Finite Group Databasebeta

← #15623029

Subgroups — #15623029

Order 2816.

2050 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2#13081945C211yesmaximal, characteristic
3#13078984C214yesmaximal, complemented
4#13078977C214yesmaximal, complemented
5#13078973C214yesmaximal, complemented
6#13078966C214yesmaximal, complemented
7#13078959C214yesmaximal, complemented
8#13078936C214yesmaximal, complemented
9#13077136C211yesmaximal, characteristic, complemented
10C2×#10622846C211yesmaximal, characteristic, complemented
11C2×#10622615C211yesmaximal, characteristic, complemented
12C2×#10622735C211yesmaximal, characteristic, complemented
13C11×#2896C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18#10623364—22no—
19#10623363C2214yes—
20#10623361C2212yes—
21#10623359—22no—
22#10623356C2212yes—
23#10623347C2212yes—
24#10623336C2212yes—
25#10623335—22no—
26#10623322—22no—
27C2×#66979C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C23×C11⋊C8C2211yescharacteristic
30#10623050—22no—
31#10623050C2214yescomplemented
32#10623048—22no—
33#10623048C2214yescomplemented
34#10623031C2214yescomplemented
35#10623014—22no—
36#10623001—22no—
37C11×#419C2212yescomplemented
38C11×#418C2212yescomplemented
39C11×#417C2214yes—
40C11×#416C2214yescomplemented
41#10622846C2214yes—
42#10622846C2212yescomplemented
43#10622846C2212yescomplemented
44C2×#66899C2212yescomplemented
45C2×#66896C2212yescomplemented
46#10622746C2214yes—
47#10622744C2212yescomplemented
48#10622735C2214yescomplemented
49#10622735C2214yescomplemented
50#10622733C2212yescomplemented
51#10622726C2214yescomplemented
52C2×#66879C2212yescomplemented
53C2×C8×Dic11C2212yescomplemented
54#10622615C2214yes—
55#10622615C2212yescomplemented
56#10622615C2212yescomplemented
57C2×#66874C2212yescomplemented
58C2×#66873C2212yescomplemented
59#10622413C2218yescomplemented
60#10622410C2218yescomplemented
61#10622408C2218yescomplemented
62#10622405C2218yescomplemented
63#10622381C2218yescomplemented
64#10622378C2218yescomplemented
65#10622377C2218yescomplemented
66#10622373C2218yescomplemented
67C2×C11×#41—21no—
68C2×C11×#41—21no—
69C2×C11×#41—24no—
70C2×C11×#41—24no—
71C2×C11×#41C2312yes—
72C2×C11×#41C2312yes—
73C22×Q8×C11C2311yescharacteristic
74C22×D4×C11—21no—
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C2×#4339—21no—
80C2×#4339—21no—
81C2×#4339—24no—
82C2×#4339—24no—
83C2×#4339C2312yes—
84C2×#4339C2312yes—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C2×C11×M16—24no—
89C2×C11×M16C2312yes—
90C2×C11×M16C2312yes—
91C22×C8×C11C2312yes—
92C11×#117—21no—
93C11×#117—21no—
94C11×#117C2312yes—
95C11×#117C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11—21no—
99#67006—24no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D412yes—
102#67000C2314yes—
103#66999—24no—
104#66997C2314yes—
105#66993C2314yes—
106#66992—28no—
107#66991—24no—
108#66990—24no—
109#66989C2314yes—
110#66988—24no—
111#66983—24no—
112#66982—24no—
113C4×C22⋊D11—28no—
114#66979—21no—
115#66979—21no—
116#66979D412yes—
117#66979D412yes—
118#66979C2312yes—
119#66979C2312yes—
120#66979C2312yes—
121#66979C2312yes—
122C2×C4⋊Dic11D412yes—
123C2×C4⋊Dic11C2312yes—
124#66977—28no—
125#66977—24no—
126C2×C4×Dic11—21no—
127C2×C4×Dic11C2312yes—
128C22×C11⋊C8—24no—
129C22×C11⋊C8C2312yes—
130C22×C11⋊C8C2312yes—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133#66943—24no—
134#66943C2318yes—
135#66941—24no—
136#66941C2318yes—
137#66931—28no—
138#66931—28no—
139#66923—24no—
140#66922—24no—
141C4×Dic22—28no—
142C11×#103C2318yes—
143C11×#102C2318yes—
144#66899C2314yes—
145#66899C2314yes—
146#66896C2314yes—
147#66896C2314yes—
148#66885C2318yes—
149#66880C2318yes—
150#66879C2318yes—
151C8×Dic11C2318yes—
152#66874C2314yes—
153#66874C2314yes—
154#66873C2314yes—
155#66873C2314yes—
156#60612—111nomaximal, Sylow
157C24×C11—21no—
158C24×C11C2×D411yescharacteristic
159C23×D11—21no—
160C11×#41—24no—
161C11×#41—24no—
162C11×#41—24no—
163C11×#41—24no—
164C11×#41—44no—
165C11×#41—44no—
166C2×Q8×C11—21no—
167C2×Q8×C11—22no—
168C2×Q8×C11—22no—
169C2×Q8×C11C2412yes—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—21no—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11—44no—
176C2×D4×C11C2412yes—
177C22×C4×C11—21no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—44no—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11#4114yes—
186C22×C4×C11#4114yes—
187C22×C4×C11C2411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—28no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—44no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11C2×D414yes—
197#4339—24no—
198#4339—24no—
199#4339—24no—
200#4339—24no—
201#4339—44no—
202#4339—44no—
203C2×D44—21no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44C2412yes—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—44no—
210C2×Dic22—28no—
211C2×Dic22—21no—
212C2×Dic22—22no—
213C2×Dic22—22no—
214C2×Dic22C2412yes—
215C11×M16—24no—
216C11×M16—24no—
217C2×C8×C11—24no—
218C2×C8×C11C2414yes—
219C11×C4⋊C4—22no—
220C11×C4⋊C4C2414yes—
221C11×C22⋊C4—22no—
222C11×C22⋊C4—22no—
223C42×C11—22no—
224C42×C11—22no—
225C22⋊Dic11—28no—
226C22⋊Dic11—22no—
227C22⋊Dic11—22no—
228C22⋊Dic11C2×D414yes—
229C22⋊Dic11C2×D414yes—
230(C2×D11)⋊C4—28no—
231C4⋊Dic11—28no—
232C4⋊Dic11—22no—
233C4⋊Dic11C2×D414yes—
234C4⋊Dic11C2×D414yes—
235C4⋊Dic11C2414yes—
236Dic11⋊C4—28no—
237Dic11⋊C4—28no—
238Dic11⋊C4—28no—
239C4×Dic11—22no—
240C4×Dic11—22no—
241C4×Dic11C2×D414yes—
242C4×Dic11C2414yes—
243C2×C11⋊C8—24no—
244C2×C11⋊C8—24no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—22no—
247C2×C11⋊C8C2412yes—
248C2×C11⋊C8C2412yes—
249#3458—111no—
250#3449—111no—
251#3137—114no—
252#3137—114no—
253#3136—114no—
254#3136—114no—
255#3135—114no—
256#3131—114no—
257#2896—111no—
258#2896D1111yescharacteristic, complemented
259C2×#416—111no—
260C2×#416—111no—
261C2×#405—111no—
262C23×C11—22no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—82no—
266C23×C11#12414yes—
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—42no—
272C22×D11—82no—
273Q8×C11—22no—
274Q8×C11—22no—
275Q8×C11—42no—
276D4×C11—22no—
277D4×C11—22no—
278D4×C11—44no—
279D4×C11—44no—
280D4×C11—42no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—42no—
284C2×C4×C11—44no—
285C2×C4×C11—44no—
286C2×C4×C11—82no—
287C2×C4×C11#12414yes—
288C2×C4×C11#12414yes—
289C2×C4×C11#12414yes—
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C2×#4112yes—
294C2×C4×C11C2×#4112yes—
295C2×C4×C11C2×#4112yes—
296C2×C4×C11C2×#4112yes—
297C2×C4×C11C2×#4112yes—
298C2×C4×C11C2×#4112yes—
299C2×C4×C11C2511yescharacteristic
300C22⋊D11—44no—
301C22⋊D11—44no—
302C22⋊D11—88no—
303C2×Dic11—24no—
304C2×Dic11—22no—
305C2×Dic11—44no—
306C2×Dic11—42no—
307C2×Dic11—82no—
308C2×Dic11C22×D418yes—
309D44—22no—
310D44—22no—
311D44—42no—
312C4×D11—44no—
313C4×D11—44no—
314Dic22—22no—
315Dic22—22no—
316Dic22—42no—
317Dic22—88no—
318C8×C11—24no—
319C11⋊C8—22no—
320C11⋊C8—22no—
321C22×#41—111no—
322C22×#41C2×D1111yescharacteristic
323C22×M16C2×D1111yescharacteristic
324C23×C8—111no—
325#544—114no—
326#544—114no—
327#544—222no—
328#543—222no—
329#537—222no—
330#536—112no—
331#536—112no—
332#535—112no—
333#535—112no—
334#534—222no—
335#533—114no—
336#533—222no—
337#533—222no—
338#532—114no—
339#525—222no—
340#525—222no—
341C2×#117—111no—
342C2×#117—111no—
343C2×#117C2×D1111yescharacteristic
344#491—118no—
345#490—118no—
346#489—118no—
347#489—118no—
348#488—118no—
349#488—118no—
350#487—118no—
351#486—118no—
352#419—112no—
353#419C2×D1112yescomplemented
354#418—112no—
355#418C2×D1112yescomplemented
356#417—114no—
357#417C2×D1114yes—
358#416—112no—
359#416—112no—
360#416—114no—
361#416—114no—
362#416—112no—
363#416—112no—
364#416—114no—
365#416C2×D1114yescomplemented
366C2×#103—112no—
367C2×#103—112no—
368C2×#102—112no—
369C2×#102—112no—
370#405—114no—
371#405—114no—
372C2×#97—112no—
373C2×C4×C8—112no—
374C22×C11—22no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—42no—
380C22×C11—84no—
381C22×C11C2×#12412yes—
382C22×C11C2×#12412yes—
383C22×C11C2×#12412yes—
384C22×C11C23×D411yescharacteristic
385C2×D11—44no—
386C2×D11—42no—
387C2×D11—84no—
388C4×C11—44no—
389C4×C11—42no—
390C4×C11C2×#12412yes—
391C4×C11C2×#12412yes—
392C4×C11C2×#12412yes—
393C4×C11C22×#4111yescharacteristic
394C4×C11C22×#4111yescharacteristic
395Dic11—28no—
396Dic11—44no—
397Dic11—42no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—24no—
401C2×#41—24no—
402C2×#41—112no—
403C2×#41—112no—
404C2×#41—221no—
405C2×#41—221no—
406C2×#41—224no—
407C2×#41—224no—
408C2×#41C22×D1112yes—
409C2×#41C22×D1112yes—
410C22×Q8—111no—
411C22×Q8C22×D1111yescharacteristic
412C22×D4—21no—
413C22×D4—111no—
414C22×D4—221no—
415C22×D4C22×D1111yescharacteristic
416C23×C4—21no—
417C23×C4—221no—
418C23×C4C22×D1111yescharacteristic
419C2×M16—24no—
420C2×M16C22×D1112yes—
421C2×M16C22×D1112yes—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—112no—
425C22×C8—112no—
426C22×C8—224no—
427C22×C8C22×D1112yes—
428C4⋊Q8—118no—
429C4⋊Q8—114no—
430C4⋊Q8—224no—
431C4⋊Q8—224no—
432#127—114no—
433#125—118no—
434#125—224no—
435#125—224no—
436#124—114no—
437#124—114no—
438#123—224no—
439#123—224no—
440C22⋊Q8—228no—
441C22⋊Q8—228no—
442C22⋊Q8—228no—
443C22⋊Q8—224no—
444C22⋊Q8—224no—
445#121—224no—
446#121—224no—
447#121—228no—
448#120—224no—
449#120—224no—
450C4×Q8—228no—
451C4×D4—228no—
452#117—21no—
453#117—21no—
454#117—112no—
455#117—112no—
456#117—112no—
457#117—112no—
458#117—112no—
459#117—112no—
460#117—221no—
461#117—221no—
462#117C22×D1112yes—
463#117C22×D1112yes—
464C2×C4⋊C4—112no—
465C2×C4⋊C4—112no—
466C2×C4⋊C4C22×D1112yes—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—221no—
470C2×C42—21no—
471C2×C42—112no—
472C2×C42—221no—
473#103—114no—
474#103—114no—
475#103—118no—
476#103—114no—
477#103—114no—
478#103C22×D1118yes—
479#102—114no—
480#102—114no—
481#102—118no—
482#102—114no—
483#102—114no—
484#102C22×D1118yes—
485#97—118no—
486C4×C8—118no—
487C2×C11—22no—
488C2×C11—22no—
489C2×C11—22no—
490C2×C11—82no—
491C2×C11C22×#12411yescharacteristic
492C2×C11#358412yes—
493D11—82no—
494C24—21no—
495C24—221no—
496C24D4×D1111yescharacteristic
497#41—24no—
498#41—24no—
499#41—24no—
500#41—24no—
501#41—44no—
502#41—44no—
503#41—224no—
504#41—224no—
505#41—224no—
506#41—224no—
507#41—444no—
508#41—444no—
509C2×Q8—21no—
510C2×Q8—22no—
511C2×Q8—22no—
512C2×Q8—112no—
513C2×Q8—228no—
514C2×Q8—221no—
515C2×Q8—222no—
516C2×Q8—222no—
517C2×Q8C23×D1112yes—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—22no—
523C2×D4—44no—
524C2×D4—112no—
525C2×D4—228no—
526C2×D4—222no—
527C2×D4—222no—
528C2×D4—222no—
529C2×D4—221no—
530C2×D4—222no—
531C2×D4—444no—
532C2×D4C23×D1112yes—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—44no—
538C22×C4—114no—
539C22×C4—221no—
540C22×C4—222no—
541C22×C4—222no—
542C22×C4—222no—
543C22×C4—444no—
544C22×C4#433914yes—
545C22×C4D4×D1111yescharacteristic
546C22×C4D4×D1111yescharacteristic
547C22×C4D4×D1111yescharacteristic
548C22×C4#434114yes—
549C22×C4C23×D1111yescharacteristic
550C22×C4C23×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552M16—24no—
553M16—24no—
554C2×C8—24no—
555C2×C8—112no—
556C2×C8—112no—
557C2×C8—224no—
558C2×C8—224no—
559C2×C8—222no—
560C2×C8—222no—
561C2×C8C23×D1114yes—
562C4⋊C4—22no—
563C4⋊C4—114no—
564C4⋊C4—114no—
565C4⋊C4—114no—
566C4⋊C4—228no—
567C4⋊C4—228no—
568C4⋊C4—228no—
569C4⋊C4—228no—
570C4⋊C4—222no—
571C4⋊C4C23×D1114yes—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—114no—
575C22⋊C4—114no—
576C22⋊C4—228no—
577C22⋊C4—228no—
578C22⋊C4—222no—
579C22⋊C4—222no—
580C42—22no—
581C42—22no—
582C42—114no—
583C42—114no—
584C42—222no—
585C42—222no—
586C11#6061211yescharacteristic, complemented, Sylow
587C23—22no—
588C23—42no—
589C23—42no—
590C23—82no—
591C23—222no—
592C23—442no—
593C23—882no—
594C23#6693814yes—
595C23C2×D4×D1111yescharacteristic
596C23C2×D4×D1111yescharacteristic
597C23C2×D4×D1111yescharacteristic
598Q8—22no—
599Q8—22no—
600Q8—42no—
601Q8—222no—
602Q8—222no—
603Q8—442no—
604Q8—888no—
605D4—22no—
606D4—22no—
607D4—44no—
608D4—44no—
609D4—42no—
610D4—222no—
611D4—222no—
612D4—444no—
613D4—444no—
614D4—442no—
615D4—888no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—82no—
622C2×C4—118no—
623C2×C4—224no—
624C2×C4—222no—
625C2×C4—444no—
626C2×C4—442no—
627C2×C4—444no—
628C2×C4—444no—
629C2×C4—882no—
630C2×C4#6693814yes—
631C2×C4#6693814yes—
632C2×C4#6693814yes—
633C2×C4C2×#433912yes—
634C2×C4C2×#433912yes—
635C2×C4C2×#433912yes—
636C2×C4C2×D4×D1111yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×#434112yes—
640C2×C4C2×#434112yes—
641C2×C4C2×#434112yes—
642C2×C4C24×D1111yescharacteristic
643C8—24no—
644C8—222no—
645C8—222no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—44no—
650C22—42no—
651C22—44no—
652C22—84no—
653C22—442no—
654C22—444no—
655C22—884no—
656C22C2×#6693812yes—
657C22C2×#6693812yes—
658C22C2×#6693812yes—
659C22C22×D4×D1111yescharacteristic
660C4—42no—
661C4—44no—
662C4—228no—
663C4—442no—
664C4—444no—
665C4C2×#6693812yes—
666C4C2×#6693812yes—
667C4C2×#6693812yes—
668C4C22×#433911yescharacteristic
669C4C22×#434111yescharacteristic
670C2—22no—
671C2—22no—
672C2—22no—
673C2—82no—
674C2—882no—
675C2C22×#6693811yescharacteristic
676C2#1308338912yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2896C2
socleC22×C11C23×D4
prime radical#13081945C2
hypercenter#2896D11
hypocenterC11#60612
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
3. #13078984C2semidirect
4. #13078977C2semidirect
5. #13078973C2semidirect
6. #13078966C2semidirect
7. #13078959C2semidirect
8. #13078936C2semidirect
9. #13077136C2semidirect
10. C2×#10622846C2semidirect
11. C2×#10622615C2semidirect
12. C2×#10622735C2semidirect
13. C11×#2896C2semidirect
31. #10623050C22semidirect
33. #10623048C22semidirect
34. #10623031C22semidirect
37. C11×#419C22semidirect
38. C11×#418C22semidirect
40. C11×#416C22semidirect
42. #10622846C22semidirect
43. #10622846C22semidirect
44. C2×#66899C22semidirect
45. C2×#66896C22semidirect
47. #10622744C22semidirect
48. #10622735C22semidirect
49. #10622735C22semidirect
50. #10622733C22semidirect
51. #10622726C22semidirect
52. C2×#66879C22semidirect
53. C2×C8×Dic11C22semidirect
55. #10622615C22semidirect
56. #10622615C22semidirect
57. C2×#66874C22semidirect
58. C2×#66873C22semidirect
59. #10622413C22semidirect
60. #10622410C22semidirect
61. #10622408C22semidirect
62. #10622405C22semidirect
63. #10622381C22semidirect
64. #10622378C22semidirect
65. #10622377C22semidirect
66. #10622373C22semidirect
258. #2896D11semidirect
353. #419C2×D11semidirect
355. #418C2×D11semidirect
365. #416C2×D11semidirect
586. C11#60612semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130819452
#130789842
#130789772
#130789732
#130789662
#130789592
#130789362
#130771362
C2×#106228462
C2×#106226152
C2×#106227352
C11×#28962
#6061211