Finite Group Databasebeta

← #14925767

Subgroups — #14925767

Order 2816.

1812 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
1#13073878C214yesmaximal, complemented
2#13073831C211yesmaximal, characteristic, complemented
3#13073611C211yesmaximal, characteristic
4#13073539C211yesmaximal, characteristic
5#13073220C212yesmaximal, complemented
6#13073014C212yesmaximal, complemented
7#13072405C212yesmaximal
8#13072122C212yesmaximal, complemented
9#13071915C214yesmaximal, complemented
10#13071183C211yesmaximal, characteristic, complemented
11#13071155C212yesmaximal
12#13071146C212yesmaximal, complemented
13#13071087C212yesmaximal, complemented
14#13071009C212yesmaximal, complemented
15C4×#66940C211yesmaximal, characteristic, complemented
16C4×#66946C211yesmaximal, characteristic
17C11×#2571C211yesmaximal, characteristic, complemented
18C2×#66950C2212yes—
19C2×#66946C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×#66940C2212yes—
23C2×#66940C2211yescharacteristic
24C2×#66928C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×C42×D11C2212yes—
27C2×#66922C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#400C2214yes—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#384C2211yescharacteristic
33C11×#382C2212yes—
34C11×#382C2212yes—
35C4×C11×C4⋊C4C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37#10622607C2214yes—
38#10622606C2214yes—
39#10622602C2214yes—
40#10622601C2212yes—
41#10622600C2212yes—
42#10622600C2212yes—
43#10622600C2212yes—
44#10622598C2212yes—
45#10622591C2214yes—
46C4⋊C4×Dic11C2214yes—
47C4⋊C4×Dic11C2212yes—
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2211yescharacteristic
50C4⋊C4×Dic11C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53#10622587C2212yes—
54#10622587C2212yes—
55#10622587C2212yes—
56#10622586C2212yes—
57#10622586C2212yes—
58C4×(C2×D11)⋊C4C2212yes—
59#10622549C2212yes—
60C4×Dic11⋊C4C2212yes—
61C42×Dic11C2212yes—
62C42×Dic11C2211yescharacteristic
63#10622542C2212yes—
64#10622542C2212yes—
65#10622288C2214yes—
66#10622287C2214yes—
67#10622282C2214yes—
68#10622282C2214yes—
69#10622279C2214yes—
70#10622279C2212yes—
71#10622279C2214yes—
72#10622279C2212yes—
73#10622277C2214yes—
74C11⋊#401C2214yes—
75#10622273C2214yes—
76#10622272C2214yes—
77#10622268C2214yes—
78#10622267C2214yes—
79#10622264C2214yes—
80#10622262C2212yes—
81#10622262C2212yes—
82#10622261C2214yes—
83C22×D44C2311yescharacteristic
84C22×C4×D11C2312yes—
85C22×C4×D11C2312yes—
86C22×C4×D11C2312yes—
87C22×Dic22C2312yes—
88C22×Dic22C2311yescharacteristic
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2312yes—
99C2×C42×C11C2311yescharacteristic
100C2×(C2×D11)⋊C4C2312yes—
101C2×(C2×D11)⋊C4C2314yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2314yes—
112C2×Dic11⋊C4C2312yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2312yes—
115C2×Dic11⋊C4C2314yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2312yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2311yescharacteristic
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130#66950—28no—
131#66946—24no—
132#66946—24no—
133#66940—24no—
134#66940—24no—
135#66940—28no—
136#66928—28no—
137C4×D44—24no—
138C42×D11—28no—
139#66922—24no—
140C4×Dic22—24no—
141C11×#95C2314yes—
142C11×#95C2312yes—
143C11×#95C2314yes—
144C11×#95C2314yes—
145C11×#95C2312yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159#34945—111nomaximal, Sylow
160C23×D11C2412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2414yes—
166C22×C4×C11C2411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C22×Dic11C2411yescharacteristic
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C22×Dic11C2414yes—
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2412yes—
175C22×Dic11C2411yescharacteristic
176C22×Dic11C2411yescharacteristic
177C2×D44—22no—
178C2×D44—22no—
179C2×D44#4114yes—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—42no—
189C2×Dic22—22no—
190C2×Dic22—22no—
191C2×Dic22—24no—
192C2×Dic22—24no—
193C2×Dic22—24no—
194C2×Dic22#4114yes—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—22no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—42no—
202C11×C4⋊C4—44no—
203C42×C11—24no—
204C42×C11—24no—
205C42×C11#4114yes—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—28no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—44no—
213C4⋊Dic11—28no—
214C4⋊Dic11—22no—
215C4⋊Dic11—24no—
216C4⋊Dic11—24no—
217C4⋊Dic11—22no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220Dic11⋊C4—28no—
221Dic11⋊C4—24no—
222C4×Dic11—24no—
223C4×Dic11—24no—
224C4×Dic11—24no—
225C4×Dic11—24no—
226C4×Dic11—28no—
227C4×Dic11—22no—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—22no—
231C4×Dic11—22no—
232C4×Dic11—41no—
233C4×Dic11—42no—
234C4×Dic11#4114yes—
235C4×Dic11#4114yes—
236#2573—114no—
237#2571D1111yescharacteristic, complemented
238#2568—111no—
239#2547—111no—
240#2538—111no—
241#2514—112no—
242#2494—112no—
243#2447—112no—
244#2421—112no—
245#2401—114no—
246C4×C4⋊Q8—111no—
247C4×#124—112no—
248C4×C22⋊Q8—112no—
249#2295—112no—
250#2283—112no—
251C42×Q8—111no—
252C42×D4—111no—
253C23×C11C2511yescharacteristic
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11C2×#4114yes—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—22no—
278C2×C4×C11C2×#4112yes—
279C2×C4×C11C2×#4112yes—
280C2×C4×C11C2×#4112yes—
281C2×C4×C11C2×#4112yes—
282C2×C4×C11C2×#4112yes—
283C2×C4×C11C2×#4112yes—
284C2×C4×C11C2×#4112yes—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—21no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—22no—
301C2×Dic11—21no—
302C2×Dic11—22no—
303C2×Dic11C2×#4112yes—
304C2×Dic11C2×#4114yes—
305C2×Dic11C2×#4112yes—
306C2×Dic11C2×#4112yes—
307C2×Dic11C2×#4112yes—
308C2×Dic112−1+412yes—
309D44—28no—
310C4×D11—48no—
311C4×D11—48no—
312C4×D11—48no—
313Dic22—28no—
314Dic22—48no—
315C2×C4⋊Q8—111no—
316C2×#124—112no—
317C2×C22⋊Q8—112no—
318C2×C4×Q8—112no—
319C2×C4×Q8—111no—
320C2×C4×Q8—111no—
321C2×C4×Q8—111no—
322C2×C4×D4—111no—
323C2×C4×D4—111no—
324C2×C4×D4—111no—
325C22×C42—112no—
326#401—114no—
327#400—114no—
328#400—114no—
329#400C2×D1114yes—
330#397—114no—
331#397—114no—
332#397—114no—
333#396—114no—
334#391—112no—
335#391—112no—
336#391—112no—
337#391—112no—
338#391—112no—
339#390—112no—
340#389—112no—
341#389—112no—
342#389—112no—
343#389C2×D1112yes—
344#389C2×D1112yes—
345#388—114no—
346#388—114no—
347#387—114no—
348#387—114no—
349#387—114no—
350#385—114no—
351#384C2×D1111yescharacteristic
352#383—114no—
353#382—112no—
354#382C2×D1112yes—
355#382C2×D1112yes—
356#381—114no—
357#380—112no—
358#380—112no—
359#380—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—112no—
362C4×C4⋊C4—114no—
363C4×C4⋊C4—111no—
364C4×C4⋊C4—111no—
365C4×C4⋊C4—111no—
366C4×C4⋊C4—111no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4—112no—
369C4×C4⋊C4—112no—
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C4⋊C4C2×D1111yescharacteristic
372C4×C22⋊C4—112no—
373C4×C22⋊C4—112no—
374C4×C22⋊C4—112no—
375C4×C22⋊C4—114no—
376C4×C22⋊C4—114no—
377#376—114no—
378C43—111no—
379C43—112no—
380C22×C11C22×#4111yescharacteristic
381C22×C11C22×#4111yescharacteristic
382C22×C11C22×#4111yescharacteristic
383C22×C11C22×#4111yescharacteristic
384C22×C11C22×#4111yescharacteristic
385C22×C11C2×2−1+411yescharacteristic
386C22×C11#58511yescharacteristic
387C2×D11—24no—
388C2×D11—24no—
389C2×D11—24no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—42no—
394C4×C11—22no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—44no—
399C4×C11—42no—
400C4×C11#52914yes—
401C4×C11#52914yes—
402Dic11—24no—
403Dic11—22no—
404Dic11—22no—
405Dic11—44no—
406Dic11—42no—
407Dic11—42no—
408Dic11—41no—
409Dic11#55614yes—
410C22×Q8—111no—
411C22×Q8—112no—
412C22×D4—111no—
413C23×C4—112no—
414C23×C4—112no—
415C23×C4—112no—
416C4⋊Q8—224no—
417#124—228no—
418C22⋊Q8—228no—
419C4×Q8—224no—
420C4×Q8—228no—
421C4×Q8—224no—
422C4×Q8—224no—
423C4×D4—224no—
424C4×D4—224no—
425C4×D4—224no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1112yes—
440C2×C4⋊C4C22×D1112yes—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1114yes—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—114no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—114no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—112no—
454C2×C42—111no—
455C2×C42—112no—
456C2×C42—112no—
457C2×C42—114no—
458C2×C42—112no—
459C2×C42—111no—
460C2×C42—112no—
461C2×C42—112no—
462C2×C42—111no—
463C2×C42—112no—
464C2×C42—228no—
465C2×C42C22×D1112yes—
466C2×C42C22×D1112yes—
467C2×C42C22×D1111yescharacteristic
468#95—114no—
469#95—114no—
470#95—114no—
471#95—112no—
472#95—112no—
473#95—114no—
474#95—114no—
475#95—112no—
476#95—112no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95C22×D1114yes—
482#95C22×D1112yes—
483#95C22×D1114yes—
484#95C22×D1114yes—
485#95C22×D1112yes—
486C2×C11C2×#52911yescharacteristic
487C2×C11C2×#52911yescharacteristic
488C2×C11#346111yescharacteristic
489C2×C11C2×#55611yescharacteristic
490C2×C11#347511yescharacteristic
491C2×C11#348011yescharacteristic
492C2×C11#348211yescharacteristic
493D11—44no—
494C24—112no—
495C2×Q8—114no—
496C2×Q8—222no—
497C2×Q8—224no—
498C2×Q8—222no—
499C2×Q8—224no—
500C2×Q8—224no—
501C2×D4—114no—
502C2×D4—222no—
503C2×D4—222no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—112no—
509C22×C4—111no—
510C22×C4—112no—
511C22×C4—114no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—224no—
519C22×C4—224no—
520C22×C4—442no—
521C22×C4C23×D1112yes—
522C22×C4C23×D1112yes—
523C22×C4C23×D1112yes—
524C22×C4C23×D1112yes—
525C22×C4C23×D1114yes—
526C22×C4C23×D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—24no—
533C4⋊C4—22no—
534C4⋊C4—24no—
535C4⋊C4—42no—
536C4⋊C4—44no—
537C4⋊C4—224no—
538C4⋊C4—228no—
539C4⋊C4—224no—
540C4⋊C4—228no—
541C4⋊C4—222no—
542C4⋊C4—224no—
543C4⋊C4—222no—
544C4⋊C4—224no—
545C4⋊C4—224no—
546C22⋊C4—224no—
547C22⋊C4—228no—
548C22⋊C4—224no—
549C22⋊C4—228no—
550C22⋊C4—228no—
551C22⋊C4—224no—
552C22⋊C4—444no—
553C42—24no—
554C42—24no—
555C42—114no—
556C42—114no—
557C42—224no—
558C42—224no—
559C42—224no—
560C42—228no—
561C42—224no—
562C42—222no—
563C42—224no—
564C42—224no—
565C42—222no—
566C42—222no—
567C42—441no—
568C42—442no—
569C42#434314yes—
570C11#3494511yescharacteristic, complemented, Sylow
571C23—114no—
572C23—222no—
573C23—222no—
574C23—222no—
575C23—222no—
576C23—222no—
577C23—222no—
578C23C24×D1111yescharacteristic
579Q8—228no—
580Q8—448no—
581D4—228no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—114no—
605C2×C4—222no—
606C2×C4—221no—
607C2×C4—222no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—224no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—448no—
624C2×C4—448no—
625C2×C4—448no—
626C2×C4C2×#434312yes—
627C2×C4C2×#434312yes—
628C2×C4C2×#434312yes—
629C2×C4#41×D1112yes—
630C2×C4#41×D1112yes—
631C2×C4#41×D1112yes—
632C2×C4#41×D1112yes—
633C22—224no—
634C22—224no—
635C22—224no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—442no—
640C22C22×#434311yescharacteristic
641C22C2×#41×D1111yescharacteristic
642C22C2×#41×D1111yescharacteristic
643C22C2×#41×D1111yescharacteristic
644C22C2×#41×D1111yescharacteristic
645C22#1062345511yescharacteristic
646C22D11×2−1+411yescharacteristic
647C4—22no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—44no—
652C4—42no—
653C4—114no—
654C4—224no—
655C4—222no—
656C4—222no—
657C4—442no—
658C4—444no—
659C4—441no—
660C4—442no—
661C4#1062322214yes—
662C4#1062322214yes—
663C2—444no—
664C2C2×#1062322211yescharacteristic
665C2C2×#1062322211yescharacteristic
666C2#1308205011yescharacteristic
667C2D11×#55611yescharacteristic
668C2#1308217311yescharacteristic
669C2#1308221211yescharacteristic
670C2#1308223511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2571C2
prime radicalC22×D44C23
hypercenter#2571D11
hypocenterC11#34945
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2571

Complements

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

NH ≅ G/Ntype
1. #13073878C2semidirect
2. #13073831C2semidirect
5. #13073220C2semidirect
6. #13073014C2semidirect
8. #13072122C2semidirect
9. #13071915C2semidirect
10. #13071183C2semidirect
12. #13071146C2semidirect
13. #13071087C2semidirect
14. #13071009C2semidirect
15. C4×#66940C2semidirect
17. C11×#2571C2semidirect
237. #2571D11semidirect
570. C11#34945semidirect

Maximal subgroups

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

subgroupindex
#130738782
#130738312
#130736112
#130735392
#130732202
#130730142
#130724052
#130721222
#130719152
#130711832
#130711552
#130711462
#130710872
#130710092
C4×#669402
C4×#669462
C11×#25712
#3494511