Finite Group Databasebeta

← #15633927

Subgroups — #15633927

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#13082437C211yesmaximal, characteristic, complemented
2#13081378C214yesmaximal, complemented
3#13081363C214yesmaximal, complemented
4#13081341C214yesmaximal, complemented
5#13081319C214yesmaximal, complemented
6#13078970C212yesmaximal, complemented
7C2×#10622684C211yesmaximal, characteristic, complemented
8#13078447C212yesmaximal, complemented
9#13078438C211yesmaximal, characteristic, complemented
10#13078151C212yesmaximal, complemented
11#13078092C211yesmaximal, characteristic, complemented
12#13077557C211yesmaximal, characteristic, complemented
13#13077448C212yesmaximal, complemented
14#13077414C211yesmaximal, characteristic, complemented
15C11×#3508C211yesmaximal, characteristic, complemented
16C11×#559C2214yes—
17C11×#550C2214yes—
18C11×#546—24no—
19C11×#540—21no—
20C11×#540—21no—
21C11×#535C2212yes—
22C11×#533C2211yescharacteristic
23C11×#532—22no—
24C2×C11×#127C2211yescharacteristic
25C11×#518C2212yes—
26C4×C11×#41C2211yescharacteristic
27C2×#67003C2211yescharacteristic
28C2×#66985C2212yes—
29#10623260—22no—
30#10623219—21no—
31D11×#125—21no—
32#10623167—24no—
33#10623110C2214yescomplemented
34#10623098C2214yescomplemented
35#10623054C2212yes—
36#10623050C2212yes—
37C4×#4339C2211yescharacteristic
38C2×#66923C2211yescharacteristic
39#10622846C2211yescharacteristic
40#10622845C2212yes—
41#10622828C2212yes—
42C2×#66896C2212yes—
43C2×#66896C2212yes—
44#10622688C2214yes—
45#10622688C2214yescomplemented
46#10622685C2214yes—
47#10622685C2214yescomplemented
48#10622684C2214yes—
49#10622684C2214yes—
50#10622684C2214yescomplemented
51#10622683C2214yescomplemented
52#10622670C2214yescomplemented
53#10622669C2214yescomplemented
54#10622668C2214yescomplemented
55#10622667C2214yescomplemented
56#10622643C2212yescomplemented
57#10622639C2212yescomplemented
58#10622637C2214yescomplemented
59#10622637C2214yescomplemented
60#10622635C2214yescomplemented
61#10622631C2214yescomplemented
62#10622631C2212yescomplemented
63C4×#4324C2214yescomplemented
64#10622627C2214yescomplemented
65#10622627C2212yescomplemented
66C4×#4323C2214yescomplemented
67#10622622C2214yescomplemented
68#10622622C2214yescomplemented
69#10622622C2214yescomplemented
70#10622621C2214yescomplemented
71#10622620C2214yescomplemented
72#10622615C2211yescharacteristic
73#10622612C2212yes—
74#10622611C2211yescharacteristic
75#10622610C2212yes—
76#10622608C2212yes—
77#10622537C2211yescharacteristic
78C2×#66867C2211yescharacteristic
79C2×C11×#41—24no—
80C2×C11×#41C2311yescharacteristic
81C22×D4×C11—22no—
82C22×D4×C11C2312yes—
83C2×#4339C2311yescharacteristic
84C11×C4⋊Q8D412yes—
85C11×#127—21no—
86C11×#127—21no—
87C11×#127C2314yes—
88C11×#127C2314yes—
89C11×#125D411yescharacteristic
90C11×#125D411yescharacteristic
91C11×#124—24no—
92C11×#124C2314yes—
93C11×#123—24no—
94C11×#123—24no—
95C11×C22⋊Q8D414yes—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—24no—
99C11×#121—24no—
100C11×#121—24no—
101C11×#120—24no—
102C4×Q8×C11C2312yes—
103C4×Q8×C11C2314yes—
104C4×D4×C11—22no—
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11—24no—
108C4×D4×C11C2312yes—
109C4×D4×C11C2314yes—
110C4×D4×C11C2314yes—
111C11×#117—21no—
112C11×#117C2311yescharacteristic
113C11×#117C2312yes—
114C2×C11×C22⋊C4—24no—
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117#67003—24no—
118#66999—24no—
119#66997—24no—
120C2×#4326C2311yescharacteristic
121C2×#4325C2311yescharacteristic
122C2×#4324C2314yes—
123C2×#4324C2311yescharacteristic
124#66985—28no—
125C2×#4323C2314yes—
126C2×#4323C2311yescharacteristic
127C4×C22⋊D11—22no—
128#66979C2311yescharacteristic
129C2×C4⋊Dic11C2312yes—
130C2×Dic11⋊C4—22no—
131C2×#4318C2312yes—
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134#66949—24no—
135#66949—24no—
136#66945—22no—
137C4⋊C4×D11—22no—
138C4⋊C4×D11—24no—
139#66943—22no—
140#66942—24no—
141#66942—24no—
142#66941—22no—
143#66940—24no—
144(C22⋊D11)⋊C4—24no—
145#66931—24no—
146C4×D44C2312yes—
147C4×D44C2314yes—
148#66925—21no—
149C42×D11—21no—
150#66923—21no—
151#66923—21no—
152#66923C2314yes—
153#66923C2314yes—
154#66922C2314yes—
155C4×Dic22C2312yes—
156C4×Dic22C2314yes—
157#66899C2314yes—
158#66899C2312yes—
159#66896C2314yes—
160#66896C2314yes—
161#66896C2314yes—
162#66896C2314yes—
163#66896C2314yes—
164#66896C2314yes—
165#66896C2314yes—
166#66896C2312yes—
167#66874C2312yes—
168#66873C2312yes—
169#66872C2314yes—
170#66872C2312yes—
171#66871C2314yes—
172#66871C2312yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176#66867C2312yes—
177#66867C2312yes—
178#66867C2314yes—
179C4×C11⋊C8C2314yes—
180#61337—111nomaximal, Sylow
181C24×C11—22no—
182C11×#41—22no—
183C11×#41—22no—
184C11×#41—88no—
185C2×Q8×C11C2×D414yes—
186C2×Q8×C11C2411yescharacteristic
187C2×D4×C11—21no—
188C2×D4×C11—22no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—24no—
193C2×D4×C11—24no—
194C2×D4×C11—24no—
195C2×D4×C11—84no—
196C2×D4×C11C2414yes—
197C2×D4×C11C2411yescharacteristic
198C22×C4×C11—21no—
199C22×C4×C11—22no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2411yescharacteristic
204C2×C22⋊D11—21no—
205C22×Dic11—22no—
206#4339—22no—
207#4339#4114yescomplemented
208C2×D44C2411yescharacteristic
209C2×C4×D11—21no—
210C2×C4×D11—22no—
211C2×C4×D11—24no—
212C2×Dic22—24no—
213C2×Dic22C2411yescharacteristic
214C11×C4⋊C4—22no—
215C11×C4⋊C4C2×D414yes—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2×D414yes—
218C11×C4⋊C4C2×D414yes—
219C11×C4⋊C4C2×D412yes—
220C11×C4⋊C4C2412yes—
221C11×C22⋊C4—21no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—24no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4C2×D414yes—
228C42×C11—21no—
229C42×C11—22no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2414yes—
233C42×C11C2412yes—
234C22⋊Dic11—21no—
235#4326—22no—
236#4325—22no—
237#4324—28no—
238#4324—22no—
239#4323—28no—
240#4323—22no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4—24no—
243C4⋊Dic11—24no—
244C4⋊Dic11—22no—
245C4⋊Dic11C2412yes—
246C4⋊Dic11C2414yes—
247Dic11⋊C4—22no—
248Dic11⋊C4—24no—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253C4×Dic11—22no—
254C4×Dic11—24no—
255C4×Dic11—21no—
256#4318—24no—
257C2×C11⋊C8—22no—
258C2×C11⋊C8—22no—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2414yes—
261C2×C11⋊C8C2411yescharacteristic
262C2×C11⋊C8C2411yescharacteristic
263#3508D1111yescharacteristic, complemented
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#2943—111no—
278C23×C11—24no—
279C23×C11—21no—
280C23×C11—44no—
281C23×C11—82no—
282C23×C11—82no—
283C23×C11C22×D411yescharacteristic
284C22×D11—21no—
285Q8×C11—21no—
286Q8×C11—21no—
287Q8×C11—44no—
288D4×C11—24no—
289D4×C11—21no—
290D4×C11—24no—
291D4×C11—21no—
292D4×C11—48no—
293D4×C11—42no—
294D4×C11—44no—
295D4×C11—84no—
296D4×C11—84no—
297D4×C11—84no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—42no—
301C2×C4×C11—44no—
302C2×C4×C11—42no—
303C2×C4×C11—84no—
304C2×C4×C11—84no—
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D414yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D414yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4112yes—
311C2×C4×C112−1+412yes—
312C2×C4×C11C2511yescharacteristic
313C22⋊D11—24no—
314C2×Dic11—21no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—82no—
318D44—21no—
319D44C2×#4112yes—
320C4×D11—24no—
321C4×D11—82no—
322C4×D11—84no—
323Dic22—21no—
324Dic22—84no—
325Dic22C2×#4112yes—
326C11⋊C8—21no—
327C11⋊C8—21no—
328C11⋊C8—24no—
329C11⋊C8—22no—
330C2×AGL(1,ℤ/8)—112no—
331C2×#135—111no—
332#559C2×D1114yes—
333#557—114no—
334#554—114no—
335#554—224no—
336#550C2×D1114yes—
337#546—24no—
338#544—112no—
339#544—222no—
340#540—21no—
341#540—21no—
342#535C2×D1112yes—
343#533—221no—
344#533C2×D1111yescharacteristic
345#532—22no—
346C2×#127C2×D1111yescharacteristic
347C2×#125—111no—
348C2×#125—221no—
349#520—112no—
350#518C2×D1112yes—
351C4×#41—111no—
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—112no—
374#442—114no—
375#441—112no—
376#440—112no—
377#440—112no—
378#440—114no—
379C4×SD16—114no—
380C4×D8—114no—
381#428—112no—
382#427—111no—
383#424—112no—
384#423—111no—
385#418—112no—
386#417—112no—
387#416—111no—
388#416—111no—
389C2×#102—112no—
390C2×#102—112no—
391#405—112no—
392C2×#97—111no—
393C22×C11—22no—
394C22×C11—42no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—41no—
398C22×C11—44no—
399C22×C11—164no—
400C22×C11#54812yes—
401C22×C11C23×D411yescharacteristic
402C2×D11—22no—
403C2×D11—42no—
404C4×C11—22no—
405C4×C11—22no—
406C4×C11—24no—
407C4×C11—24no—
408C4×C11—42no—
409C4×C11—41no—
410C4×C11#54812yes—
411C4×C11C22×#4111yescharacteristic
412C4×C11C2×2−1+411yescharacteristic
413Dic11—22no—
414Dic11—42no—
415Dic11—44no—
416C2×#41—24no—
417C2×#41—111no—
418C2×#41C22×D1111yescharacteristic
419C22×D4—22no—
420C22×D4C22×D1112yes—
421AGL(1,ℤ/8)—228no—
422#135—224no—
423C2×Q16—111no—
424C2×SD16—111no—
425C2×SD16—111no—
426C2×SD16—114no—
427C2×D8—111no—
428C2×D8—114no—
429C2×M16—112no—
430C22×C8—111no—
431C22×C8—111no—
432C4⋊Q8—114no—
433C4⋊Q8—224no—
434C4⋊Q8—222no—
435C4⋊Q8C22⋊D1112yes—
436#127—21no—
437#127—21no—
438#127C22×D1114yes—
439#127C22×D1114yes—
440#125—114no—
441#125—114no—
442#125—222no—
443#125—224no—
444#125—224no—
445#125—221no—
446#125—221no—
447#125C22⋊D1111yescharacteristic
448#125C22⋊D1111yescharacteristic
449#124—24no—
450#124C22×D1114yes—
451#123—24no—
452#123—24no—
453C22⋊Q8—224no—
454C22⋊Q8—224no—
455C22⋊Q8—224no—
456C22⋊Q8—224no—
457C22⋊Q8C22⋊D1114yes—
458#121—22no—
459#121—22no—
460#121—24no—
461#121—24no—
462#121—24no—
463#120—24no—
464C4×Q8—112no—
465C4×Q8—114no—
466C4×Q8—224no—
467C4×Q8C22×D1112yes—
468C4×Q8C22×D1114yes—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—22no—
472C4×D4—24no—
473C4×D4—112no—
474C4×D4—114no—
475C4×D4—222no—
476C4×D4—224no—
477C4×D4C22×D1112yes—
478C4×D4C22×D1114yes—
479C4×D4C22×D1114yes—
480#117—21no—
481#117—111no—
482#117—222no—
483#117—221no—
484#117C22×D1111yescharacteristic
485#117C22×D1112yes—
486C2×C4⋊C4—112no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—224no—
490C2×C22⋊C4—24no—
491C2×C42—21no—
492C2×C42—221no—
493C2×C42C22×D1111yescharacteristic
494#107—112no—
495#107—114no—
496#106—112no—
497#106—114no—
498C4⋊C8—114no—
499C4⋊C8—114no—
500C4⋊C8—114no—
501#103—112no—
502#103—114no—
503#103—112no—
504#102—114no—
505#102—114no—
506#102—114no—
507#102—114no—
508#102—112no—
509#102—114no—
510#102—114no—
511#102—114no—
512#102—112no—
513#97—112no—
514#97—112no—
515#97—114no—
516C4×C8—114no—
517C2×C11—22no—
518C2×C11—81no—
519C2×C11—84no—
520C2×C11C2×#54811yescharacteristic
521C2×C11#358512yes—
522D11—42no—
523C24—22no—
524#41—22no—
525#41—22no—
526#41—88no—
527#41—114no—
528#41—222no—
529C2×Q8—111no—
530C2×Q8—224no—
531C2×Q8C2×C22⋊D1114yes—
532C2×Q8C23×D1111yescharacteristic
533C2×D4—21no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—22no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—84no—
542C2×D4—111no—
543C2×D4—221no—
544C2×D4C23×D1114yes—
545C2×D4C23×D1111yescharacteristic
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—221no—
551C22×C4—222no—
552C22×C4—222no—
553C22×C4—224no—
554C22×C4C2×C22⋊D1112yes—
555C22×C4C23×D1111yescharacteristic
556Q16—222no—
557SD16—222no—
558SD16—228no—
559SD16—222no—
560D8—222no—
561D8—228no—
562M16—224no—
563C2×C8—112no—
564C2×C8—114no—
565C2×C8—111no—
566C2×C8—111no—
567C2×C8—222no—
568C2×C8—222no—
569C4⋊C4—22no—
570C4⋊C4—114no—
571C4⋊C4—112no—
572C4⋊C4—222no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—224no—
576C4⋊C4—224no—
577C4⋊C4—224no—
578C4⋊C4—222no—
579C4⋊C4—224no—
580C4⋊C4C2×C22⋊D1112yes—
581C4⋊C4C2×C22⋊D1114yes—
582C4⋊C4C2×C22⋊D1112yes—
583C4⋊C4C2×C22⋊D1114yes—
584C4⋊C4C2×C22⋊D1114yes—
585C4⋊C4C23×D1112yes—
586C22⋊C4—21no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C22⋊C4—22no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—221no—
593C22⋊C4—222no—
594C22⋊C4—224no—
595C22⋊C4C2×C22⋊D1114yes—
596C42—21no—
597C42—22no—
598C42—221no—
599C42—222no—
600C42—224no—
601C42C2×C22⋊D1111yescharacteristic
602C42C2×C22⋊D1111yescharacteristic
603C42C23×D1114yes—
604C42C23×D1112yes—
605C11#6133711yescharacteristic, complemented, Sylow
606C23—24no—
607C23—21no—
608C23—44no—
609C23—82no—
610C23—82no—
611C23—221no—
612C23C22×C22⋊D1111yescharacteristic
613Q8—21no—
614Q8—21no—
615Q8—44no—
616Q8—112no—
617Q8—221no—
618Q8—884no—
619D4—24no—
620D4—21no—
621D4—24no—
622D4—21no—
623D4—48no—
624D4—42no—
625D4—44no—
626D4—84no—
627D4—84no—
628D4—84no—
629D4—112no—
630D4—224no—
631D4—221no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—42no—
635C2×C4—44no—
636C2×C4—42no—
637C2×C4—84no—
638C2×C4—84no—
639C2×C4—221no—
640C2×C4—224no—
641C2×C4—222no—
642C2×C4—224no—
643C2×C4—882no—
644C2×C4—884no—
645C2×C4—882no—
646C2×C4#41×D1112yes—
647C2×C4#6704312yes—
648C2×C4C22×C22⋊D1112yes—
649C2×C4C22×C22⋊D1112yes—
650C2×C4C22×C22⋊D1114yes—
651C2×C4C22×C22⋊D1114yes—
652C2×C4C22×C22⋊D1111yescharacteristic
653C2×C4C24×D1111yescharacteristic
654C8—221no—
655C8—221no—
656C8—224no—
657C8—222no—
658C22—22no—
659C22—42no—
660C22—44no—
661C22—44no—
662C22—41no—
663C22—44no—
664C22—164no—
665C22—222no—
666C22—442no—
667C22#1062336212yes—
668C22C23×C22⋊D1111yescharacteristic
669C4—22no—
670C4—22no—
671C4—24no—
672C4—24no—
673C4—42no—
674C4—41no—
675C4—222no—
676C4—444no—
677C4—442no—
678C4#1062336212yes—
679C4C2×#41×D1111yescharacteristic
680C4C2×#6704311yescharacteristic
681C2—22no—
682C2—84no—
683C2—81no—
684C2—442no—
685C2C2×#1062336211yescharacteristic
686C2#1308339612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3508C2
socleC22×C11C23×D4
hypercenter#3508D11
hypocenterC11#61337
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13082437C2semidirect
2. #13081378C2semidirect
3. #13081363C2semidirect
4. #13081341C2semidirect
5. #13081319C2semidirect
6. #13078970C2semidirect
7. C2×#10622684C2semidirect
8. #13078447C2semidirect
9. #13078438C2semidirect
10. #13078151C2semidirect
11. #13078092C2semidirect
12. #13077557C2semidirect
13. #13077448C2semidirect
14. #13077414C2semidirect
15. C11×#3508C2semidirect
33. #10623110C22semidirect
34. #10623098C22semidirect
45. #10622688C22semidirect
47. #10622685C22semidirect
50. #10622684C22semidirect
51. #10622683C22semidirect
52. #10622670C22semidirect
53. #10622669C22semidirect
54. #10622668C22semidirect
55. #10622667C22semidirect
56. #10622643C22semidirect
57. #10622639C22semidirect
58. #10622637C22semidirect
59. #10622637C22semidirect
60. #10622635C22semidirect
61. #10622631C22semidirect
62. #10622631C22semidirect
63. C4×#4324C22semidirect
64. #10622627C22semidirect
65. #10622627C22semidirect
66. C4×#4323C22semidirect
67. #10622622C22semidirect
68. #10622622C22semidirect
69. #10622622C22semidirect
70. #10622621C22semidirect
71. #10622620C22semidirect
207. #4339#41semidirect
263. #3508D11semidirect
605. C11#61337semidirect

Maximal subgroups

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

subgroupindex
#130824372
#130813782
#130813632
#130813412
#130813192
#130789702
C2×#106226842
#130784472
#130784382
#130781512
#130780922
#130775572
#130774482
#130774142
C11×#35082
#6133711