Finite Group Databasebeta

← #15638540

Subgroups — #15638540

Order 2816.

2194 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#13082468C211yesmaximal, characteristic, complemented
2#13080566C214yesmaximal, complemented
3#13080555C214yesmaximal, complemented
4#13080372C214yesmaximal, complemented
5#13080346C214yesmaximal, complemented
6#13079557C211yesmaximal, characteristic, complemented
7#13079534C211yesmaximal, characteristic, complemented
8#13079381C214yesmaximal, complemented
9#13078655C211yesmaximal, characteristic, complemented
10#13078647C211yesmaximal, characteristic, complemented
11#13077834C214yesmaximal, complemented
12#13077640C211yesmaximal, characteristic, complemented
13C2×C11×#550C211yesmaximal, characteristic, complemented
14C22×C11×#41C2212yes—
15C11×#550—22no—
16C11×#550—22no—
17C11×#550C2214yes—
18C11×#550C2214yes—
19C2×C11×#127—21no—
20C2×C11×#127C2211yescharacteristic
21C2×C11×#121—22no—
22C2×C11×#121C2212yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×D4×C11—21no—
25C2×C4×D4×C11C2211yescharacteristic
26C2×#67003C2218yescomplemented
27#10623336—21no—
28#10623322C2214yes—
29#10623094C2212yescomplemented
30#10623090—22no—
31#10623089—22no—
32#10623084C2212yescomplemented
33#10623082C2212yescomplemented
34#10623073C2212yescomplemented
35#10623035—21no—
36#10623025—22no—
37#10623008C2211yescharacteristic
38#10623001C2211yescharacteristic
39#10622852C2218yescomplemented
40#10622851C2218yescomplemented
41#10622846C2218yescomplemented
42#10622841C2212yes—
43#10622840C2212yes—
44#10622831C2214yes—
45#10622830C2214yes—
46C2×C22⋊(C11⋊C8)C2214yes—
47#10622689C2212yescomplemented
48#10622688C2214yescomplemented
49#10622686C2212yescomplemented
50#10622685C2214yescomplemented
51#10622683C2212yescomplemented
52#10622683C2212yescomplemented
53#10622654C2218yescomplemented
54#10622651C2218yescomplemented
55#10622650C2218yescomplemented
56#10622648C2218yescomplemented
57#10622644C2212yescomplemented
58C4×#4326C2214yescomplemented
59#10622640C2212yescomplemented
60C4×#4325C2214yescomplemented
61#10622634C2212yescomplemented
62#10622633C2212yescomplemented
63D4×C11⋊C8C2214yescomplemented
64D4×C11⋊C8C2214yescomplemented
65#10622583C2212yes—
66#10622581C2212yes—
67#10622538C2211yescharacteristic
68#10622538C2211yescharacteristic
69C2×C11×#41—24no—
70C2×C11×#41—48no—
71C2×C11×#41C2318yes—
72C22×Q8×C11C2311yescharacteristic
73C22×D4×C11—22no—
74C22×D4×C11—22no—
75C22×D4×C11—21no—
76C22×D4×C11—21no—
77C22×D4×C11D411yescharacteristic
78C22×D4×C11C2312yes—
79C23×C4×C11—22no—
80C23×C4×C11C2312yes—
81C2×#4339—21no—
82C2×#4339C2314yes—
83C11×#127—24no—
84C11×#127—24no—
85C11×#127—21no—
86C11×#127—21no—
87C11×#127C2312yes—
88C11×#127C2312yes—
89C11×#121—24no—
90C11×#121—28no—
91C11×#121—28no—
92C11×#121C2318yes—
93C4×Q8×C11—21no—
94C4×Q8×C11—21no—
95C4×Q8×C11C2312yes—
96C4×Q8×C11C2312yes—
97C4×D4×C11—24no—
98C4×D4×C11—24no—
99C4×D4×C11D412yes—
100C4×D4×C11D412yes—
101C4×D4×C11C2312yes—
102C4×D4×C11C2312yes—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4D411yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4D412yes—
108C2×C42×C11—21no—
109C2×C42×C11C2311yescharacteristic
110#67006—24no—
111#67003—416no—
112C2×#4326C2314yes—
113C2×#4325C2314yes—
114#66993—22no—
115#66991—22no—
116#66991—22no—
117#66989—22no—
118C2×#4324C2318yes—
119C2×#4323C2318yes—
120#66983—21no—
121#66983C2312yes—
122#66983C2314yes—
123#66982—24no—
124C4×C22⋊D11—24no—
125C4×C22⋊D11—24no—
126#66979—21no—
127#66979C2314yes—
128#66977—21no—
129#66977C2312yes—
130#66977C2314yes—
131C22×C11⋊C8C2318yes—
132#66946—22no—
133#66945—22no—
134C4⋊C4×D11—22no—
135#66940—22no—
136#66938—24no—
137#66937—24no—
138#66936—24no—
139#66932—24no—
140#66928—21no—
141#66927C2311yescharacteristic
142C4×D44—21no—
143C4×D44C2312yes—
144#66923—21no—
145#66922C2311yescharacteristic
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22C2312yes—
150#66899C2314yes—
151#66899C2314yes—
152#66896C2318yes—
153#66896C2318yes—
154C22⋊(C11⋊C8)C2312yes—
155C22⋊(C11⋊C8)C2312yes—
156C22⋊(C11⋊C8)C2318yes—
157#66874C2314yes—
158#66873C2314yes—
159#66872C2314yes—
160#66871C2314yes—
161C4⋊(C11⋊C8)C2312yes—
162C4⋊(C11⋊C8)C2312yes—
163C4×C11⋊C8C2312yes—
164C4×C11⋊C8C2312yes—
165#61566—111nomaximal, Sylow
166C24×C11—22no—
167C24×C11C2×D412yes—
168C11×#41—216no—
169C11×#41—48no—
170C11×#41—416no—
171C2×Q8×C11—24no—
172C2×Q8×C11—21no—
173C2×Q8×C11C2412yes—
174C2×D4×C11—28no—
175C2×D4×C11—28no—
176C2×D4×C11—24no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—44no—
183C2×D4×C11—48no—
184C2×D4×C11—44no—
185C2×D4×C11—82no—
186C2×D4×C11—84no—
187C2×D4×C11C2×D412yes—
188C2×D4×C11C2×D412yes—
189C2×D4×C11C2414yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—28no—
193C22×C4×C11—44no—
194C22×C4×C11—48no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D414yes—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2414yes—
201C2×C22⋊D11—22no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204#4339—48no—
205#4339—44no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44C2412yes—
209C2×C4×D11—22no—
210C2×C4×D11—24no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22C2412yes—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4C2×D412yes—
218C11×C4⋊C4C2×D412yes—
219C11×C4⋊C4C2412yes—
220C11×C22⋊C4—28no—
221C11×C22⋊C4C2×D414yes—
222C11×C22⋊C4C2×D414yes—
223C42×C11—22no—
224C42×C11—22no—
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228C42×C11C2411yescharacteristic
229C22⋊Dic11—24no—
230C22⋊Dic11—24no—
231C22⋊Dic11—22no—
232#4326—28no—
233#4325—28no—
234#4324—48no—
235#4323—48no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—22no—
238(C2×D11)⋊C4—24no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11C2412yes—
244C4⋊Dic11C2412yes—
245Dic11⋊C4—22no—
246Dic11⋊C4—22no—
247Dic11⋊C4—24no—
248C4×Dic11—22no—
249C4×Dic11—24no—
250C2×C11⋊C8—48no—
251C2×C11⋊C8C2414yes—
252C2×C11⋊C8C2414yes—
253#3506—111no—
254C2×#550D1111yescharacteristic, complemented
255#3305—114no—
256#3304—114no—
257#3287—114no—
258#3284—114no—
259#3208—111no—
260#3205—111no—
261#3188—114no—
262#3104—111no—
263#3103—111no—
264#3002—114no—
265#2972—111no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—44no—
271C23×C11—44no—
272C23×C11—44no—
273C23×C11C22×D414yes—
274C23×C11C22×D411yescharacteristic
275C22×D11—22no—
276Q8×C11—24no—
277Q8×C11—22no—
278Q8×C11H(5,𝔽2)14yes—
279D4×C11—24no—
280D4×C11—24no—
281D4×C11—28no—
282D4×C11—416no—
283D4×C11—44no—
284D4×C11—44no—
285D4×C11—44no—
286D4×C11—82no—
287D4×C11—82no—
288D4×C11—88no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—28no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—42no—
295C2×C4×C11—44no—
296C2×C4×C11—41no—
297C2×C4×C11—416no—
298C2×C4×C11—42no—
299C2×C4×C11#13514yescomplemented
300C2×C4×C11C22×D414yes—
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2511yescharacteristic
307C22⋊D11—44no—
308C22⋊D11—84no—
309C22⋊D11—84no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313D44—24no—
314D44—42no—
315D44—81no—
316C4×D11—44no—
317C4×D11—84no—
318Dic22—24no—
319Dic22—42no—
320Dic22—81no—
321C11⋊C8—24no—
322C11⋊C8—24no—
323C22×#41C2×D1112yes—
324C2×#135—118no—
325#559—222no—
326#556—112no—
327#555—112no—
328#553—222no—
329#550—22no—
330#550—22no—
331#550—112no—
332#550C2×D1114yes—
333#550C2×D1114yes—
334#547—112no—
335#538—222no—
336#535—221no—
337#533—111no—
338#532—111no—
339C2×#127—21no—
340C2×#127C2×D1111yescharacteristic
341#525—114no—
342C2×#121—22no—
343C2×#121C2×D1112yes—
344#520—221no—
345C2×C4×Q8C2×D1111yescharacteristic
346C2×C4×D4—21no—
347C2×C4×D4C2×D1111yescharacteristic
348#493—112no—
349#492—112no—
350#486—112no—
351#486—112no—
352#484—112no—
353#482—118no—
354#481—112no—
355#477—112no—
356#475—112no—
357#466—118no—
358#465—118no—
359#462—112no—
360#460—114no—
361#460—112no—
362#459—114no—
363#452—118no—
364#451—112no—
365#450—114no—
366#449—118no—
367#449—118no—
368#448—112no—
369#447—114no—
370C4×Q16—114no—
371C4×SD16—114no—
372C8×D4—114no—
373C8×D4—114no—
374#431—111no—
375#431—111no—
376#416—118no—
377C2×C22⋊C8—114no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—24no—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—44no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—84no—
387C22×C11—88no—
388C22×C11C2×#13512yes—
389C22×C11C23×D411yescharacteristic
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—42no—
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—24no—
396C4×C11—24no—
397C4×C11—21no—
398C4×C11—42no—
399C4×C11C2×#13512yes—
400C4×C11C2×#13512yes—
401C4×C11C2×H(5,𝔽2)12yes—
402Dic11—42no—
403Dic11—42no—
404Dic11—42no—
405C2×#41—24no—
406C2×#41—48no—
407C2×#41—114no—
408C2×#41—221no—
409C2×#41C22×D1118yes—
410C22×Q8C22×D1111yescharacteristic
411C22×D4—22no—
412C22×D4—22no—
413C22×D4—21no—
414C22×D4—21no—
415C22×D4C22⋊D1111yescharacteristic
416C22×D4C22×D1112yes—
417C23×C4—22no—
418C23×C4C22×D1112yes—
419#135—4416no—
420C2×Q16—114no—
421C2×SD16—114no—
422C2×SD16—118no—
423C2×D8—118no—
424C22×C8—118no—
425C4⋊Q8—111no—
426C4⋊Q8—111no—
427C4⋊Q8—111no—
428#127—24no—
429#127—24no—
430#127—21no—
431#127—21no—
432#127—111no—
433#127—222no—
434#127C22×D1112yes—
435#127C22×D1112yes—
436#126—224no—
437#125—221no—
438#124—222no—
439#124—224no—
440#124—221no—
441#123—224no—
442#123—224no—
443C22⋊Q8—112no—
444C22⋊Q8—114no—
445C22⋊Q8—221no—
446#121—24no—
447#121—28no—
448#121—28no—
449#121—112no—
450#121—114no—
451#121—222no—
452#121—222no—
453#121—221no—
454#121—224no—
455#121C22×D1118yes—
456#120—224no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—112no—
460C4×Q8—222no—
461C4×Q8—221no—
462C4×Q8C22×D1112yes—
463C4×Q8C22×D1112yes—
464C4×D4—24no—
465C4×D4—24no—
466C4×D4—112no—
467C4×D4—224no—
468C4×D4—224no—
469C4×D4—222no—
470C4×D4—221no—
471C4×D4C22⋊D1112yes—
472C4×D4C22⋊D1112yes—
473C4×D4C22×D1112yes—
474C4×D4C22×D1112yes—
475#117—114no—
476#117—221no—
477#117—222no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—222no—
480C2×C4⋊C4C22⋊D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C22⋊C4—22no—
483C2×C22⋊C4C22⋊D1112yes—
484C2×C42—21no—
485C2×C42C22×D1111yescharacteristic
486#107—114no—
487#106—114no—
488C4⋊C8—112no—
489C4⋊C8—112no—
490#103—114no—
491#103—114no—
492#103—114no—
493#102—118no—
494#102—118no—
495#102—114no—
496C22⋊C8—112no—
497C22⋊C8—112no—
498C22⋊C8—118no—
499C4×C8—112no—
500C4×C8—112no—
501C2×C11—22no—
502C2×C11—44no—
503C2×C11—84no—
504C2×C11#348411yescharacteristic
505C2×C11C22×#13511yescharacteristic
506C2×C11#358511yescharacteristic
507D11—82no—
508C24—22no—
509C24C2×C22⋊D1112yes—
510#41—216no—
511#41—48no—
512#41—416no—
513#41—448no—
514#41—444no—
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—112no—
518C2×Q8—221no—
519C2×Q8—221no—
520C2×Q8C23×D1112yes—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—24no—
524C2×D4—22no—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—44no—
530C2×D4—48no—
531C2×D4—44no—
532C2×D4—82no—
533C2×D4—84no—
534C2×D4—112no—
535C2×D4—222no—
536C2×D4—224no—
537C2×D4—224no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4C2×C22⋊D1112yes—
541C2×D4C2×C22⋊D1112yes—
542C2×D4C23×D1114yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—28no—
546C22×C4—44no—
547C22×C4—48no—
548C22×C4—222no—
549C22×C4—224no—
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C2×C22⋊D1112yes—
552C22×C4C2×C22⋊D1114yes—
553C22×C4C2×C22⋊D1111yescharacteristic
554C22×C4C23×D1111yescharacteristic
555C22×C4C23×D1114yes—
556Q16—228no—
557SD16—228no—
558SD16—448no—
559D8—448no—
560C2×C8—114no—
561C2×C8—114no—
562C2×C8—448no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—112no—
567C4⋊C4—112no—
568C4⋊C4—221no—
569C4⋊C4—224no—
570C4⋊C4—221no—
571C4⋊C4—222no—
572C4⋊C4—221no—
573C4⋊C4—222no—
574C4⋊C4—221no—
575C4⋊C4C2×C22⋊D1112yes—
576C4⋊C4C2×C22⋊D1112yes—
577C4⋊C4C23×D1112yes—
578C22⋊C4—28no—
579C22⋊C4—224no—
580C22⋊C4—222no—
581C22⋊C4—224no—
582C22⋊C4—224no—
583C22⋊C4—222no—
584C22⋊C4—222no—
585C22⋊C4C2×C22⋊D1114yes—
586C22⋊C4C2×C22⋊D1114yes—
587C42—22no—
588C42—22no—
589C42—224no—
590C42—222no—
591C42C2×C22⋊D1111yescharacteristic
592C42C2×C22⋊D1111yescharacteristic
593C42C23×D1111yescharacteristic
594C42C23×D1111yescharacteristic
595C11#6156611yescharacteristic, complemented, Sylow
596C23—24no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—222no—
604C23C22×C22⋊D1114yes—
605C23C22×C22⋊D1111yescharacteristic
606Q8—24no—
607Q8—22no—
608Q8—224no—
609Q8—442no—
610Q8—881no—
611Q8#6703714yes—
612D4—24no—
613D4—24no—
614D4—28no—
615D4—416no—
616D4—44no—
617D4—44no—
618D4—44no—
619D4—82no—
620D4—82no—
621D4—88no—
622D4—224no—
623D4—444no—
624D4—442no—
625D4—881no—
626D4—884no—
627D4—884no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—28no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—42no—
634C2×C4—44no—
635C2×C4—41no—
636C2×C4—416no—
637C2×C4—42no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—444no—
642C2×C4—884no—
643C2×C4#6700314yescomplemented
644C2×C4C22×C22⋊D1114yes—
645C2×C4C22×C22⋊D1111yescharacteristic
646C2×C4C22×C22⋊D1111yescharacteristic
647C2×C4C22×C22⋊D1111yescharacteristic
648C2×C4C22×C22⋊D1111yescharacteristic
649C2×C4C22×C22⋊D1111yescharacteristic
650C2×C4C24×D1111yescharacteristic
651C8—224no—
652C8—224no—
653C22—21no—
654C22—21no—
655C22—24no—
656C22—24no—
657C22—24no—
658C22—44no—
659C22—44no—
660C22—44no—
661C22—84no—
662C22—88no—
663C22—442no—
664C22—442no—
665C22—442no—
666C22C2×#6700312yes—
667C22C23×C22⋊D1111yescharacteristic
668C4—21no—
669C4—21no—
670C4—24no—
671C4—24no—
672C4—21no—
673C4—42no—
674C4—442no—
675C4—442no—
676C4—442no—
677C4C2×#6700312yes—
678C4C2×#6700312yes—
679C4C2×#6703712yes—
680C2—22no—
681C2—44no—
682C2—84no—
683C2—882no—
684C2#1308225111yescharacteristic
685C2C22×#6700311yescharacteristic
686C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC22×C11C23×D4
hypercenterC2×#550D11
hypocenterC11#61566
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13082468C2semidirect
2. #13080566C2semidirect
3. #13080555C2semidirect
4. #13080372C2semidirect
5. #13080346C2semidirect
6. #13079557C2semidirect
7. #13079534C2semidirect
8. #13079381C2semidirect
9. #13078655C2semidirect
10. #13078647C2semidirect
11. #13077834C2semidirect
12. #13077640C2semidirect
13. C2×C11×#550C2semidirect
26. C2×#67003C22semidirect
29. #10623094C22semidirect
32. #10623084C22semidirect
33. #10623082C22semidirect
34. #10623073C22semidirect
39. #10622852C22semidirect
40. #10622851C22semidirect
41. #10622846C22semidirect
47. #10622689C22semidirect
48. #10622688C22semidirect
49. #10622686C22semidirect
50. #10622685C22semidirect
51. #10622683C22semidirect
52. #10622683C22semidirect
53. #10622654C22semidirect
54. #10622651C22semidirect
55. #10622650C22semidirect
56. #10622648C22semidirect
57. #10622644C22semidirect
58. C4×#4326C22semidirect
59. #10622640C22semidirect
60. C4×#4325C22semidirect
61. #10622634C22semidirect
62. #10622633C22semidirect
63. D4×C11⋊C8C22semidirect
64. D4×C11⋊C8C22semidirect
254. C2×#550D11semidirect
299. C2×C4×C11#135semidirect
595. C11#61566semidirect
643. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
#130824682
#130805662
#130805552
#130803722
#130803462
#130795572
#130795342
#130793812
#130786552
#130786472
#130778342
#130776402
C2×C11×#5502
#6156611