Finite Group Databasebeta

← #15638529

Subgroups — #15638529

Order 2816.

2142 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#13082468C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13080545C214yesmaximal, complemented
4#13080534C214yesmaximal, complemented
5#13080348C214yesmaximal, complemented
6#13080338C214yesmaximal, complemented
7#13079566C211yesmaximal, characteristic, complemented
8#13079543C211yesmaximal, characteristic, complemented
9#13079399C214yesmaximal, complemented
10#13078625C211yesmaximal, characteristic, complemented
11#13078617C211yesmaximal, characteristic, complemented
12#13077838C214yesmaximal, complemented
13C11×#2972C211yesmaximal, characteristic, complemented
14C22×#4339C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16#10623336—21no—
17C2×#66991—21no—
18#10623322C2214yes—
19C2×#66977C2212yes—
20C2×#66957C2218yescomplemented
21#10623094C2212yescomplemented
22#10623090—22no—
23#10623089—22no—
24#10623084C2212yescomplemented
25#10623082—22no—
26#10623082—22no—
27#10623082C2214yes—
28#10623082C2214yes—
29#10623082C2212yescomplemented
30#10623073C2212yescomplemented
31#10623035—21no—
32C2×C4⋊C4×D11—21no—
33#10623025—22no—
34C2×#66936—22no—
35#10623008C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37#10623001C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C8×D4×C11C2214yescomplemented
40C8×D4×C11C2214yescomplemented
41C11×#431C2211yescharacteristic
42C11×#431C2211yescharacteristic
43C2×C11×C22⋊C8C2214yes—
44#10622729C2218yescomplemented
45#10622727C2218yescomplemented
46#10622726C2218yescomplemented
47#10622462C2214yescomplemented
48#10622459C2212yescomplemented
49#10622456C2212yescomplemented
50#10622455C2212yescomplemented
51#10622454C2212yescomplemented
52#10622454C2214yescomplemented
53#10622352C2214yes—
54#10622351C2214yes—
55#10622349C2212yes—
56#10622347C2218yescomplemented
57#10622346C2218yescomplemented
58#10622346C2218yescomplemented
59#10622345C2212yes—
60#10622344C2212yes—
61#10622336C2218yescomplemented
62#10622334C2212yes—
63#10622312C2212yescomplemented
64#10622306C2212yescomplemented
65C4×D88C2214yescomplemented
66C4×#4314C2214yescomplemented
67#10622294C2212yescomplemented
68#10622294C2212yescomplemented
69C22×D4×C11D411yescharacteristic
70C23×C4×C11C2312yes—
71C22×C22⋊D11—22no—
72C2×#4339—21no—
73C2×#4339—24no—
74C2×#4339—48no—
75C2×#4339C2318yes—
76C2×#4339C2314yes—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×C4×D11—22no—
80C22×Dic22C2312yes—
81C22×C8×C11C2318yes—
82C4×D4×C11D412yes—
83C4×D4×C11D412yes—
84C4×D4×C11C2312yes—
85C4×D4×C11C2312yes—
86C2×C11×C4⋊C4D411yescharacteristic
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11C2311yescharacteristic
89#67006—24no—
90C2×C22⋊Dic11—22no—
91#66993—22no—
92#66991—24no—
93#66991—24no—
94#66991—22no—
95#66991—22no—
96#66989—22no—
97#66983—21no—
98#66983C2314yes—
99#66983C2312yes—
100#66982—24no—
101C4×C22⋊D11—24no—
102C4×C22⋊D11—24no—
103C2×(C2×D11)⋊C4—21no—
104#66979—21no—
105#66979C2314yes—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11C2311yescharacteristic
109#66977—21no—
110#66977—24no—
111#66977C2318yes—
112#66977C2314yes—
113#66977C2312yes—
114C2×Dic11⋊C4—22no—
115C2×Dic44C2318yes—
116#66957—416no—
117C2×D88C2314yes—
118C2×#4314C2314yes—
119C2×#4314C2318yes—
120#66946—22no—
121#66945—22no—
122C4⋊C4×D11—24no—
123C4⋊C4×D11—24no—
124C4⋊C4×D11—22no—
125#66940—22no—
126#66938—24no—
127#66937—24no—
128#66936—28no—
129#66936—28no—
130#66936—24no—
131#66932—24no—
132#66928—21no—
133#66927C2311yescharacteristic
134C4×D44—21no—
135C4×D44—21no—
136C4×D44—21no—
137C4×D44C2312yes—
138C4×D44C2312yes—
139C4×D44C2312yes—
140#66923—21no—
141#66922—21no—
142#66922—21no—
143#66922C2312yes—
144#66922C2312yes—
145#66922C2311yescharacteristic
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22C2312yes—
150C11×C4⋊C8C2312yes—
151C11×C4⋊C8C2312yes—
152C11×C22⋊C8C2312yes—
153C11×C22⋊C8C2318yes—
154C11×C22⋊C8C2312yes—
155C4×C8×C11C2312yes—
156C4×C8×C11C2312yes—
157#66885C2314yes—
158#66885C2314yes—
159#66885C2314yes—
160#66882C2314yes—
161#66881C2314yes—
162#66880C2318yes—
163#66880C2318yes—
164#66880C2314yes—
165#61565—111nomaximal, Sylow
166C24×C11C2×D412yes—
167C23×D11—21no—
168C2×D4×C11—24no—
169C2×D4×C11C2×D412yes—
170C2×D4×C11C2×D412yes—
171C22×C4×C11—44no—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×C4×C11C2414yes—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—22no—
180C2×C22⋊D11—24no—
181C2×C22⋊D11—24no—
182C2×C22⋊D11—48no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185#4339—216no—
186#4339—48no—
187#4339—48no—
188#4339—416no—
189#4339—44no—
190C2×D44—24no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44—21no—
194C2×D44C2412yes—
195C2×D44C2412yes—
196C2×C4×D11—22no—
197C2×C4×D11—22no—
198C2×C4×D11—22no—
199C2×C4×D11—28no—
200C2×C4×D11—24no—
201C2×C4×D11—48no—
202C2×C4×D11—44no—
203C2×Dic22—22no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—44no—
207C2×Dic22C2414yes—
208C2×Dic22C2412yes—
209C2×C8×C11—48no—
210C2×C8×C11C2414yes—
211C2×C8×C11C2414yes—
212C11×C4⋊C4C2×D412yes—
213C11×C4⋊C4C2×D412yes—
214C11×C22⋊C4C2×D414yes—
215C11×C22⋊C4C2×D414yes—
216C42×C11C2×D411yescharacteristic
217C42×C11C2×D411yescharacteristic
218C42×C11C2411yescharacteristic
219C42×C11C2411yescharacteristic
220C22⋊Dic11—24no—
221C22⋊Dic11—24no—
222C22⋊Dic11—28no—
223C22⋊Dic11—22no—
224(C2×D11)⋊C4—22no—
225(C2×D11)⋊C4—22no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—24no—
229C4⋊Dic11—21no—
230C4⋊Dic11—22no—
231C4⋊Dic11—22no—
232C4⋊Dic11—22no—
233C4⋊Dic11—22no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11C2412yes—
239C4⋊Dic11C2412yes—
240C4⋊Dic11C2412yes—
241Dic11⋊C4—22no—
242Dic11⋊C4—22no—
243Dic11⋊C4—24no—
244Dic11⋊C4—28no—
245C4×Dic11—22no—
246C4×Dic11—24no—
247Dic44—48no—
248D88—28no—
249#4314—28no—
250#4314—48no—
251#3506—111no—
252C2×#547—111no—
253#3303—114no—
254#3302—114no—
255#3284—114no—
256#3283—114no—
257#3209—111no—
258#3206—111no—
259#3190—114no—
260#3101—111no—
261#3100—111no—
262#3002—114no—
263#2972D1111yescharacteristic, complemented
264C23×C11—24no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11C22×D414yes—
268C23×C11C22×D411yescharacteristic
269C22×D11—24no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—42no—
273C22×D11—42no—
274D4×C11—24no—
275D4×C11—24no—
276C2×C4×C11—28no—
277C2×C4×C11—22no—
278C2×C4×C11—42no—
279C2×C4×C11—44no—
280C2×C4×C11—41no—
281C2×C4×C11#13514yescomplemented
282C2×C4×C11C22×D414yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2511yescharacteristic
289C22⋊D11—416no—
290C22⋊D11—44no—
291C22⋊D11—84no—
292C22⋊D11—84no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—24no—
298C2×Dic11—44no—
299C2×Dic11—42no—
300D44—24no—
301D44—22no—
302D44—24no—
303D44—42no—
304D44—81no—
305D44H(5,𝔽2)14yes—
306C4×D11—416no—
307C4×D11—44no—
308C4×D11—44no—
309C4×D11—44no—
310C4×D11—84no—
311Dic22—24no—
312Dic22—28no—
313Dic22—44no—
314Dic22—42no—
315Dic22—81no—
316C8×C11—24no—
317C8×C11—24no—
318C22×#41—112no—
319C2×#135—118no—
320#559—222no—
321#556—112no—
322#555—112no—
323#553—222no—
324#550—112no—
325#547—114no—
326#547—114no—
327#547—112no—
328#547—222no—
329#547—222no—
330#538—222no—
331#535—221no—
332#533—111no—
333#532—111no—
334C2×C4⋊Q8—111no—
335#525—114no—
336C2×#123—222no—
337C2×C22⋊Q8—112no—
338C2×#121—221no—
339#520—221no—
340C2×C4×D4—111no—
341C2×C4×D4C2×D1111yescharacteristic
342C22×C4⋊C4—221no—
343#494—112no—
344#492—112no—
345#487—112no—
346#487—112no—
347#485—118no—
348#483—112no—
349#480—112no—
350#476—112no—
351#474—112no—
352#467—118no—
353#465—118no—
354#462—114no—
355#461—112no—
356#461—114no—
357#459—112no—
358#452—118no—
359#452—118no—
360#451—114no—
361#450—112no—
362#449—118no—
363#448—114no—
364#447—112no—
365C4×SD16—114no—
366C4×D8—114no—
367C8×D4C2×D1114yescomplemented
368C8×D4C2×D1114yescomplemented
369#431C2×D1111yescharacteristic
370#431C2×D1111yescharacteristic
371#416—118no—
372C2×C22⋊C8C2×D1114yes—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—84no—
379C22×C11C2×#13512yes—
380C22×C11C23×D411yescharacteristic
381C2×D11—24no—
382C2×D11—48no—
383C2×D11—42no—
384C2×D11—42no—
385C2×D11—42no—
386C2×D11—42no—
387C2×D11—42no—
388C4×C11—21no—
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—24no—
392C4×C11C2×#13512yes—
393C4×C11C2×#13512yes—
394C4×C11C2×H(5,𝔽2)12yes—
395Dic11—42no—
396Dic11—44no—
397Dic11—42no—
398Dic11—42no—
399Dic11—42no—
400C2×#41—118no—
401C2×#41—114no—
402C2×#41—221no—
403C2×#41—224no—
404C2×#41—448no—
405C22×Q8—112no—
406C22×D4—111no—
407C22×D4—222no—
408C22×D4D4411yescharacteristic
409C23×C4—221no—
410C23×C4—222no—
411C23×C4C22×D1112yes—
412#135—4416no—
413C2×Q16—118no—
414C2×SD16—114no—
415C2×SD16—118no—
416C2×D8—114no—
417C22×C8C22×D1118yes—
418C4⋊Q8—111no—
419C4⋊Q8—111no—
420C4⋊Q8—112no—
421C4⋊Q8—112no—
422C4⋊Q8—111no—
423C4⋊Q8—221no—
424C4⋊Q8—221no—
425#127—111no—
426#127—222no—
427#126—224no—
428#125—221no—
429#124—222no—
430#124—224no—
431#124—221no—
432#123—224no—
433#123—228no—
434#123—228no—
435#123—224no—
436C22⋊Q8—118no—
437C22⋊Q8—112no—
438C22⋊Q8—114no—
439C22⋊Q8—224no—
440C22⋊Q8—221no—
441#121—112no—
442#121—114no—
443#121—224no—
444#121—224no—
445#121—222no—
446#121—222no—
447#121—221no—
448#121—224no—
449#120—224no—
450C4×Q8—112no—
451C4×Q8—222no—
452C4×Q8—221no—
453C4×D4—112no—
454C4×D4—112no—
455C4×D4—112no—
456C4×D4—224no—
457C4×D4—224no—
458C4×D4—222no—
459C4×D4—221no—
460C4×D4—221no—
461C4×D4—221no—
462C4×D4D4412yes—
463C4×D4D4412yes—
464C4×D4C22×D1112yes—
465C4×D4C22×D1112yes—
466#117—114no—
467#117—221no—
468#117—222no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—222no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—224no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—222no—
476C2×C4⋊C4D4411yescharacteristic
477C2×C22⋊C4—222no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4D4412yes—
480C2×C42C22×D1111yescharacteristic
481#107—114no—
482#106—114no—
483C4⋊C8C22×D1112yes—
484C4⋊C8C22×D1112yes—
485#103—118no—
486#103—118no—
487#103—114no—
488#102—114no—
489#102—114no—
490#102—114no—
491C22⋊C8C22×D1112yes—
492C22⋊C8C22×D1112yes—
493C22⋊C8C22×D1118yes—
494C4×C8C22×D1112yes—
495C4×C8C22×D1112yes—
496C2×C11—22no—
497C2×C11—44no—
498C2×C11#348411yescharacteristic
499C2×C11C22×#13511yescharacteristic
500C2×C11#358611yescharacteristic
501D11—44no—
502D11—82no—
503C24—221no—
504C24C2×D4412yes—
505#41—2216no—
506#41—448no—
507#41—448no—
508#41—4416no—
509#41—444no—
510C2×Q8—114no—
511C2×Q8—112no—
512C2×Q8—221no—
513C2×Q8—222no—
514C2×Q8—221no—
515C2×Q8—444no—
516C2×D4—24no—
517C2×D4—112no—
518C2×D4—112no—
519C2×D4—224no—
520C2×D4—222no—
521C2×D4—228no—
522C2×D4—224no—
523C2×D4—224no—
524C2×D4—221no—
525C2×D4—221no—
526C2×D4—221no—
527C2×D4—448no—
528C2×D4C2×D4412yes—
529C2×D4C2×D4412yes—
530C22×C4—44no—
531C22×C4—221no—
532C22×C4—222no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—228no—
536C22×C4—222no—
537C22×C4—224no—
538C22×C4—448no—
539C22×C4—444no—
540C22×C4C2×D4411yescharacteristic
541C22×C4C2×D4412yes—
542C22×C4C2×D4414yes—
543C22×C4C2×D4411yescharacteristic
544C22×C4C23×D1111yescharacteristic
545C22×C4C23×D1114yes—
546Q16—448no—
547SD16—228no—
548SD16—448no—
549D8—228no—
550C2×C8—48no—
551C2×C8C23×D1114yes—
552C2×C8C23×D1114yes—
553C4⋊C4—112no—
554C4⋊C4—112no—
555C4⋊C4—112no—
556C4⋊C4—221no—
557C4⋊C4—222no—
558C4⋊C4—222no—
559C4⋊C4—228no—
560C4⋊C4—221no—
561C4⋊C4—224no—
562C4⋊C4—222no—
563C4⋊C4—222no—
564C4⋊C4—221no—
565C4⋊C4—222no—
566C4⋊C4—221no—
567C4⋊C4—222no—
568C4⋊C4—221no—
569C4⋊C4C2×D4412yes—
570C4⋊C4C2×D4412yes—
571C22⋊C4—228no—
572C22⋊C4—224no—
573C22⋊C4—222no—
574C22⋊C4—224no—
575C22⋊C4—222no—
576C22⋊C4—222no—
577C22⋊C4—224no—
578C22⋊C4—222no—
579C22⋊C4—222no—
580C22⋊C4C2×D4414yes—
581C22⋊C4C2×D4414yes—
582C42—224no—
583C42—222no—
584C42C2×D4411yescharacteristic
585C42C2×D4411yescharacteristic
586C42C23×D1111yescharacteristic
587C42C23×D1111yescharacteristic
588C11#6156511yescharacteristic, complemented, Sylow
589C23—24no—
590C23—42no—
591C23—42no—
592C23—224no—
593C23—222no—
594C23—222no—
595C23—442no—
596C23—442no—
597C23C22×D4414yes—
598C23C22×D4411yescharacteristic
599Q8—224no—
600Q8—228no—
601Q8—444no—
602Q8—442no—
603Q8—881no—
604D4—24no—
605D4—24no—
606D4—114no—
607D4—224no—
608D4—222no—
609D4—224no—
610D4—4416no—
611D4—444no—
612D4—442no—
613D4—881no—
614D4—884no—
615D4—884no—
616C2×C4—28no—
617C2×C4—22no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—41no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—224no—
626C2×C4—4416no—
627C2×C4—444no—
628C2×C4—442no—
629C2×C4—444no—
630C2×C4—444no—
631C2×C4—444no—
632C2×C4—884no—
633C2×C4#6695714yescomplemented
634C2×C4C22×D4414yes—
635C2×C4C22×D4411yescharacteristic
636C2×C4C22×D4411yescharacteristic
637C2×C4C22×D4411yescharacteristic
638C2×C4C22×D4411yescharacteristic
639C2×C4C22×D4411yescharacteristic
640C2×C4C24×D1111yescharacteristic
641C8—24no—
642C8—24no—
643C22—21no—
644C22—21no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—84no—
649C22—224no—
650C22—448no—
651C22—442no—
652C22—442no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22C2×#6695712yes—
657C22C23×D4411yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—24no—
662C4—442no—
663C4—444no—
664C4—442no—
665C4—442no—
666C4—442no—
667C4C2×#6695712yes—
668C4C2×#6695712yes—
669C4D11×H(5,𝔽2)12yes—
670C2—22no—
671C2—44no—
672C2—444no—
673C2—882no—
674C2#1308225211yescharacteristic
675C2C22×#6695711yescharacteristic
676C2#1308340411yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2972C2
socleC22×C11C23×D4
hypercenter#2972D11
hypocenterC11#61565
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13082468C2semidirect
2. C2×#10623082C2semidirect
3. #13080545C2semidirect
4. #13080534C2semidirect
5. #13080348C2semidirect
6. #13080338C2semidirect
7. #13079566C2semidirect
8. #13079543C2semidirect
9. #13079399C2semidirect
10. #13078625C2semidirect
11. #13078617C2semidirect
12. #13077838C2semidirect
13. C11×#2972C2semidirect
20. C2×#66957C22semidirect
21. #10623094C22semidirect
24. #10623084C22semidirect
29. #10623082C22semidirect
30. #10623073C22semidirect
39. C8×D4×C11C22semidirect
40. C8×D4×C11C22semidirect
44. #10622729C22semidirect
45. #10622727C22semidirect
46. #10622726C22semidirect
47. #10622462C22semidirect
48. #10622459C22semidirect
49. #10622456C22semidirect
50. #10622455C22semidirect
51. #10622454C22semidirect
52. #10622454C22semidirect
56. #10622347C22semidirect
57. #10622346C22semidirect
58. #10622346C22semidirect
61. #10622336C22semidirect
63. #10622312C22semidirect
64. #10622306C22semidirect
65. C4×D88C22semidirect
66. C4×#4314C22semidirect
67. #10622294C22semidirect
68. #10622294C22semidirect
263. #2972D11semidirect
281. C2×C4×C11#135semidirect
367. C8×D4C2×D11semidirect
368. C8×D4C2×D11semidirect
588. C11#61565semidirect
633. C2×C4#66957semidirect

Maximal subgroups

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

subgroupindex
#130824682
C2×#106230822
#130805452
#130805342
#130803482
#130803382
#130795662
#130795432
#130793992
#130786252
#130786172
#130778382
C11×#29722
#6156511