Finite Group Databasebeta

← #14960731

Subgroups — #14960731

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623175C211yesmaximal, characteristic
2C22×#66950C211yesmaximal, characteristic, complemented
3#13076911C212yesmaximal, complemented
4#13075213C214yesmaximal, complemented
5#13075185C214yesmaximal, complemented
6#13074963C214yesmaximal, complemented
7#13074957C214yesmaximal, complemented
8#13074394C212yesmaximal, complemented
9#13074096C211yesmaximal, characteristic, complemented
10#13073966C212yesmaximal, complemented
11#13073108C211yesmaximal, characteristic, complemented
12#13073095C211yesmaximal, characteristic, complemented
13#13071980C212yesmaximal, complemented
14#13071211C211yesmaximal, characteristic, complemented
15C11×#2583C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#67000C2212yes—
21C2×#66983C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26#10623175—28no—
27C2×#66951C2212yes—
28C2×#66950—28no—
29C2×#66950C2214yes—
30C2×#66950C2214yes—
31C2×#66949C2214yescomplemented
32C2×#66948C2212yes—
33C2×#66947C2212yes—
34C2×#66947C2214yes—
35C2×#66935C2212yes—
36C2×(C22⋊D11)⋊C4C2212yes—
37C11×#398C2212yescomplemented
38C11×#395C2212yescomplemented
39C11×#389C2214yescomplemented
40C11×#385C2212yes—
41C11×#385C2212yes—
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622843C2212yescomplemented
44#10622826C2212yes—
45#10622826C2212yes—
46C4×C22⋊Dic11C2211yescharacteristic
47#10622607C2214yescomplemented
48#10622606C2214yes—
49#10622604C2214yes—
50#10622604C2212yescomplemented
51#10622603C2214yescomplemented
52#10622602C2214yes—
53#10622599C2212yescomplemented
54#10622596C2214yescomplemented
55#10622594C2214yescomplemented
56#10622592C2214yescomplemented
57#10622589C2212yescomplemented
58#10622571C2212yes—
59#10622571C2212yes—
60#10622568C2212yes—
61#10622559C2212yes—
62#10622559C2212yes—
63#10622555C2212yes—
64#10622553C2214yes—
65#10622552C2212yescomplemented
66#10622549C2212yescomplemented
67#10622288C2214yes—
68#10622287C2214yescomplemented
69#10622286C2214yescomplemented
70#10622285C2214yes—
71#10622282C2214yes—
72#10622281C2214yescomplemented
73#10622278C2214yes—
74#10622277C2214yes—
75#10622270C2214yescomplemented
76#10622259C2214yescomplemented
77C24×D11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11C2312yes—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C22×D44C2312yes—
87C22×D44C2312yes—
88C22×D44C2311yescharacteristic
89C22×C4×D11—24no—
90C22×C4×D11—44no—
91C22×C4×D11C2314yes—
92C22×C4×D11C2312yes—
93C22×Dic22—24no—
94C22×Dic22—44no—
95C22×Dic22C2314yes—
96C11×C22⋊Q8—24no—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2314yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2314yes—
104C2×C11×C22⋊C4C2312yes—
105C2×C11×C22⋊C4C2312yes—
106C2×C42×C11C2312yes—
107C2×C22⋊Dic11C2312yes—
108#67000—28no—
109#66983—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4D418yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2314yes—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×C4⋊Dic11—24no—
126C2×C4⋊Dic11—24no—
127C2×C4⋊Dic11C2314yes—
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2312yes—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2312yes—
137#66951—28no—
138#66950—216no—
139#66950—216no—
140#66949—48no—
141#66948—28no—
142#66947—28no—
143#66947—48no—
144#66935—28no—
145(C22⋊D11)⋊C4—28no—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157#36716—111nomaximal, Sylow
158C24×C11C2411yescharacteristic
159C23×D11—24no—
160C23×D11—42no—
161C23×D11—42no—
162C23×D11C2×D414yes—
163C23×D11C2412yes—
164C23×D11C2412yes—
165C2×Q8×C11—22no—
166C2×Q8×C11—42no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2414yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2412yes—
180C2×C22⋊D11—24no—
181C2×C22⋊D11—28no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11—42no—
187C22×Dic11C2×D414yes—
188C22×Dic11C2412yes—
189C22×Dic11C2414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C2×D44—24no—
194C2×D44—24no—
195C2×D44—22no—
196C2×D44—44no—
197C2×D44—42no—
198C2×D44—44no—
199C2×C4×D11—24no—
200C2×C4×D11—28no—
201C2×C4×D11—28no—
202C2×C4×D11—44no—
203C2×C4×D11—44no—
204C2×C4×D11—416no—
205C2×Dic22—28no—
206C2×Dic22—28no—
207C2×Dic22—44no—
208C2×Dic22—416no—
209C11×C4⋊C4—22no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—28no—
214C11×C4⋊C4—44no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C42×C11—42no—
218C22⋊Dic11—24no—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—24no—
221(C2×D11)⋊C4—24no—
222(C2×D11)⋊C4—28no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—44no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4—44no—
228(C2×D11)⋊C4—44no—
229(C2×D11)⋊C4—44no—
230(C2×D11)⋊C4C2×D418yes—
231(C2×D11)⋊C4C2×D418yes—
232C4⋊Dic11—28no—
233C4⋊Dic11—24no—
234C4⋊Dic11—24no—
235C4⋊Dic11—22no—
236Dic11⋊C4—24no—
237Dic11⋊C4—44no—
238Dic11⋊C4—44no—
239Dic11⋊C4—44no—
240C4×Dic11—24no—
241C4×Dic11—42no—
242C2×#538—111no—
243C22×C22⋊Q8—111no—
244#2849—112no—
245#2700—114no—
246#2698—114no—
247#2681—114no—
248#2680—114no—
249#2622—112no—
250#2591—111no—
251#2583D1111yescharacteristic, complemented
252#2579—112no—
253#2504—111no—
254#2502—111no—
255#2409—112no—
256#2312—111no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11C22×D412yes—
260C23×C112−1+414yes—
261C23×C11C2511yescharacteristic
262C22×D11—28no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—24no—
266C22×D11—22no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—44no—
271C22×D11—44no—
272C22×D11—416no—
273C22×D11C22×D414yes—
274Q8×C11—82no—
275C2×C4×C11—28no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—44no—
290C2×C4×C11—44no—
291C2×C4×C11C22×D412yes—
292C2×C4×C11C22×D412yes—
293C2×C4×C11H(5,𝔽2)14yes—
294C22⋊D11—48no—
295C2×Dic11—24no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—44no—
306C2×Dic11—44no—
307C2×Dic11—44no—
308C2×Dic11C22×D414yes—
309D44—82no—
310D44—84no—
311D44—84no—
312C4×D11—416no—
313C4×D11—84no—
314Dic22—416no—
315C23×Q8—111no—
316C24×C4—111no—
317#538—228no—
318C2×#126—112no—
319C2×#124—112no—
320C2×#123—112no—
321C2×#123—114no—
322C2×C22⋊Q8—114no—
323C2×C22⋊Q8—114no—
324C2×C22⋊Q8—114no—
325C2×C22⋊Q8—228no—
326C2×C22⋊Q8C2×D1111yescharacteristic
327C2×#121—111no—
328C2×#121—112no—
329C2×#120—112no—
330C2×C4×D4—112no—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—111no—
333C22×C4⋊C4C2×D1111yescharacteristic
334C22×C22⋊C4—111no—
335C22×C22⋊C4—111no—
336#400—112no—
337#398—114no—
338#398—114no—
339#398C2×D1112yescomplemented
340#397—114no—
341#397—114no—
342#397—114no—
343#396—114no—
344#395—114no—
345#395C2×D1112yescomplemented
346#394—112no—
347#394—114no—
348#394—114no—
349#393—114no—
350#391—112no—
351#391—114no—
352#390—112no—
353#389C2×D1114yescomplemented
354#388—114no—
355#388—114no—
356#388—114no—
357#387—114no—
358#386—112no—
359#386—112no—
360#386—112no—
361#386—112no—
362#386—114no—
363#385—114no—
364#385—112no—
365#385—112no—
366#385—114no—
367#385C2×D1112yes—
368#385C2×D1112yes—
369#384—112no—
370#382—112no—
371#381—114no—
372#380—112no—
373#379—112no—
374C4×C22⋊C4—111no—
375C4×C22⋊C4C2×D1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—28no—
379C22×C11#53614yes—
380C22×C11C23×D411yescharacteristic
381C22×C11C2×H(5,𝔽2)12yes—
382C22×C11C2×2−1+412yes—
383C22×C11#58512yes—
384C2×D11—24no—
385C2×D11—24no—
386C2×D11—24no—
387C2×D11—416no—
388C2×D11—48no—
389C2×D11—42no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—48no—
393C4×C11—24no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—44no—
400Dic11—24no—
401Dic11—42no—
402Dic11—42no—
403Dic11—42no—
404Dic11—44no—
405C25—111no—
406C22×Q8—114no—
407C22×Q8—224no—
408C22×Q8—444no—
409C22×Q8C22×D1111yescharacteristic
410C22×D4—112no—
411C22×D4—112no—
412C22×D4—112no—
413C22×D4—111no—
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—111no—
417C23×C4—114no—
418C23×C4—112no—
419C23×C4—224no—
420C23×C4—444no—
421C23×C4C22×D1111yescharacteristic
422C23×C4C22×D1111yescharacteristic
423C23×C4C22×D1111yescharacteristic
424#126—228no—
425#124—228no—
426#123—228no—
427#123—448no—
428C22⋊Q8—24no—
429C22⋊Q8—2216no—
430C22⋊Q8—2216no—
431C22⋊Q8—448no—
432#121—228no—
433#121—224no—
434#120—228no—
435C4×D4—228no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—224no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4C22×D1112yes—
448C2×C4⋊C4C22×D1112yes—
449C2×C4⋊C4C22×D1112yes—
450C2×C4⋊C4C22×D1114yes—
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1114yes—
453C2×C22⋊C4—118no—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—112no—
457C2×C22⋊C4—114no—
458C2×C22⋊C4—112no—
459C2×C22⋊C4—112no—
460C2×C22⋊C4—112no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4C22×D1112yes—
470C2×C22⋊C4C22×D1112yes—
471C2×C42—112no—
472C2×C42—112no—
473C2×C42C22×D1112yes—
474#95—112no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95C22×D1112yes—
483#95C22×D1114yes—
484#95C22×D1114yes—
485C2×C11—24no—
486C2×C11C2×#53611yescharacteristic
487C2×C11#348411yescharacteristic
488C2×C11#348511yescharacteristic
489C2×C11#354114yes—
490D11—44no—
491D11—82no—
492C24—112no—
493C24—114no—
494C24—112no—
495C24—224no—
496C24—442no—
497C24—442no—
498C24C23×D1111yescharacteristic
499C2×Q8—22no—
500C2×Q8—42no—
501C2×Q8—228no—
502C2×Q8—228no—
503C2×Q8—444no—
504C2×Q8—4416no—
505C2×D4—224no—
506C2×D4—224no—
507C2×D4—224no—
508C2×D4—228no—
509C2×D4—222no—
510C2×D4—444no—
511C2×D4—442no—
512C2×D4—444no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—112no—
519C22×C4—114no—
520C22×C4—112no—
521C22×C4—114no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—224no—
525C22×C4—228no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—228no—
529C22×C4—444no—
530C22×C4—444no—
531C22×C4—4416no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—442no—
535C22×C4D4×D1114yes—
536C22×C4C23×D1112yes—
537C22×C4C23×D1114yes—
538C22×C4C23×D1112yes—
539C22×C4C23×D1112yes—
540C22×C4C23×D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542C22×C4C23×D1112yes—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—28no—
548C4⋊C4—44no—
549C4⋊C4—228no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4—222no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C4⋊C4—444no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—118no—
560C22⋊C4—118no—
561C22⋊C4—224no—
562C22⋊C4—228no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—224no—
567C22⋊C4—228no—
568C22⋊C4—444no—
569C22⋊C4—444no—
570C22⋊C4—444no—
571C22⋊C4—444no—
572C22⋊C4—444no—
573C42—42no—
574C42—224no—
575C42—442no—
576C11#3671611yescharacteristic, complemented, Sylow
577C23—22no—
578C23—22no—
579C23—114no—
580C23—228no—
581C23—224no—
582C23—224no—
583C23—224no—
584C23—222no—
585C23—224no—
586C23—224no—
587C23—224no—
588C23—444no—
589C23—444no—
590C23—4416no—
591C23C2×D4×D1112yes—
592C23#6704014yes—
593C23C24×D1111yescharacteristic
594Q8—82no—
595Q8—4416no—
596D4—448no—
597D4—882no—
598D4—884no—
599D4—884no—
600C2×C4—28no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—44no—
615C2×C4—44no—
616C2×C4—114no—
617C2×C4—224no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—4416no—
628C2×C4—444no—
629C2×C4—444no—
630C2×C4—444no—
631C2×C4—884no—
632C2×C4C2×D4×D1112yes—
633C2×C4C2×D4×D1112yes—
634C2×C4#6704214yes—
635C22—28no—
636C22—22no—
637C22—22no—
638C22—224no—
639C22—224no—
640C22—224no—
641C22—4416no—
642C22—448no—
643C22—448no—
644C22—442no—
645C22—442no—
646C22—442no—
647C22#1062325514yes—
648C22C22×D4×D1111yescharacteristic
649C22C2×#6704012yes—
650C22C2×#6704212yes—
651C22#1062345512yes—
652C4—24no—
653C4—22no—
654C4—22no—
655C4—44no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—224no—
660C4—444no—
661C4—442no—
662C4—442no—
663C4—442no—
664C2—24no—
665C2—444no—
666C2—882no—
667C2C2×#1062325511yescharacteristic
668C2#1308224911yescharacteristic
669C2#1308225711yescharacteristic
670C2#1308291014yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2583C2
prime radicalC2×#10623175C2
hypercenter#2583D11
hypocenterC11#36716
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2583

Complements

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

NH ≅ G/Ntype
2. C22×#66950C2semidirect
3. #13076911C2semidirect
4. #13075213C2semidirect
5. #13075185C2semidirect
6. #13074963C2semidirect
7. #13074957C2semidirect
8. #13074394C2semidirect
9. #13074096C2semidirect
10. #13073966C2semidirect
11. #13073108C2semidirect
12. #13073095C2semidirect
13. #13071980C2semidirect
14. #13071211C2semidirect
15. C11×#2583C2semidirect
31. C2×#66949C22semidirect
37. C11×#398C22semidirect
38. C11×#395C22semidirect
39. C11×#389C22semidirect
43. #10622843C22semidirect
47. #10622607C22semidirect
50. #10622604C22semidirect
51. #10622603C22semidirect
53. #10622599C22semidirect
54. #10622596C22semidirect
55. #10622594C22semidirect
56. #10622592C22semidirect
57. #10622589C22semidirect
65. #10622552C22semidirect
66. #10622549C22semidirect
68. #10622287C22semidirect
69. #10622286C22semidirect
72. #10622281C22semidirect
75. #10622270C22semidirect
76. #10622259C22semidirect
251. #2583D11semidirect
339. #398C2×D11semidirect
345. #395C2×D11semidirect
353. #389C2×D11semidirect
576. C11#36716semidirect

Maximal subgroups

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

subgroupindex
C2×#106231752
C22×#669502
#130769112
#130752132
#130751852
#130749632
#130749572
#130743942
#130740962
#130739662
#130731082
#130730952
#130719802
#130712112
C11×#25832
#3671611