Finite Group Databasebeta

← #15625296

Subgroups — #15625296

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082008C211yesmaximal, characteristic, complemented
2C2×#10623205C211yesmaximal, characteristic, complemented
3#13079711C218yesmaximal, complemented
4#13079691C214yesmaximal, complemented
5#13079669C214yesmaximal, complemented
6#13079080C211yesmaximal, characteristic, complemented
7#13079068C211yesmaximal, characteristic, complemented
8#13078992C211yesmaximal, characteristic, complemented
9#13078113C212yesmaximal, complemented
10#13078095C212yesmaximal, complemented
11#13077862C212yesmaximal, complemented
12#13077845C212yesmaximal, complemented
13#13077252C211yesmaximal, characteristic, complemented
14C11×#3140C211yesmaximal, characteristic, complemented
15C22×#4343C2211yescharacteristic
16C22×D4×D11C2211yescharacteristic
17C11×#533C2211yescharacteristic, complemented
18C2×C11×#124C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66995C2212yescomplemented
21C2×#66993C2211yescharacteristic
22C2×#66985C2212yes—
23C2×#66961C2212yes—
24C2×#66961C2212yescomplemented
25#10623264C2214yescomplemented
26#10623229C2212yescomplemented
27#10623228C2212yescomplemented
28#10623205—24no—
29#10623205C2214yes—
30#10623205C2214yes—
31#10623176—22no—
32#10623175—22no—
33#10623111—24no—
34#10623055C2212yes—
35#10623053C2212yescomplemented
36C2×#66937—22no—
37C2×#66935—22no—
38#10623008C2211yescharacteristic, complemented
39C2×#66927C2211yescharacteristic
40C2×#66925C2211yescharacteristic
41C11×#489C2214yescomplemented
42C11×#488C2214yescomplemented
43C11×#419C2212yescomplemented
44C11×#418C2212yes—
45C4×C11×M16C2211yescharacteristic, complemented
46#10622739C2212yes—
47#10622731C2212yescomplemented
48#10622701C2214yescomplemented
49#10622680C2214yescomplemented
50#10622673C2212yescomplemented
51#10622672C2214yescomplemented
52#10622671C2212yescomplemented
53#10622614C2212yes—
54#10622614C2212yescomplemented
55C4×#4318C2211yescharacteristic, complemented
56#10622432C2218yescomplemented
57#10622424C2218yescomplemented
58#10622423C2218yescomplemented
59#10622411C2218yescomplemented
60#10622399C2218yescomplemented
61#10622389C2218yescomplemented
62#10622386C2218yescomplemented
63#10622375C2218yescomplemented
64#10622325C2214yescomplemented
65#10622322C2214yescomplemented
66#10622308C2212yescomplemented
67#10622306C2212yescomplemented
68#10622303C2214yescomplemented
69C24×D11—21no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C22×C22⋊D11—21no—
73C22×C22⋊D11—22no—
74C2×#4343—22no—
75C2×#4343—44no—
76C2×#4343C2314yes—
77C2×D4×D11—22no—
78C2×D4×D11—44no—
79C2×D4×D11C2314yes—
80C2×#4339C2312yes—
81C22×D44—21no—
82C22×D44—22no—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C2×C11×M16C2312yes—
88C11×C4⋊Q8C2312yescomplemented
89C11×#125C2312yescomplemented
90C11×#124—22no—
91C11×#124C2312yes—
92C11×#124C2312yes—
93C11×C22⋊Q8—22no—
94C4×Q8×C11—22no—
95C11×#117C2312yes—
96C2×C11×C22⋊C4—22no—
97C2×C42×C11C2311yescharacteristic
98#67000—24no—
99#67000—22no—
100#67000C2314yes—
101#66999—24no—
102C2×#4326C2314yescomplemented
103#66995—44no—
104C2×#4325C2314yescomplemented
105#66993—22no—
106#66993C2314yes—
107C2×#4324C2314yes—
108#66985—44no—
109C2×#4323C2314yes—
110#66983—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4D412yes—
113C2×Dic11⋊C4D412yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×#4318C2312yes—
116#66961—44no—
117#66961—44no—
118C2×D88C2314yes—
119C2×D88C2314yescomplemented
120C2×#4314C2314yes—
121C2×#4314C2314yescomplemented
122#66951—24no—
123#66951—24no—
124#66950C2314yes—
125#66948—24no—
126#66948C2314yes—
127#66947—24no—
128#66947—24no—
129#66946C2314yescomplemented
130#66943—24no—
131#66940C2314yescomplemented
132#66939—22no—
133#66937—28no—
134#66937—28no—
135#66935—22no—
136#66935—28no—
137#66935—28no—
138(C22⋊D11)⋊C4—24no—
139#66928C2312yescomplemented
140#66927—22no—
141#66927C2312yes—
142#66927C2312yes—
143#66927C2311yescharacteristic, complemented
144C4×D44—24no—
145C4×D44—22no—
146#66925—22no—
147#66925D414yes—
148#66925C2312yes—
149#66925C2312yes—
150C42×D11—22no—
151#66922C2311yescharacteristic, complemented
152C11×#103C2318yescomplemented
153C11×#102C2318yes—
154C11×#97C2312yescomplemented
155C4×C8×C11C2312yescomplemented
156(C2×D11)⋊C8C2318yes—
157Dic11⋊C8C2318yescomplemented
158#66873C2318yes—
159#66873C2318yescomplemented
160#66867C2312yescomplemented
161C4×C11⋊C8C2312yescomplemented
162#60806—111nomaximal, Sylow
163C24×C11—21no—
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—24no—
167C23×D11—44no—
168C23×D11—84no—
169C23×D11C2×D411yescharacteristic
170C2×Q8×C11—21no—
171C2×Q8×C11—22no—
172C2×Q8×C11—24no—
173C2×Q8×C11C2412yes—
174C2×D4×C11—21no—
175C2×D4×C11—24no—
176C2×D4×C11C2412yes—
177C22×C4×C11—21no—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2411yescharacteristic
180C2×C22⋊D11—24no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—22no—
183C2×C22⋊D11—44no—
184C2×C22⋊D11—84no—
185C22×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D412yes—
187#4343—48no—
188#4343—48no—
189D4×D11—48no—
190D4×D11—48no—
191#4339—24no—
192#4339—24no—
193C2×D44—24no—
194C2×D44—24no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—22no—
198C2×D44—24no—
199C2×D44—24no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—44no—
203C2×D44—84no—
204C2×D44C2412yes—
205C2×D44C2412yes—
206C2×D44C2412yes—
207C2×C4×D11—24no—
208C2×C4×D11—24no—
209C2×C4×D11—22no—
210C2×C4×D11—24no—
211C2×C4×D11—44no—
212C2×C4×D11C2×D412yes—
213C2×C4×D11C2412yes—
214C2×Dic22C2412yes—
215C11×M16—24no—
216C2×C8×C11C2414yes—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4C2414yes—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—24no—
223C42×C11—22no—
224C42×C11C2×D412yes—
225C42×C11C2411yescharacteristic
226C42×C11C2411yescharacteristic
227#4326—44no—
228#4325—44no—
229#4324—44no—
230#4323—44no—
231(C2×D11)⋊C4—24no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—28no—
234(C2×D11)⋊C4—24no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4C2×D414yes—
237(C2×D11)⋊C4C2×D414yes—
238C4⋊Dic11—24no—
239C4⋊Dic11—22no—
240Dic11⋊C4—24no—
241Dic11⋊C4C2×D414yes—
242Dic11⋊C4C2×D414yes—
243C4×Dic11—24no—
244C4×Dic11C2×D412yes—
245C4×Dic11C2412yes—
246#4318—24no—
247C2×C11⋊C8C2414yes—
248D88—44no—
249D88—44no—
250#4314—44no—
251#4314—44no—
252#3455—111no—
253C2×#535—111no—
254#3224—118no—
255#3222—114no—
256#3220—114no—
257#3153—111no—
258#3151—111no—
259#3140D1111yescharacteristic, complemented
260#3138—111no—
261#3040—112no—
262#3038—112no—
263#3005—112no—
264#3003—112no—
265#2921—111no—
266C23×C11—22no—
267C23×C11—44no—
268C23×C11—42no—
269C23×C11C22×D411yescharacteristic
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—22no—
273C22×D11—22no—
274C22×D11—42no—
275C22×D11—48no—
276C22×D11—44no—
277C22×D11—44no—
278C22×D11—42no—
279C22×D11—42no—
280C22×D11—88no—
281C22×D11—816no—
282C22×D11C22×D412yes—
283Q8×C11—24no—
284Q8×C11—42no—
285Q8×C11—82no—
286D4×C11—24no—
287D4×C11—42no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11C22×D412yes—
293C2×C4×C11C22×D412yes—
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11H(5,𝔽2)14yes—
296C2×C4×C11C2511yescharacteristic
297C22⋊D11—48no—
298C22⋊D11—44no—
299C22⋊D11—88no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—42no—
303C2×Dic11C22×D414yes—
304C2×Dic11C22×D412yes—
305D44—24no—
306D44—24no—
307D44—22no—
308D44—22no—
309D44—48no—
310D44—42no—
311D44—42no—
312D44—82no—
313D44—84no—
314D44—84no—
315D44—84no—
316C4×D11—24no—
317C4×D11—24no—
318C4×D11—48no—
319C4×D11—44no—
320C4×D11—84no—
321Dic22—22no—
322Dic22—22no—
323C8×C11—24no—
324C11⋊C8—24no—
325C22×#41—111no—
326C23×D4—111no—
327C2×#137—112no—
328C2×AGL(1,ℤ/8)—112no—
329C2×AGL(1,ℤ/8)—112no—
330C2×AGL(1,ℤ/8)—112no—
331#542—114no—
332#541—112no—
333#540—112no—
334#539—222no—
335#538—222no—
336#535—114no—
337#535—114no—
338#535—224no—
339#533C2×D1111yescharacteristic, complemented
340#532—111no—
341C2×#127—111no—
342C2×#127—111no—
343#529—224no—
344C2×#124—111no—
345C2×#124C2×D1111yescharacteristic
346#525—112no—
347C2×#121—222no—
348C2×#120—222no—
349C4×#41—112no—
350C2×#117—111no—
351#497—112no—
352#496—112no—
353#496—114no—
354#495—114no—
355#493—112no—
356#492—112no—
357#490—114no—
358#489C2×D1114yescomplemented
359#488C2×D1114yescomplemented
360#486—114no—
361#464—118no—
362#463—118no—
363#460—118no—
364#459—118no—
365#452—118no—
366#450—118no—
367#449—118no—
368#447—118no—
369#433—114no—
370#433—114no—
371#423—112no—
372#419C2×D1112yescomplemented
373#418—112no—
374#418—112no—
375#418C2×D1112yes—
376#407—112no—
377C4×M16—111no—
378C4×M16C2×D1111yescharacteristic, complemented
379C22×C11—22no—
380C22×C11—44no—
381C22×C11—42no—
382C22×C11—84no—
383C22×C11#53512yes—
384C22×C11C23×D411yescharacteristic
385C2×D11—24no—
386C2×D11—22no—
387C2×D11—44no—
388C2×D11—44no—
389C2×D11—44no—
390C2×D11—44no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—42no—
394C2×D11—816no—
395C2×D11—84no—
396C2×D11—84no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—44no—
400C4×C11—42no—
401C4×C11#53512yes—
402C4×C11C2×H(5,𝔽2)12yes—
403Dic11—24no—
404Dic11—22no—
405Dic11—42no—
406C25—221no—
407C2×#41—114no—
408C2×#41—112no—
409C2×#41—222no—
410C2×#41—444no—
411C22×Q8C22×D1111yescharacteristic
412C22×D4—114no—
413C22×D4—111no—
414C22×D4—111no—
415C22×D4—221no—
416C22×D4—222no—
417C22×D4—221no—
418C22×D4—222no—
419C22×D4—222no—
420C22×D4—444no—
421C22×D4C22×D1111yescharacteristic
422C23×C4—111no—
423C23×C4—221no—
424#137—444no—
425AGL(1,ℤ/8)—444no—
426AGL(1,ℤ/8)—444no—
427AGL(1,ℤ/8)—444no—
428C2×Q16—114no—
429C2×SD16—114no—
430C2×SD16—114no—
431C2×SD16—114no—
432C2×SD16—114no—
433C2×D8—114no—
434C2×D8—114no—
435C2×D8—114no—
436C2×M16—112no—
437C2×M16C22×D1112yes—
438C4⋊Q8—111no—
439C4⋊Q8C22×D1112yescomplemented
440#127—114no—
441#127—112no—
442#127—112no—
443#127—111no—
444#127—222no—
445#127—222no—
446#126—224no—
447#126—224no—
448#125—224no—
449#125C22×D1112yescomplemented
450#124—22no—
451#124—114no—
452#124—112no—
453#124—222no—
454#124—224no—
455#124C22×D1112yes—
456#124C22×D1112yes—
457#123—222no—
458#123—224no—
459#123—224no—
460C22⋊Q8—22no—
461C22⋊Q8—114no—
462C22⋊Q8—224no—
463#121—114no—
464#121—228no—
465#121—228no—
466#121—224no—
467#121—222no—
468#120—228no—
469#120—228no—
470#120—222no—
471C4×Q8—22no—
472C4×Q8—114no—
473C4×D4—114no—
474C4×D4—224no—
475C4×D4—224no—
476C4×D4—222no—
477#117—114no—
478#117—112no—
479#117—112no—
480#117—222no—
481#117C22×D1112yes—
482C2×C4⋊C4—112no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—112no—
485C2×C22⋊C4—222no—
486C2×C42—111no—
487C2×C42—222no—
488C2×C42C22×D1111yescharacteristic
489C4⋊C8—118no—
490#103C22×D1118yescomplemented
491#102—118no—
492#102—118no—
493#102C22×D1118yes—
494C22⋊C8—118no—
495#97—112no—
496#97C22×D1112yescomplemented
497C4×C8—112no—
498C4×C8C22×D1112yescomplemented
499C2×C11—22no—
500C2×C11—82no—
501C2×C11C2×#53511yescharacteristic
502C2×C11#358512yes—
503D11—42no—
504D11—82no—
505D11—82no—
506D11—82no—
507C24—21no—
508C24—111no—
509C24—224no—
510C24—221no—
511C24—221no—
512C24—444no—
513C24—884no—
514#41—224no—
515#41—224no—
516#41—448no—
517#41—448no—
518C2×Q8—21no—
519C2×Q8—22no—
520C2×Q8—24no—
521C2×Q8—112no—
522C2×Q8C23×D1112yes—
523C2×D4—21no—
524C2×D4—24no—
525C2×D4—112no—
526C2×D4—112no—
527C2×D4—112no—
528C2×D4—224no—
529C2×D4—224no—
530C2×D4—224no—
531C2×D4—228no—
532C2×D4—222no—
533C2×D4—221no—
534C2×D4—221no—
535C2×D4—222no—
536C2×D4—224no—
537C2×D4—224no—
538C2×D4—224no—
539C2×D4—224no—
540C2×D4—444no—
541C2×D4—448no—
542C2×D4—448no—
543C2×D4—444no—
544C2×D4—884no—
545C2×D4—884no—
546C2×D4C23×D1112yes—
547C22×C4—21no—
548C22×C4—111no—
549C22×C4—112no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—224no—
553C22×C4—224no—
554C22×C4—224no—
555C22×C4—222no—
556C22×C4—444no—
557C22×C4D4×D1112yes—
558C22×C4C23×D1111yescharacteristic
559Q16—444no—
560SD16—444no—
561SD16—444no—
562SD16—444no—
563SD16—444no—
564D8—444no—
565D8—444no—
566D8—444no—
567M16—24no—
568M16—224no—
569C2×C8—114no—
570C2×C8C23×D1114yes—
571C4⋊C4—24no—
572C4⋊C4—22no—
573C4⋊C4—114no—
574C4⋊C4—114no—
575C4⋊C4—224no—
576C4⋊C4—224no—
577C4⋊C4—222no—
578C4⋊C4C23×D1114yes—
579C22⋊C4—22no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—114no—
583C22⋊C4—114no—
584C22⋊C4—228no—
585C22⋊C4—224no—
586C22⋊C4—224no—
587C22⋊C4—224no—
588C22⋊C4—224no—
589C42—22no—
590C42—112no—
591C42—112no—
592C42—224no—
593C42D4×D1112yes—
594C42C23×D1111yescharacteristic
595C42C23×D1111yescharacteristic
596C11#6080611yescharacteristic, complemented, Sylow
597C23—22no—
598C23—44no—
599C23—42no—
600C23—112no—
601C23—222no—
602C23—222no—
603C23—222no—
604C23—222no—
605C23—442no—
606C23—444no—
607C23—444no—
608C23—448no—
609C23—442no—
610C23—442no—
611C23—888no—
612C23—8816no—
613C23C2×D4×D1111yescharacteristic
614Q8—24no—
615Q8—42no—
616Q8—82no—
617Q8—222no—
618Q8—222no—
619D4—24no—
620D4—42no—
621D4—222no—
622D4—222no—
623D4—224no—
624D4—224no—
625D4—448no—
626D4—448no—
627D4—444no—
628D4—442no—
629D4—442no—
630D4—884no—
631D4—884no—
632D4—882no—
633D4—884no—
634D4—888no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—114no—
640C2×C4—112no—
641C2×C4—222no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—222no—
645C2×C4—448no—
646C2×C4—442no—
647C2×C4—444no—
648C2×C4—884no—
649C2×C4C2×D4×D1112yes—
650C2×C4C2×D4×D1112yes—
651C2×C4C2×D4×D1111yescharacteristic
652C2×C4#6704214yes—
653C2×C4C24×D1111yescharacteristic
654C8—24no—
655C8—224no—
656C22—22no—
657C22—44no—
658C22—42no—
659C22—84no—
660C22—224no—
661C22—222no—
662C22—444no—
663C22—444no—
664C22—444no—
665C22—444no—
666C22—442no—
667C22—442no—
668C22—442no—
669C22—884no—
670C22—884no—
671C22—8816no—
672C22#1062320512yes—
673C22C22×D4×D1111yescharacteristic
674C4—22no—
675C4—22no—
676C4—44no—
677C4—42no—
678C4—224no—
679C4—222no—
680C4—442no—
681C4#1062320512yes—
682C4C2×#6704212yes—
683C2—22no—
684C2—82no—
685C2—442no—
686C2—882no—
687C2—882no—
688C2—882no—
689C2C2×#1062320511yescharacteristic
690C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3140C2
socleC22×C11C23×D4
hypercenter#3140D11
hypocenterC11#60806
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3140

Complements

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

NH ≅ G/Ntype
1. #13082008C2semidirect
2. C2×#10623205C2semidirect
3. #13079711C2semidirect
4. #13079691C2semidirect
5. #13079669C2semidirect
6. #13079080C2semidirect
7. #13079068C2semidirect
8. #13078992C2semidirect
9. #13078113C2semidirect
10. #13078095C2semidirect
11. #13077862C2semidirect
12. #13077845C2semidirect
13. #13077252C2semidirect
14. C11×#3140C2semidirect
17. C11×#533C22semidirect
20. C2×#66995C22semidirect
24. C2×#66961C22semidirect
25. #10623264C22semidirect
26. #10623229C22semidirect
27. #10623228C22semidirect
35. #10623053C22semidirect
38. #10623008C22semidirect
41. C11×#489C22semidirect
42. C11×#488C22semidirect
43. C11×#419C22semidirect
45. C4×C11×M16C22semidirect
47. #10622731C22semidirect
48. #10622701C22semidirect
49. #10622680C22semidirect
50. #10622673C22semidirect
51. #10622672C22semidirect
52. #10622671C22semidirect
54. #10622614C22semidirect
55. C4×#4318C22semidirect
56. #10622432C22semidirect
57. #10622424C22semidirect
58. #10622423C22semidirect
59. #10622411C22semidirect
60. #10622399C22semidirect
61. #10622389C22semidirect
62. #10622386C22semidirect
63. #10622375C22semidirect
64. #10622325C22semidirect
65. #10622322C22semidirect
66. #10622308C22semidirect
67. #10622306C22semidirect
68. #10622303C22semidirect
88. C11×C4⋊Q8C23semidirect
89. C11×#125C23semidirect
102. C2×#4326C23semidirect
104. C2×#4325C23semidirect
119. C2×D88C23semidirect
121. C2×#4314C23semidirect
129. #66946C23semidirect
131. #66940C23semidirect
139. #66928C23semidirect
143. #66927C23semidirect
151. #66922C23semidirect
152. C11×#103C23semidirect
154. C11×#97C23semidirect
155. C4×C8×C11C23semidirect
157. Dic11⋊C8C23semidirect
159. #66873C23semidirect
160. #66867C23semidirect
161. C4×C11⋊C8C23semidirect
259. #3140D11semidirect
339. #533C2×D11semidirect
358. #489C2×D11semidirect
359. #488C2×D11semidirect
372. #419C2×D11semidirect
378. C4×M16C2×D11semidirect
439. C4⋊Q8C22×D11semidirect
449. #125C22×D11semidirect
490. #103C22×D11semidirect
496. #97C22×D11semidirect
498. C4×C8C22×D11semidirect
596. C11#60806semidirect

Maximal subgroups

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

subgroupindex
#130820082
C2×#106232052
#130797112
#130796912
#130796692
#130790802
#130790682
#130789922
#130781132
#130780952
#130778622
#130778452
#130772522
C11×#31402
#6080611