Finite Group Databasebeta

← #14755355

Subgroups — #14755355

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3#13077135C211yesmaximal, characteristic, complemented
4C22×#66887C211yesmaximal, characteristic, complemented
5#13069011C214yesmaximal, complemented
6#13069001C214yesmaximal, complemented
7#13068327C211yesmaximal, characteristic, complemented
8#13068325C211yesmaximal, characteristic, complemented
9C11×#2896C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623361—24no—
15#10623361C418yescomplemented
16C2×#67000C2212yes—
17C2×#66993C2212yes—
18C2×#66990—22no—
19C2×#66983—22no—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623052—22no—
24#10623052—22no—
25#10623052—22no—
26#10623052C2214yes—
27C2×#66946—22no—
28C2×C22⋊C4×D11—22no—
29C2×C4×D44—22no—
30C11×#419C2212yescomplemented
31C11×#418C2212yescomplemented
32C11×#417—22no—
33C11×#416—22no—
34#10622846—22no—
35#10622845—22no—
36#10622838C2212yescomplemented
37#10622828C2212yescomplemented
38C2×#66887—24no—
39C2×#66887C2214yes—
40#10622193C2214yescomplemented
41#10622170C2214yescomplemented
42C24×D11D412yes—
43C2×C11×#41—22no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41C2×C414yescomplemented
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—22no—
62C22×D44—22no—
63C22×D44C2×C414yes—
64C22×D44D412yes—
65C22×D44D414yes—
66C22×D44C2312yes—
67C22×C4×D11—24no—
68C2×C11×M16—21no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C2×C11×M16C2312yes—
72C22×C8×C11—21no—
73C11×#117—21no—
74C11×#117—21no—
75C11×#117D412yescomplemented
76C11×#117C2312yes—
77C2×C11×C4⋊C4D412yescomplemented
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#67000—24no—
83#67000C2×C418yescomplemented
84#66993—24no—
85#66993C2×C418yescomplemented
86#66990—216no—
87#66983—216no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—24no—
90#66979—21no—
91#66979—21no—
92#66979—22no—
93#66979C2×C414yescomplemented
94#66979D412yescomplemented
95#66979C2312yes—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D412yescomplemented
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2312yes—
100C2×#4318—21no—
101C2×#4318—22no—
102C2×#4318—22no—
103C2×#4318C2312yes—
104C22×C11⋊C8—21no—
105#66946—28no—
106#66946—28no—
107C22⋊C4×D11—28no—
108C22⋊C4×D11—28no—
109C4×D44—28no—
110C4×D44—28no—
111C11×#103—24no—
112C11×#102—24no—
113#66899—24no—
114#66896—24no—
115#66887—28no—
116#20953—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—84no—
123C23×D11C22⋊C418yes—
124C23×D11C2×D414yes—
125C11×#41—24no—
126C11×#41—24no—
127C11×#41—24no—
128C11×#41—24no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—42no—
132C11×#41—42no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C22×C412yescomplemented
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—41no—
146C2×D4×C11—41no—
147C2×D4×C11—42no—
148C2×D4×C11C22×C412yescomplemented
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—24no—
152C22×C4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11—42no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—216no—
166C2×C22⋊D11—88no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—24no—
172C2×D44—24no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—24no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—24no—
179C2×D44—24no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—22no—
183C2×D44—22no—
184C2×D44C22⋊C418yes—
185C2×D44C22×C414yes—
186C2×D44C2×D414yes—
187C2×C4×D11—216no—
188C2×C4×D11—88no—
189C11×M16—22no—
190C11×M16—22no—
191C11×M16—42no—
192C2×C8×C11—22no—
193C2×C8×C11—42no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4C2×D414yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C42×C11—22no—
199C42×C11—22no—
200C22⋊Dic11—24no—
201C22⋊Dic11—22no—
202C22⋊Dic11—22no—
203(C2×D11)⋊C4—216no—
204(C2×D11)⋊C4—216no—
205C4⋊Dic11—24no—
206C4⋊Dic11—22no—
207C4⋊Dic11C2×D414yes—
208C4×Dic11—22no—
209C4×Dic11—22no—
210C4×Dic11—22no—
211C4×Dic11C22×C414yescomplemented
212#4318—22no—
213#4318—22no—
214#4318—42no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—42no—
217C2×#535—111no—
218C2×#518—111no—
219#2896—111no—
220#2896D1111yescharacteristic, complemented
221C22×#100—111no—
222#1887—114no—
223#1885—114no—
224#1733—111no—
225#1733—111no—
226C23×C11—22no—
227C23×C11—42no—
228C23×C11—44no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11C2×C22⋊C412yes—
232C23×C11#12011yescharacteristic
233C23×C11#12011yescharacteristic
234C23×C11#12312yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—24no—
237C22×D11—28no—
238C22×D11—24no—
239C22×D11—28no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—88no—
243C22×D11—84no—
244C22×D11—88no—
245C22×D11C2×C22⋊C418yes—
246Q8×C11—22no—
247Q8×C11—22no—
248Q8×C11—41no—
249Q8×C11—41no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—44no—
253D4×C11—44no—
254D4×C11—41no—
255D4×C11—41no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—44no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C4×D412yes—
265C2×C4×C11C4×D412yes—
266C2×C4×C11C4×D412yes—
267C2×C4×C11C4×D412yes—
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12112yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12112yes—
274C2×C4×C11#12312yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C22⋊D11—816no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286D44—24no—
287D44—24no—
288D44—24no—
289D44—24no—
290D44—28no—
291D44—28no—
292C4×D11—816no—
293C8×C11—42no—
294C11⋊C8—42no—
295C22×#41C2×D1111yescharacteristic
296C23×D4—111no—
297C22×M16—111no—
298C22×M16C2×D1111yescharacteristic
299#535—118no—
300#535—224no—
301C2×#127—112no—
302C2×#124—112no—
303C2×#121—222no—
304C2×#120—222no—
305#518—114no—
306#518—222no—
307#518—222no—
308#518—222no—
309C2×C4×D4—222no—
310C2×C4×D4—222no—
311C2×#117—111no—
312C2×#117—111no—
313C2×#117C2×D1111yescharacteristic
314C22×C22⋊C4—222no—
315#419—112no—
316#419C2×D1112yescomplemented
317#418—112no—
318#418C2×D1112yescomplemented
319#417—22no—
320#417—222no—
321#416—22no—
322#416—222no—
323C2×#100—114no—
324C2×#100—224no—
325#339—114no—
326#339—114no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—44no—
333C22×C11—42no—
334C22×C11—82no—
335C22×C11—82no—
336C22×C11#38612yes—
337C22×C11#38612yes—
338C22×C11C22×C22⋊C411yescharacteristic
339C22×C11C2×#12011yescharacteristic
340C22×C11C2×#12311yescharacteristic
341C2×D11—28no—
342C2×D11—416no—
343C2×D11—48no—
344C2×D11—48no—
345C2×D11—84no—
346C2×D11—88no—
347C4×C11—44no—
348C4×C11—42no—
349C4×C11#38612yes—
350C4×C11#38612yes—
351C4×C11C2×C4×D411yescharacteristic
352C4×C11C2×C4×D411yescharacteristic
353C4×C11C2×#12111yescharacteristic
354C4×C11C2×#12111yescharacteristic
355Dic11—44no—
356Dic11—44no—
357C25—112no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—22no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41C4×D1114yescomplemented
366C22×Q8C22×D1111yescharacteristic
367C22×D4—21no—
368C22×D4—114no—
369C22×D4—112no—
370C22×D4—114no—
371C22×D4—112no—
372C22×D4—224no—
373C22×D4—222no—
374C22×D4—221no—
375C22×D4—221no—
376C22×D4—222no—
377C22×D4—221no—
378C22×D4—221no—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—224no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—21no—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—112no—
387C2×M16—221no—
388C2×M16—222no—
389C2×M16—222no—
390C2×M16C22×D1112yes—
391C22×C8—21no—
392C22×C8—221no—
393#127—118no—
394#127—224no—
395#124—118no—
396#124—224no—
397#121—2216no—
398#120—2216no—
399C4×D4—228no—
400C4×D4—228no—
401C4×D4—228no—
402C4×D4—228no—
403#117—21no—
404#117—21no—
405#117—114no—
406#117—112no—
407#117—112no—
408#117—221no—
409#117—222no—
410#117—221no—
411#117C22⋊D1112yescomplemented
412#117C22×D1112yes—
413C2×C4⋊C4—112no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4C22⋊D1112yescomplemented
416C2×C22⋊C4—21no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—224no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—21no—
424C2×C42—112no—
425C2×C42—221no—
426#103—24no—
427#103—224no—
428#102—24no—
429#102—224no—
430#100—228no—
431C2×C11—21no—
432C2×C11—22no—
433C2×C11—21no—
434C2×C11—22no—
435C2×C11—82no—
436C2×C11C2×#38611yescharacteristic
437C2×C11#301912yes—
438D11—48no—
439C24—21no—
440C24—114no—
441C24—118no—
442C24—222no—
443C24—224no—
444C24—222no—
445C24—884no—
446C24D4×D1111yescharacteristic
447#41—24no—
448#41—24no—
449#41—24no—
450#41—24no—
451#41—42no—
452#41—42no—
453#41—42no—
454#41—42no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×C4×D1112yescomplemented
461C2×D4—24no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—118no—
471C2×D4—114no—
472C2×D4—114no—
473C2×D4—2216no—
474C2×D4—224no—
475C2×D4—224no—
476C2×D4—224no—
477C2×D4—224no—
478C2×D4—224no—
479C2×D4—224no—
480C2×D4—224no—
481C2×D4—222no—
482C2×D4—222no—
483C2×D4—224no—
484C2×D4—224no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—222no—
488C2×D4—222no—
489C2×D4—888no—
490C2×D4C2×C4×D1112yescomplemented
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—24no—
494C22×C4—42no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—2216no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—888no—
501C22×C4C2×C4×D1112yes—
502C22×C4#433912yes—
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1112yes—
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1111yescharacteristic
507C22×C4#434112yes—
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511M16—22no—
512M16—22no—
513M16—42no—
514M16—222no—
515M16—222no—
516M16—442no—
517C2×C8—22no—
518C2×C8—42no—
519C2×C8—222no—
520C2×C8—442no—
521C4⋊C4—22no—
522C4⋊C4—114no—
523C4⋊C4—224no—
524C4⋊C4—222no—
525C4⋊C4C2×C22⋊D1114yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—2216no—
529C22⋊C4—2216no—
530C22⋊C4—224no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C42—22no—
534C42—22no—
535C42—114no—
536C42—222no—
537C42—222no—
538C42—222no—
539C11#2095311yescharacteristic, complemented, Sylow
540C23—22no—
541C23—42no—
542C23—44no—
543C23—41no—
544C23—41no—
545C23—118no—
546C23—224no—
547C23—228no—
548C23—224no—
549C23—228no—
550C23—448no—
551C23—448no—
552C23—884no—
553C23—888no—
554C23—888no—
555C23C22⋊C4×D1112yes—
556C23#6693612yes—
557C23#6699011yescharacteristic
558C23#6699011yescharacteristic
559C23C2×D4×D1111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564D4—22no—
565D4—22no—
566D4—44no—
567D4—44no—
568D4—41no—
569D4—41no—
570D4—224no—
571D4—224no—
572D4—224no—
573D4—224no—
574D4—228no—
575D4—228no—
576D4—8816no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—44no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—8816no—
589C2×C4C22⋊C4×D1112yes—
590C2×C4(C22⋊D11)⋊C412yes—
591C2×C4(C22⋊D11)⋊C412yes—
592C2×C4#6693612yes—
593C2×C4#6693712yes—
594C2×C4#6693712yes—
595C2×C4C4×C22⋊D1112yes—
596C2×C4C4×C22⋊D1112yes—
597C2×C4#6699011yescharacteristic
598C2×C4#6699011yescharacteristic
599C2×C4#6699112yes—
600C2×C4#6699112yes—
601C2×C4C22×C4×D1111yescharacteristic
602C2×C4C2×#433911yescharacteristic
603C2×C4C2×D4×D1111yescharacteristic
604C2×C4C2×D4×D1111yescharacteristic
605C2×C4C2×#434111yescharacteristic
606C2×C4C22×C22⋊D1111yescharacteristic
607C8—42no—
608C8—442no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—42no—
613C22—42no—
614C22—44no—
615C22—42no—
616C22—82no—
617C22—82no—
618C22—228no—
619C22—448no—
620C22—4416no—
621C22—448no—
622C22—884no—
623C22—888no—
624C22#1062256912yes—
625C22#1062256912yes—
626C22C2×C22⋊C4×D1111yescharacteristic
627C22C2×#6693611yescharacteristic
628C22C2×#6699011yescharacteristic
629C4—42no—
630C4—44no—
631C4—444no—
632C4—444no—
633C4#1062256912yes—
634C4#1062256912yes—
635C4C2×(C22⋊D11)⋊C411yescharacteristic
636C4C2×#6693711yescharacteristic
637C4C2×C4×C22⋊D1111yescharacteristic
638C4C2×#6699111yescharacteristic
639C2—21no—
640C2—21no—
641C2—22no—
642C2—22no—
643C2—82no—
644C2—448no—
645C2C2×#1062256911yescharacteristic
646C2#1307797112yes—
subgroupG/H
centerC22C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2896C2
socleC22×C11C2×#120
prime radicalC2×#10623361C2
cosocleC22×C4×C11C24
hypercenter#2896D11
hypocenterC11#20953
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. #13077135C2semidirect
4. C22×#66887C2semidirect
5. #13069011C2semidirect
6. #13069001C2semidirect
7. #13068327C2semidirect
8. #13068325C2semidirect
9. C11×#2896C2semidirect
15. #10623361C4semidirect
30. C11×#419C22semidirect
31. C11×#418C22semidirect
36. #10622838C22semidirect
37. #10622828C22semidirect
40. #10622193C22semidirect
41. #10622170C22semidirect
50. C2×C11×#41C2×C4semidirect
75. C11×#117D4semidirect
77. C2×C11×C4⋊C4D4semidirect
83. #67000C2×C4semidirect
85. #66993C2×C4semidirect
93. #66979C2×C4semidirect
94. #66979D4semidirect
97. C2×C4⋊Dic11D4semidirect
138. C2×Q8×C11C22×C4semidirect
148. C2×D4×C11C22×C4semidirect
211. C4×Dic11C22×C4semidirect
220. #2896D11semidirect
316. #419C2×D11semidirect
318. #418C2×D11semidirect
365. C2×#41C4×D11semidirect
411. #117C22⋊D11semidirect
415. C2×C4⋊C4C22⋊D11semidirect
460. C2×Q8C2×C4×D11semidirect
490. C2×D4C2×C4×D11semidirect
539. C11#20953semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
C2×#106230522
#130771352
C22×#668872
#130690112
#130690012
#130683272
#130683252
C11×#28962
#2095311