Finite Group Databasebeta

← #14762813

Subgroups — #14762813

Order 2816.

1590 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×D11×C22⋊C8C211yesmaximal, characteristic, complemented
3D11×#380C211yesmaximal, characteristic, complemented
4#13069041C212yesmaximal, complemented
5#13069036C212yesmaximal, complemented
6#13068930C212yesmaximal, complemented
7#13068920C212yesmaximal, complemented
8#13068712C211yesmaximal, characteristic, complemented
9#13068708C211yesmaximal, characteristic, complemented
10#13068556C211yesmaximal, characteristic, complemented
11C11×#1788C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14#10623359—24no—
15#10623359C418yescomplemented
16C2×#66999C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×#66990—21no—
21C2×#66988—21no—
22C2×C4×C22⋊D11—21no—
23C2×C4×C22⋊D11—21no—
24C2×#66979C2211yescharacteristic
25C22×C8×D11C2212yes—
26C2×C4⋊C4×D11C2212yes—
27C2×C22⋊C4×D11—21no—
28C2×C11×#103C2212yescomplemented
29C2×C11×#102C2212yescomplemented
30C2×C11×C22⋊C8C2211yescharacteristic
31C11×#380C2211yescharacteristic
32C2×#66899C2212yescomplemented
33C2×#66896C2212yescomplemented
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×(C2×D11)⋊C8C2212yes—
37#10622600C2212yes—
38#10622555—21no—
39D11×C22⋊C8—24no—
40#10622280—21no—
41D11×#95—21no—
42#10622189C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C2×C11×#41—22no—
48C2×C11×#41—42no—
49C2×C11×#41—42no—
50C2×C11×#41C2×C414yescomplemented
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—21no—
57C22×C22⋊D11—21no—
58C23×Dic11D411yescharacteristic
59C22×C4×D11—22no—
60C22×C4×D11—42no—
61C22×C4×D11—42no—
62C22×C4×D11C2×C414yes—
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D414yes—
66C22×C4×D11C2311yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2312yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66999—22no—
76#66999—22no—
77#66999C2×C414yes—
78#66999C2×C414yescomplemented
79#66991—22no—
80#66991—22no—
81#66991C2×C414yes—
82#66991C2×C414yescomplemented
83#66990—28no—
84#66988—28no—
85C4×C22⋊D11—28no—
86C4×C22⋊D11—28no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—22no—
90#66979—22no—
91#66979C2×C414yescomplemented
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2312yes—
100C2×C8×D11—24no—
101C2×C8×D11—42no—
102C2×C8×D11—42no—
103C4⋊C4×D11—42no—
104C4⋊C4×D11—42no—
105C22⋊C4×D11—44no—
106C11×#103—42no—
107C11×#102—42no—
108C11×C22⋊C8—22no—
109C11×#95—21no—
110#66899—42no—
111#66896—42no—
112C11⋊#95—21no—
113C11⋊#95—22no—
114C22⋊(C11⋊C8)—22no—
115(C2×D11)⋊C8—24no—
116#21763—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—42no—
123C23×D11C22⋊C414yes—
124C23×D11C2×D411yescharacteristic
125C23×D11C2×D411yescharacteristic
126C11×#41—44no—
127C11×#41—44no—
128C11×#41—48no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C22×C412yes—
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—44no—
138C2×D4×C11C22×C412yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—44no—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—24no—
150C2×C22⋊D11—24no—
151C2×C22⋊D11—44no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—42no—
158C22×Dic11C22⋊C414yes—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11—48no—
170C2×C4×D11—44no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11C22⋊C414yes—
174C2×C4×D11C22⋊C414yes—
175C2×C4×D11C22×C412yes—
176C2×C4×D11C22×C412yes—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×D412yes—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C22⋊C4—42no—
185C22⋊Dic11—24no—
186C22⋊Dic11—24no—
187C22⋊Dic11—24no—
188C22⋊Dic11—42no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—44no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11C22×C412yes—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200Dic11⋊C4—44no—
201C4×Dic11—24no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C8×D11—48no—
206C2×#525—111no—
207C22×C22⋊C8—111no—
208C2×#380—111no—
209#1893—112no—
210#1892—112no—
211#1874—112no—
212#1872—112no—
213#1825—111no—
214#1825—111no—
215#1788—111no—
216#1788D1111yescharacteristic, complemented
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C2×C22⋊C412yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—28no—
234C22×D11—28no—
235C22×D11—44no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11C2×C22⋊C412yes—
239C22×D11C2×C22⋊C412yes—
240C22×D11#13514yes—
241C22×D11AGL(1,ℤ/8)12yes—
242C22×D11#13712yes—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—42no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—48no—
249D4×C11—42no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—48no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11H(5,𝔽2)12yes—
264C2×C4×C11H(5,𝔽2)12yes—
265C22⋊D11—48no—
266C22⋊D11—48no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11C2×C22⋊C412yes—
279C2×Dic11C2×C22⋊C412yes—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—24no—
285C4×D11—24no—
286C4×D11—44no—
287C4×D11—44no—
288C4×D11—88no—
289C8×C11—42no—
290C11⋊C8—42no—
291C22×#41C2×D1111yescharacteristic
292C24×C4—111no—
293C23×C8—112no—
294#525—118no—
295#525—224no—
296C2×#123—221no—
297C2×C22⋊Q8—111no—
298C2×C22⋊Q8—111no—
299C2×#121—111no—
300C2×#121—111no—
301C2×#120—221no—
302C2×C4×D4—221no—
303C2×C4×D4—221no—
304C2×#117—111no—
305C22×C4⋊C4—112no—
306C22×C22⋊C4—221no—
307C2×#103—112no—
308C2×#103C2×D1112yescomplemented
309C2×#102—112no—
310C2×#102C2×D1112yescomplemented
311C2×C22⋊C8—111no—
312C2×C22⋊C8—112no—
313C2×C22⋊C8—224no—
314C2×C22⋊C8C2×D1111yescharacteristic
315#380—111no—
316#380—112no—
317#380—221no—
318#380—221no—
319#380C2×D1111yescharacteristic
320C2×#95—221no—
321#340—112no—
322#340—112no—
323#340—112no—
324#340—112no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11C22×C22⋊C411yescharacteristic
336C22×C11#53412yes—
337C22×C11C2×#13512yes—
338C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C11C2×#13711yescharacteristic
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—24no—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—416no—
349C2×D11#41614yes—
350C2×D11#41714yes—
351C4×C11—22no—
352C4×C11—42no—
353C4×C11—82no—
354C4×C11#51811yescharacteristic
355C4×C11#51811yescharacteristic
356C4×C11#53412yes—
357Dic11—22no—
358Dic11—22no—
359Dic11—42no—
360Dic11—42no—
361Dic11—82no—
362C25—111no—
363C2×#41—22no—
364C2×#41—42no—
365C2×#41—42no—
366C2×#41C4×D1114yescomplemented
367C22×Q8C22×D1111yescharacteristic
368C22×D4—21no—
369C22×D4—221no—
370C22×D4—221no—
371C22×D4C22×D1111yescharacteristic
372C23×C4—21no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—114no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—222no—
381C23×C4—442no—
382C23×C4—442no—
383C23×C4C22×D1111yescharacteristic
384C22×C8—112no—
385C22×C8—224no—
386C22×C8—442no—
387C22×C8—442no—
388C22×C8C22×D1112yes—
389#123—228no—
390C22⋊Q8—114no—
391C22⋊Q8—114no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394#121—114no—
395#121—114no—
396#121—222no—
397#121—222no—
398#120—228no—
399C4×D4—228no—
400C4×D4—228no—
401#117—114no—
402#117—222no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—442no—
410C2×C4⋊C4—442no—
411C2×C4⋊C4C22×D1112yes—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—444no—
421C2×C42—221no—
422#103—42no—
423#103—442no—
424#102—42no—
425#102—442no—
426C22⋊C8—22no—
427C22⋊C8—224no—
428C22⋊C8—222no—
429#95—21no—
430#95—222no—
431#95—221no—
432C2×C11—42no—
433C2×C11—82no—
434C2×C11#230811yescharacteristic
435C2×C11C2×#41611yescharacteristic
436C2×C11C2×#41711yescharacteristic
437C2×C11#318812yes—
438C2×C11#319012yes—
439D11—24no—
440D11—24no—
441C24—21no—
442C24—111no—
443C24—111no—
444C24—114no—
445C24—222no—
446C24—224no—
447C24—222no—
448C24—442no—
449C24D4×D1111yescharacteristic
450#41—44no—
451#41—44no—
452#41—48no—
453C2×Q8—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8C2×C4×D1112yes—
457C2×D4—24no—
458C2×D4—21no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—44no—
462C2×D4—224no—
463C2×D4—224no—
464C2×D4—444no—
465C2×D4—442no—
466C2×D4—442no—
467C2×D4C2×C4×D1112yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—44no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—222no—
490C22×C4—444no—
491C22×C4—444no—
492C22×C4—448no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—444no—
496C22×C4—444no—
497C22×C4—444no—
498C22×C4—442no—
499C22×C4C2×C4×D1112yes—
500C22×C4D4×D1111yescharacteristic
501C22×C4D4×D1112yes—
502C22×C4C23×D1111yescharacteristic
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—448no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—112no—
513C4⋊C4—112no—
514C4⋊C4—224no—
515C4⋊C4—224no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—444no—
521C22⋊C4—42no—
522C22⋊C4—224no—
523C22⋊C4—224no—
524C22⋊C4—224no—
525C22⋊C4—224no—
526C22⋊C4—224no—
527C22⋊C4—444no—
528C22⋊C4—442no—
529C42—224no—
530C11#2176311yescharacteristic, complemented, Sylow
531C23—22no—
532C23—21no—
533C23—21no—
534C23—22no—
535C23—22no—
536C23—42no—
537C23—41no—
538C23—41no—
539C23—42no—
540C23—112no—
541C23—112no—
542C23—114no—
543C23—112no—
544C23—112no—
545C23—228no—
546C23—228no—
547C23—222no—
548C23—221no—
549C23—221no—
550C23—222no—
551C23—222no—
552C23—444no—
553C23—448no—
554C23—448no—
555C23C22⋊C4×D1112yes—
556C23C2×D4×D1111yescharacteristic
557Q8—22no—
558Q8—22no—
559Q8—42no—
560D4—22no—
561D4—22no—
562D4—48no—
563D4—42no—
564D4—448no—
565D4—448no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—48no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—444no—
589C2×C4—444no—
590C2×C4—444no—
591C2×C4—442no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—888no—
598C2×C4C22⋊C4×D1112yes—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×D4×D1111yescharacteristic
601C2×C4#6703712yes—
602C2×C4#6703712yes—
603C8—42no—
604C8—442no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—82no—
614C22—82no—
615C22—114no—
616C22—114no—
617C22—224no—
618C22—224no—
619C22—222no—
620C22—222no—
621C22—224no—
622C22—224no—
623C22—222no—
624C22—222no—
625C22—4416no—
626C22C2×C22⋊C4×D1111yescharacteristic
627C22#1062312012yes—
628C22D11×#13512yes—
629C22D11×AGL(1,ℤ/8)11yescharacteristic
630C22D11×#13711yescharacteristic
631C4—22no—
632C4—42no—
633C4—82no—
634C4—222no—
635C4—222no—
636C4—442no—
637C4—442no—
638C4—882no—
639C4#1062301711yescharacteristic
640C4#1062301711yescharacteristic
641C4#1062312012yes—
642C2—42no—
643C2—82no—
644C2—224no—
645C2—224no—
646C2#1307119211yescharacteristic
647C2D11×#41611yescharacteristic
648C2D11×#41711yescharacteristic
649C2#1307937912yes—
650C2#1307939512yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#21763
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊C8C2semidirect
3. D11×#380C2semidirect
4. #13069041C2semidirect
5. #13069036C2semidirect
6. #13068930C2semidirect
7. #13068920C2semidirect
8. #13068712C2semidirect
9. #13068708C2semidirect
10. #13068556C2semidirect
11. C11×#1788C2semidirect
15. #10623359C4semidirect
28. C2×C11×#103C22semidirect
29. C2×C11×#102C22semidirect
32. C2×#66899C22semidirect
33. C2×#66896C22semidirect
42. #10622189C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
50. C2×C11×#41C2×C4semidirect
78. #66999C2×C4semidirect
82. #66991C2×C4semidirect
91. #66979C2×C4semidirect
216. #1788D11semidirect
308. C2×#103C2×D11semidirect
310. C2×#102C2×D11semidirect
366. C2×#41C4×D11semidirect
530. C11#21763semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×D11×C22⋊C82
D11×#3802
#130690412
#130690362
#130689302
#130689202
#130687122
#130687082
#130685562
C11×#17882
#2176311