Finite Group Databasebeta

← D11×#1463 #14719611

Subgroups — D11×#1463 #14719611

Order 2816.

1718 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
1C22×C4⋊C4×D11C211yesmaximal, characteristic
2D11×#407C212yesmaximal
3#13066946C211yesmaximal, characteristic, complemented
4#13066945C212yesmaximal, complemented
5#13066944C214yesmaximal, complemented
6D11×#324C214yesmaximal, complemented
7C11×#1463C211yesmaximal, characteristic, complemented
8C23×C4×D11C411yescharacteristic
9C23×C4×D11C411yescharacteristic
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C411yescharacteristic
13C22×Dic11⋊C4C411yescharacteristic
14C22×Dic11⋊C4C2211yescharacteristic
15C2×M16×D11—22no—
16C2×C4⋊C4×D11—22no—
17C2×C4⋊C4×D11—22no—
18C2×C4⋊C4×D11—22no—
19C2×C4⋊C4×D11—22no—
20C2×C4⋊C4×D11C412yes—
21C2×C4⋊C4×D11C412yes—
22C2×C4⋊C4×D11C2212yes—
23C2×C4⋊C4×D11C2212yes—
24C11×#407C2212yes—
25#10622820C2212yes—
26#10622739—22no—
27#10622339—22no—
28#10622339C2214yes—
29D11×C22⋊C8—22no—
30D11×C22⋊C8C2214yes—
31C11×#324C2214yescomplemented
32#10622166C2214yescomplemented
33#10622107C2218yescomplemented
34C24×D11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2×C411yescharacteristic
39C23×Dic11C2×C411yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C22×C4×D11—21no—
42C22×C4×D11—21no—
43C22×C4×D11—21no—
44C22×C4×D11—21no—
45C22×C4×D11—28no—
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—21no—
50C22×C4×D11—44no—
51C22×C4×D11—44no—
52C22×C4×D11C2×C412yes—
53C22×C4×D11C2×C412yes—
54C22×C4×D11C2×C412yes—
55C22×C4×D11C2×C412yes—
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D412yes—
59C22×C4×D11D412yes—
60C22×C4×D11D412yes—
61C22×C4×D11D412yes—
62C22×C4×D11C2311yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C2×C11×M16—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4C2×C412yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11C2×C412yes—
72C2×C4⋊Dic11C2×C412yes—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4C2×C412yes—
78C2×Dic11⋊C4C2×C412yes—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2312yes—
81C2×#4318—22no—
82M16×D11—48no—
83C2×#4313—24no—
84C2×C8×D11—24no—
85C4⋊C4×D11—24no—
86C4⋊C4×D11—24no—
87C4⋊C4×D11—24no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—24no—
90C4⋊C4×D11—24no—
91C4⋊C4×D11—24no—
92C4⋊C4×D11—24no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8C2314yes—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)C2314yes—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—24no—
99C2×#1463—111nomaximal, Sylow
100C24×C11C22×C411yescharacteristic
101C23×D11—24no—
102C23×D11—24no—
103C23×D11—24no—
104C23×D11C22⋊C411yescharacteristic
105C23×D11C22⋊C411yescharacteristic
106C23×D11C22⋊C411yescharacteristic
107C23×D11C22⋊C411yescharacteristic
108C23×D11C22×C411yescharacteristic
109C23×D11C22×C411yescharacteristic
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—24no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—24no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11C22⋊C412yes—
131C22×Dic11C22⋊C412yes—
132C22×Dic11C22×C412yes—
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C2×C4×D11—28no—
137C2×C4×D11—28no—
138C2×C4×D11—28no—
139C2×C4×D11—28no—
140C2×C4×D11—24no—
141C2×C4×D11—28no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—24no—
151C2×C4×D11—24no—
152C2×C4×D11—44no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—44no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11C22⋊C412yes—
166C2×C4×D11C22⋊C412yes—
167C2×C4×D11C22⋊C412yes—
168C2×C4×D11C22⋊C412yes—
169C2×C4×D11M1618yescomplemented
170C2×C4×D11C2×D412yes—
171C2×C4×D11C2×D412yes—
172C2×C4×D11C2×D412yes—
173C2×C4×D11C2×D412yes—
174C11×M16—44no—
175C2×C8×C11—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C4⋊Dic11—24no—
179C4⋊Dic11—24no—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184#4318—44no—
185C2×C11⋊C8—24no—
186#4313—48no—
187C8×D11—48no—
188C23×C4⋊C4—111no—
189C2×#407—112no—
190#1463—112no—
191#1463—114no—
192#1463—111no—
193#1463D1111yescharacteristic, direct product factor
194C2×#324—114no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11C2×C22⋊C411yescharacteristic
199C23×C11C2×C22⋊C411yescharacteristic
200C23×C11C23×C411yescharacteristic
201C22×D11—232no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11#9914yes—
218C22×D11#10114yes—
219C22×D11C2×C22⋊C411yescharacteristic
220C22×D11C2×C22⋊C411yescharacteristic
221C22×D11C2×C22⋊C411yescharacteristic
222C22×D11C2×C22⋊C411yescharacteristic
223C22×D11C2×M1614yes—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C2×M1614yescomplemented
238C2×C4×C11C22×D412yes—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—42no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11C2×C22⋊C412yes—
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×M1614yescomplemented
254C4×D11—28no—
255C4×D11—28no—
256C4×D11—28no—
257C4×D11—28no—
258C4×D11—24no—
259C4×D11—24no—
260C4×D11—24no—
261C4×D11—24no—
262C4×D11—42no—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—42no—
266C4×D11—44no—
267C4×D11—44no—
268C4×D11—44no—
269C4×D11—44no—
270C8×C11—44no—
271C11⋊C8—44no—
272C24×C4—111no—
273C24×C4—111no—
274C24×C4—111no—
275C22×M16—222no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—112no—
283C22×C4⋊C4—222no—
284C22×C4⋊C4—222no—
285C22×C4⋊C4—222no—
286C22×C4⋊C4—222no—
287C22×C4⋊C4C2×D1111yescharacteristic
288#407—112no—
289#407—114no—
290#407—222no—
291#407—222no—
292#407C2×D1112yes—
293C2×C22⋊C8—114no—
294C2×C22⋊C8—222no—
295#324—114no—
296#324—118no—
297#324C2×D1114yescomplemented
298C22×C11—28no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11C2×#9912yes—
306C22×C11C2×#10112yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C22×M1612yes—
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—21no—
313C2×D11—21no—
314C2×D11—21no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—28no—
319C2×D11—28no—
320C2×D11—28no—
321C2×D11#40712yes—
322C2×D11#40712yes—
323C2×D11C2×#9912yes—
324C2×D11C2×#9912yes—
325C2×D11C2×#10112yes—
326C2×D11C2×#10112yes—
327C4×C11—24no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—42no—
331Dic11—24no—
332Dic11—22no—
333Dic11—22no—
334Dic11—42no—
335C25—111no—
336C23×C4—111no—
337C23×C4—112no—
338C23×C4—112no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4—112no—
343C23×C4—112no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4—112no—
351C23×C4—228no—
352C23×C4—221no—
353C23×C4—221no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4—444no—
361C23×C4—444no—
362C23×C4C4×D1111yescharacteristic
363C23×C4C4×D1111yescharacteristic
364C23×C4C22×D1111yescharacteristic
365C2×M16—22no—
366C2×M16—224no—
367C2×M16—222no—
368C2×M16—448no—
369C22×C8—224no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4C4×D1112yes—
393C2×C4⋊C4C22×D1112yes—
394C22⋊C8—22no—
395C22⋊C8—114no—
396C22⋊C8—224no—
397C22⋊C8—224no—
398C22⋊C8—222no—
399C22⋊C8C22×D1114yes—
400C2×C11—22no—
401C2×C11—22no—
402C2×C11—22no—
403C2×C11C2×#40711yescharacteristic
404C2×C11C22×#9911yescharacteristic
405C2×C11C22×#10111yescharacteristic
406D11—22no—
407D11—22no—
408D11—22no—
409D11#146314yesdirect product factor
410C24—111no—
411C24—111no—
412C24—111no—
413C24—111no—
414C24—111no—
415C24—111no—
416C24—224no—
417C24—224no—
418C24—224no—
419C24C2×C4×D1111yescharacteristic
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—112no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—118no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—228no—
448C22×C4—224no—
449C22×C4—228no—
450C22×C4—228no—
451C22×C4—228no—
452C22×C4—228no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—224no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—444no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—444no—
471C22×C4—444no—
472C22×C4—444no—
473C22×C4—444no—
474C22×C4—444no—
475C22×C4—444no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4C2×C4×D1112yes—
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4D4×D1112yes—
482C22×C4D4×D1112yes—
483C22×C4C23×D1111yescharacteristic
484M16—44no—
485M16—448no—
486M16—444no—
487C2×C8—24no—
488C2×C8—224no—
489C2×C8—448no—
490C4⋊C4—24no—
491C4⋊C4—24no—
492C4⋊C4—224no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—224no—
496C4⋊C4—224no—
497C4⋊C4—224no—
498C11C2×#146311yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—22no—
502C23—111no—
503C23—111no—
504C23—111no—
505C23—111no—
506C23—114no—
507C23—114no—
508C23—114no—
509C23—222no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—222no—
514C23—222no—
515C23—222no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—2232no—
522C23—222no—
523C23—222no—
524C23—222no—
525C23C22⋊C4×D1111yescharacteristic
526C23C22⋊C4×D1111yescharacteristic
527C23C22×C4×D1111yescharacteristic
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—114no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—228no—
546C2×C4—228no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—228no—
550C2×C4—228no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—222no—
554C2×C4—222no—
555C2×C4—224no—
556C2×C4—222no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—444no—
564C2×C4—444no—
565C2×C4—442no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4C22⋊C4×D1112yes—
572C2×C4M16×D1114yescomplemented
573C2×C4C2×D4×D1112yes—
574C8—44no—
575C8—444no—
576C22—28no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—112no—
584C22—112no—
585C22—112no—
586C22—112no—
587C22—112no—
588C22—112no—
589C22—228no—
590C22—228no—
591C22—228no—
592C22—228no—
593C22—228no—
594C22—228no—
595C22—221no—
596C22—221no—
597C22—221no—
598C22—221no—
599C22—221no—
600C22—221no—
601C22D11×#9912yes—
602C22D11×#10112yes—
603C22C2×C22⋊C4×D1111yescharacteristic
604C22C2×M16×D1112yes—
605C4—24no—
606C4—22no—
607C4—22no—
608C4—42no—
609C4—224no—
610C4—222no—
611C4—222no—
612C4—442no—
613C2—22no—
614C2—22no—
615C2—22no—
616C2—114no—
617C2—222no—
618C2—222no—
619C2—222no—
620C2D11×#40711yescharacteristic
621C2C2×D11×#9911yescharacteristic
622C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11C2×#1463
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13066946C2semidirect
4. #13066945C2semidirect
5. #13066944C2semidirect
6. D11×#324C2semidirect
7. C11×#1463C2semidirect
31. C11×#324C22semidirect
32. #10622166C22semidirect
33. #10622107C22semidirect
169. C2×C4×D11M16semidirect
193. #1463D11direct (N × H)
237. C2×C4×C11C2×M16semidirect
253. C2×Dic11C2×M16semidirect
297. #324C2×D11semidirect
409. D11#1463direct (N × H)
498. C11C2×#1463semidirect
572. C2×C4M16×D11semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D112
D11×#4072
#130669462
#130669452
#130669442
D11×#3242
C11×#14632
C2×#146311