112yes—
540C2×C4#41×D1112yes—
541C2×C4#41×D1111yescharacteristic
542C8—42no—
543C8—442no—
544C22—114no—
545C22—114no—
546C22—114no—
547C22—114no—
548C22—114no—
549C22—114no—
550C22—114no—
551C22D11×#12011yescharacteristic
552C22D11×#12111yescharacteristic
553C22D11×#12411yescharacteristic
554C22C2×SD16×D1111yescharacteristic
555C22C2×Q16×D1111yescharacteristic
556C22D11×#13711yescharacteristic
557C22D11×#13711yescharacteristic
558C4—22no—
559C4—22no—
560C4—42no—
561C4—44no—
562C4—81no—
563C4—114no—
564C4—222no—
565C4—222no—
566C4—442no—
567C4—444no—
568C4—881no—
569C4D11×#12112yes—
570C4D11×#12312yes—
571C2—118no—
572C2D11×#39411yescharacteristic
573C2D11×#44811yescharacteristic
574C2D11×#45111yescharacteristic
575C2D11×#46111yescharacteristic
576C2D11×#46211yescharacteristic
577C2D11×#48711yescharacteristic
578C2D11×#49111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2043C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2043D11
hypocenterC11C2×#2043
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
5. #13069863C2semidirect
6. #13069862C2semidirect
7. #13069861C2semidirect
8. #13069860C2semidirect
9. #13069859C2semidirect
11. C11×#2043C2semidirect
201. #2043D11direct (N × H)
399. D11#2043direct (N × H)
480. C11C2×#2043semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×D11×#1032
D11×#3892
#130698632
#130698622
#130698612
#130698602
#130698592
D11×#3362
C11×#20432
C2×#204311