Finite Group Databasebeta

← #14762858

Subgroups — #14762858

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×#10622739C211yesmaximal, characteristic, complemented
3D11×#380C211yesmaximal, characteristic, complemented
4#13069054C211yesmaximal, characteristic, complemented
5#13069052C211yesmaximal, characteristic, complemented
6#13069050C211yesmaximal, characteristic, complemented
7#13068932C212yesmaximal, complemented
8#13068920C212yesmaximal, complemented
9#13068710C212yesmaximal, complemented
10#13068555C212yesmaximal, complemented
11C11×#1894C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10623158—24no—
20#10623158C418yescomplemented
21C2×#66948C2211yescharacteristic
22C2×#66947—21no—
23C2×#66946—21no—
24C2×#66945C2211yescharacteristic
25C2×C4⋊C4×D11C2212yes—
26C2×#66935—21no—
27C2×(C22⋊D11)⋊C4—21no—
28C2×C22⋊C4×D11—21no—
29C2×C11×#103C2212yescomplemented
30C11×#380C2211yescharacteristic
31C2×#66899C2212yescomplemented
32#10622825C2211yescharacteristic
33#10622739—24no—
34C2×#66885C2212yescomplemented
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37#10622600C2212yes—
38C2×#66873C2212yescomplemented
39#10622555—21no—
40#10622280—21no—
41D11×#95—21no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C23×Dic11D411yescharacteristic
51C2×#4343—22no—
52C2×#4343—42no—
53C2×#4343—42no—
54C2×#4343C2×C414yescomplemented
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2311yescharacteristic
58C22×C4×D11—21no—
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
68C2×C11×M16—22no—
69C2×C11×M16—42no—
70C22×C8×C11C2312yes—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8C2×C414yescomplemented
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79#66999—22no—
80#66999C2×C414yes—
81#66983—22no—
82#66983C2×C414yescomplemented
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—22no—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—22no—
92C2×C4×Dic11—21no—
93C2×#4318—22no—
94C2×#4318—42no—
95C22×C11⋊C8C2312yes—
96#66948—22no—
97#66948C2×C414yes—
98#66947—28no—
99#66946—28no—
100#66945—22no—
101#66945C2×C414yescomplemented
102C4⋊C4×D11—42no—
103C4⋊C4×D11—42no—
104#66935—28no—
105(C22⋊D11)⋊C4—28no—
106C22⋊C4×D11—44no—
107C11×#103—42no—
108C11×#95—21no—
109#66899—42no—
110C11⋊#95—21no—
111C11⋊#95—22no—
112#66885—42no—
113(C2×D11)⋊C8—24no—
114(C2×D11)⋊C8—24no—
115#66873—42no—
116#21769—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—42no—
122C23×D11—42no—
123C23×D11C22⋊C414yes—
124C23×D11C2×D411yescharacteristic
125C23×D11C2×D411yescharacteristic
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11C22×C412yes—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—44no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—42no—
144C22×Dic11C22⋊C414yes—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147#4343—48no—
148#4343—44no—
149#4343—44no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—21no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—44no—
156C2×D44—42no—
157C2×D44—42no—
158C2×D44C22×C412yes—
159C2×C4×D11—24no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—48no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11—44no—
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—
179C11×M16—44no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C22×C412yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—42no—
190C22⋊Dic11—42no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—44no—
196C4⋊Dic11—21no—
197C4⋊Dic11—22no—
198C4⋊Dic11—22no—
199C4⋊Dic11C22×C412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—44no—
202C4×Dic11—24no—
203#4318—44no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×#525—111no—
208C2×#407—111no—
209C2×#380—111no—
210#1895—111no—
211#1895—111no—
212#1894—111no—
213#1894D1111yescharacteristic, complemented
214#1874—112no—
215#1872—112no—
216#1825—112no—
217#1788—112no—
218C23×C11—22no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—22no—
222C23×C11C2×C22⋊C412yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—22no—
230C22×D11—28no—
231C22×D11—22no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—42no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—42no—
240C22×D11C2×C22⋊C412yes—
241C22×D11C2×C22⋊C412yes—
242C22×D11AGL(1,ℤ/8)12yes—
243C22×D11#13712yes—
244Q8×C11—24no—
245Q8×C11—41no—
246Q8×C11—41no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11H(5,𝔽2)12yes—
263C2×C4×C11H(5,𝔽2)12yes—
264C22⋊D11—48no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11C2×C22⋊C412yes—
274C2×Dic11C2×C22⋊C412yes—
275D44—24no—
276D44—48no—
277D44—48no—
278D44—41no—
279D44—41no—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—44no—
287C4×D11—44no—
288C4×D11—48no—
289C4×D11—88no—
290C8×C11—42no—
291C11⋊C8—42no—
292C22×#41—111no—
293C24×C4—111no—
294C22×M16—111no—
295C22×M16C2×D1111yescharacteristic
296#525—118no—
297#525—224no—
298C2×#123—221no—
299C2×C22⋊Q8—111no—
300C2×C22⋊Q8C2×D1111yescharacteristic
301C2×#121—111no—
302C2×#121—111no—
303C2×#120—221no—
304C2×C4×D4—221no—
305C2×C4×D4—221no—
306C2×#117—111no—
307C22×C4⋊C4—112no—
308C22×C22⋊C4—221no—
309C2×#103—112no—
310C2×#103C2×D1112yescomplemented
311C2×#102—112no—
312C2×#102—112no—
313#407—224no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316#380—111no—
317#380—112no—
318#380—221no—
319#380—221no—
320#380C2×D1111yescharacteristic
321C2×#95—221no—
322#340—112no—
323#340—112no—
324#340—112no—
325#340C2×D1112yescomplemented
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11#53412yes—
333C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11#57512yes—
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—416no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—82no—
350C2×D11—82no—
351C2×D11#41714yes—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—82no—
356C4×C11#51812yes—
357C4×C11#53411yescharacteristic
358C4×C11#53411yescharacteristic
359Dic11—22no—
360Dic11—22no—
361Dic11—42no—
362Dic11—82no—
363C25—111no—
364C2×#41—114no—
365C2×#41—222no—
366C2×#41—442no—
367C2×#41—442no—
368C22×Q8C22×D1111yescharacteristic
369C22×D4—111no—
370C22×D4—221no—
371C22×D4—221no—
372C22×D4—221no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—114no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—221no—
381C23×C4—222no—
382C23×C4—442no—
383C23×C4—442no—
384C23×C4C22×D1111yescharacteristic
385C2×M16—22no—
386C2×M16—42no—
387C2×M16—222no—
388C2×M16—442no—
389C22×C8—112no—
390C22×C8C22×D1112yes—
391#123—228no—
392C22⋊Q8—22no—
393C22⋊Q8—114no—
394C22⋊Q8—222no—
395C22⋊Q8C4×D1114yescomplemented
396#121—114no—
397#121—114no—
398#121—222no—
399#121—222no—
400#120—228no—
401C4×D4—228no—
402C4×D4—228no—
403#117—114no—
404#117—222no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—442no—
411C2×C4⋊C4—442no—
412C2×C4⋊C4C22×D1112yes—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—444no—
423C2×C42—221no—
424#103—42no—
425#103—442no—
426#102—442no—
427#102—442no—
428C22⋊C8—224no—
429C22⋊C8—224no—
430#95—21no—
431#95—222no—
432#95—221no—
433C2×C11—42no—
434C2×C11#230811yescharacteristic
435C2×C11C2×#41711yescharacteristic
436C2×C11#289611yescharacteristic
437C2×C11#319412yes—
438C2×C11#319612yes—
439D11—24no—
440D11—42no—
441D11—82no—
442C24—111no—
443C24—111no—
444C24—114no—
445C24—222no—
446C24—222no—
447C24—221no—
448C24—442no—
449C24—442no—
450C24D4×D1111yescharacteristic
451#41—448no—
452#41—444no—
453#41—444no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8C2×C4×D1112yes—
458C2×D4—112no—
459C2×D4—224no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—221no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—442no—
466C2×D4—442no—
467C2×D4—444no—
468C2×D4—444no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
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—224no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—221no—
489C22×C4—222no—
490C22×C4—448no—
491C22×C4—444no—
492C22×C4—444no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—444no—
496C22×C4—444no—
497C22×C4—444no—
498C22×C4—444no—
499C22×C4—442no—
500C22×C4C2×C4×D1112yes—
501C22×C4D4×D1111yescharacteristic
502C22×C4D4×D1112yes—
503C22×C4C23×D1111yescharacteristic
504M16—44no—
505M16—444no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C4⋊C4—24no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—112no—
517C4⋊C4—224no—
518C4⋊C4—221no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—444no—
522C4⋊C4C2×C4×D1112yes—
523C22⋊C4—24no—
524C22⋊C4—42no—
525C22⋊C4—224no—
526C22⋊C4—224no—
527C22⋊C4—224no—
528C22⋊C4—224no—
529C22⋊C4—444no—
530C22⋊C4—442no—
531C42—224no—
532C11#2176911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—21no—
535C23—22no—
536C23—22no—
537C23—112no—
538C23—112no—
539C23—112no—
540C23—112no—
541C23—228no—
542C23—222no—
543C23—222no—
544C23—221no—
545C23—221no—
546C23—222no—
547C23—222no—
548C23—222no—
549C23—444no—
550C23—444no—
551C23—448no—
552C23—448no—
553C23—441no—
554C23—441no—
555C23—442no—
556C23—442no—
557C23C22⋊C4×D1112yes—
558C23C2×D4×D1111yescharacteristic
559Q8—24no—
560Q8—41no—
561Q8—41no—
562D4—224no—
563D4—448no—
564D4—448no—
565D4—448no—
566D4—441no—
567D4—441no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—444no—
592C2×C4—444no—
593C2×C4—448no—
594C2×C4—444no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—888no—
600C2×C4C22⋊C4×D1112yes—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4#6703712yes—
604C2×C4#6704212yes—
605C8—42no—
606C8—442no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—42no—
611C22—42no—
612C22—114no—
613C22—222no—
614C22—224no—
615C22—222no—
616C22—224no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—4416no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22—882no—
627C22—882no—
628C22C2×C22⋊C4×D1111yescharacteristic
629C22#1062313612yes—
630C22D11×AGL(1,ℤ/8)11yescharacteristic
631C22D11×#13711yescharacteristic
632C22#1062330812yes—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—82no—
637C4—222no—
638C4—222no—
639C4—442no—
640C4—882no—
641C4#1062307612yes—
642C4#1062312011yescharacteristic
643C4#1062318411yescharacteristic
644C2—42no—
645C2—224no—
646C2—442no—
647C2—882no—
648C2#1307119011yescharacteristic
649C2D11×#41711yescharacteristic
650C2#1307713411yescharacteristic
651C2#1307943112yes—
652C2#1307944712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC2×#10623158C2
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#21769
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#10622739C2semidirect
3. D11×#380C2semidirect
4. #13069054C2semidirect
5. #13069052C2semidirect
6. #13069050C2semidirect
7. #13068932C2semidirect
8. #13068920C2semidirect
9. #13068710C2semidirect
10. #13068555C2semidirect
11. C11×#1894C2semidirect
20. #10623158C4semidirect
29. C2×C11×#103C22semidirect
31. C2×#66899C22semidirect
34. C2×#66885C22semidirect
38. C2×#66873C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
54. C2×#4343C2×C4semidirect
72. C11×C22⋊Q8C2×C4semidirect
82. #66983C2×C4semidirect
101. #66945C2×C4semidirect
213. #1894D11semidirect
310. C2×#103C2×D11semidirect
325. #340C2×D11semidirect
395. C22⋊Q8C4×D11semidirect
532. C11#21769semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106227392
D11×#3802
#130690542
#130690522
#130690502
#130689322
#130689202
#130687102
#130685552
C11×#18942
#2176911