Finite Group Databasebeta

← #15625306

Subgroups — #15625306

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#13082006C211yesmaximal, characteristic, complemented
2#13079725C218yesmaximal, complemented
3#13079699C214yesmaximal, complemented
4#13079677C214yesmaximal, complemented
5#13079080C211yesmaximal, characteristic, complemented
6#13079073C211yesmaximal, characteristic, complemented
7#13079002C211yesmaximal, characteristic, complemented
8#13078996C211yesmaximal, characteristic, complemented
9#13078106C212yesmaximal, complemented
10#13078099C212yesmaximal, complemented
11#13077858C212yesmaximal, complemented
12#13077850C212yesmaximal, complemented
13#13077254C211yesmaximal, characteristic, complemented
14C2×C11×#536C211yesmaximal, characteristic, complemented
15C22×C11×#41C2211yescharacteristic
16C23×Q8×C11C2211yescharacteristic
17C11×#536—24no—
18C11×#536C2214yes—
19C11×#536C2214yes—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×#123—22no—
25C2×C11×C22⋊Q8—22no—
26C2×C11×#117C2211yescharacteristic
27C2×#66995C2212yes—
28C2×#66995C2212yes—
29C2×#66995C2212yes—
30C2×#66985C2212yes—
31#10623322C2212yes—
32#10623066C2212yescomplemented
33#10623065C2214yescomplemented
34#10623059—24no—
35#10623049C2212yescomplemented
36#10623046—22no—
37#10623025—22no—
38#10623008C2211yescharacteristic
39C4×#4339C2212yes—
40#10623001C2211yescharacteristic
41#10622852C2218yes—
42#10622851C2218yes—
43#10622841C2218yescomplemented
44#10622840C2218yescomplemented
45#10622838C2212yes—
46#10622838C2212yes—
47#10622838C2212yes—
48#10622828C2212yes—
49#10622820C2212yes—
50#10622705C2212yescomplemented
51#10622703C2218yescomplemented
52#10622699C2214yescomplemented
53#10622698C2212yescomplemented
54#10622696C2218yescomplemented
55#10622695C2214yescomplemented
56#10622694C2214yescomplemented
57#10622673C2212yescomplemented
58#10622672C2214yescomplemented
59#10622671C2212yescomplemented
60#10622670C2218yescomplemented
61#10622669C2214yescomplemented
62#10622668C2214yescomplemented
63#10622667C2218yescomplemented
64#10622613C2214yescomplemented
65#10622613C2214yescomplemented
66#10622537C2212yes—
67C4×#4318C2211yescharacteristic
68C4×#4318C2211yescharacteristic
69C2×C11×#41—22no—
70C2×C11×#41—44no—
71C2×C11×#41C2314yes—
72C22×Q8×C11—21no—
73C22×Q8×C11—22no—
74C22×Q8×C11—44no—
75C22×Q8×C11C2311yescharacteristic
76C22×Q8×C11C2311yescharacteristic
77C22×Q8×C11C2311yescharacteristic
78C22×Q8×C11C2314yes—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C23×C4×C11—21no—
83C23×C4×C11C2311yescharacteristic
84C2×#4339C2312yes—
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8—22no—
87C11×C4⋊Q8C2312yes—
88C11×C4⋊Q8C2312yes—
89C11×C4⋊Q8C2314yes—
90C11×#124—22no—
91C11×#124—22no—
92C11×#124C2314yes—
93C11×#124C2312yes—
94C11×#124C2312yes—
95C11×#123—28no—
96C11×#123—28no—
97C11×C22⋊Q8—28no—
98C11×C22⋊Q8—28no—
99C11×#117D414yes—
100C11×#117C2312yes—
101C11×#117C2312yes—
102C2×C11×C4⋊C4—22no—
103C2×C11×C4⋊C4—22no—
104C2×C11×C4⋊C4D412yes—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4D412yes—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110#67006—22no—
111C2×#4326C2314yes—
112C2×#4326C2314yes—
113C2×#4326C2314yes—
114#66995—44no—
115#66995—44no—
116#66995—44no—
117C2×#4325C2314yes—
118C2×#4325C2314yes—
119C2×#4325C2314yes—
120C2×#4324C2314yes—
121#66985—44no—
122C2×#4323C2314yes—
123#66983—22no—
124#66983C2314yes—
125#66982—22no—
126C4×C22⋊D11—24no—
127C4×C22⋊D11—24no—
128#66979C2312yes—
129#66977—22no—
130#66977C2314yes—
131C2×#4318C2312yes—
132C2×#4318C2312yes—
133#66951—24no—
134#66949—24no—
135#66947—24no—
136#66942—24no—
137#66938—24no—
138#66937—24no—
139#66936—24no—
140#66932—24no—
141#66928C2312yes—
142#66927C2311yescharacteristic
143C4×D44—22no—
144C4×D44C2314yes—
145#66925—22no—
146C42×D11—22no—
147#66923C2312yes—
148#66922C2311yescharacteristic
149#66922C2312yes—
150C4×Dic22—22no—
151C4×Dic22C2314yes—
152#66899C2318yes—
153#66899C2318yes—
154#66899C2318yes—
155#66896C2318yes—
156C22⋊(C11⋊C8)C2318yes—
157C4⋊(C11⋊C8)C2318yes—
158#66867C2312yes—
159#66867C2312yes—
160C4×C11⋊C8C2312yes—
161C4×C11⋊C8C2312yes—
162#60807—111nomaximal, Sylow
163C24×C11—21no—
164C24×C11C2×D411yescharacteristic
165C11×#41—48no—
166C11×#41—48no—
167C2×Q8×C11—24no—
168C2×Q8×C11—21no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—24no—
172C2×Q8×C11—24no—
173C2×Q8×C11—24no—
174C2×Q8×C11—48no—
175C2×Q8×C11—44no—
176C2×Q8×C11—48no—
177C2×Q8×C11C2412yes—
178C2×Q8×C11C2412yes—
179C2×Q8×C11C2412yes—
180C2×D4×C11—24no—
181C2×D4×C11—21no—
182C2×D4×C11—24no—
183C2×D4×C11—44no—
184C2×D4×C11C2412yes—
185C22×C4×C11—24no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—24no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11C2×D412yes—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—22no—
200C2×C22⋊D11—24no—
201#4339—24no—
202#4339—24no—
203C2×D44—22no—
204C2×D44C2412yes—
205C2×C4×D11—22no—
206C2×C4×D11—24no—
207C2×Dic22—22no—
208C2×Dic22C2412yes—
209C11×C4⋊C4—28no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4C2×D414yes—
213C11×C4⋊C4C2×D414yes—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4C2×D414yes—
218C11×C22⋊C4C2×D414yes—
219C42×C11C2×D412yes—
220C42×C11C2×D412yes—
221C42×C11C2411yescharacteristic
222C42×C11C2411yescharacteristic
223C42×C11C2412yes—
224C22⋊Dic11—24no—
225C22⋊Dic11—22no—
226#4326—44no—
227#4326—44no—
228#4326—44no—
229#4325—44no—
230#4325—44no—
231#4325—44no—
232#4324—44no—
233#4323—44no—
234(C2×D11)⋊C4—24no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—24no—
237C4⋊Dic11—22no—
238C4⋊Dic11—22no—
239C4⋊Dic11C2414yes—
240Dic11⋊C4—24no—
241Dic11⋊C4—24no—
242Dic11⋊C4—24no—
243C4×Dic11—22no—
244C4×Dic11—24no—
245#4318—24no—
246#4318—24no—
247C2×C11⋊C8C2414yes—
248C2×C11⋊C8C2414yes—
249#3455—111no—
250C2×#536D1111yescharacteristic, complemented
251#3225—118no—
252#3223—114no—
253#3221—114no—
254#3153—111no—
255#3152—111no—
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×C11—22no—
265C23×C11—42no—
266C23×C11—44no—
267C23×C11—42no—
268C23×C11C22×D412yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271Q8×C11—24no—
272Q8×C11—24no—
273Q8×C11—24no—
274Q8×C11—48no—
275Q8×C11—42no—
276Q8×C11—42no—
277Q8×C11—42no—
278D4×C11—24no—
279D4×C11—48no—
280D4×C11—42no—
281C2×C4×C11—22no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—48no—
290C2×C4×C11—48no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11C22×D414yes—
295C2×C4×C11C22×D412yes—
296C2×C4×C11C22×D412yes—
297C2×C4×C11C22×D412yes—
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11H(5,𝔽2)14yes—
300C2×C4×C11C2511yescharacteristic
301C22⋊D11—44no—
302C22⋊D11—84no—
303C2×Dic11—22no—
304C2×Dic11—24no—
305D44—22no—
306D44—22no—
307D44—82no—
308C4×D11—44no—
309C4×D11—84no—
310Dic22—22no—
311Dic22—22no—
312Dic22—82no—
313C11⋊C8—24no—
314C11⋊C8—24no—
315C22×#41C2×D1111yescharacteristic
316C23×Q8C2×D1111yescharacteristic
317C2×#137—112no—
318C2×#137—112no—
319C2×#137—112no—
320C2×AGL(1,ℤ/8)—112no—
321#542—114no—
322#541—112no—
323#540—112no—
324#539—222no—
325#538—222no—
326#536—24no—
327#536C2×D1114yes—
328#536C2×D1114yes—
329#533—111no—
330#532—111no—
331C2×C4⋊Q8C2×D1111yescharacteristic
332C2×C4⋊Q8C2×D1111yescharacteristic
333#529—224no—
334C2×#124C2×D1111yescharacteristic
335C2×#124C2×D1111yescharacteristic
336#525—112no—
337C2×#123—22no—
338C2×C22⋊Q8—22no—
339C4×#41—112no—
340C2×#117C2×D1111yescharacteristic
341#497—114no—
342#497—112no—
343#496—112no—
344#495—114no—
345#494—112no—
346#492—112no—
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×M16—111no—
369C22×C11—22no—
370C22×C11—24no—
371C22×C11—22no—
372C22×C11—44no—
373C22×C11—44no—
374C22×C11—42no—
375C22×C11—84no—
376C22×C11#53512yes—
377C22×C11C23×D411yescharacteristic
378C2×D11—44no—
379C2×D11—42no—
380C4×C11—22no—
381C4×C11—24no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—42no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11#53512yes—
388C4×C11C2×H(5,𝔽2)12yes—
389Dic11—44no—
390Dic11—42no—
391C2×#41—22no—
392C2×#41—44no—
393C2×#41—112no—
394C2×#41C22×D1114yes—
395C22×Q8—21no—
396C22×Q8—22no—
397C22×Q8—44no—
398C22×Q8C22×D1111yescharacteristic
399C22×Q8C22×D1111yescharacteristic
400C22×Q8C22×D1111yescharacteristic
401C22×Q8C22×D1114yes—
402C22×D4—21no—
403C22×D4C22×D1111yescharacteristic
404C23×C4—21no—
405C23×C4—21no—
406C23×C4C22×D1111yescharacteristic
407#137—444no—
408#137—444no—
409#137—444no—
410AGL(1,ℤ/8)—444no—
411C2×Q16—114no—
412C2×Q16—114no—
413C2×Q16—114no—
414C2×SD16—114no—
415C2×SD16—114no—
416C2×SD16—114no—
417C2×SD16—114no—
418C2×D8—114no—
419C2×M16—112no—
420C2×M16—112no—
421C4⋊Q8—22no—
422C4⋊Q8—22no—
423C4⋊Q8—112no—
424C4⋊Q8—111no—
425C4⋊Q8C22×D1114yes—
426C4⋊Q8C22×D1112yes—
427C4⋊Q8C22×D1112yes—
428#127—111no—
429#126—224no—
430#126—224no—
431#125—112no—
432#125—224no—
433#124—22no—
434#124—22no—
435#124—112no—
436#124—224no—
437#124C22×D1114yes—
438#124C22×D1112yes—
439#124C22×D1112yes—
440#123—28no—
441#123—28no—
442#123—222no—
443#123—224no—
444#123—224no—
445C22⋊Q8—28no—
446C22⋊Q8—28no—
447C22⋊Q8—114no—
448C22⋊Q8—222no—
449C22⋊Q8—224no—
450#121—114no—
451#121—222no—
452#121—224no—
453#120—222no—
454C4×Q8—114no—
455C4×Q8—222no—
456C4×D4—114no—
457C4×D4—224no—
458C4×D4—224no—
459C4×D4—222no—
460#117—112no—
461#117—222no—
462#117C22⋊D1114yes—
463#117C22×D1112yes—
464#117C22×D1112yes—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4C22⋊D1112yes—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4C22⋊D1112yes—
471C2×C42—222no—
472C2×C42C22×D1111yescharacteristic
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#97—112no—
482C4×C8—112no—
483C4×C8—112no—
484C2×C11—22no—
485C2×C11—42no—
486C2×C11—82no—
487C2×C11C2×#53511yescharacteristic
488C2×C11#358612yes—
489D11—82no—
490C24—21no—
491C24C2×C22⋊D1111yescharacteristic
492#41—48no—
493#41—48no—
494#41—224no—
495#41—224no—
496C2×Q8—24no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—24no—
501C2×Q8—24no—
502C2×Q8—24no—
503C2×Q8—48no—
504C2×Q8—44no—
505C2×Q8—48no—
506C2×Q8—112no—
507C2×Q8—222no—
508C2×Q8C23×D1112yes—
509C2×Q8C23×D1112yes—
510C2×Q8C23×D1112yes—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—21no—
514C2×D4—44no—
515C2×D4—112no—
516C2×D4—222no—
517C2×D4—224no—
518C2×D4—222no—
519C2×D4C23×D1112yes—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—222no—
529C22×C4—224no—
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1112yes—
532C22×C4C2×C22⋊D1112yes—
533C22×C4C2×C22⋊D1112yes—
534C22×C4C23×D1112yes—
535C22×C4C23×D1111yescharacteristic
536Q16—444no—
537Q16—444no—
538Q16—444no—
539SD16—444no—
540SD16—444no—
541SD16—444no—
542SD16—444no—
543D8—444no—
544M16—224no—
545M16—224no—
546C2×C8—114no—
547C2×C8—114no—
548C4⋊C4—28no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—114no—
552C4⋊C4—224no—
553C4⋊C4—222no—
554C4⋊C4—224no—
555C4⋊C4—224no—
556C4⋊C4—222no—
557C4⋊C4C2×C22⋊D1114yes—
558C4⋊C4C2×C22⋊D1114yes—
559C22⋊C4—28no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—222no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—224no—
567C22⋊C4C2×C22⋊D1114yes—
568C22⋊C4C2×C22⋊D1114yes—
569C42—222no—
570C42—224no—
571C42C2×C22⋊D1112yes—
572C42C2×C22⋊D1112yes—
573C42C23×D1111yescharacteristic
574C42C23×D1111yescharacteristic
575C42C23×D1112yes—
576C11#6080711yescharacteristic, complemented, Sylow
577C23—22no—
578C23—22no—
579C23—42no—
580C23—44no—
581C23—42no—
582C23—222no—
583C23C22×C22⋊D1112yes—
584C23C22×C22⋊D1111yescharacteristic
585Q8—24no—
586Q8—24no—
587Q8—24no—
588Q8—48no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592Q8—222no—
593Q8—222no—
594Q8—882no—
595D4—24no—
596D4—48no—
597D4—42no—
598D4—222no—
599D4—222no—
600D4—444no—
601D4—882no—
602D4—884no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—48no—
612C2×C4—48no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—444no—
619C2×C4—884no—
620C2×C4#6703714yes—
621C2×C4C22×C22⋊D1114yes—
622C2×C4C22×C22⋊D1112yes—
623C2×C4C22×C22⋊D1112yes—
624C2×C4C22×C22⋊D1112yes—
625C2×C4C22×C22⋊D1111yescharacteristic
626C2×C4C24×D1111yescharacteristic
627C8—224no—
628C8—224no—
629C22—22no—
630C22—24no—
631C22—22no—
632C22—44no—
633C22—44no—
634C22—42no—
635C22—84no—
636C22—444no—
637C22—442no—
638C22#1062333612yes—
639C22C23×C22⋊D1111yescharacteristic
640C4—24no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—444no—
648C4—442no—
649C4#1062333612yes—
650C4C2×#6703712yes—
651C2—22no—
652C2—42no—
653C2—82no—
654C2—882no—
655C2C2×#1062333611yescharacteristic
656C2#1308340312yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#536C2
socleC22×C11C23×D4
hypercenterC2×#536D11
hypocenterC11#60807
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13082006C2semidirect
2. #13079725C2semidirect
3. #13079699C2semidirect
4. #13079677C2semidirect
5. #13079080C2semidirect
6. #13079073C2semidirect
7. #13079002C2semidirect
8. #13078996C2semidirect
9. #13078106C2semidirect
10. #13078099C2semidirect
11. #13077858C2semidirect
12. #13077850C2semidirect
13. #13077254C2semidirect
14. C2×C11×#536C2semidirect
32. #10623066C22semidirect
33. #10623065C22semidirect
35. #10623049C22semidirect
43. #10622841C22semidirect
44. #10622840C22semidirect
50. #10622705C22semidirect
51. #10622703C22semidirect
52. #10622699C22semidirect
53. #10622698C22semidirect
54. #10622696C22semidirect
55. #10622695C22semidirect
56. #10622694C22semidirect
57. #10622673C22semidirect
58. #10622672C22semidirect
59. #10622671C22semidirect
60. #10622670C22semidirect
61. #10622669C22semidirect
62. #10622668C22semidirect
63. #10622667C22semidirect
64. #10622613C22semidirect
65. #10622613C22semidirect
250. C2×#536D11semidirect
576. C11#60807semidirect

Maximal subgroups

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

subgroupindex
#130820062
#130797252
#130796992
#130796772
#130790802
#130790732
#130790022
#130789962
#130781062
#130780992
#130778582
#130778502
#130772542
C2×C11×#5362
#6080711