Finite Group Databasebeta

← #14762836

Subgroups — #14762836

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic, complemented
3#13070998C211yesmaximal, characteristic, complemented
4#13069051C212yesmaximal, complemented
5#13069046C212yesmaximal, complemented
6#13068935C212yesmaximal, complemented
7#13068925C212yesmaximal, 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×#4313C2212yes—
26C2×#66945C2212yes—
27C2×C11×#103C2212yescomplemented
28C2×C11×#102C2212yescomplemented
29C2×C11×C22⋊C8C2211yescharacteristic
30C11×#380C2211yescharacteristic
31C2×#66899C2212yescomplemented
32C2×#66896C2212yescomplemented
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×(C2×D11)⋊C8C2212yes—
36#10622600C2212yes—
37#10622568—21no—
38C22⋊C4×Dic11—21no—
39#10622339—24no—
40#10622279—21no—
41#10622277—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×C414yes—
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—42no—
60C22×C4×D11—42no—
61C22×C4×D11C2×C414yes—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D414yes—
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2312yes—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66999—22no—
75#66999—22no—
76#66999C2×C414yes—
77#66999C2×C414yes—
78#66991—22no—
79#66991—22no—
80#66991C2×C414yes—
81#66991C2×C414yes—
82#66990—28no—
83#66988—28no—
84C4×C22⋊D11—28no—
85C4×C22⋊D11—28no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90#66979—22no—
91#66979C2×C414yes—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—22no—
99C22×C11⋊C8C2312yes—
100C2×#4313—24no—
101C2×#4313—42no—
102C2×#4313—42no—
103#66945—42no—
104#66945—42no—
105C11×#103—42no—
106C11×#102—42no—
107C11×C22⋊C8—22no—
108C11×#95—21no—
109#66899—42no—
110#66896—42no—
111C11⋊#95—21no—
112C11⋊#95—22no—
113C22⋊(C11⋊C8)—22no—
114(C2×D11)⋊C8—24no—
115#21766—111nomaximal, Sylow
116C24×C11—21no—
117C24×C11C2×D411yescharacteristic
118C23×D11—42no—
119C23×D11—42no—
120C23×D11—41no—
121C23×D11—41no—
122C23×D11C22⋊C414yes—
123C23×D11C2×D411yescharacteristic
124C23×D11C2×D411yescharacteristic
125C11×#41—44no—
126C11×#41—44no—
127C11×#41—48no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C22×C412yes—
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—24no—
142C22×C4×C11—22no—
143C22×C4×C11—44no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—24no—
150C2×C22⋊D11—44no—
151C2×C22⋊D11—42no—
152C2×C22⋊D11—42no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—42no—
157C22×Dic11C22⋊C414yes—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
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—44no—
167C2×C4×D11—44no—
168C2×C4×D11—48no—
169C2×C4×D11C22⋊C414yes—
170C2×C4×D11C22⋊C414yes—
171C2×C4×D11C22×C412yes—
172C2×C4×D11C22×C412yes—
173C2×C4×D11C2×D412yes—
174C2×C4×D11C2×D412yes—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C22⋊C4—42no—
181C22⋊Dic11—24no—
182C22⋊Dic11—24no—
183C22⋊Dic11—24no—
184C22⋊Dic11—42no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—44no—
188(C2×D11)⋊C4—44no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11C22×C412yes—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—24no—
197C4×Dic11—24no—
198C4×Dic11—44no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202#4313—48no—
203C2×#525—111no—
204C2×#407—111no—
205#2280—111no—
206#1895—112no—
207#1894—112no—
208#1875—112no—
209#1873—112no—
210#1825—111no—
211#1825—111no—
212#1788—111no—
213#1788D1111yescharacteristic, complemented
214C23×C11—22no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11C2×C22⋊C412yes—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11C2×C22⋊C412yes—
239C22×D11C2×C22⋊C412yes—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—42no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—48no—
246D4×C11—42no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—48no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11H(5,𝔽2)12yes—
261C2×C4×C11H(5,𝔽2)12yes—
262C22⋊D11—48no—
263C22⋊D11—48no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—44no—
269C2×Dic11—42no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11C2×C22⋊C412yes—
276C2×Dic11C2×C22⋊C412yes—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—44no—
284C4×D11—44no—
285C8×C11—42no—
286C11⋊C8—42no—
287C22×#41C2×D1111yescharacteristic
288C24×C4—111no—
289C22×M16—112no—
290#525—118no—
291#525—224no—
292C2×#123—221no—
293C2×C22⋊Q8—111no—
294C2×C22⋊Q8—111no—
295C2×#121—111no—
296C2×#121—111no—
297C2×#120—221no—
298C2×C4×D4—221no—
299C2×C4×D4—221no—
300C2×#117—111no—
301C2×#117—112no—
302C2×#103—112no—
303C2×#103C2×D1112yescomplemented
304C2×#102—112no—
305C2×#102C2×D1112yescomplemented
306#407—224no—
307C2×C22⋊C8—111no—
308C2×C22⋊C8—112no—
309C2×C22⋊C8C2×D1111yescharacteristic
310#381—221no—
311#380—111no—
312#380—112no—
313#380C2×D1111yescharacteristic
314#379—221no—
315C4×C22⋊C4—221no—
316C4×C22⋊C4—221no—
317#340—112no—
318#340—112no—
319#340—112no—
320#340—112no—
321C22×C11—22no—
322C22×C11—22no—
323C22×C11—22no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—82no—
330C22×C11—82no—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11#53412yes—
333C22×C11#57512yes—
334C22×C11#57511yescharacteristic
335C22×C11#57511yescharacteristic
336C2×D11—22no—
337C2×D11—22no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—416no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C4×C11—22no—
348C4×C11—42no—
349C4×C11—82no—
350C4×C11#51811yescharacteristic
351C4×C11#51811yescharacteristic
352C4×C11#53412yes—
353Dic11—22no—
354Dic11—22no—
355Dic11—42no—
356Dic11—42no—
357Dic11—82no—
358C25—111no—
359C2×#41—22no—
360C2×#41—42no—
361C2×#41—42no—
362C2×#41C4×D1114yes—
363C22×Q8C22×D1111yescharacteristic
364C22×D4—21no—
365C22×D4—221no—
366C22×D4—221no—
367C22×D4C22×D1111yescharacteristic
368C23×C4—21no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—114no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—114no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4C22×D1111yescharacteristic
379C2×M16—224no—
380C2×M16—442no—
381C2×M16—442no—
382C22×C8—112no—
383C22×C8C22×D1112yes—
384#123—228no—
385C22⋊Q8—114no—
386C22⋊Q8—114no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389#121—114no—
390#121—114no—
391#121—222no—
392#121—222no—
393#120—228no—
394C4×D4—228no—
395C4×D4—228no—
396#117—114no—
397#117—222no—
398#117—442no—
399#117—442no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1112yes—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—222no—
413C2×C22⋊C4—222no—
414C2×C22⋊C4—221no—
415C2×C42—221no—
416C2×C42—222no—
417#103—42no—
418#103—442no—
419#102—42no—
420#102—442no—
421C22⋊C8—22no—
422C22⋊C8—224no—
423C22⋊C8—222no—
424#95—21no—
425#95—222no—
426#95—221no—
427C2×C11—42no—
428C2×C11—82no—
429C2×C11#230811yescharacteristic
430C2×C11#289611yescharacteristic
431C2×C11#289611yescharacteristic
432C2×C11#319712yes—
433C2×C11#319712yes—
434D11—42no—
435D11—42no—
436C24—21no—
437C24—111no—
438C24—111no—
439C24—114no—
440C24—442no—
441C24—442no—
442C24—441no—
443C24—441no—
444C24D4×D1111yescharacteristic
445#41—44no—
446#41—44no—
447#41—48no—
448C2×Q8—21no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8C2×C4×D1112yes—
452C2×D4—24no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—44no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—444no—
460C2×D4—442no—
461C2×D4—442no—
462C2×D4C2×C4×D1112yes—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—222no—
485C22×C4—444no—
486C22×C4—444no—
487C22×C4—448no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4C2×C4×D1112yes—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1112yes—
494C22×C4C23×D1111yescharacteristic
495M16—448no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—222no—
500C2×C8—222no—
501C2×C8—222no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—112no—
505C4⋊C4—112no—
506C4⋊C4—224no—
507C4⋊C4—224no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C22⋊C4—42no—
513C22⋊C4—224no—
514C22⋊C4—224no—
515C22⋊C4—224no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—444no—
519C22⋊C4—444no—
520C22⋊C4—442no—
521C42—224no—
522C42—444no—
523C11#2176611yescharacteristic, complemented, Sylow
524C23—22no—
525C23—21no—
526C23—21no—
527C23—22no—
528C23—22no—
529C23—42no—
530C23—41no—
531C23—41no—
532C23—42no—
533C23—112no—
534C23—112no—
535C23—222no—
536C23—222no—
537C23—221no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23—222no—
542C23—222no—
543C23—444no—
544C23—444no—
545C23—444no—
546C23—448no—
547C23—448no—
548C23C22⋊C4×D1112yes—
549C23C2×D4×D1111yescharacteristic
550Q8—22no—
551Q8—22no—
552Q8—42no—
553D4—22no—
554D4—22no—
555D4—48no—
556D4—42no—
557D4—448no—
558D4—448no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—48no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—112no—
570C2×C4—112no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—442no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4C22⋊C4×D1112yes—
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703712yes—
594C2×C4#6703712yes—
595C8—42no—
596C8—442no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—42no—
601C22—42no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—82no—
606C22—82no—
607C22—222no—
608C22—222no—
609C22—222no—
610C22—222no—
611C22—222no—
612C22—222no—
613C22—4416no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—442no—
618C22C2×C22⋊C4×D1111yescharacteristic
619C22#1062312012yes—
620C22#1062329912yes—
621C22#1062330411yescharacteristic
622C22#1062330811yescharacteristic
623C4—22no—
624C4—42no—
625C4—82no—
626C4—222no—
627C4—222no—
628C4—442no—
629C4—442no—
630C4—882no—
631C4#1062301711yescharacteristic
632C4#1062301711yescharacteristic
633C4#1062312012yes—
634C2—42no—
635C2—82no—
636C2—442no—
637C2—442no—
638C2#1307119211yescharacteristic
639C2#1307713111yescharacteristic
640C2#1307713211yescharacteristic
641C2#1307945512yes—
642C2#1307945712yes—
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#21766
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×#10622339C2semidirect
3. #13070998C2semidirect
4. #13069051C2semidirect
5. #13069046C2semidirect
6. #13068935C2semidirect
7. #13068925C2semidirect
8. #13068712C2semidirect
9. #13068708C2semidirect
10. #13068556C2semidirect
11. C11×#1788C2semidirect
15. #10623359C4semidirect
27. C2×C11×#103C22semidirect
28. C2×C11×#102C22semidirect
31. C2×#66899C22semidirect
32. C2×#66896C22semidirect
42. #10622189C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
213. #1788D11semidirect
303. C2×#103C2×D11semidirect
305. C2×#102C2×D11semidirect
523. C11#21766semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
C2×#106223392
#130709982
#130690512
#130690462
#130689352
#130689252
#130687122
#130687082
#130685562
C11×#17882
#2176611