Finite Group Databasebeta

← #14762842

Subgroups — #14762842

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C2×#10622739C211yesmaximal, characteristic, complemented
3#13070998C211yesmaximal, characteristic, complemented
4#13069055C211yesmaximal, characteristic, complemented
5#13069054C211yesmaximal, characteristic, complemented
6#13069052C211yesmaximal, characteristic, complemented
7#13068937C212yesmaximal, complemented
8#13068935C212yesmaximal, complemented
9#13068701C212yesmaximal, complemented
10#13068545C212yesmaximal, complemented
11C11×#1895C211yesmaximal, characteristic, complemented
12C22×D4×D11—21no—
13C22×D4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×#66992—21no—
18C2×#66991C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C22×#4318C2211yescharacteristic, complemented
21D11×#121—24no—
22D11×#121C418yescomplemented
23C2×#66948C2211yescharacteristic
24C2×#66945C2212yescomplemented
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×#66937—21no—
27C2×C22⋊C4×D11—21no—
28C2×C11×#102C2212yescomplemented
29C11×#380C2211yescharacteristic, complemented
30C2×#66896C2212yescomplemented
31#10622825C2211yescharacteristic, complemented
32#10622739—24no—
33C2×#66885C2212yescomplemented
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yescomplemented
36#10622600C2212yes—
37C2×#66873C2212yescomplemented
38#10622568—21no—
39C22⋊C4×Dic11—21no—
40#10622279—21no—
41#10622277—21no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11—21no—
47C24×D11D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C22×C22⋊D11—21no—
53C22×C22⋊D11—21no—
54C23×Dic11D411yescharacteristic
55C2×D4×D11—28no—
56C2×D4×D11—22no—
57C2×D4×D11—42no—
58C2×D4×D11—42no—
59C2×D4×D11—48no—
60C2×D4×D11C2×C414yes—
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—42no—
65C22×C4×D11—42no—
66C22×C4×D11C2×C414yes—
67C22×C4×D11D411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D414yes—
70C22×C4×D11C2311yescharacteristic
71C22×C4×D11C2311yescharacteristic
72C2×C11×M16—22no—
73C2×C11×M16—42no—
74C22×C8×C11C2312yes—
75C11×#121—22no—
76C11×#121C2×C414yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83#66992—28no—
84#66991—22no—
85#66991C2×C414yes—
86#66983—22no—
87#66983C2×C414yes—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—22no—
96C2×#4318—22no—
97C2×#4318—42no—
98C22×C11⋊C8C2312yes—
99#66948—22no—
100#66948C2×C414yes—
101#66945—42no—
102#66945—42no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11C2×C414yes—
105#66937—28no—
106C22⋊C4×D11—28no—
107C11×#102—42no—
108C11×#95—21no—
109#66896—42no—
110C11⋊#95—21no—
111C11⋊#95—22no—
112#66885—42no—
113(C2×D11)⋊C8—24no—
114(C2×D11)⋊C8—24no—
115#66873—42no—
116#21767—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C23×D11—24no—
120C23×D11—21no—
121C23×D11—24no—
122C23×D11—42no—
123C23×D11—41no—
124C23×D11—41no—
125C23×D11—44no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11—44no—
129C23×D11C22⋊C414yes—
130C23×D11C2×D411yescharacteristic
131C23×D11C2×D411yescharacteristic
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—44no—
137C2×D4×C11C22×C412yes—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—24no—
147C2×C22⋊D11—24no—
148C2×C22⋊D11—24no—
149C2×C22⋊D11—44no—
150C2×C22⋊D11—44no—
151C2×C22⋊D11—44no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—42no—
155C22×Dic11C22⋊C414yes—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158D4×D11—48no—
159D4×D11—432no—
160D4×D11—44no—
161D4×D11—44no—
162C2×D44—24no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44—44no—
167C2×D44C22×C412yes—
168C2×C4×D11—24no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—48no—
176C2×C4×D11—44no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×C4×D11C22⋊C414yes—
180C2×C4×D11C22⋊C414yes—
181C2×C4×D11C22×C412yes—
182C2×C4×D11C22×C412yes—
183C2×C4×D11C2×D412yes—
184C2×C4×D11C2×D412yes—
185C11×M16—44no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4C22×C412yes—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—42no—
195C22⋊Dic11—24no—
196C22⋊Dic11—42no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—44no—
200(C2×D11)⋊C4—44no—
201C4⋊Dic11—21no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11C22×C412yes—
205Dic11⋊C4—24no—
206C4×Dic11—44no—
207#4318—44no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C22×#121—111no—
212C2×#407—111no—
213#2280—111no—
214#1895—111no—
215#1895—111no—
216#1895—111no—
217#1895D1111yescharacteristic, complemented
218#1875—112no—
219#1875—112no—
220#1823—112no—
221#1786—112no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C2×C22⋊C412yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—28no—
241C22×D11—22no—
242C22×D11—44no—
243C22×D11—44no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—48no—
253C22×D11—88no—
254C22×D11—88no—
255C22×D11C2×C22⋊C412yes—
256C22×D11C2×C22⋊C412yes—
257C22×D11AGL(1,ℤ/8)14yes—
258D4×C11—24no—
259D4×C11—48no—
260D4×C11—41no—
261D4×C11—41no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11C2×C22⋊C412yes—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11H(5,𝔽2)12yes—
275C2×C4×C11H(5,𝔽2)12yes—
276C22⋊D11—48no—
277C22⋊D11—48no—
278C22⋊D11—48no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—44no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11C2×C22⋊C412yes—
288C2×Dic11C2×C22⋊C412yes—
289D44—24no—
290D44—48no—
291D44—41no—
292D44—41no—
293C4×D11—24no—
294C4×D11—24no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—44no—
300C4×D11—44no—
301C4×D11—48no—
302C8×C11—42no—
303C11⋊C8—42no—
304C23×D4—111no—
305C23×D4—221no—
306C24×C4—111no—
307C22×M16—111no—
308C22×M16C2×D1111yescharacteristic, complemented
309C2×#121—111no—
310C2×#121—111no—
311C2×#121—118no—
312C2×#121—111no—
313C2×#121—221no—
314C2×#121—224no—
315C2×#121—221no—
316C2×#121C2×D1111yescharacteristic
317C2×#117—112no—
318C22×C4⋊C4—111no—
319C22×C22⋊C4—221no—
320C2×#102—112no—
321C2×#102—112no—
322C2×#102—112no—
323C2×#102C2×D1112yescomplemented
324#407—224no—
325C2×C22⋊C8—112no—
326C2×C22⋊C8—112no—
327#381—221no—
328#380—111no—
329#380—112no—
330#380C2×D1111yescharacteristic, complemented
331#379—221no—
332C4×C22⋊C4—221no—
333C4×C22⋊C4—221no—
334#340—112no—
335#340—112no—
336#340—112no—
337#340C2×D1112yescomplemented
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—82no—
347C22×C11—82no—
348C22×C11C22×C22⋊C411yescharacteristic
349C22×C11#53412yes—
350C22×C11C2×AGL(1,ℤ/8)12yes—
351C22×C11#57511yescharacteristic
352C22×C11#57511yescharacteristic
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—24no—
356C2×D11—24no—
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—416no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—816no—
367C2×D11—82no—
368C2×D11—82no—
369C2×D11#41814yes—
370C4×C11—22no—
371C4×C11—42no—
372C4×C11—82no—
373C4×C11#51812yes—
374C4×C11#53411yescharacteristic
375C4×C11#53411yescharacteristic
376Dic11—22no—
377Dic11—22no—
378Dic11—42no—
379Dic11—82no—
380C25—111no—
381C25—221no—
382C22×D4—21no—
383C22×D4—114no—
384C22×D4—111no—
385C22×D4—221no—
386C22×D4—222no—
387C22×D4—221no—
388C22×D4—228no—
389C22×D4—221no—
390C22×D4—221no—
391C22×D4—442no—
392C22×D4—442no—
393C22×D4—448no—
394C22×D4C22×D1111yescharacteristic
395C23×C4—111no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—114no—
399C23×C4—111no—
400C23×C4—111no—
401C23×C4—114no—
402C23×C4—221no—
403C23×C4—442no—
404C23×C4—442no—
405C23×C4C22×D1111yescharacteristic
406C2×M16—22no—
407C2×M16—42no—
408C2×M16—222no—
409C2×M16—442no—
410C22×C8—112no—
411C22×C8C22×D1112yes—
412#121—22no—
413#121—114no—
414#121—114no—
415#121—114no—
416#121—228no—
417#121—222no—
418#121—222no—
419#121—228no—
420#121—222no—
421#121C4×D1114yes—
422#117—442no—
423#117—442no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C22×D1112yes—
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—228no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—221no—
440C2×C42—222no—
441#102—42no—
442#102—442no—
443#102—442no—
444#102—442no—
445C22⋊C8—224no—
446C22⋊C8—224no—
447#95—21no—
448#95—222no—
449#95—221no—
450C2×C11—42no—
451C2×C11—82no—
452C2×C11#230811yescharacteristic
453C2×C11C2×#41811yescharacteristic
454C2×C11#289611yescharacteristic
455C2×C11#319412yes—
456C2×C11#319412yes—
457D11—24no—
458D11—42no—
459D11—82no—
460C24—21no—
461C24—111no—
462C24—111no—
463C24—114no—
464C24—224no—
465C24—224no—
466C24—221no—
467C24—442no—
468C24—441no—
469C24—441no—
470C24—444no—
471C24—444no—
472C24—442no—
473C24—442no—
474C24D4×D1111yescharacteristic
475C2×D4—24no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—44no—
480C2×D4—112no—
481C2×D4—224no—
482C2×D4—224no—
483C2×D4—224no—
484C2×D4—224no—
485C2×D4—221no—
486C2×D4—222no—
487C2×D4—222no—
488C2×D4—444no—
489C2×D4—448no—
490C2×D4—444no—
491C2×D4—444no—
492C2×D4—444no—
493C2×D4—4432no—
494C2×D4—444no—
495C2×D4—444no—
496C2×D4C2×C4×D1112yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—114no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—114no—
509C22×C4—114no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—221no—
516C22×C4—222no—
517C22×C4—448no—
518C22×C4—444no—
519C22×C4—444no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—444no—
523C22×C4—442no—
524C22×C4C2×C4×D1112yes—
525C22×C4D4×D1111yescharacteristic
526C22×C4D4×D1112yes—
527C22×C4C23×D1111yescharacteristic
528M16—44no—
529M16—444no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—222no—
534C2×C8—222no—
535C2×C8—222no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—112no—
540C4⋊C4—224no—
541C4⋊C4—221no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C4⋊C4C2×C4×D1112yes—
545C22⋊C4—24no—
546C22⋊C4—42no—
547C22⋊C4—224no—
548C22⋊C4—224no—
549C22⋊C4—224no—
550C22⋊C4—444no—
551C22⋊C4—444no—
552C22⋊C4—442no—
553C42—444no—
554C11#2176711yescharacteristic, complemented, Sylow
555C23—22no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—22no—
560C23—42no—
561C23—41no—
562C23—41no—
563C23—42no—
564C23—112no—
565C23—114no—
566C23—112no—
567C23—228no—
568C23—221no—
569C23—221no—
570C23—222no—
571C23—222no—
572C23—221no—
573C23—221no—
574C23—222no—
575C23—222no—
576C23—444no—
577C23—444no—
578C23—448no—
579C23—448no—
580C23—448no—
581C23—448no—
582C23—448no—
583C23—442no—
584C23—441no—
585C23—441no—
586C23—442no—
587C23—888no—
588C23—888no—
589C23C22⋊C4×D1112yes—
590C23C2×D4×D1111yescharacteristic
591D4—24no—
592D4—48no—
593D4—41no—
594D4—41no—
595D4—224no—
596D4—448no—
597D4—448no—
598D4—448no—
599D4—448no—
600D4—441no—
601D4—441no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—112no—
612C2×C4—112no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—444no—
623C2×C4—444no—
624C2×C4—448no—
625C2×C4—444no—
626C2×C4—442no—
627C2×C4—442no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4C22⋊C4×D1112yes—
631C2×C4C22×C4×D1111yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4#6703712yes—
634C2×C4#6704212yes—
635C8—42no—
636C8—442no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—82no—
646C22—82no—
647C22—114no—
648C22—222no—
649C22—224no—
650C22—224no—
651C22—222no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22—4416no—
656C22—442no—
657C22—442no—
658C22—442no—
659C22—442no—
660C22—442no—
661C22—8816no—
662C22—882no—
663C22—882no—
664C22C2×C22⋊C4×D1111yescharacteristic
665C22#1062313612yes—
666C22D11×AGL(1,ℤ/8)12yes—
667C22#1062330411yescharacteristic
668C22#1062330811yescharacteristic
669C4—22no—
670C4—42no—
671C4—82no—
672C4—222no—
673C4—222no—
674C4—442no—
675C4—882no—
676C4#1062307612yes—
677C4#1062312011yescharacteristic
678C4#1062318411yescharacteristic
679C2—42no—
680C2—82no—
681C2—224no—
682C2—442no—
683C2—882no—
684C2#1307119011yescharacteristic
685C2D11×#41811yescharacteristic
686C2#1307713211yescharacteristic
687C2#1307942512yes—
688C2#1307943112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×D11×#121C2
cosocleC22×C4×C11C24
hypercenter#1895D11
hypocenterC11#21767
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
2. C2×#10622739C2semidirect
3. #13070998C2semidirect
4. #13069055C2semidirect
5. #13069054C2semidirect
6. #13069052C2semidirect
7. #13068937C2semidirect
8. #13068935C2semidirect
9. #13068701C2semidirect
10. #13068545C2semidirect
11. C11×#1895C2semidirect
15. C22×C11×M16C22semidirect
20. C22×#4318C22semidirect
22. D11×#121C4semidirect
24. C2×#66945C22semidirect
28. C2×C11×#102C22semidirect
29. C11×#380C22semidirect
30. C2×#66896C22semidirect
31. #10622825C22semidirect
33. C2×#66885C22semidirect
35. C2×(C2×D11)⋊C8C22semidirect
37. C2×#66873C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
217. #1895D11semidirect
308. C22×M16C2×D11semidirect
323. C2×#102C2×D11semidirect
330. #380C2×D11semidirect
337. #340C2×D11semidirect
554. C11#21767semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C2×#106227392
#130709982
#130690552
#130690542
#130690522
#130689372
#130689352
#130687012
#130685452
C11×#18952
#2176711