Finite Group Databasebeta

← #15625298

Subgroups — #15625298

Order 2816.

2030 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082005C211yesmaximal, characteristic, complemented
2C2×#10623255C211yesmaximal, characteristic, complemented
3#13079720C218yesmaximal, complemented
4#13079692C214yesmaximal, complemented
5#13079670C214yesmaximal, complemented
6#13079084C211yesmaximal, characteristic, complemented
7#13079003C211yesmaximal, characteristic, complemented
8#13078996C211yesmaximal, characteristic, complemented
9#13078112C212yesmaximal, complemented
10#13078101C212yesmaximal, complemented
11#13077857C212yesmaximal, complemented
12#13077848C212yesmaximal, complemented
13#13077252C211yesmaximal, characteristic, complemented
14C11×#3152C211yesmaximal, characteristic, complemented
15C22×#4343C2211yescharacteristic
16C22×Q8×D11C2211yescharacteristic
17C2×C11×#137C2212yes—
18C2×C11×#137C2212yes—
19C11×#532C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21#10623359C2212yes—
22#41×Dic11C2212yes—
23C2×#67004C2212yes—
24C2×#67002C2212yes—
25C2×#67000C2211yescharacteristic
26C2×#66997C2211yescharacteristic
27#10623262C2212yescomplemented
28#10623255—24no—
29#10623255C2214yes—
30#10623255C2214yes—
31#10623250C2212yescomplemented
32#10623213C2214yescomplemented
33#10623148—22no—
34#10623133—22no—
35#10623069—24no—
36C2×#66949—22no—
37C2×#66947—22no—
38C2×#66928C2211yescharacteristic
39C2×#66925C2211yescharacteristic
40#10623001C2211yescharacteristic
41C11×#497C2214yescomplemented
42C11×#494C2212yescomplemented
43C11×#492C2212yescomplemented
44C4×C11×M16C2211yescharacteristic
45#10622838C2212yes—
46#10622838C2212yes—
47#10622800C2218yes—
48#10622799C2218yescomplemented
49#10622798C2218yescomplemented
50#10622795C2218yescomplemented
51#10622785C2218yes—
52#10622783C2218yescomplemented
53#10622778C2218yescomplemented
54#10622775C2218yescomplemented
55#10622744C2212yes—
56#10622739C2212yes—
57#10622733C2212yes—
58#10622731C2212yes—
59#10622699C2212yescomplemented
60#10622695C2214yescomplemented
61#10622694C2214yescomplemented
62#10622687C2212yescomplemented
63#10622672C2214yescomplemented
64C4×#4318C2211yescharacteristic
65#10622327C2214yescomplemented
66#10622322C2214yescomplemented
67#10622310C2214yescomplemented
68#10622303C2214yescomplemented
69C2×C11×#41C2312yes—
70C22×Q8×C11C2311yescharacteristic
71C22×Q8×C11C2311yescharacteristic
72C2×#4343—22no—
73C2×#4343—44no—
74C2×#4343C2314yes—
75C2×Q8×D11—22no—
76C2×Q8×D11—44no—
77C2×Q8×D11C2314yes—
78C22×D44—21no—
79C22×D44C2311yescharacteristic
80C22×C4×D11—21no—
81C22×C4×D11—21no—
82C22×C4×D11C2311yescharacteristic
83C22×Dic22—21no—
84C22×Dic22C2311yescharacteristic
85C11×#137—44no—
86C11×#137—44no—
87C2×C11×Q16C2314yes—
88C2×C11×Q16C2314yes—
89C2×C11×SD16C2314yes—
90C2×C11×SD16C2314yes—
91C2×C11×M16C2312yes—
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8C2312yes—
94C11×C4⋊Q8C2311yescharacteristic
95C11×C4⋊Q8C2312yes—
96C11×#127C2311yescharacteristic
97C11×#124C2312yes—
98C11×#121—22no—
99C4×D4×C11—22no—
100C2×C11×C4⋊C4—22no—
101C2×C42×C11C2311yescharacteristic
102#67004—44no—
103#67002—44no—
104#67000—22no—
105#67000C2314yes—
106#66999C2314yes—
107Q8×Dic11C2314yes—
108#66997—22no—
109#66997C2314yes—
110C2×#4326C2314yes—
111C2×#4325C2314yes—
112#66992—24no—
113#66991C2314yes—
114#66990—22no—
115#66988—22no—
116#66988—24no—
117D4×Dic11—24no—
118D4×Dic11C2314yes—
119C2×#4324C2314yes—
120C2×#4323C2314yes—
121C4×C22⋊D11—24no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4D412yes—
125#66979—22no—
126#66979C2312yes—
127#66977—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4D412yes—
130C2×C4×Dic11—22no—
131C2×C4×Dic11C2311yescharacteristic
132C2×#4318C2312yes—
133#66951—24no—
134#66949—28no—
135#66949—28no—
136#66947—28no—
137#66947—28no—
138#66942—24no—
139#66939—24no—
140#66938—24no—
141#66932—24no—
142#66931—24no—
143#66928—22no—
144#66928C2312yes—
145#66928C2312yes—
146#66925D414yes—
147#66925C2312yes—
148#66925C2312yes—
149#66923C2312yes—
150#66922C2312yes—
151C4×Dic22—22no—
152C11×#97C2312yes—
153C4×C8×C11C2312yes—
154#66899C2318yes—
155#66899C2318yes—
156#66885C2318yes—
157(C2×D11)⋊C8C2318yes—
158#66880C2318yes—
159Dic11⋊C8C2318yes—
160#66867C2312yes—
161C4×C11⋊C8C2312yes—
162#60807—111nomaximal, Sylow
163C23×D11—21no—
164C23×D11C2×D411yescharacteristic
165C11×#41—24no—
166C11×#41—24no—
167C2×Q8×C11—21no—
168C2×Q8×C11—21no—
169C2×Q8×C11—24no—
170C2×Q8×C11—24no—
171C2×Q8×C11C2412yes—
172C2×Q8×C11C2412yes—
173C2×Q8×C11C2412yes—
174C2×D4×C11—22no—
175C2×D4×C11—22no—
176C2×D4×C11C2412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—24no—
183C22×Dic11—24no—
184C22×Dic11—21no—
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D412yes—
187#4343—48no—
188#4343—48no—
189Q8×D11—48no—
190Q8×D11—48no—
191C2×D44—24no—
192C2×D44—21no—
193C2×D44—24no—
194C2×D44—44no—
195C2×D44C2412yes—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—24no—
199C2×C4×D11—44no—
200C2×C4×D11—44no—
201C2×C4×D11C2×D412yes—
202C2×C4×D11C2412yes—
203C2×Dic22—24no—
204C2×Dic22—21no—
205C2×Dic22—22no—
206C2×Dic22—24no—
207C2×Dic22—44no—
208C2×Dic22C2412yes—
209C11×Q16—44no—
210C11×Q16—44no—
211C11×SD16—44no—
212C11×SD16—44no—
213C11×M16—24no—
214C2×C8×C11C2414yes—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—24no—
218C11×C22⋊C4—24no—
219C42×C11C2×D412yes—
220C42×C11C2411yescharacteristic
221C42×C11C2411yescharacteristic
222C22⋊Dic11—24no—
223C22⋊Dic11—24no—
224C22⋊Dic11—22no—
225#4326—44no—
226#4325—44no—
227#4324—44no—
228#4323—44no—
229(C2×D11)⋊C4—28no—
230(C2×D11)⋊C4—24no—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4C2×D414yes—
234(C2×D11)⋊C4C2×D414yes—
235C4⋊Dic11—24no—
236C4⋊Dic11—22no—
237C4⋊Dic11C2414yes—
238Dic11⋊C4—24no—
239Dic11⋊C4—28no—
240Dic11⋊C4—24no—
241Dic11⋊C4C2×D414yes—
242Dic11⋊C4C2×D414yes—
243C4×Dic11—24no—
244C4×Dic11—22no—
245C4×Dic11C2×D412yes—
246C4×Dic11C2412yes—
247#4318—24no—
248C2×C11⋊C8C2414yes—
249#3455—111no—
250C2×#536—111no—
251#3225—118no—
252#3223—114no—
253#3221—114no—
254#3153—111no—
255#3152D1111yescharacteristic, complemented
256#3140—111no—
257#3139—111no—
258#3040—112no—
259#3039—112no—
260#3005—112no—
261#3004—112no—
262#2921—111no—
263C23×C11—22no—
264C23×C11C22×D411yescharacteristic
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—42no—
268C22×D11—44no—
269C22×D11—42no—
270C22×D11C22×D412yes—
271Q8×C11—22no—
272Q8×C11—22no—
273Q8×C11—24no—
274Q8×C11—24no—
275Q8×C11—42no—
276Q8×C11—42no—
277D4×C11—22no—
278D4×C11—22no—
279D4×C11—44no—
280D4×C11—82no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—42no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—44no—
288C2×C4×C11C22×D412yes—
289C2×C4×C11C22×D412yes—
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11H(5,𝔽2)14yes—
292C2×C4×C11C2511yescharacteristic
293C22⋊D11—84no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—22no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—84no—
300C2×Dic11C22×D414yes—
301C2×Dic11C22×D412yes—
302D44—24no—
303D44—48no—
304D44—42no—
305C4×D11—24no—
306C4×D11—24no—
307C4×D11—48no—
308C4×D11—48no—
309Dic22—24no—
310Dic22—48no—
311Dic22—42no—
312Dic22—82no—
313C8×C11—24no—
314C11⋊C8—24no—
315C22×#41—111no—
316C23×Q8—111no—
317C2×#137—112no—
318C2×#137C2×D1112yes—
319C2×#137C2×D1112yes—
320C2×AGL(1,ℤ/8)—112no—
321#542—114no—
322#541—112no—
323#540—112no—
324#539—222no—
325#538—222no—
326#536—114no—
327#536—114no—
328#536—224no—
329#533—111no—
330#532C2×D1111yescharacteristic
331C2×C4⋊Q8—111no—
332C2×C4⋊Q8C2×D1111yescharacteristic
333#529—224no—
334C2×#124—111no—
335C2×#124—111no—
336#525—112no—
337C2×#123—222no—
338C2×C22⋊Q8—222no—
339C4×#41—112no—
340C2×#117—111no—
341#497—112no—
342#497C2×D1114yescomplemented
343#496—112no—
344#495—114no—
345#494C2×D1112yescomplemented
346#492C2×D1112yescomplemented
347#491—114no—
348#489—114no—
349#488—114no—
350#487—114no—
351#464—118no—
352#463—118no—
353#462—118no—
354#461—118no—
355#452—118no—
356#451—118no—
357#449—118no—
358#448—118no—
359#433—114no—
360#433—114no—
361#423—112no—
362#419—112no—
363#419—112no—
364#419—112no—
365#418—112no—
366#407—112no—
367C4×M16—111no—
368C4×M16C2×D1111yescharacteristic
369C22×C11—22no—
370C22×C11—44no—
371C22×C11—42no—
372C22×C11#53512yes—
373C22×C11C23×D411yescharacteristic
374C2×D11—24no—
375C2×D11—22no—
376C2×D11—44no—
377C2×D11—44no—
378C2×D11—42no—
379C2×D11—84no—
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—42no—
383C4×C11—42no—
384C4×C11—42no—
385C4×C11#53512yes—
386C4×C11C2×H(5,𝔽2)12yes—
387Dic11—24no—
388Dic11—22no—
389Dic11—44no—
390Dic11—42no—
391C2×#41—114no—
392C2×#41—222no—
393C2×#41—444no—
394C2×#41C22×D1112yes—
395C22×Q8—114no—
396C22×Q8—111no—
397C22×Q8—221no—
398C22×Q8—222no—
399C22×Q8—444no—
400C22×Q8C22×D1111yescharacteristic
401C22×Q8C22×D1111yescharacteristic
402C22×D4—111no—
403C22×D4—221no—
404C23×C4—111no—
405C23×C4—221no—
406C23×C4—221no—
407#137—44no—
408#137—44no—
409#137—444no—
410AGL(1,ℤ/8)—444no—
411C2×Q16—114no—
412C2×Q16C22×D1114yes—
413C2×Q16C22×D1114yes—
414C2×SD16—114no—
415C2×SD16—114no—
416C2×SD16C22×D1114yes—
417C2×SD16C22×D1114yes—
418C2×D8—114no—
419C2×M16—112no—
420C2×M16C22×D1112yes—
421C4⋊Q8—22no—
422C4⋊Q8—114no—
423C4⋊Q8—112no—
424C4⋊Q8—222no—
425C4⋊Q8C22×D1112yes—
426C4⋊Q8C22×D1112yes—
427C4⋊Q8C22×D1111yescharacteristic
428#127C22×D1111yescharacteristic
429#126—224no—
430#126—224no—
431#125—112no—
432#125—224no—
433#124—114no—
434#124—112no—
435#124—112no—
436#124—222no—
437#124—224no—
438#124—222no—
439#124C22×D1112yes—
440#123—224no—
441#123—228no—
442#123—228no—
443#123—224no—
444#123—222no—
445C22⋊Q8—114no—
446C22⋊Q8—224no—
447C22⋊Q8—228no—
448C22⋊Q8—228no—
449C22⋊Q8—222no—
450#121—22no—
451#121—114no—
452#121—224no—
453#120—222no—
454C4×Q8—114no—
455C4×Q8—222no—
456C4×D4—22no—
457C4×D4—114no—
458C4×D4—224no—
459C4×D4—224no—
460#117—114no—
461#117—112no—
462#117—112no—
463#117—112no—
464#117—222no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—222no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—222no—
471C2×C42—111no—
472C2×C42—222no—
473C2×C42C22×D1111yescharacteristic
474C4⋊C8—118no—
475#103—118no—
476#103—118no—
477#103—118no—
478#102—118no—
479C22⋊C8—118no—
480#97—112no—
481#97C22×D1112yes—
482C4×C8—112no—
483C4×C8C22×D1112yes—
484C2×C11—22no—
485C2×C11—82no—
486C2×C11C2×#53511yescharacteristic
487C2×C11#358612yes—
488D11—42no—
489D11—82no—
490C24—111no—
491C24—221no—
492#41—24no—
493#41—24no—
494#41—448no—
495#41—448no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—24no—
499C2×Q8—24no—
500C2×Q8—112no—
501C2×Q8—224no—
502C2×Q8—221no—
503C2×Q8—222no—
504C2×Q8—224no—
505C2×Q8—444no—
506C2×Q8—448no—
507C2×Q8—448no—
508C2×Q8C23×D1112yes—
509C2×Q8C23×D1112yes—
510C2×Q8C23×D1112yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—112no—
514C2×D4—224no—
515C2×D4—224no—
516C2×D4—221no—
517C2×D4—224no—
518C2×D4—444no—
519C2×D4C23×D1112yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—111no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—112no—
527C22×C4—224no—
528C22×C4—224no—
529C22×C4—224no—
530C22×C4—224no—
531C22×C4—221no—
532C22×C4—444no—
533C22×C4—444no—
534C22×C4D4×D1112yes—
535C22×C4C23×D1111yescharacteristic
536Q16—44no—
537Q16—44no—
538Q16—444no—
539SD16—44no—
540SD16—44no—
541SD16—444no—
542SD16—444no—
543D8—444no—
544M16—24no—
545M16—224no—
546C2×C8—114no—
547C2×C8C23×D1114yes—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—22no—
551C4⋊C4—114no—
552C4⋊C4—114no—
553C4⋊C4—114no—
554C4⋊C4—228no—
555C4⋊C4—224no—
556C4⋊C4—224no—
557C4⋊C4—224no—
558C4⋊C4—222no—
559C22⋊C4—24no—
560C22⋊C4—114no—
561C22⋊C4—114no—
562C22⋊C4—228no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—222no—
567C22⋊C4—224no—
568C22⋊C4—224no—
569C42—112no—
570C42—112no—
571C42—224no—
572C42—222no—
573C42D4×D1112yes—
574C42C23×D1111yescharacteristic
575C42C23×D1111yescharacteristic
576C11#6080711yescharacteristic, complemented, Sylow
577C23—22no—
578C23—112no—
579C23—222no—
580C23—222no—
581C23—442no—
582C23—444no—
583C23—442no—
584C23C2×D4×D1111yescharacteristic
585Q8—24no—
586Q8—24no—
587Q8—22no—
588Q8—22no—
589Q8—42no—
590Q8—42no—
591Q8—224no—
592Q8—448no—
593Q8—442no—
594Q8—882no—
595D4—22no—
596D4—22no—
597D4—44no—
598D4—82no—
599D4—224no—
600D4—448no—
601D4—442no—
602D4—884no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—114no—
611C2×C4—112no—
612C2×C4—222no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—448no—
618C2×C4—448no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—884no—
622C2×C4C2×D4×D1112yes—
623C2×C4C2×D4×D1112yes—
624C2×C4C2×D4×D1111yescharacteristic
625C2×C4#6703714yes—
626C2×C4C24×D1111yescharacteristic
627C8—24no—
628C8—224no—
629C22—22no—
630C22—44no—
631C22—42no—
632C22—224no—
633C22—222no—
634C22—444no—
635C22—444no—
636C22—442no—
637C22—884no—
638C22#1062324612yes—
639C22C22×D4×D1111yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—224no—
646C4—222no—
647C4—444no—
648C4—442no—
649C4#1062324612yes—
650C4C2×#6703712yes—
651C2—22no—
652C2—82no—
653C2—442no—
654C2—882no—
655C2C2×#1062324611yescharacteristic
656C2#1308339912yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3152C2
socleC22×C11C23×D4
hypercenter#3152D11
hypocenterC11#60807
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
1. #13082005C2semidirect
2. C2×#10623255C2semidirect
3. #13079720C2semidirect
4. #13079692C2semidirect
5. #13079670C2semidirect
6. #13079084C2semidirect
7. #13079003C2semidirect
8. #13078996C2semidirect
9. #13078112C2semidirect
10. #13078101C2semidirect
11. #13077857C2semidirect
12. #13077848C2semidirect
13. #13077252C2semidirect
14. C11×#3152C2semidirect
27. #10623262C22semidirect
31. #10623250C22semidirect
32. #10623213C22semidirect
41. C11×#497C22semidirect
42. C11×#494C22semidirect
43. C11×#492C22semidirect
48. #10622799C22semidirect
49. #10622798C22semidirect
50. #10622795C22semidirect
52. #10622783C22semidirect
53. #10622778C22semidirect
54. #10622775C22semidirect
59. #10622699C22semidirect
60. #10622695C22semidirect
61. #10622694C22semidirect
62. #10622687C22semidirect
63. #10622672C22semidirect
65. #10622327C22semidirect
66. #10622322C22semidirect
67. #10622310C22semidirect
68. #10622303C22semidirect
255. #3152D11semidirect
342. #497C2×D11semidirect
345. #494C2×D11semidirect
346. #492C2×D11semidirect
576. C11#60807semidirect

Maximal subgroups

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

subgroupindex
#130820052
C2×#106232552
#130797202
#130796922
#130796702
#130790842
#130790032
#130789962
#130781122
#130781012
#130778572
#130778482
#130772522
C11×#31522
#6080711