Finite Group Databasebeta

← D11×#1588 #14723332

Subgroups — D11×#1588 #14723332

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×Q8×D11C211yesmaximal, characteristic, complemented
2C4×SD16×D11C211yesmaximal, characteristic
3D11×#436C211yesmaximal, characteristic
4#13067497C211yesmaximal, characteristic, complemented
5#13067496C211yesmaximal, characteristic, complemented
6#13067495C211yesmaximal, characteristic, complemented
7#13067494C211yesmaximal, characteristic, complemented
8#13067493C211yesmaximal, characteristic, complemented
9#13067492C211yesmaximal, characteristic, complemented
10#13067491C211yesmaximal, characteristic, complemented
11D11×#335C211yesmaximal, characteristic, complemented
12D11×Q8⋊C8C211yesmaximal, characteristic, complemented
13D11×D4⋊C8C211yesmaximal, characteristic
14D11×#322C211yesmaximal, characteristic, complemented
15C11×#1588C211yesmaximal, characteristic, complemented
16C2×SD16×D11C411yescharacteristic
17C2×M16×D11—21no—
18C4×Q8×D11C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic, complemented
21C4×C11×SD16C2211yescharacteristic
22C11×#436C2211yescharacteristic
23SD16×Dic11C411yescharacteristic
24#10622741—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29D11×#106C411yescharacteristic
30#10622465C411yescharacteristic
31#10622451C2211yescharacteristic
32D11×C4⋊C8—21no—
33D11×C4⋊C8C2211yescharacteristic
34D11×C4⋊C8C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic, complemented
37D11×#103C411yescharacteristic
38#10622401C411yescharacteristic
39D11×#102C411yescharacteristic
40#10622371C411yescharacteristic
41#10622342—21no—
42D11×C22⋊C8—21no—
43C4×#4314C2211yescharacteristic
44#10622301C2211yescharacteristic
45C4×C8×D11—21no—
46C4×C8×D11C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49C8×Dic22—21no—
50C8×Dic22C2211yescharacteristic, complemented
51C11×#335C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622117C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×Q8×D11C2×C411yescharacteristic
68C2×D4×D11C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×M16—21no—
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74Q8×Dic11C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80SD16×D11—24no—
81M16×D11—44no—
82C2×#4314C2×C411yescharacteristic
83C2×#4313—21no—
84C2×#4313—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11C2×C411yescharacteristic
89C2×C8×D11C2×C411yescharacteristic
90C2×C8×D11D411yescharacteristic
91C2×C8×D11D411yescharacteristic
92#66946C2×C411yescharacteristic
93C4⋊C4×D11—21no—
94C4⋊C4×D11C2×C411yescharacteristic
95C4⋊C4×D11C2×C411yescharacteristic
96#66940—21no—
97#66940C2×C411yescharacteristic
98(C22⋊D11)⋊C4—21no—
99C22⋊C4×D11—21no—
100C4×D44C2311yescharacteristic
101C42×D11—21no—
102C42×D11C2311yescharacteristic
103C4×Dic22—21no—
104C4×Dic22C2311yescharacteristic
105C11×#106C2×C411yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×C22⋊C8—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116#66899C2×C411yescharacteristic
117#66896C2×C411yescharacteristic
118C22⋊(C11⋊C8)—21no—
119#66885C2×C411yescharacteristic
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66881C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11—21no—
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11C2×C411yescharacteristic
133C8×Dic11D411yescharacteristic
134C8×Dic11D411yescharacteristic
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146C2×#1588—111nomaximal, Sylow
147C23×D11—21no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153Q8×D11—22no—
154Q8×D11M1614yescomplemented
155D4×D11—22no—
156D4×D11—22no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11C22×C411yescharacteristic
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11#4111yescharacteristic
168C2×Dic22—21no—
169C2×Dic22C22×C411yescharacteristic
170C11×SD16—22no—
171C11×M16—42no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C42×C11—21no—
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186#4325—22no—
187#4324—22no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11C22×C411yescharacteristic
192C4⋊Dic11C22×C411yescharacteristic
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11C22×C411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11#4111yescharacteristic
203#4318—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#4314—22no—
212#4313—42no—
213#4313—42no—
214C8×D11—24no—
215C8×D11—22no—
216C8×D11—22no—
217C8×D11—22no—
218C8×D11—22no—
219C8×D11—42no—
220C8×D11—42no—
221C2×C8×Q8—111no—
222C2×C4×SD16—111no—
223C2×#436—111no—
224#1588—111no—
225#1588—111no—
226#1588—111no—
227#1588—111no—
228#1588—111no—
229#1588—111no—
230#1588—111no—
231#1588D1111yescharacteristic, direct product factor
232C2×#335—111no—
233C2×Q8⋊C8—111no—
234C2×D4⋊C8—111no—
235C2×#322—111no—
236C23×C11—21no—
237C22×D11—21no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11C4×D411yescharacteristic
242Q8×C11—21no—
243Q8×C11C2×M1612yescomplemented
244D4×C11—21no—
245D4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—42no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—42no—
259C2×Dic11C4×D411yescharacteristic
260C2×Dic11C4×D411yescharacteristic
261C2×Dic11C4×D411yescharacteristic
262D44—21no—
263D44—21no—
264C4×D11—24no—
265C4×D11—22no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—42no—
271C4×D11C2×M1612yes—
272C4×D11#13112yes—
273C4×D11AGL(1,ℤ/8)12yes—
274C4×D11#13712yes—
275Dic22—21no—
276Dic22—24no—
277Dic22C2×M1612yescomplemented
278C8×C11—22no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—21no—
287C11⋊C8—21no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×SD16—111no—
293C22×M16—221no—
294C2×C4×Q8—111no—
295C2×C4×D4—111no—
296C8×Q8—111no—
297C8×Q8—111no—
298C8×Q8—111no—
299C8×Q8—221no—
300C8×Q8—221no—
301C8×Q8C2×D1111yescharacteristic, complemented
302C4×SD16—111no—
303C4×SD16—111no—
304C4×SD16—111no—
305C4×SD16—111no—
306C4×SD16—111no—
307C4×SD16—111no—
308C4×SD16—111no—
309C4×SD16C2×D1111yescharacteristic
310#436—111no—
311#436—111no—
312#436—111no—
313#436—221no—
314#436—221no—
315#436C2×D1111yescharacteristic
316C2×#106—111no—
317C2×C4⋊C8—111no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—221no—
320C2×#103—111no—
321C2×#102—111no—
322C2×C22⋊C8—221no—
323C2×C4×C8—111no—
324C2×C4×C8—111no—
325C2×C4×C8—111no—
326C2×C4×C8—221no—
327#335—111no—
328#335—111no—
329#335—111no—
330#335C2×D1111yescharacteristic, complemented
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333Q8⋊C8—111no—
334Q8⋊C8C2×D1111yescharacteristic, complemented
335D4⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8C2×D1111yescharacteristic
339#322—111no—
340#322—111no—
341#322—111no—
342#322C2×D1111yescharacteristic, complemented
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11C2×C4×D411yescharacteristic
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—84no—
351C2×D11#43512yes—
352C2×D11#44012yes—
353C2×D11#44312yes—
354C4×C11—22no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11C22×M1611yescharacteristic
359C4×C11C2×#13111yescharacteristic
360C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C11C2×#13711yescharacteristic
362Dic11—22no—
363Dic11—21no—
364Dic11—41no—
365Dic11—41no—
366Dic11#43512yes—
367Dic11#44012yes—
368C22×Q8—111no—
369C22×D4—111no—
370C23×C4—221no—
371C2×SD16—111no—
372C2×SD16—111no—
373C2×SD16—111no—
374C2×SD16—224no—
375C2×SD16C4×D1111yescharacteristic
376C2×M16—21no—
377C2×M16—221no—
378C2×M16—221no—
379C2×M16—221no—
380C2×M16—444no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8—111no—
385C22×C8—221no—
386C22×C8—221no—
387C22×C8—221no—
388C4×Q8—111no—
389C4×Q8—111no—
390C4×Q8—111no—
391C4×Q8—221no—
392C4×Q8—221no—
393C4×Q8C22×D1111yescharacteristic
394C4×D4—111no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—221no—
398C4×D4—221no—
399C4×D4C22×D1111yescharacteristic
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—221no—
406#106—111no—
407#106—111no—
408#106—111no—
409#106C4×D1111yescharacteristic
410C4⋊C8—21no—
411C4⋊C8—111no—
412C4⋊C8—111no—
413C4⋊C8—221no—
414C4⋊C8—221no—
415C4⋊C8—221no—
416C4⋊C8—221no—
417C4⋊C8—221no—
418C4⋊C8C22×D1111yescharacteristic
419C4⋊C8C22×D1111yescharacteristic
420#103—111no—
421#103—111no—
422#103—111no—
423#103C4×D1111yescharacteristic
424#102—111no—
425#102—111no—
426#102—111no—
427#102C4×D1111yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432C4×C8—21no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—221no—
441C4×C8—221no—
442C4×C8—221no—
443C4×C8—221no—
444C4×C8C22×D1111yescharacteristic
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C2×C11—81no—
448C2×C11C2×#43511yescharacteristic
449C2×C11C2×#44011yescharacteristic
450C2×C11C2×#44311yescharacteristic
451D11—81no—
452D11#158814yesdirect product factor
453C24—221no—
454C2×Q8—114no—
455C2×Q8—111no—
456C2×Q8—221no—
457C2×Q8—222no—
458C2×Q8C2×C4×D1111yescharacteristic
459C2×D4—111no—
460C2×D4—222no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4C2×C4×D1111yescharacteristic
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476SD16—22no—
477SD16—222no—
478SD16—222no—
479SD16—222no—
480M16—42no—
481M16—442no—
482M16—442no—
483M16—442no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—111no—
490C2×C8—111no—
491C2×C8—222no—
492C2×C8—222no—
493C2×C8—222no—
494C2×C8—222no—
495C2×C8—224no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—442no—
500C2×C8—442no—
501C2×C8C2×C4×D1111yescharacteristic
502C2×C8C2×C4×D1111yescharacteristic
503C2×C8D4×D1111yescharacteristic
504C2×C8D4×D1111yescharacteristic
505C4⋊C4—21no—
506C4⋊C4—111no—
507C4⋊C4—111no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4C2×C4×D1111yescharacteristic
514C4⋊C4C2×C4×D1111yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—221no—
517C22⋊C4—221no—
518C22⋊C4—221no—
519C42—21no—
520C42—111no—
521C42—111no—
522C42—111no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42C23×D1111yescharacteristic
527C11C2×#158811yescharacteristic, complemented, Sylow
528C23—21no—
529C23—111no—
530C23—221no—
531C23—442no—
532C23—442no—
533C23—442no—
534Q8—21no—
535Q8—112no—
536Q8—224no—
537Q8—221no—
538Q8M16×D1112yescomplemented
539D4—21no—
540D4—21no—
541D4—221no—
542D4—221no—
543D4—442no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—111no—
550C2×C4—111no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—111no—
556C2×C4—222no—
557C2×C4—224no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4C22×C4×D1111yescharacteristic
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4#41×D1111yescharacteristic
570C8—22no—
571C8—21no—
572C8—21no—
573C8—21no—
574C8—21no—
575C8—41no—
576C8—41no—
577C8—222no—
578C8—221no—
579C8—221no—
580C8—221no—
581C8—221no—
582C8—441no—
583C8—441no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—112no—
588C22—112no—
589C22—112no—
590C22—441no—
591C22—441no—
592C22—441no—
593C22—884no—
594C22C4×D4×D1111yescharacteristic
595C4—22no—
596C4—21no—
597C4—41no—
598C4—41no—
599C4—112no—
600C4—112no—
601C4—222no—
602C4—221no—
603C4—441no—
604C4—441no—
605C4C2×M16×D1111yescharacteristic
606C4D11×#13111yescharacteristic
607C4D11×AGL(1,ℤ/8)11yescharacteristic
608C4D11×#13711yescharacteristic
609C2—81no—
610C2—114no—
611C2—881no—
612C2D11×#43511yescharacteristic
613C2D11×#44011yescharacteristic
614C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1588C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenter#1588D11
hypocenterC11C2×#1588
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
1. C8×Q8×D11C2semidirect
4. #13067497C2semidirect
5. #13067496C2semidirect
6. #13067495C2semidirect
7. #13067494C2semidirect
8. #13067493C2semidirect
9. #13067492C2semidirect
10. #13067491C2semidirect
11. D11×#335C2semidirect
12. D11×Q8⋊C8C2semidirect
14. D11×#322C2semidirect
15. C11×#1588C2semidirect
20. C8×Q8×C11C22semidirect
26. Q8×C11⋊C8C22semidirect
36. #10622443C22semidirect
50. C8×Dic22C22semidirect
51. C11×#335C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622117C22semidirect
60. #10622117C22semidirect
62. #10622096C22semidirect
63. #10622094C22semidirect
64. #10622093C22semidirect
65. #10622092C22semidirect
66. #10622092C22semidirect
154. Q8×D11M16semidirect
231. #1588D11direct (N × H)
243. Q8×C11C2×M16semidirect
277. Dic22C2×M16semidirect
301. C8×Q8C2×D11semidirect
330. #335C2×D11semidirect
334. Q8⋊C8C2×D11semidirect
342. #322C2×D11semidirect
452. D11#1588direct (N × H)
527. C11C2×#1588semidirect
538. Q8M16×D11semidirect

Maximal subgroups

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

subgroupindex
C8×Q8×D112
C4×SD16×D112
D11×#4362
#130674972
#130674962
#130674952
#130674942
#130674932
#130674922
#130674912
D11×#3352
D11×Q8⋊C82
D11×D4⋊C82
D11×#3222
C11×#15882
C2×#158811