Finite Group Databasebeta

← #14684513

Subgroups — #14684513

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622606C211yesmaximal, characteristic
2C2×#10622598C211yesmaximal, characteristic, complemented
3C2×#10622282C211yesmaximal, characteristic
4#13066880C212yesmaximal, complemented
5#13066880C211yesmaximal, characteristic, complemented
6#13066877C212yesmaximal, complemented
7#13066862C211yesmaximal, characteristic
8#13066862C212yesmaximal
9#13066860C212yesmaximal
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1445C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2212yes—
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35#10622606C418yescomplemented
36#10622598—24no—
37#10622282—24no—
38C24×D11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C414yes—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—42no—
57C2×(C2×D11)⋊C4—42no—
58C2×(C2×D11)⋊C4—42no—
59C2×(C2×D11)⋊C4—42no—
60C2×(C2×D11)⋊C4—42no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4C2×C414yes—
64C2×(C2×D11)⋊C4C2×C418yes—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—24no—
67C2×C4⋊Dic11—42no—
68C2×C4⋊Dic11—42no—
69C2×C4⋊Dic11—42no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—42no—
72C2×Dic11⋊C4—42no—
73C2×Dic11⋊C4—42no—
74C2×Dic11⋊C4—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11D414yes—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—42no—
80C11×#95—42no—
81C11⋊#95—22no—
82C11⋊#95—24no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95C2×C418yes—
88C11⋊#95C2×C414yes—
89#14630—111nomaximal, Sylow
90C24×C11C2411yescharacteristic
91C23×D11—21no—
92C23×D11—21no—
93C23×D11—21no—
94C23×D11—21no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—21no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—21no—
101C23×D11C22×C412yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11#4112yes—
131C22×Dic11—21no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C414yes—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D412yes—
160C11×C4⋊C4—28no—
161(C2×D11)⋊C4—28no—
162(C2×D11)⋊C4—48no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165(C2×D11)⋊C4—48no—
166C4⋊Dic11—44no—
167C4⋊Dic11—48no—
168Dic11⋊C4—44no—
169Dic11⋊C4—48no—
170C4×Dic11—44no—
171C2×#397—111no—
172C2×#389—111no—
173C2×#388—111no—
174#1445D1111yescharacteristic, complemented
175#1444—112no—
176#1444—111no—
177#1443—112no—
178#1439—112no—
179#1439—111no—
180#1439—112no—
181#1434—111no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C2×#4111yescharacteristic
185C23×C11H(5,𝔽2)11yescharacteristic
186C23×C11H(5,𝔽2)11yescharacteristic
187C23×C11H(5,𝔽2)11yescharacteristic
188C23×C11H(5,𝔽2)12yes—
189C23×C11H(5,𝔽2)12yes—
190C23×C112−1+412yes—
191C23×C112−1+412yes—
192C23×C112−1+411yescharacteristic
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—24no—
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—42no—
205C22×D11—41no—
206C22×D11—42no—
207C22×D11—41no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11C4×D414yes—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—112no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4C2×D1111yescharacteristic
279C22×C22⋊C4—111no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—111no—
282C22×C22⋊C4—111no—
283C22×C22⋊C4—112no—
284C22×C42—111no—
285#397—118no—
286#389—224no—
287#388—224no—
288C2×#95—111no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95C2×D1111yescharacteristic
297C2×#95C2×D1111yescharacteristic
298C2×#95C2×D1112yes—
299C2×#95C2×D1112yes—
300C22×C11C2×C4×D411yescharacteristic
301C22×C11#51811yescharacteristic
302C22×C11#52012yes—
303C22×C11#52011yescharacteristic
304C22×C11#52012yes—
305C22×C11#53411yescharacteristic
306C22×C11#53511yescharacteristic
307C22×C11#53511yescharacteristic
308C22×C11#53611yescharacteristic
309C22×C11#53611yescharacteristic
310C22×C11#53711yescharacteristic
311C22×C11#53912yes—
312C22×C11#54011yescharacteristic
313C22×C11#54212yes—
314C22×C11#54211yescharacteristic
315C22×C11#56012yes—
316C22×C11#56012yes—
317C22×C11#56212yes—
318C22×C11#56212yes—
319C22×C11#56312yes—
320C22×C11#56312yes—
321C22×C11#56312yes—
322C22×C11#56312yes—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—24no—
335C4×C11—44no—
336C4×C11—81no—
337C4×C11—82no—
338C4×C11—81no—
339Dic11—42no—
340Dic11—44no—
341Dic11—42no—
342Dic11—42no—
343Dic11—82no—
344C25—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—112no—
348C23×C4—111no—
349C23×C4—112no—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1112yes—
353C23×C4C22×D1112yes—
354C23×C4C22×D1111yescharacteristic
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—442no—
361C2×C4⋊C4—442no—
362C2×C4⋊C4—442no—
363C2×C4⋊C4—442no—
364C2×C4⋊C4—442no—
365C2×C4⋊C4—442no—
366C2×C4⋊C4—442no—
367C2×C4⋊C4C4×D1114yes—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—442no—
375C2×C22⋊C4—442no—
376C2×C22⋊C4—442no—
377C2×C22⋊C4—442no—
378C2×C22⋊C4—442no—
379C2×C22⋊C4—442no—
380C2×C22⋊C4—442no—
381C2×C42—114no—
382C2×C42—442no—
383#95—22no—
384#95—22no—
385#95—42no—
386#95—42no—
387#95—118no—
388#95—114no—
389#95—222no—
390#95—224no—
391#95—442no—
392#95—442no—
393#95—442no—
394#95—442no—
395C2×C11#232211yescharacteristic
396C2×C11#232411yescharacteristic
397C2×C11#232611yescharacteristic
398C2×C11#237612yes—
399C2×C11#238312yes—
400C2×C11#281411yescharacteristic
401C2×C11#281511yescharacteristic
402C2×C11#282011yescharacteristic
403C2×C11#282111yescharacteristic
404C2×C11#283712yes—
405C2×C11#283812yes—
406D11—82no—
407C24—112no—
408C24—221no—
409C24—221no—
410C24—221no—
411C24—221no—
412C24—222no—
413C24—222no—
414C24—221no—
415C24—222no—
416C24—222no—
417C24—221no—
418C24C23×D1111yescharacteristic
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4C2×C4×D1114yes—
474C22×C4C2×C4×D1112yes—
475C22×C4D4×D1112yes—
476C22×C4#434112yes—
477C4⋊C4—28no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C4⋊C4—448no—
481C4⋊C4—448no—
482C22⋊C4—228no—
483C22⋊C4—448no—
484C22⋊C4—444no—
485C22⋊C4—444no—
486C22⋊C4—448no—
487C42—444no—
488C11#1463011yescharacteristic, complemented, Sylow
489C23—222no—
490C23—224no—
491C23—222no—
492C23—222no—
493C23—224no—
494C23—442no—
495C23—442no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—442no—
501C23—442no—
502C23—442no—
503C23—441no—
504C23—441no—
505C23—442no—
506C23—442no—
507C23—442no—
508C23—441no—
509C23—441no—
510C23—442no—
511C23—442no—
512C23C22×C4×D1111yescharacteristic
513C23C2×D4×D1111yescharacteristic
514C23C2×#434111yescharacteristic
515C23#6703711yescharacteristic
516C23#6703711yescharacteristic
517C23#6704012yes—
518C23#6704211yescharacteristic
519C23#6704212yes—
520C23#6704212yes—
521C23#6704311yescharacteristic
522C23#6704312yes—
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—222no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—441no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—441no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4(C22⋊D11)⋊C414yes—
581C22—444no—
582C22—442no—
583C22—444no—
584C22—442no—
585C22—442no—
586C22—882no—
587C22—882no—
588C22—881no—
589C22—881no—
590C22—881no—
591C22—881no—
592C22C2×(C22⋊D11)⋊C411yescharacteristic
593C22#1062305412yes—
594C22#1062307611yescharacteristic
595C22#1062307711yescharacteristic
596C22#1062310512yes—
597C22#1062313811yescharacteristic
598C22#1062313911yescharacteristic
599C22#1062317412yes—
600C22#1062317712yes—
601C22#1062317812yes—
602C22#1062317911yescharacteristic
603C22#1062318411yescharacteristic
604C22#1062319612yes—
605C22#1062319712yes—
606C22#1062319812yes—
607C22#1062320511yescharacteristic
608C22#1062321311yescharacteristic
609C22#1062323012yes—
610C22#1062323012yes—
611C22#1062324212yes—
612C22#1062324312yes—
613C22#1062325011yescharacteristic
614C22#1062325511yescharacteristic
615C4—24no—
616C4—44no—
617C4—82no—
618C4—81no—
619C4—81no—
620C4—444no—
621C4—442no—
622C4—442no—
623C4—442no—
624C4—882no—
625C2—882no—
626C2#1307128211yescharacteristic
627C2#1307131211yescharacteristic
628C2#1307133011yescharacteristic
629C2#1307176312yes—
630C2#1307180612yes—
631C2#1307663211yescharacteristic
632C2#1307663911yescharacteristic
633C2#1307667211yescharacteristic
634C2#1307667611yescharacteristic
635C2#1307683012yes—
636C2#1307684512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#14630
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622598C2semidirect
4. #13066880C2semidirect
5. #13066880C2semidirect
6. #13066877C2semidirect
10. #13066841C2semidirect
11. C11×#1445C2semidirect
35. #10622606C4semidirect
174. #1445D11semidirect
488. C11#14630semidirect

Maximal subgroups

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

subgroupindex
C2×#106226062
C2×#106225982
C2×#106222822
#130668802
#130668772
#130668622
#130668602
#130668412
C11×#14452
#1463011