Finite Group Databasebeta

← #14960541

Subgroups — #14960541

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623148C211yesmaximal, characteristic
2C22×#66949C211yesmaximal, characteristic, complemented
3#13076907C212yesmaximal, complemented
4#13075060C214yesmaximal, complemented
5#13075034C214yesmaximal, complemented
6#13074894C214yesmaximal, complemented
7#13074860C214yesmaximal, complemented
8#13074393C212yesmaximal, complemented
9#13073996C211yesmaximal, characteristic, complemented
10#13073962C212yesmaximal, complemented
11#13072930C212yesmaximal, complemented
12#13072275C211yesmaximal, characteristic, complemented
13#13072260C211yesmaximal, characteristic, complemented
14#13071211C211yesmaximal, characteristic, complemented
15C11×#2591C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66992C2212yes—
21C2×#66990C2212yes—
22C2×#66989C2212yescomplemented
23C2×D4×Dic11C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29#10623148—28no—
30C2×#66951C2212yes—
31C2×#66949—28no—
32C2×#66949C2214yes—
33C2×#66949C2214yes—
34C2×#66939C2212yes—
35C2×#66938C2212yes—
36C2×#66936C2214yes—
37C2×#66922C2212yescomplemented
38C11×#400C2212yescomplemented
39C11×#394C2212yescomplemented
40C11×#388C2214yescomplemented
41C11×#386C2212yes—
42C11×#386C2212yes—
43C4×C11×C22⋊C4C2211yescharacteristic
44#10622833C2212yes—
45#10622833C2212yes—
46#10622823C2212yes—
47#10622823C2212yes—
48C4×C22⋊Dic11C2211yescharacteristic
49#10622596C2212yescomplemented
50#10622592C2212yescomplemented
51#10622587C2212yescomplemented
52#10622585C2214yescomplemented
53#10622574C2214yes—
54#10622572C2214yes—
55#10622569C2214yes—
56#10622568C2212yes—
57#10622563C2212yes—
58#10622563C2212yes—
59#10622562C2214yescomplemented
60#10622561C2214yescomplemented
61#10622560C2214yescomplemented
62#10622559C2214yescomplemented
63#10622555C2212yes—
64#10622555C2214yescomplemented
65#10622553C2214yes—
66#10622542C2212yescomplemented
67#10622288C2214yes—
68#10622287C2214yes—
69#10622282C2214yes—
70#10622281C2214yes—
71#10622277C2214yes—
72#10622273C2214yescomplemented
73#10622270C2214yescomplemented
74#10622269C2214yescomplemented
75#10622267C2214yescomplemented
76#10622260C2214yescomplemented
77C24×D11C2311yescharacteristic
78C22×D4×C11C2312yes—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11C2312yes—
84C22×C22⋊D11C2312yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—24no—
90C22×C4×D11—44no—
91C22×C4×D11C2314yes—
92C22×Dic22—24no—
93C22×Dic22—44no—
94C22×Dic22C2312yes—
95C22×Dic22C2312yes—
96C22×Dic22C2311yescharacteristic
97C11×#121—24no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C42×C11C2312yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2312yes—
111C2×C22⋊Dic11C2314yes—
112#66992—28no—
113#66990—28no—
114#66989—44no—
115D4×Dic11—28no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4D418yes—
118C2×(C2×D11)⋊C4C2312yes—
119C2×(C2×D11)⋊C4C2312yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2312yes—
128C2×C4⋊Dic11C2314yes—
129#66977—24no—
130C2×Dic11⋊C4—24no—
131C2×Dic11⋊C4—24no—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2312yes—
140#66951—28no—
141#66949—216no—
142#66949—216no—
143#66939—28no—
144#66938—28no—
145#66936—48no—
146#66922—44no—
147C11×#95C2314yes—
148C11×#95C2314yes—
149C11×#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158#36705—111nomaximal, Sylow
159C24×C11C2412yes—
160C24×C11C2411yescharacteristic
161C23×D11—24no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11C2×D414yes—
165C23×D11C2412yes—
166C2×D4×C11—24no—
167C2×D4×C11—28no—
168C2×D4×C11—22no—
169C2×D4×C11—42no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11—42no—
175C22×C4×C11C2×D414yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2414yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C2×C22⋊D11—24no—
183C2×C22⋊D11—24no—
184C2×C22⋊D11—44no—
185C2×C22⋊D11—44no—
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—42no—
191C22×Dic11—42no—
192C22×Dic11—44no—
193C22×Dic11C2×D414yes—
194C22×Dic11C2414yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C22×Dic11C2412yes—
200C2×C4×D11—28no—
201C2×C4×D11—28no—
202C2×C4×D11—44no—
203C2×C4×D11—416no—
204C2×Dic22—24no—
205C2×Dic22—24no—
206C2×Dic22—24no—
207C2×Dic22—24no—
208C2×Dic22—22no—
209C2×Dic22—42no—
210C2×Dic22—42no—
211C2×Dic22—42no—
212C2×Dic22—416no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—44no—
219C11×C22⋊C4—44no—
220C42×C11—42no—
221C22⋊Dic11—24no—
222C22⋊Dic11—28no—
223C22⋊Dic11—24no—
224C22⋊Dic11—24no—
225C22⋊Dic11—44no—
226(C2×D11)⋊C4—24no—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—28no—
229(C2×D11)⋊C4—44no—
230(C2×D11)⋊C4—44no—
231(C2×D11)⋊C4C2×D418yes—
232(C2×D11)⋊C4C2×D418yes—
233C4⋊Dic11—24no—
234C4⋊Dic11—28no—
235C4⋊Dic11—22no—
236C4⋊Dic11—44no—
237Dic11⋊C4—28no—
238Dic11⋊C4—28no—
239Dic11⋊C4—24no—
240Dic11⋊C4—44no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243C4×Dic11—24no—
244C4×Dic11—42no—
245C2×#538—111no—
246C22×C22⋊Q8—111no—
247#2849—112no—
248#2689—114no—
249#2687—114no—
250#2674—114no—
251#2672—114no—
252#2622—112no—
253#2591D1111yescharacteristic, complemented
254#2583—111no—
255#2579—112no—
256#2487—112no—
257#2436—111no—
258#2434—111no—
259#2312—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11C22×D412yes—
267C23×C112−1+414yes—
268C23×C11C2511yescharacteristic
269C22×D11—28no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11—416no—
276C22×D11C22×D414yes—
277D4×C11—48no—
278D4×C11—82no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—44no—
292C2×C4×C11—44no—
293C2×C4×C11—44no—
294C2×C4×C11C22×D412yes—
295C2×C4×C11C22×D412yes—
296C22⋊D11—84no—
297C22⋊D11—84no—
298C2×Dic11—28no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—44no—
313C2×Dic11—44no—
314C2×Dic11—84no—
315C2×Dic11C22×D414yes—
316C2×Dic11H(5,𝔽2)14yes—
317C4×D11—416no—
318Dic22—48no—
319Dic22—48no—
320Dic22—82no—
321C23×Q8—111no—
322C24×C4—111no—
323#538—228no—
324C2×C4⋊Q8—112no—
325C2×#126—112no—
326C2×#124—112no—
327C2×#124—112no—
328C2×#123—112no—
329C2×#123—114no—
330C2×C22⋊Q8—111no—
331C2×C22⋊Q8—114no—
332C2×C22⋊Q8—114no—
333C2×C22⋊Q8—228no—
334C2×#121—112no—
335C2×#121C2×D1111yescharacteristic
336C2×#120—112no—
337C2×C4×D4—112no—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343#400—114no—
344#400C2×D1112yescomplemented
345#399—114no—
346#398—112no—
347#398—114no—
348#397—114no—
349#397—114no—
350#396—114no—
351#395—112no—
352#395—114no—
353#394—114no—
354#394—114no—
355#394C2×D1112yescomplemented
356#393—114no—
357#391—112no—
358#391—112no—
359#389—114no—
360#389—114no—
361#388—114no—
362#388—114no—
363#388C2×D1114yescomplemented
364#387—114no—
365#386—112no—
366#386—112no—
367#386—114no—
368#386C2×D1112yes—
369#386C2×D1112yes—
370#385—112no—
371#385—112no—
372#385—112no—
373#385—114no—
374#385—112no—
375#385—114no—
376#381—114no—
377#380—112no—
378#380—114no—
379#379—112no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4C2×D1111yescharacteristic
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—28no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—48no—
389C22×C11#53614yes—
390C22×C11C23×D411yescharacteristic
391C22×C11C2×H(5,𝔽2)12yes—
392C22×C11C2×2−1+412yes—
393C22×C11#58512yes—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—24no—
397C2×D11—416no—
398C2×D11—48no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—44no—
405Dic11—24no—
406Dic11—24no—
407Dic11—42no—
408Dic11—42no—
409Dic11—42no—
410Dic11—44no—
411C25—111no—
412C22×Q8—112no—
413C22×Q8—112no—
414C22×Q8—111no—
415C22×Q8—224no—
416C22×Q8—444no—
417C22×D4—112no—
418C22×D4—112no—
419C22×D4C22×D1112yes—
420C22×D4C22×D1111yescharacteristic
421C23×C4—111no—
422C23×C4—111no—
423C23×C4—111no—
424C23×C4—112no—
425C23×C4—114no—
426C23×C4—224no—
427C23×C4—444no—
428C23×C4C22×D1111yescharacteristic
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C4⋊Q8—444no—
432#126—228no—
433#124—228no—
434#124—444no—
435#123—228no—
436#123—448no—
437C22⋊Q8—2216no—
438C22⋊Q8—2216no—
439C22⋊Q8—224no—
440#121—24no—
441#121—228no—
442#120—228no—
443C4×D4—228no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—111no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—224no—
457C2×C4⋊C4C22×D1112yes—
458C2×C4⋊C4C22×D1112yes—
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C22⋊C4—118no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4—112no—
464C2×C22⋊C4—112no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—112no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4C22×D1112yes—
475C2×C22⋊C4C22×D1112yes—
476C2×C22⋊C4C22×D1114yes—
477C2×C22⋊C4C22×D1114yes—
478C2×C42—112no—
479C2×C42—112no—
480C2×C42C22×D1112yes—
481#95—112no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95C22×D1112yes—
490#95C22×D1114yes—
491#95C22×D1114yes—
492C2×C11—24no—
493C2×C11—82no—
494C2×C11C2×#53611yescharacteristic
495C2×C11#348411yescharacteristic
496C2×C11#348511yescharacteristic
497C2×C11#354114yes—
498D11—44no—
499C24—112no—
500C24—114no—
501C24—224no—
502C24—442no—
503C24—442no—
504C24C23×D1112yes—
505C24C23×D1111yescharacteristic
506C2×Q8—224no—
507C2×Q8—224no—
508C2×Q8—224no—
509C2×Q8—224no—
510C2×Q8—222no—
511C2×Q8—442no—
512C2×Q8—442no—
513C2×Q8—442no—
514C2×Q8—4416no—
515C2×D4—24no—
516C2×D4—28no—
517C2×D4—22no—
518C2×D4—42no—
519C2×D4—224no—
520C2×D4—224no—
521C2×D4—444no—
522C2×D4—444no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—114no—
531C22×C4—114no—
532C22×C4—112no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—228no—
536C22×C4—228no—
537C22×C4—224no—
538C22×C4—224no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—444no—
542C22×C4—4416no—
543C22×C4—442no—
544C22×C4—442no—
545C22×C4—444no—
546C22×C4D4×D1114yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1114yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1112yes—
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1111yescharacteristic
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—228no—
557C4⋊C4—228no—
558C4⋊C4—224no—
559C4⋊C4—228no—
560C4⋊C4—224no—
561C4⋊C4—222no—
562C4⋊C4—444no—
563C4⋊C4—444no—
564C4⋊C4—444no—
565C4⋊C4—444no—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—118no—
571C22⋊C4—118no—
572C22⋊C4—228no—
573C22⋊C4—224no—
574C22⋊C4—224no—
575C22⋊C4—224no—
576C22⋊C4—228no—
577C22⋊C4—224no—
578C22⋊C4—224no—
579C22⋊C4—444no—
580C22⋊C4—444no—
581C22⋊C4—444no—
582C42—42no—
583C42—224no—
584C42—442no—
585C11#3670511yescharacteristic, complemented, Sylow
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—114no—
593C23—224no—
594C23—224no—
595C23—224no—
596C23—228no—
597C23—444no—
598C23—444no—
599C23—4416no—
600C23C2×D4×D1112yes—
601C23#6704314yes—
602C23C24×D1111yescharacteristic
603Q8—448no—
604Q8—448no—
605Q8—882no—
606D4—48no—
607D4—82no—
608D4—884no—
609D4—884no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—44no—
623C2×C4—44no—
624C2×C4—44no—
625C2×C4—114no—
626C2×C4—114no—
627C2×C4—228no—
628C2×C4—222no—
629C2×C4—224no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—224no—
635C2×C4—224no—
636C2×C4—224no—
637C2×C4—224no—
638C2×C4—222no—
639C2×C4—224no—
640C2×C4—222no—
641C2×C4—4416no—
642C2×C4—444no—
643C2×C4—444no—
644C2×C4—884no—
645C2×C4C2×D4×D1112yes—
646C2×C4C2×D4×D1112yes—
647C22—28no—
648C22—22no—
649C22—22no—
650C22—48no—
651C22—42no—
652C22—42no—
653C22—42no—
654C22—224no—
655C22—224no—
656C22—224no—
657C22—4416no—
658C22—448no—
659C22#1062320614yes—
660C22C22×D4×D1111yescharacteristic
661C22C2×#6704312yes—
662C22#1062345312yes—
663C22D11×H(5,𝔽2)12yes—
664C4—22no—
665C4—22no—
666C4—44no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—224no—
671C4—224no—
672C4—444no—
673C4—442no—
674C4—442no—
675C4—442no—
676C2—24no—
677C2—82no—
678C2—444no—
679C2C2×#1062320611yescharacteristic
680C2#1308224811yescharacteristic
681C2#1308225811yescharacteristic
682C2#1308289414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2591C2
prime radicalC2×#10623148C2
hypercenter#2591D11
hypocenterC11#36705
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2591

Complements

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

NH ≅ G/Ntype
2. C22×#66949C2semidirect
3. #13076907C2semidirect
4. #13075060C2semidirect
5. #13075034C2semidirect
6. #13074894C2semidirect
7. #13074860C2semidirect
8. #13074393C2semidirect
9. #13073996C2semidirect
10. #13073962C2semidirect
11. #13072930C2semidirect
12. #13072275C2semidirect
13. #13072260C2semidirect
14. #13071211C2semidirect
15. C11×#2591C2semidirect
22. C2×#66989C22semidirect
37. C2×#66922C22semidirect
38. C11×#400C22semidirect
39. C11×#394C22semidirect
40. C11×#388C22semidirect
49. #10622596C22semidirect
50. #10622592C22semidirect
51. #10622587C22semidirect
52. #10622585C22semidirect
59. #10622562C22semidirect
60. #10622561C22semidirect
61. #10622560C22semidirect
62. #10622559C22semidirect
64. #10622555C22semidirect
66. #10622542C22semidirect
72. #10622273C22semidirect
73. #10622270C22semidirect
74. #10622269C22semidirect
75. #10622267C22semidirect
76. #10622260C22semidirect
253. #2591D11semidirect
344. #400C2×D11semidirect
355. #394C2×D11semidirect
363. #388C2×D11semidirect
585. C11#36705semidirect

Maximal subgroups

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

subgroupindex
C2×#106231482
C22×#669492
#130769072
#130750602
#130750342
#130748942
#130748602
#130743932
#130739962
#130739622
#130729302
#130722752
#130722602
#130712112
C11×#25912
#3670511