Finite Group Databasebeta

← #15633930

Subgroups — #15633930

Order 2816.

1852 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082492C211yesmaximal, characteristic, complemented
2#13082442C211yesmaximal, characteristic, complemented
3#13081385C214yesmaximal, complemented
4#13081370C214yesmaximal, complemented
5#13081346C214yesmaximal, complemented
6#13081324C214yesmaximal, complemented
7#13078974C212yesmaximal, complemented
8C2×#10622326C211yesmaximal, characteristic, complemented
9#13078450C212yesmaximal, complemented
10#13078438C211yesmaximal, characteristic, complemented
11#13078153C212yesmaximal, complemented
12#13078096C211yesmaximal, characteristic, complemented
13#13077556C211yesmaximal, characteristic, complemented
14#13077451C212yesmaximal, complemented
15C11×#2943C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623361C2212yes—
20#10623358C2212yes—
21C2×#67002C2212yes—
22#10623116C2214yes—
23#10623100C2214yescomplemented
24#10623084C2214yes—
25#10623081—24no—
26#10623070—24no—
27#10623070C2214yescomplemented
28#10623066—21no—
29#10623066—21no—
30#10623052C2212yes—
31#10623050—22no—
32#10623050C2212yes—
33#10623008—22no—
34C2×#66927C2211yescharacteristic
35#10623001—21no—
36#10623001C2211yescharacteristic
37C2×#66923—21no—
38C2×#66923C2211yescharacteristic
39C11×#442C2212yescomplemented
40C11×#441C2212yescomplemented
41C11×#440C2212yescomplemented
42C11×#440C2212yescomplemented
43C11×#427C2211yescharacteristic
44C11×#416C2211yescharacteristic
45C11×#416C2211yescharacteristic
46C2×C11×#97C2211yescharacteristic
47#10622845C2212yes—
48#10622798C2214yescomplemented
49#10622778C2214yescomplemented
50#10622776C2214yescomplemented
51#10622763C2214yescomplemented
52C2×#66885C2212yes—
53C2×#66885C2212yes—
54#10622715C2212yes—
55#10622714C2212yes—
56#10622640C2214yes—
57#10622635C2214yescomplemented
58#10622628C2214yes—
59#10622622C2214yescomplemented
60#10622614C2212yes—
61#10622608C2212yes—
62#10622537C2211yescharacteristic
63#10622504C2214yescomplemented
64#10622503C2214yescomplemented
65#10622484C2214yescomplemented
66#10622483C2214yescomplemented
67#10622430C2214yescomplemented
68#10622413C2214yescomplemented
69#10622408C2214yescomplemented
70#10622401C2214yescomplemented
71#10622398C2214yescomplemented
72#10622377C2214yescomplemented
73#10622373C2214yescomplemented
74#10622369C2214yescomplemented
75#10622326C2214yes—
76#10622326C2214yes—
77#10622314C2214yescomplemented
78#10622314C2214yescomplemented
79C2×C11×#41C2311yescharacteristic
80C2×C11×#41C2311yescharacteristic
81C2×#4339—24no—
82C22×D44—22no—
83C22×D44C2312yes—
84C11×#135—24no—
85C2×C11×Q16C2311yescharacteristic
86C2×C11×SD16C2311yescharacteristic
87C2×C11×SD16C2311yescharacteristic
88C2×C11×D8C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C4×Q8×C11C2312yes—
92C4×Q8×C11C2312yes—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11C2312yes—
96C4×D4×C11C2312yes—
97C11×#117—21no—
98C11×#117—21no—
99C11×#117C2311yescharacteristic
100C11×#117C2311yescharacteristic
101C2×C42×C11—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104#67002—28no—
105#67000C2314yes—
106Q8×Dic11C2314yes—
107C2×#4325C2314yes—
108#66993C2314yes—
109#66990—24no—
110D4×Dic11—24no—
111D4×Dic11C2314yes—
112C2×#4323C2314yes—
113#66983—22no—
114#66983—22no—
115#66983—24no—
116#66979—22no—
117#66979C2312yes—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11C2312yes—
120#66977—24no—
121#66977D414yes—
122C2×Dic11⋊C4—22no—
123C2×Dic11⋊C4—24no—
124C2×#4318C2312yes—
125#66947—24no—
126#66947—24no—
127#66946C2314yes—
128#66946C2314yes—
129#66943—24no—
130#66943C2314yes—
131#66941—24no—
132#66941C2314yes—
133#66937—24no—
134#66937—24no—
135C22⋊C4×D11—24no—
136#66931—24no—
137#66931—24no—
138#66931—24no—
139#66928—24no—
140#66927—21no—
141#66927—21no—
142#66927C2314yes—
143C4×D44—22no—
144C4×D44—22no—
145C4×D44—24no—
146#66923—21no—
147#66923—21no—
148#66923—22no—
149#66923—24no—
150#66923D411yescharacteristic
151#66923D411yescharacteristic
152#66923C2314yes—
153#66922—22no—
154#66922D412yes—
155C4×Dic22—24no—
156C4×Dic22C2314yes—
157C11×#107C2312yes—
158C11×#106C2312yes—
159C11×#103C2312yes—
160C11×#103C2312yes—
161C11×#102C2312yes—
162C11×#102C2312yes—
163C11×#97C2312yes—
164C11×#97C2312yes—
165#66899C2314yes—
166#66896C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66885C2314yes—
170#66885C2314yes—
171#66879C2314yes—
172Dic11⋊C8C2314yes—
173Dic11⋊C8C2314yes—
174C8×Dic11C2314yes—
175#66873C2314yes—
176#66873C2314yes—
177#66872C2314yes—
178#66871C2314yes—
179C4⋊(C11⋊C8)C2314yes—
180#61337—111nomaximal, Sylow
181C23×D11—22no—
182C11×#41—22no—
183C11×#41—22no—
184C11×#41—22no—
185C11×#41#4114yescomplemented
186C2×Q8×C11C2411yescharacteristic
187C2×Q8×C11C2411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11C2411yescharacteristic
191C2×D4×C11C2411yescharacteristic
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C22×Dic11—24no—
201C22×Dic11—22no—
202#4339—88no—
203C2×D44—22no—
204C2×D44—24no—
205C2×D44—24no—
206C2×D44—24no—
207C2×D44—24no—
208C2×D44—84no—
209C2×D44C2414yes—
210C2×C4×D11—24no—
211C2×C4×D11—24no—
212C2×Dic22—24no—
213C2×Dic22C2×D414yes—
214C11×Q16—22no—
215C11×SD16—22no—
216C11×SD16—22no—
217C11×D8—22no—
218C2×C8×C11—22no—
219C2×C8×C11—22no—
220C2×C8×C11C2412yes—
221C2×C8×C11C2411yescharacteristic
222C2×C8×C11C2411yescharacteristic
223C11×C4⋊C4—22no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4C2412yes—
226C11×C4⋊C4C2412yes—
227C11×C22⋊C4—21no—
228C11×C22⋊C4—21no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C42×C11—22no—
232C42×C11—21no—
233C42×C11—21no—
234C42×C11—22no—
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237C42×C11C2412yes—
238C22⋊Dic11—24no—
239C22⋊Dic11C2×D414yes—
240#4325—28no—
241#4323—28no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—22no—
249C4⋊Dic11C2×D414yes—
250C4⋊Dic11C2×D412yes—
251C4⋊Dic11C2×D412yes—
252C4⋊Dic11C2414yes—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4C2×D414yes—
258Dic11⋊C4C2×D414yes—
259C4×Dic11—24no—
260C4×Dic11C2414yes—
261#4318—24no—
262C2×C11⋊C8C2414yes—
263#3508—111no—
264#3504—111no—
265#3371—114no—
266#3370—114no—
267#3368—114no—
268#3366—114no—
269#3136—112no—
270C2×#490—111no—
271#3081—112no—
272#3080—111no—
273#3045—112no—
274#3038—111no—
275#2961—111no—
276#2946—112no—
277#2943D1111yescharacteristic, complemented
278C23×C11—21no—
279C23×C11—21no—
280C23×C11C22×D411yescharacteristic
281C22×D11—24no—
282C22×D11—44no—
283C22×D11—82no—
284C22×D11—82no—
285Q8×C11—21no—
286Q8×C11—21no—
287Q8×C11—21no—
288Q8×C11C2×#4112yes—
289D4×C11—24no—
290D4×C11—21no—
291D4×C11—21no—
292D4×C11—21no—
293D4×C11—42no—
294D4×C11C2×#4112yes—
295C2×C4×C11—21no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—42no—
301C2×C4×C11—44no—
302C2×C4×C11—42no—
303C2×C4×C11—82no—
304C2×C4×C11C22×D412yes—
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4112yes—
308C2×C4×C112−1+412yes—
309C2×C4×C11C2511yescharacteristic
310C22⋊D11—84no—
311C22⋊D11—84no—
312C2×Dic11—24no—
313C2×Dic11—84no—
314C2×Dic11—82no—
315C2×Dic11C22×D414yes—
316C2×Dic11C22×D414yes—
317D44—24no—
318D44—24no—
319D44—48no—
320D44—44no—
321D44—84no—
322C4×D11—84no—
323C4×D11—84no—
324Dic22—44no—
325Dic22—84no—
326C8×C11—21no—
327C8×C11—21no—
328C8×C11—22no—
329C11⋊C8—24no—
330C2×AGL(1,ℤ/8)—112no—
331C2×#135C2×D1111yescharacteristic
332#559—114no—
333#557—114no—
334#554—114no—
335#554—224no—
336#550—114no—
337#546—224no—
338#544—112no—
339#544—222no—
340#540—221no—
341#540—221no—
342#535—112no—
343#533—111no—
344#533—221no—
345#532—222no—
346C2×#127—111no—
347C2×#125—111no—
348C2×#125—221no—
349#520—112no—
350#518—112no—
351C4×#41C2×D1111yescharacteristic
352C4×#41C2×D1111yescharacteristic
353#490—114no—
354#490—114no—
355#490—114no—
356#489—114no—
357#488—114no—
358#486—114no—
359#479—114no—
360#478—114no—
361#478—114no—
362#478—114no—
363#476—114no—
364#474—114no—
365#464—114no—
366#463—114no—
367#460—114no—
368#460—114no—
369#459—114no—
370#459—114no—
371#446—114no—
372#446—114no—
373#442—114no—
374#442C2×D1112yescomplemented
375#441C2×D1112yescomplemented
376#440—114no—
377#440C2×D1112yescomplemented
378#440C2×D1112yescomplemented
379C4×SD16—114no—
380C4×D8—114no—
381#428—112no—
382#427C2×D1111yescharacteristic
383#424—112no—
384#423—111no—
385#418—112no—
386#417—112no—
387#416C2×D1111yescharacteristic
388#416C2×D1111yescharacteristic
389C2×#102—112no—
390C2×#102—112no—
391#405—112no—
392C2×#97C2×D1111yescharacteristic
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—41no—
398C22×C11#54812yes—
399C22×C11C23×D411yescharacteristic
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—164no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—42no—
408C4×C11—42no—
409C4×C11—41no—
410C4×C11#54812yes—
411C4×C11C22×#4111yescharacteristic
412C4×C11C2×2−1+411yescharacteristic
413Dic11—24no—
414Dic11—24no—
415Dic11—44no—
416C2×#41—224no—
417C2×#41C22×D1111yescharacteristic
418C2×#41C22×D1111yescharacteristic
419C22×D4—112no—
420C22×D4—222no—
421AGL(1,ℤ/8)—228no—
422#135—24no—
423C2×Q16C22×D1111yescharacteristic
424C2×SD16—114no—
425C2×SD16C22×D1111yescharacteristic
426C2×SD16C22×D1111yescharacteristic
427C2×D8—114no—
428C2×D8C22×D1111yescharacteristic
429C2×M16—112no—
430C22×C8C22×D1111yescharacteristic
431C22×C8C22×D1111yescharacteristic
432C4⋊Q8—114no—
433C4⋊Q8—112no—
434C4⋊Q8—222no—
435C4⋊Q8—224no—
436#127—114no—
437#127—114no—
438#127—221no—
439#127—221no—
440#125—114no—
441#125—111no—
442#125—111no—
443#125—114no—
444#125—222no—
445#125—224no—
446#125—224no—
447#125—221no—
448#125—221no—
449#124—114no—
450#124—224no—
451#123—224no—
452#123—224no—
453C22⋊Q8—114no—
454C22⋊Q8—224no—
455C22⋊Q8—224no—
456C22⋊Q8—224no—
457C22⋊Q8—224no—
458#121—224no—
459#121—224no—
460#121—222no—
461#121—222no—
462#121—224no—
463#120—224no—
464C4×Q8—114no—
465C4×Q8—114no—
466C4×Q8—224no—
467C4×Q8C22×D1112yes—
468C4×Q8C22×D1112yes—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—114no—
472C4×D4—114no—
473C4×D4—114no—
474C4×D4—222no—
475C4×D4—222no—
476C4×D4—224no—
477C4×D4—224no—
478C4×D4C22×D1112yes—
479C4×D4C22×D1112yes—
480#117—21no—
481#117—21no—
482#117—112no—
483#117—222no—
484#117C22×D1111yescharacteristic
485#117C22×D1111yescharacteristic
486C2×C4⋊C4—112no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—224no—
489C2×C4⋊C4—222no—
490C2×C22⋊C4—224no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42C22×D1111yescharacteristic
494#107—114no—
495#107C22×D1112yes—
496#106—114no—
497#106C22×D1112yes—
498C4⋊C8—114no—
499C4⋊C8—114no—
500C4⋊C8—114no—
501#103—114no—
502#103C22×D1112yes—
503#103C22×D1112yes—
504#102—114no—
505#102—114no—
506#102—114no—
507#102—114no—
508#102—114no—
509#102—114no—
510#102—114no—
511#102C22×D1112yes—
512#102C22×D1112yes—
513#97—114no—
514#97C22×D1112yes—
515#97C22×D1112yes—
516C4×C8—114no—
517C2×C11—22no—
518C2×C11—42no—
519C2×C11—81no—
520C2×C11C2×#54811yescharacteristic
521C2×C11#358512yes—
522D11—84no—
523C24—222no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—888no—
528#41#433914yescomplemented
529C2×Q8—114no—
530C2×Q8—224no—
531C2×Q8C23×D1111yescharacteristic
532C2×Q8C23×D1111yescharacteristic
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—114no—
536C2×D4—224no—
537C2×D4—224no—
538C2×D4—224no—
539C2×D4—222no—
540C2×D4—224no—
541C2×D4—224no—
542C2×D4—224no—
543C2×D4—884no—
544C2×D4C23×D1111yescharacteristic
545C2×D4C23×D1111yescharacteristic
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—224no—
551C22×C4—224no—
552C22×C4—224no—
553C22×C4—222no—
554C22×C4D4×D1112yes—
555C22×C4C23×D1111yescharacteristic
556Q16—22no—
557SD16—22no—
558SD16—22no—
559SD16—228no—
560D8—22no—
561D8—228no—
562M16—224no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—114no—
566C2×C8C23×D1112yes—
567C2×C8C23×D1111yescharacteristic
568C2×C8C23×D1111yescharacteristic
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—112no—
572C4⋊C4—114no—
573C4⋊C4—112no—
574C4⋊C4—114no—
575C4⋊C4—114no—
576C4⋊C4—114no—
577C4⋊C4—224no—
578C4⋊C4—224no—
579C4⋊C4—224no—
580C4⋊C4—224no—
581C4⋊C4—222no—
582C4⋊C4—224no—
583C4⋊C4—224no—
584C4⋊C4C23×D1112yes—
585C4⋊C4C23×D1112yes—
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—114no—
591C22⋊C4—224no—
592C22⋊C4—224no—
593C22⋊C4—224no—
594C22⋊C4—224no—
595C22⋊C4—224no—
596C42—21no—
597C42—21no—
598C42—22no—
599C42—22no—
600C42—114no—
601C42—224no—
602C42D4×D1111yescharacteristic
603C42D4×D1111yescharacteristic
604C42C23×D1112yes—
605C11#6133711yescharacteristic, complemented, Sylow
606C23—21no—
607C23—21no—
608C23—224no—
609C23—444no—
610C23—882no—
611C23—882no—
612C23C2×D4×D1111yescharacteristic
613Q8—21no—
614Q8—21no—
615Q8—21no—
616Q8—444no—
617Q8—884no—
618Q8C2×#433912yes—
619D4—24no—
620D4—21no—
621D4—21no—
622D4—21no—
623D4—42no—
624D4—224no—
625D4—224no—
626D4—448no—
627D4—444no—
628D4—884no—
629D4—884no—
630D4—884no—
631D4C2×#433912yes—
632C2×C4—21no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—42no—
638C2×C4—44no—
639C2×C4—42no—
640C2×C4—82no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—224no—
644C2×C4—884no—
645C2×C4—884no—
646C2×C4—884no—
647C2×C4—882no—
648C2×C4C2×#433912yes—
649C2×C4C2×D4×D1112yes—
650C2×C4C2×D4×D1112yes—
651C2×C4C2×D4×D1111yescharacteristic
652C2×C4#6704312yes—
653C2×C4C24×D1111yescharacteristic
654C8—21no—
655C8—21no—
656C8—22no—
657C8—224no—
658C22—22no—
659C22—22no—
660C22—42no—
661C22—42no—
662C22—41no—
663C22—444no—
664C22—444no—
665C22—444no—
666C22—1764no—
667C22#1062308312yes—
668C22C22×D4×D1111yescharacteristic
669C4—22no—
670C4—22no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—41no—
675C4—224no—
676C4—224no—
677C4—444no—
678C4#1062308312yes—
679C4C22×#433911yescharacteristic
680C4C2×#6704311yescharacteristic
681C2—22no—
682C2—42no—
683C2—81no—
684C2—884no—
685C2C2×#1062308311yescharacteristic
686C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2943C2
socleC22×C11C23×D4
hypercenter#2943D11
hypocenterC11#61337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2943

Complements

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

NH ≅ G/Ntype
1. #13082492C2semidirect
2. #13082442C2semidirect
3. #13081385C2semidirect
4. #13081370C2semidirect
5. #13081346C2semidirect
6. #13081324C2semidirect
7. #13078974C2semidirect
8. C2×#10622326C2semidirect
9. #13078450C2semidirect
10. #13078438C2semidirect
11. #13078153C2semidirect
12. #13078096C2semidirect
13. #13077556C2semidirect
14. #13077451C2semidirect
15. C11×#2943C2semidirect
23. #10623100C22semidirect
27. #10623070C22semidirect
39. C11×#442C22semidirect
40. C11×#441C22semidirect
41. C11×#440C22semidirect
42. C11×#440C22semidirect
48. #10622798C22semidirect
49. #10622778C22semidirect
50. #10622776C22semidirect
51. #10622763C22semidirect
57. #10622635C22semidirect
59. #10622622C22semidirect
63. #10622504C22semidirect
64. #10622503C22semidirect
65. #10622484C22semidirect
66. #10622483C22semidirect
67. #10622430C22semidirect
68. #10622413C22semidirect
69. #10622408C22semidirect
70. #10622401C22semidirect
71. #10622398C22semidirect
72. #10622377C22semidirect
73. #10622373C22semidirect
74. #10622369C22semidirect
77. #10622314C22semidirect
78. #10622314C22semidirect
185. C11×#41#41semidirect
277. #2943D11semidirect
374. #442C2×D11semidirect
375. #441C2×D11semidirect
377. #440C2×D11semidirect
378. #440C2×D11semidirect
528. #41#4339semidirect
605. C11#61337semidirect

Maximal subgroups

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

subgroupindex
#130824922
#130824422
#130813852
#130813702
#130813462
#130813242
#130789742
C2×#106223262
#130784502
#130784382
#130781532
#130780962
#130775562
#130774512
C11×#29432
#6133711