Finite Group Databasebeta

← #15638535

Subgroups — #15638535

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
1C2×#10623084C211yesmaximal, characteristic, complemented
2#13080560C214yesmaximal, complemented
3#13080549C214yesmaximal, complemented
4#13080372C214yesmaximal, complemented
5#13080342C214yesmaximal, complemented
6#13079554C211yesmaximal, characteristic, complemented
7#13079531C211yesmaximal, characteristic, complemented
8#13079377C214yesmaximal, complemented
9#13078651C211yesmaximal, characteristic, complemented
10#13078643C211yesmaximal, characteristic, complemented
11#13077832C214yesmaximal, complemented
12#13077640C211yesmaximal, characteristic, complemented
13C11×#3506C211yesmaximal, characteristic, complemented
14C22×#4339C2212yes—
15C11×#559—22no—
16C11×#556C2212yescomplemented
17C11×#555C2212yescomplemented
18C11×#553—22no—
19C11×#550C2212yescomplemented
20C11×#547C2212yescomplemented
21C11×#538—22no—
22C11×#535—21no—
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#525C2214yes—
26C11×#520—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×#67003C2218yescomplemented
29C2×#66993—21no—
30C2×#66983C2212yes—
31#10623084—22no—
32#10623084—22no—
33#10623084C2214yes—
34#10623084C2214yes—
35C2×#66946—21no—
36C2×#66937—22no—
37C2×#66927C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39#10622851C2218yescomplemented
40C2×C22⋊(C11⋊C8)C2214yes—
41#10622707C2212yescomplemented
42#10622704C2212yescomplemented
43#10622703C2212yescomplemented
44#10622701C2212yescomplemented
45#10622701C2212yescomplemented
46#10622698C2212yescomplemented
47#10622688C2212yescomplemented
48#10622686C2212yescomplemented
49#10622663C2212yes—
50#10622661C2218yescomplemented
51#10622660C2218yescomplemented
52#10622659C2214yes—
53#10622657C2212yes—
54#10622653C2212yes—
55#10622651C2218yescomplemented
56#10622650C2218yescomplemented
57#10622649C2214yes—
58#10622647C2212yes—
59C4×#4326C2214yescomplemented
60#10622640C2214yescomplemented
61C4×#4324C2214yescomplemented
62#10622628C2214yescomplemented
63D4×C11⋊C8C2214yescomplemented
64D4×C11⋊C8C2214yescomplemented
65#10622616C2218yescomplemented
66#10622615C2218yescomplemented
67#10622538C2211yescharacteristic
68#10622538C2211yescharacteristic
69C2×C11×#41—21no—
70C2×C11×#41C2314yes—
71C22×D4×C11D411yescharacteristic
72C23×C4×C11C2312yes—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C2×#4339—24no—
76C2×#4339—48no—
77C2×#4339C2318yes—
78C22×D44—21no—
79C22×D44—21no—
80C22×D44C2312yes—
81C22×C4×D11—22no—
82C22×Dic22C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×C4⋊Q8C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#127—22no—
87C11×#127C2311yescharacteristic
88C11×#126—24no—
89C11×#125—21no—
90C11×#124—22no—
91C11×#124—24no—
92C11×#124—21no—
93C11×#123—24no—
94C11×#123—24no—
95C11×C22⋊Q8—21no—
96C11×C22⋊Q8C2312yes—
97C11×C22⋊Q8C2314yes—
98C11×#121—22no—
99C11×#121—22no—
100C11×#121—21no—
101C11×#121—24no—
102C11×#121C2312yes—
103C11×#121C2314yes—
104C11×#120—24no—
105C4×Q8×C11—22no—
106C4×Q8×C11—21no—
107C4×Q8×C11C2312yes—
108C4×D4×C11—24no—
109C4×D4×C11—24no—
110C4×D4×C11—22no—
111C4×D4×C11—21no—
112C4×D4×C11D412yes—
113C4×D4×C11D412yes—
114C4×D4×C11C2312yes—
115C4×D4×C11C2312yes—
116C4×D4×C11C2312yes—
117C11×#117—21no—
118C11×#117—22no—
119C11×#117C2314yes—
120C2×C11×C4⋊C4—22no—
121C2×C11×C4⋊C4D411yescharacteristic
122C2×C11×C22⋊C4D412yes—
123C2×C42×C11C2311yescharacteristic
124#67003—416no—
125C2×#4326C2314yes—
126C2×#4325C2318yes—
127#66993—24no—
128#66993—24no—
129C2×#4324C2314yes—
130C2×#4323C2318yes—
131#66983—24no—
132#66983C2318yes—
133C2×(C2×D11)⋊C4—22no—
134C2×C4⋊Dic11C2311yescharacteristic
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C22×C11⋊C8C2318yes—
138#66946—24no—
139#66946—24no—
140#66937—28no—
141#66937—28no—
142#66927—21no—
143#66927—21no—
144#66927C2312yes—
145#66927C2312yes—
146C4×Dic22—21no—
147C4×Dic22—21no—
148C4×Dic22C2312yes—
149C4×Dic22C2312yes—
150#66899C2314yes—
151#66896C2314yes—
152C22⋊(C11⋊C8)C2312yes—
153C22⋊(C11⋊C8)C2312yes—
154C22⋊(C11⋊C8)C2318yes—
155#66874C2314yes—
156#66874C2314yes—
157#66873C2318yes—
158#66873C2318yes—
159#66872C2314yes—
160#66871C2314yes—
161C4⋊(C11⋊C8)C2312yes—
162C4⋊(C11⋊C8)C2312yes—
163C4×C11⋊C8C2312yes—
164C4×C11⋊C8C2312yes—
165#61566—111nomaximal, Sylow
166C24×C11C2×D412yes—
167C23×D11—22no—
168C11×#41—48no—
169C11×#41—44no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C2412yes—
173C2×D4×C11—22no—
174C2×D4×C11—24no—
175C2×D4×C11—24no—
176C2×D4×C11—24no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
181C2×D4×C11C2412yes—
182C22×C4×C11—22no—
183C22×C4×C11—24no—
184C22×C4×C11—44no—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D414yes—
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×C4×C11C2414yes—
191C2×C22⋊D11—28no—
192C2×C22⋊D11—28no—
193C2×C22⋊D11—48no—
194C2×C22⋊D11—84no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197#4339—216no—
198#4339—48no—
199#4339—416no—
200C2×D44—22no—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—44no—
206C2×D44—44no—
207C2×D44—82no—
208C2×D44C2414yes—
209C2×C4×D11—28no—
210C2×C4×D11—48no—
211C2×Dic22—24no—
212C2×Dic22—21no—
213C2×Dic22C2412yes—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4C2×D412yes—
222C11×C4⋊C4C2×D412yes—
223C11×C4⋊C4C2412yes—
224C11×C4⋊C4C2412yes—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4C2×D414yes—
232C11×C22⋊C4C2×D414yes—
233C42×C11—24no—
234C42×C11—22no—
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237C42×C11C2411yescharacteristic
238C42×C11C2411yescharacteristic
239#4326—28no—
240#4325—48no—
241#4324—28no—
242#4323—48no—
243(C2×D11)⋊C4—28no—
244C4⋊Dic11—21no—
245C4⋊Dic11C2412yes—
246Dic11⋊C4—22no—
247Dic11⋊C4—22no—
248C4×Dic11—22no—
249C4×Dic11—22no—
250C2×C11⋊C8—48no—
251C2×C11⋊C8C2414yes—
252C2×C11⋊C8C2414yes—
253#3506D1111yescharacteristic, complemented
254C2×#550—111no—
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—22no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11C22×D414yes—
271C23×C11C22×D411yescharacteristic
272C22×D11—24no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11—44no—
276Q8×C11—24no—
277Q8×C11—42no—
278Q8×C11—81no—
279D4×C11—24no—
280D4×C11—24no—
281D4×C11—24no—
282D4×C11—44no—
283D4×C11—42no—
284D4×C11—81no—
285D4×C11—84no—
286D4×C11—84no—
287C2×C4×C11—28no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—42no—
293C2×C4×C11—41no—
294C2×C4×C11—44no—
295C2×C4×C11—44no—
296C2×C4×C11—84no—
297C2×C4×C11#13514yescomplemented
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D414yes—
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C2511yescharacteristic
305C22⋊D11—416no—
306C22⋊D11—88no—
307C2×Dic11—24no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—42no—
311D44—28no—
312D44—44no—
313D44—44no—
314D44—44no—
315D44—82no—
316D44—82no—
317C4×D11—416no—
318Dic22—24no—
319Dic22—22no—
320Dic22H(5,𝔽2)14yes—
321C11⋊C8—24no—
322C11⋊C8—24no—
323C22×#41—112no—
324C2×#135—118no—
325#559—22no—
326#556C2×D1112yescomplemented
327#555C2×D1112yescomplemented
328#553—22no—
329#550—114no—
330#550—114no—
331#550—222no—
332#550—222no—
333#550C2×D1112yescomplemented
334#547C2×D1112yescomplemented
335#538—22no—
336#535—21no—
337#533C2×D1111yescharacteristic
338#532C2×D1111yescharacteristic
339C2×#127—111no—
340C2×#127—221no—
341#525C2×D1114yes—
342C2×#121—112no—
343C2×#121—222no—
344#520—21no—
345C2×C4×Q8—111no—
346C2×C4×D4—221no—
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—112no—
361#460—114no—
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—42no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—84no—
387C22×C11C2×#13512yes—
388C22×C11C23×D411yescharacteristic
389C2×D11—44no—
390C2×D11—44no—
391C2×D11—44no—
392C2×D11—88no—
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—24no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11C2×#13512yes—
401C4×C11C2×#13512yes—
402C4×C11C2×H(5,𝔽2)12yes—
403Dic11—24no—
404Dic11—42no—
405C2×#41—21no—
406C2×#41—118no—
407C2×#41—224no—
408C2×#41—448no—
409C2×#41C22×D1114yes—
410C22×Q8—111no—
411C22×D4—112no—
412C22×D4—222no—
413C22×D4—222no—
414C22×D4—221no—
415C22×D4—221no—
416C22×D4C22⋊D1111yescharacteristic
417C23×C4—222no—
418C23×C4C22×D1112yes—
419#135—4416no—
420C2×Q16—114no—
421C2×SD16—114no—
422C2×SD16—118no—
423C2×D8—118no—
424C22×C8—118no—
425C4⋊Q8C22×D1111yescharacteristic
426C4⋊Q8C22×D1111yescharacteristic
427C4⋊Q8C22×D1111yescharacteristic
428#127—22no—
429#127—112no—
430#127—112no—
431#127—224no—
432#127—224no—
433#127—221no—
434#127—221no—
435#127C22×D1111yescharacteristic
436#126—24no—
437#125—21no—
438#124—22no—
439#124—24no—
440#124—21no—
441#123—24no—
442#123—24no—
443C22⋊Q8—21no—
444C22⋊Q8C22×D1112yes—
445C22⋊Q8C22×D1114yes—
446#121—22no—
447#121—22no—
448#121—21no—
449#121—24no—
450#121—118no—
451#121—224no—
452#121—228no—
453#121—228no—
454#121C22×D1112yes—
455#121C22×D1114yes—
456#120—24no—
457C4×Q8—22no—
458C4×Q8—21no—
459C4×Q8—112no—
460C4×Q8—112no—
461C4×Q8—221no—
462C4×Q8—221no—
463C4×Q8C22×D1112yes—
464C4×D4—24no—
465C4×D4—24no—
466C4×D4—22no—
467C4×D4—21no—
468C4×D4—224no—
469C4×D4—224no—
470C4×D4C22⋊D1112yes—
471C4×D4C22⋊D1112yes—
472C4×D4C22×D1112yes—
473C4×D4C22×D1112yes—
474C4×D4C22×D1112yes—
475#117—21no—
476#117—22no—
477#117C22×D1114yes—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4C22⋊D1111yescharacteristic
482C2×C22⋊C4—222no—
483C2×C22⋊C4C22⋊D1112yes—
484C2×C42—221no—
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—114no—
494#102—118no—
495#102—118no—
496C22⋊C8—112no—
497C22⋊C8—112no—
498C22⋊C8—118no—
499C4×C8—112no—
500C4×C8—112no—
501C2×C11—22no—
502C2×C11—44no—
503C2×C11—82no—
504C2×C11#348411yescharacteristic
505C2×C11C22×#13511yescharacteristic
506C2×C11#358511yescharacteristic
507D11—84no—
508C24—222no—
509C24C2×C22⋊D1112yes—
510#41—48no—
511#41—44no—
512#41—2216no—
513#41—448no—
514#41—4416no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—112no—
518C2×Q8—224no—
519C2×Q8—221no—
520C2×Q8C23×D1112yes—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—114no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—222no—
531C2×D4—222no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—444no—
536C2×D4—448no—
537C2×D4—444no—
538C2×D4—882no—
539C2×D4—884no—
540C2×D4C2×C22⋊D1112yes—
541C2×D4C2×C22⋊D1112yes—
542C2×D4C23×D1112yes—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—44no—
546C22×C4—221no—
547C22×C4—221no—
548C22×C4—228no—
549C22×C4—448no—
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—21no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—22no—
570C4⋊C4—112no—
571C4⋊C4—221no—
572C4⋊C4—222no—
573C4⋊C4—222no—
574C4⋊C4C2×C22⋊D1112yes—
575C4⋊C4C2×C22⋊D1112yes—
576C4⋊C4C23×D1112yes—
577C4⋊C4C23×D1112yes—
578C22⋊C4—22no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—228no—
585C22⋊C4C2×C22⋊D1114yes—
586C22⋊C4C2×C22⋊D1114yes—
587C42—24no—
588C42—22no—
589C42—222no—
590C42—222no—
591C42C2×C22⋊D1111yescharacteristic
592C42C2×C22⋊D1111yescharacteristic
593C42C23×D1111yescharacteristic
594C42C23×D1111yescharacteristic
595C11#6156611yescharacteristic, complemented, Sylow
596C23—24no—
597C23—22no—
598C23—42no—
599C23—42no—
600C23—224no—
601C23—444no—
602C23—444no—
603C23—444no—
604C23C22×C22⋊D1114yes—
605C23C22×C22⋊D1111yescharacteristic
606Q8—24no—
607Q8—42no—
608Q8—81no—
609Q8—114no—
610Q8—224no—
611Q8—222no—
612D4—24no—
613D4—24no—
614D4—24no—
615D4—44no—
616D4—42no—
617D4—81no—
618D4—84no—
619D4—84no—
620D4—228no—
621D4—444no—
622D4—4416no—
623D4—444no—
624D4—444no—
625D4—882no—
626D4—882no—
627D4—888no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—42no—
634C2×C4—44no—
635C2×C4—41no—
636C2×C4—44no—
637C2×C4—84no—
638C2×C4—224no—
639C2×C4—222no—
640C2×C4—222no—
641C2×C4—4416no—
642C2×C4—442no—
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—42no—
659C22—42no—
660C22—42no—
661C22—84no—
662C22—444no—
663C22—444no—
664C22—444no—
665C22—888no—
666C22C2×#6700312yes—
667C22C23×C22⋊D1111yescharacteristic
668C4—21no—
669C4—21no—
670C4—21no—
671C4—24no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—224no—
676C4—442no—
677C4C2×#6700312yes—
678C4C2×#6700312yes—
679C4D11×H(5,𝔽2)12yes—
680C2—22no—
681C2—44no—
682C2—82no—
683C2—884no—
684C2#1308224711yescharacteristic
685C2C22×#6700311yescharacteristic
686C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3506C2
socleC22×C11C23×D4
hypercenter#3506D11
hypocenterC11#61566
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. #13080560C2semidirect
3. #13080549C2semidirect
4. #13080372C2semidirect
5. #13080342C2semidirect
6. #13079554C2semidirect
7. #13079531C2semidirect
8. #13079377C2semidirect
9. #13078651C2semidirect
10. #13078643C2semidirect
11. #13077832C2semidirect
12. #13077640C2semidirect
13. C11×#3506C2semidirect
16. C11×#556C22semidirect
17. C11×#555C22semidirect
19. C11×#550C22semidirect
20. C11×#547C22semidirect
28. C2×#67003C22semidirect
39. #10622851C22semidirect
41. #10622707C22semidirect
42. #10622704C22semidirect
43. #10622703C22semidirect
44. #10622701C22semidirect
45. #10622701C22semidirect
46. #10622698C22semidirect
47. #10622688C22semidirect
48. #10622686C22semidirect
50. #10622661C22semidirect
51. #10622660C22semidirect
55. #10622651C22semidirect
56. #10622650C22semidirect
59. C4×#4326C22semidirect
60. #10622640C22semidirect
61. C4×#4324C22semidirect
62. #10622628C22semidirect
63. D4×C11⋊C8C22semidirect
64. D4×C11⋊C8C22semidirect
65. #10622616C22semidirect
66. #10622615C22semidirect
253. #3506D11semidirect
297. C2×C4×C11#135semidirect
326. #556C2×D11semidirect
327. #555C2×D11semidirect
333. #550C2×D11semidirect
334. #547C2×D11semidirect
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
C2×#106230842
#130805602
#130805492
#130803722
#130803422
#130795542
#130795312
#130793772
#130786512
#130786432
#130778322
#130776402
C11×#35062
#6156611