Finite Group Databasebeta

← #14960626

Subgroups — #14960626

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic, complemented
2C22×#66939C211yesmaximal, characteristic
3#13076901C212yesmaximal, complemented
4#13075143C214yesmaximal, complemented
5#13075139C214yesmaximal, complemented
6#13074903C214yesmaximal, complemented
7#13074895C214yesmaximal, complemented
8#13074427C212yesmaximal, complemented
9#13073993C212yesmaximal, complemented
10#13072892C211yesmaximal, characteristic, complemented
11#13072890C211yesmaximal, characteristic, complemented
12#13072886C211yesmaximal, characteristic, complemented
13#13072265C212yesmaximal
14#13071217C211yesmaximal, characteristic, complemented
15C11×#2482C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25#10623050—28no—
26C2×#66943C2212yescomplemented
27C2×#66941C2212yescomplemented
28C2×#66939—28no—
29C2×#66939C2214yes—
30C2×#66939C2214yes—
31C2×#66938C2214yes—
32C2×#66931C2212yes—
33C2×#66931C2212yes—
34C2×#66931C2214yescomplemented
35C2×#66923C2212yescomplemented
36C2×#66922C2212yescomplemented
37C11×#399C2212yescomplemented
38C11×#397C2212yescomplemented
39C11×#388C2214yescomplemented
40C11×#385C2212yes—
41C11×#381C2211yescharacteristic
42C11×#379C2212yes—
43#10622860C2212yes—
44#10622824C2211yescharacteristic
45#10622823C2212yes—
46#10622607C2214yescomplemented
47#10622606C2212yescomplemented
48#10622605C2214yescomplemented
49#10622605C2212yescomplemented
50#10622598C2214yescomplemented
51#10622597C2214yescomplemented
52#10622574C2214yes—
53#10622572C2214yes—
54#10622570C2214yes—
55#10622568C2212yes—
56#10622568C2212yes—
57#10622566C2212yescomplemented
58#10622563C2212yes—
59#10622563C2214yescomplemented
60#10622562C2212yescomplemented
61#10622559C2212yes—
62#10622559C2214yescomplemented
63#10622557C2214yescomplemented
64#10622555C2212yes—
65#10622555C2214yescomplemented
66C22⋊C4×Dic11C2212yes—
67#10622553C2214yescomplemented
68#10622290C2212yescomplemented
69#10622289C2214yescomplemented
70#10622287C2212yescomplemented
71#10622286C2214yescomplemented
72#10622283C2214yescomplemented
73#10622269C2214yescomplemented
74#10622267C2214yescomplemented
75#10622266C2214yescomplemented
76#10622260C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—24no—
82C22×C22⋊D11—44no—
83C22×C22⋊D11C2314yes—
84C23×Dic11—24no—
85C23×Dic11—44no—
86C23×Dic11C2314yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C22×Dic22C2312yes—
91C22×Dic22C2312yes—
92C11×#117—24no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4—24no—
97C2×C11×C22⋊C4C2312yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C42×C11C2312yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2314yes—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117#66979—24no—
118C2×C4⋊Dic11—24no—
119C2×C4⋊Dic11D418yes—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2314yes—
125C2×C4⋊Dic11C2314yes—
126C2×C4⋊Dic11C2312yes—
127C2×C4⋊Dic11C2312yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2314yes—
133C2×Dic11⋊C4C2314yes—
134C2×Dic11⋊C4C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2314yes—
137#66943—28no—
138#66941—28no—
139#66939—216no—
140#66939—216no—
141#66938—48no—
142#66931—28no—
143#66931—28no—
144#66931—48no—
145#66923—28no—
146#66922—28no—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157#36711—111nomaximal, Sylow
158C24×C11—22no—
159C24×C11—24no—
160C24×C11—24no—
161C24×C11—42no—
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C23×D11—22no—
165C23×D11—24no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11C2412yes—
169C22×C4×C11—24no—
170C22×C4×C11—22no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D414yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—44no—
182C2×C22⋊D11—416no—
183C22×Dic11—28no—
184C22×Dic11—22no—
185C22×Dic11—28no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C22×Dic11—44no—
189C22×Dic11—42no—
190C22×Dic11—416no—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D414yes—
193C22×Dic11C2414yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C2×Dic22—24no—
200C2×Dic22—24no—
201C2×Dic22—44no—
202C2×Dic22—44no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4—22no—
205C11×C4⋊C4—44no—
206C11×C22⋊C4—24no—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—24no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—24no—
211C11×C22⋊C4—44no—
212C42×C11—24no—
213C22⋊Dic11—24no—
214C22⋊Dic11—28no—
215C22⋊Dic11—24no—
216C22⋊Dic11—44no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—24no—
219(C2×D11)⋊C4—24no—
220(C2×D11)⋊C4—44no—
221(C2×D11)⋊C4—44no—
222(C2×D11)⋊C4—44no—
223(C2×D11)⋊C4—44no—
224C4⋊Dic11—24no—
225C4⋊Dic11—24no—
226C4⋊Dic11—28no—
227C4⋊Dic11—22no—
228C4⋊Dic11—22no—
229C4⋊Dic11—44no—
230C4⋊Dic11C2×D418yes—
231C4⋊Dic11C2×D418yes—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—44no—
237Dic11⋊C4—44no—
238Dic11⋊C4—44no—
239C4×Dic11—24no—
240C4×Dic11—44no—
241C2×#544—111no—
242C22×#123—111no—
243#2848—112no—
244#2694—114no—
245#2694—114no—
246#2674—114no—
247#2674—114no—
248#2626—112no—
249#2583—112no—
250#2482—111no—
251#2482—111no—
252#2482—111no—
253#2482D1111yescharacteristic, complemented
254#2435—112no—
255#2313—111no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—28no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—416no—
264C23×C11—44no—
265C23×C11—44no—
266C23×C11C22×D412yes—
267C23×C11H(5,𝔽2)14yes—
268C23×C112−1+414yes—
269C23×C11C2511yescharacteristic
270C22×D11—22no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—44no—
276C22×D11—44no—
277C22×D11—44no—
278C22×D11—88no—
279C2×C4×C11—28no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—44no—
292C2×C4×C11C22×D412yes—
293C2×C4×C11C22×D412yes—
294C22⋊D11—416no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—44no—
307C2×Dic11—44no—
308C2×Dic11—416no—
309C2×Dic11—44no—
310C2×Dic11C22×D414yes—
311C2×Dic11C22×D414yes—
312Dic22—84no—
313Dic22—84no—
314C23×D4—111no—
315C24×C4—111no—
316#544—228no—
317C2×C4⋊Q8—112no—
318C2×C4⋊Q8—112no—
319C2×#125—112no—
320C2×#125—112no—
321C2×#124—114no—
322C2×#123—114no—
323C2×#123—114no—
324C2×#123—228no—
325C2×C22⋊Q8—112no—
326C2×C22⋊Q8—112no—
327C2×C22⋊Q8—114no—
328C2×#117—111no—
329C2×#117C2×D1111yescharacteristic
330C22×C4⋊C4—111no—
331C22×C4⋊C4—111no—
332C22×C22⋊C4—111no—
333C22×C22⋊C4—111no—
334C22×C22⋊C4C2×D1111yescharacteristic
335#399—114no—
336#399—112no—
337#399—112no—
338#399—112no—
339#399C2×D1112yescomplemented
340#398—114no—
341#397—112no—
342#397—112no—
343#397—112no—
344#397C2×D1112yescomplemented
345#396—114no—
346#396—114no—
347#395—114no—
348#394—114no—
349#394—114no—
350#393—114no—
351#390—114no—
352#389—114no—
353#389—114no—
354#388—114no—
355#388—114no—
356#388—114no—
357#388C2×D1114yescomplemented
358#387—114no—
359#387—114no—
360#385—112no—
361#385—112no—
362#385—112no—
363#385—114no—
364#385—114no—
365#385C2×D1112yes—
366#381—111no—
367#381C2×D1111yescharacteristic
368#380—112no—
369#380—114no—
370#379—112no—
371#379—112no—
372#379—112no—
373#379C2×D1112yes—
374C4×C22⋊C4—112no—
375C22×C11—22no—
376C22×C11—22no—
377C22×C11—28no—
378C22×C11—24no—
379C22×C11—28no—
380C22×C11—416no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—44no—
384C22×C11#53614yes—
385C22×C11C23×D411yescharacteristic
386C22×C11C2×H(5,𝔽2)12yes—
387C22×C11C2×2−1+412yes—
388C22×C11#58512yes—
389C2×D11—42no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—44no—
393C2×D11—44no—
394C2×D11—88no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—44no—
401Dic11—24no—
402Dic11—24no—
403Dic11—42no—
404Dic11—42no—
405Dic11—42no—
406Dic11—44no—
407C25—111no—
408C25C22×D1111yescharacteristic
409C22×Q8—112no—
410C22×Q8—112no—
411C22×D4—114no—
412C22×D4—224no—
413C22×D4—444no—
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—114no—
417C23×C4—111no—
418C23×C4—224no—
419C23×C4—444no—
420C23×C4C22×D1111yescharacteristic
421C23×C4C22×D1111yescharacteristic
422C4⋊Q8—228no—
423C4⋊Q8—228no—
424#125—228no—
425#125—228no—
426#124—448no—
427#123—2216no—
428#123—2216no—
429C22⋊Q8—228no—
430C22⋊Q8—228no—
431C22⋊Q8—448no—
432#117—24no—
433#117—224no—
434C2×C4⋊C4—118no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—112no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4—112no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—224no—
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C4⋊C4C22×D1114yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—114no—
457C2×C22⋊C4—112no—
458C2×C22⋊C4—112no—
459C2×C22⋊C4—112no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4C22×D1112yes—
469C2×C22⋊C4C22×D1112yes—
470C2×C22⋊C4C22×D1112yes—
471C2×C22⋊C4C22×D1114yes—
472C2×C22⋊C4C22×D1112yes—
473C2×C22⋊C4C22×D1114yes—
474C2×C42—112no—
475C2×C42—114no—
476C2×C42C22×D1112yes—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—112no—
482#95—112no—
483#95—114no—
484#95C22×D1112yes—
485#95C22×D1112yes—
486#95C22×D1114yes—
487C2×C11—24no—
488C2×C11—44no—
489C2×C11C2×#53611yescharacteristic
490C2×C11#348411yescharacteristic
491C2×C11#348711yescharacteristic
492C2×C11#353514yes—
493D11—82no—
494C24—22no—
495C24—24no—
496C24—24no—
497C24—42no—
498C24—112no—
499C24—222no—
500C24—224no—
501C24—442no—
502C24—442no—
503C24C23×D1112yes—
504C24C23×D1111yescharacteristic
505C2×Q8—224no—
506C2×Q8—224no—
507C2×Q8—444no—
508C2×Q8—444no—
509C2×D4—228no—
510C2×D4—228no—
511C2×D4—444no—
512C2×D4—4416no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—42no—
516C22×C4—112no—
517C22×C4—112no—
518C22×C4—114no—
519C22×C4—114no—
520C22×C4—114no—
521C22×C4—112no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—228no—
525C22×C4—222no—
526C22×C4—228no—
527C22×C4—442no—
528C22×C4—444no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—4416no—
532C22×C4D4×D1114yes—
533C22×C4C23×D1114yes—
534C22×C4C23×D1112yes—
535C22×C4C23×D1112yes—
536C22×C4C23×D1112yes—
537C22×C4C23×D1111yescharacteristic
538C22×C4C23×D1111yescharacteristic
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—44no—
542C4⋊C4—118no—
543C4⋊C4—118no—
544C4⋊C4—228no—
545C4⋊C4—224no—
546C4⋊C4—224no—
547C4⋊C4—224no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—222no—
552C4⋊C4—222no—
553C4⋊C4—444no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C4⋊C4—444no—
557C22⋊C4—24no—
558C22⋊C4—28no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—44no—
563C22⋊C4—228no—
564C22⋊C4—224no—
565C22⋊C4—228no—
566C22⋊C4—224no—
567C22⋊C4—224no—
568C22⋊C4—224no—
569C22⋊C4—444no—
570C22⋊C4—444no—
571C22⋊C4—444no—
572C22⋊C4—444no—
573C22⋊C4—444no—
574C42—24no—
575C42—224no—
576C42—444no—
577C11#3671111yescharacteristic, complemented, Sylow
578C23—22no—
579C23—22no—
580C23—28no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—416no—
586C23—44no—
587C23—44no—
588C23—222no—
589C23—224no—
590C23—224no—
591C23—222no—
592C23—222no—
593C23—444no—
594C23—444no—
595C23—444no—
596C23—888no—
597C23C2×D4×D1112yes—
598C23#6704214yes—
599C23#6704314yes—
600C23C24×D1111yescharacteristic
601Q8—884no—
602Q8—884no—
603D4—4416no—
604C2×C4—28no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—44no—
617C2×C4—114no—
618C2×C4—114no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—224no—
629C2×C4—224no—
630C2×C4—444no—
631C2×C4—444no—
632C2×C4—4416no—
633C2×C4—444no—
634C2×C4C2×D4×D1112yes—
635C2×C4C2×D4×D1112yes—
636C22—22no—
637C22—22no—
638C22—28no—
639C22—24no—
640C22—28no—
641C22—416no—
642C22—42no—
643C22—42no—
644C22—44no—
645C22—442no—
646C22—442no—
647C22—442no—
648C22—444no—
649C22—444no—
650C22—888no—
651C22#1062317914yes—
652C22C22×D4×D1111yescharacteristic
653C22C2×#6704212yes—
654C22C2×#6704312yes—
655C22#1062345512yes—
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—42no—
661C4—44no—
662C4—224no—
663C4—224no—
664C4—442no—
665C4—442no—
666C4—442no—
667C4—444no—
668C2—24no—
669C2—44no—
670C2—882no—
671C2C2×#1062317911yescharacteristic
672C2#1308224911yescharacteristic
673C2#1308227211yescharacteristic
674C2#1308282114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2482C2
prime radicalC23×C22⋊D11C22
hypercenter#2482D11
hypocenterC11#36711
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2482

Complements

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

NH ≅ G/Ntype
1. C2×#10623050C2semidirect
3. #13076901C2semidirect
4. #13075143C2semidirect
5. #13075139C2semidirect
6. #13074903C2semidirect
7. #13074895C2semidirect
8. #13074427C2semidirect
9. #13073993C2semidirect
10. #13072892C2semidirect
11. #13072890C2semidirect
12. #13072886C2semidirect
14. #13071217C2semidirect
15. C11×#2482C2semidirect
26. C2×#66943C22semidirect
27. C2×#66941C22semidirect
34. C2×#66931C22semidirect
35. C2×#66923C22semidirect
36. C2×#66922C22semidirect
37. C11×#399C22semidirect
38. C11×#397C22semidirect
39. C11×#388C22semidirect
46. #10622607C22semidirect
47. #10622606C22semidirect
48. #10622605C22semidirect
49. #10622605C22semidirect
50. #10622598C22semidirect
51. #10622597C22semidirect
57. #10622566C22semidirect
59. #10622563C22semidirect
60. #10622562C22semidirect
62. #10622559C22semidirect
63. #10622557C22semidirect
65. #10622555C22semidirect
67. #10622553C22semidirect
68. #10622290C22semidirect
69. #10622289C22semidirect
70. #10622287C22semidirect
71. #10622286C22semidirect
72. #10622283C22semidirect
73. #10622269C22semidirect
74. #10622267C22semidirect
75. #10622266C22semidirect
76. #10622260C22semidirect
253. #2482D11semidirect
339. #399C2×D11semidirect
344. #397C2×D11semidirect
357. #388C2×D11semidirect
577. C11#36711semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
C22×#669392
#130769012
#130751432
#130751392
#130749032
#130748952
#130744272
#130739932
#130728922
#130728902
#130728862
#130722652
#130712172
C11×#24822
#3671111