Finite Group Databasebeta

← #14754516

Subgroups — #14754516

Order 2816.

1630 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622494C212yesmaximal, complemented
3C2×#10622339C211yesmaximal, characteristic
4D11×#380C211yesmaximal, characteristic
5#13068816C212yesmaximal, complemented
6#13068812C212yesmaximal, complemented
7#13068811C211yesmaximal, characteristic, complemented
8#13068808C211yesmaximal, characteristic, complemented
9#13068804C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C11×#1852C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11—21no—
17C22×#4313C2212yes—
18C2×#66945—21no—
19C2×#66945—21no—
20C2×#66945—28no—
21C2×#66945C2212yes—
22C2×#66945C2212yes—
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C4⋊C4×D11C2211yescharacteristic
25C2×C22⋊C4×D11—21no—
26C2×C11×#107C2212yescomplemented
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66881C2212yescomplemented
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35C2×#66872C2212yescomplemented
36C2×#66871C2212yescomplemented
37#10622555—21no—
38#10622494—28no—
39#10622339C418yescomplemented
40#10622280—21no—
41D11×#95—21no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C23×Dic11D411yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11C2×C414yes—
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11Q814yes—
59C22×C4×D11C2311yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—21no—
68C2×C22⋊Dic11—21no—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×C4×Dic11—28no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C22×C11⋊C8C2312yes—
85C2×#4313—24no—
86C2×#4313—24no—
87C2×#4313C2×C418yescomplemented
88#66945—28no—
89#66945—28no—
90#66945—24no—
91#66945—24no—
92#66945—24no—
93#66945D418yes—
94C4⋊C4×D11—24no—
95C4⋊C4×D11—24no—
96C22⋊C4×D11—44no—
97C11×#107—24no—
98C11×C22⋊C8C2×C414yescomplemented
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C22⋊(C11⋊C8)C2×C414yescomplemented
104(C2×D11)⋊C8C2×C418yescomplemented
105#66881—24no—
106#66872—24no—
107#66871—24no—
108#20846—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—41no—
115C23×D11—41no—
116C23×D11C4⋊C414yes—
117C23×D11C2×D411yescharacteristic
118C23×D11C2×D411yescharacteristic
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×Q812yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11C4⋊C414yes—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—216no—
145C2×C4×D11—216no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11C4⋊C414yes—
157C2×C4×D11C4⋊C414yes—
158C2×C4×D11C22×C412yes—
159C2×C4×D11C22×C412yes—
160C2×C4×D11C2×D414yes—
161C2×C4×D11C2×Q812yes—
162C2×C4×D11C2×Q812yes—
163C2×C4×D11#4114yes—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11C22×C414yes—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C2×D414yes—
172C11×C22⋊C4—42no—
173C22⋊Dic11—42no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—24no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11C2×D414yes—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185C4×Dic11—28no—
186C4×Dic11—28no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C22×C414yes—
190#4313—216no—
191C22×#117—111no—
192C2×#428—112no—
193C2×#407—111no—
194C2×#380—111no—
195#1854—112no—
196#1854—112no—
197#1853—111no—
198#1853—111no—
199#1852—111no—
200#1852D1111yescharacteristic, complemented
201#1736—112no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11C2×C4⋊C412yes—
207C23×C11AGL(1,ℤ/8)12yes—
208C23×C11#13712yes—
209C23×C11C22×D411yescharacteristic
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—44no—
223C22×D11—44no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11C2×C4⋊C412yes—
228C22×D11C2×C4⋊C412yes—
229C22×D11#12012yes—
230C22×D11#12312yes—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—48no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C2×C4⋊C412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4112yes—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—28no—
253C2×Dic11—24no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11C2×C4⋊C412yes—
264C2×Dic11C2×C4⋊C412yes—
265C2×Dic11#12012yes—
266C2×Dic11#12312yes—
267C4×D11—28no—
268C4×D11—24no—
269C4×D11—24no—
270C4×D11—28no—
271C4×D11—84no—
272C4×D11—84no—
273C4×D11C4×D418yes—
274C4×D11C22⋊Q818yes—
275C8×C11—24no—
276C11⋊C8—24no—
277C24×C4—111no—
278C22×M16—112no—
279C2×#117—112no—
280C2×#117—112no—
281C2×#117—228no—
282C2×#117—221no—
283C2×#117—221no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4—221no—
289C22×C22⋊C4—221no—
290C22×C42—221no—
291#428—228no—
292C2×#107—112no—
293C2×#107C2×D1112yescomplemented
294C2×#106—112no—
295C2×#106—112no—
296#407—118no—
297C2×C22⋊C8—111no—
298C2×C22⋊C8—112no—
299C2×C22⋊C8C2×D1111yescharacteristic
300#380—111no—
301#380—111no—
302#380—111no—
303#380—221no—
304#380—221no—
305#380C2×D1111yescharacteristic
306C2×#95—221no—
307#340—112no—
308#340—112no—
309#340—112no—
310#340C2×D1112yescomplemented
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11#42814yescomplemented
318C22×C11C22×C4⋊C411yescharacteristic
319C22×C11C2×#12011yescharacteristic
320C22×C11C2×#12311yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11C2×#13711yescharacteristic
323C22×C11#57511yescharacteristic
324C22×C11#57511yescharacteristic
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—416no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11#38514yes—
340C4×C11—22no—
341C4×C11—44no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11C2×C4×D412yes—
345C4×C11C2×C22⋊Q812yes—
346Dic11—22no—
347Dic11—44no—
348Dic11—81no—
349Dic11—81no—
350Dic11#38514yes—
351C25—111no—
352C23×C4—21no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—114no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—114no—
359C23×C4—111no—
360C23×C4—224no—
361C23×C4—224no—
362C23×C4—221no—
363C23×C4—221no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—118no—
367C2×M16—224no—
368C2×M16—224no—
369C22×C8—112no—
370C22×C8C22×D1112yes—
371#117—118no—
372#117—224no—
373#117—224no—
374#117—228no—
375#117—228no—
376#117—224no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—224no—
383C2×C4⋊C4—224no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1112yes—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—228no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—444no—
399C2×C42—222no—
400C2×C42—222no—
401C2×C42—228no—
402#107—24no—
403#107—224no—
404#106—224no—
405#106—224no—
406C22⋊C8—114no—
407C22⋊C8—118no—
408C22⋊C8C4×D1114yescomplemented
409#95—21no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11—24no—
414C2×C11C2×#38511yescharacteristic
415C2×C11C2×#42811yescharacteristic
416C2×C11#291111yescharacteristic
417C2×C11#300611yescharacteristic
418C2×C11#300711yescharacteristic
419C2×C11#309411yescharacteristic
420C2×C11#309511yescharacteristic
421D11—24no—
422D11—42no—
423C24—111no—
424C24—111no—
425C24—114no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—441no—
431C24—441no—
432C24D4×D1111yescharacteristic
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—111no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—111no—
448C22×C4—114no—
449C22×C4—114no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—2216no—
455C22×C4—2216no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—442no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4C2×C4×D1112yes—
475C22×C4D4×D1111yescharacteristic
476C22×C4Q8×D1112yes—
477C22×C4C23×D1111yescharacteristic
478M16—2216no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—114no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8C2×C4×D1114yes—
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—114no—
490C4⋊C4—224no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4D4×D1114yes—
497C22⋊C4—42no—
498C22⋊C4—228no—
499C22⋊C4—228no—
500C22⋊C4—442no—
501C22⋊C4—442no—
502C22⋊C4—442no—
503C42—228no—
504C42—228no—
505C11#2084611yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—112no—
511C23—112no—
512C23—112no—
513C23—112no—
514C23—228no—
515C23—221no—
516C23—221no—
517C23—221no—
518C23—221no—
519C23—228no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—221no—
524C23—221no—
525C23—221no—
526C23—444no—
527C23—444no—
528C23—444no—
529C23—444no—
530C23—444no—
531C23C4⋊C4×D1112yes—
532C23#6696412yes—
533C23#6697112yes—
534C23C2×D4×D1111yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—48no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—112no—
550C2×C4—112no—
551C2×C4—112no—
552C2×C4—118no—
553C2×C4—118no—
554C2×C4—112no—
555C2×C4—228no—
556C2×C4—228no—
557C2×C4—228no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—448no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—884no—
573C2×C4—884no—
574C2×C4C4⋊C4×D1112yes—
575C2×C4C22×C4×D1111yescharacteristic
576C2×C4C2×D4×D1112yes—
577C2×C4C2×Q8×D1111yescharacteristic
578C2×C4#41×D1112yes—
579C8—24no—
580C8—224no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—114no—
588C22—222no—
589C22—222no—
590C22—222no—
591C22—222no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—222no—
597C22—4416no—
598C22—441no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22#1062249414yescomplemented
603C22C2×C4⋊C4×D1111yescharacteristic
604C22D11×#12011yescharacteristic
605C22D11×#12311yescharacteristic
606C22C2×#6696411yescharacteristic
607C22C2×#6697111yescharacteristic
608C22#1062330411yescharacteristic
609C22#1062330811yescharacteristic
610C4—22no—
611C4—44no—
612C4—81no—
613C4—81no—
614C4—114no—
615C4—222no—
616C4—444no—
617C4—881no—
618C4—881no—
619C4C4×D4×D1112yes—
620C4D11×C22⋊Q812yes—
621C2—24no—
622C2—224no—
623C2—442no—
624C2D11×#38511yescharacteristic
625C2C2×#1062249411yescharacteristic
626C2#1307720311yescharacteristic
627C2#1307786311yescharacteristic
628C2#1307787511yescharacteristic
629C2#1307855111yescharacteristic
630C2#1307856111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1852D11
hypocenterC11#20846
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
2. C2×#10622494C2semidirect
5. #13068816C2semidirect
6. #13068812C2semidirect
7. #13068811C2semidirect
8. #13068808C2semidirect
9. #13068804C2semidirect
10. #13068334C2semidirect
11. C11×#1852C2semidirect
26. C2×C11×#107C22semidirect
32. C2×#66881C22semidirect
35. C2×#66872C22semidirect
36. C2×#66871C22semidirect
39. #10622339C4semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
87. C2×#4313C2×C4semidirect
98. C11×C22⋊C8C2×C4semidirect
103. C22⋊(C11⋊C8)C2×C4semidirect
104. (C2×D11)⋊C8C2×C4semidirect
200. #1852D11semidirect
293. C2×#107C2×D11semidirect
310. #340C2×D11semidirect
317. C22×C11#428semidirect
408. C22⋊C8C4×D11semidirect
505. C11#20846semidirect
602. C22#10622494semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106224942
C2×#106223392
D11×#3802
#130688162
#130688122
#130688112
#130688082
#130688042
#130683342
C11×#18522
#2084611