Finite Group Databasebeta

← #14684740

Subgroups — #14684740

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2#13066876C212yesmaximal, complemented
3#13066864C212yesmaximal, complemented
4#13066856C212yesmaximal, complemented
5#13066855C212yesmaximal, complemented
6#13066855C212yesmaximal, complemented
7#13066853C211yesmaximal, characteristic, complemented
8#13066852C212yesmaximal, complemented
9C11×#1440C211yesmaximal, characteristic, complemented
10C23×C22⋊D11C2212yes—
11C23×D44C2211yescharacteristic
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C22⋊Dic11C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622573C418yescomplemented
32C25×C11C2311yescharacteristic
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C22×C22⋊D11—42no—
39C22×C22⋊D11—42no—
40C22×C22⋊D11—42no—
41C22×C22⋊D11—42no—
42C22×C22⋊D11—42no—
43C22×C22⋊D11—42no—
44C22×C22⋊D11C2×C418yes—
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C22×D44—42no—
49C22×D44—42no—
50C22×D44—41no—
51C22×D44—41no—
52C22×D44C2×C414yes—
53C2×C11×C22⋊C4—41no—
54C2×C11×C22⋊C4—41no—
55C2×C11×C22⋊C4—42no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—41no—
58C2×C11×C22⋊C4—41no—
59C2×C11×C22⋊C4C2×C414yes—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4—42no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4—42no—
77C2×(C2×D11)⋊C4C2×C418yes—
78C2×C4×Dic11—41no—
79C2×C4×Dic11—42no—
80C11×#95—42no—
81C11×#95—42no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—41no—
88C11⋊#95C2×C414yes—
89#14651—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11C22×C412yes—
99C24×C11C2411yescharacteristic
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11C22×C414yes—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C2×C22⋊D11—48no—
140C2×C22⋊D11—48no—
141C2×C22⋊D11—48no—
142C2×C22⋊D11—48no—
143C2×C22⋊D11—48no—
144C2×C22⋊D11—48no—
145C2×C22⋊D11—48no—
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—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11C22×C414yes—
166C22×Dic11#4114yes—
167C2×D44—44no—
168C2×D44—48no—
169C2×D44—48no—
170C2×D44—44no—
171C2×D44—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—44no—
174C11×C22⋊C4—44no—
175C22⋊Dic11—48no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181C4×Dic11—44no—
182C2×#392—111no—
183#1443—112no—
184#1440—112no—
185#1440D1111yescharacteristic, complemented
186#1438—112no—
187#1438—112no—
188#1438—112no—
189#1437—112no—
190#1437—111no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11C23×C411yescharacteristic
213C23×C11C2×#4112yes—
214C23×C11H(5,𝔽2)11yescharacteristic
215C23×C11H(5,𝔽2)12yes—
216C23×C11H(5,𝔽2)11yescharacteristic
217C23×C11H(5,𝔽2)12yes—
218C23×C11H(5,𝔽2)12yes—
219C23×C11H(5,𝔽2)12yes—
220C23×C11H(5,𝔽2)12yes—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—42no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—42no—
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—42no—
246C22×D11—42no—
247C22×D11—42no—
248C22×D11—42no—
249C22×D11—42no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—42no—
255C22×D11—42no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C22⋊D11—432no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—42no—
302D44—416no—
303C23×D4—112no—
304C23×D4—111no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4C2×D1111yescharacteristic
312C22×C22⋊C4C2×D1111yescharacteristic
313C22×C22⋊C4C2×D1111yescharacteristic
314C22×C42—111no—
315#392—118no—
316C2×#95—111no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—111no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95C2×D1112yes—
324C2×#95C2×D1112yes—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—42no—
328C22×C11—44no—
329C22×C11—42no—
330C22×C11—82no—
331C22×C11—82no—
332C22×C11—82no—
333C22×C11—82no—
334C22×C11C4×#4111yescharacteristic
335C22×C11#51811yescharacteristic
336C22×C11#51811yescharacteristic
337C22×C11#51812yes—
338C22×C11#51812yes—
339C22×C11#53812yes—
340C22×C11#53812yes—
341C22×C11#53812yes—
342C22×C11#54012yes—
343C22×C11#54012yes—
344C22×C11#54012yes—
345C22×C11#56012yes—
346C22×C11#56011yescharacteristic
347C22×C11#56012yes—
348C22×C11#56012yes—
349C22×C11#56012yes—
350C22×C11#56011yescharacteristic
351C22×C11#56012yes—
352C22×C11#56011yescharacteristic
353C22×C11H(3,𝔽4)11yescharacteristic
354C22×C11H(3,𝔽4)12yes—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—44no—
362C2×D11—82no—
363C2×D11—82no—
364C2×D11—82no—
365C2×D11—82no—
366C2×D11—82no—
367C2×D11—82no—
368C2×D11—82no—
369C2×D11—82no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—82no—
373C4×C11—82no—
374Dic11—44no—
375Dic11—44no—
376Dic11—82no—
377C25—112no—
378C25C22×D1111yescharacteristic
379C22×D4—118no—
380C22×D4—114no—
381C22×D4—442no—
382C22×D4—441no—
383C22×D4—441no—
384C22×D4—442no—
385C22×D4—442no—
386C22×D4—442no—
387C22×D4—442no—
388C22×D4—442no—
389C22×D4—442no—
390C22×D4—442no—
391C23×C4—112no—
392C23×C4—112no—
393C23×C4—112no—
394C23×C4C22×D1112yes—
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—118no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—442no—
409C2×C22⋊C4—442no—
410C2×C22⋊C4—442no—
411C2×C22⋊C4—442no—
412C2×C22⋊C4—442no—
413C2×C22⋊C4—442no—
414C2×C22⋊C4—442no—
415C2×C22⋊C4—442no—
416C2×C22⋊C4—442no—
417C2×C22⋊C4—442no—
418C2×C22⋊C4—442no—
419C2×C22⋊C4—442no—
420C2×C22⋊C4—442no—
421C2×C22⋊C4—442no—
422C2×C22⋊C4C4×D1114yes—
423C2×C42—441no—
424C2×C42—442no—
425#95—42no—
426#95—42no—
427#95—114no—
428#95—441no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95—442no—
433#95—442no—
434C2×C11—82no—
435C2×C11#233311yescharacteristic
436C2×C11#233312yes—
437C2×C11#237511yescharacteristic
438C2×C11#237512yes—
439C2×C11#238011yescharacteristic
440C2×C11#282512yes—
441C2×C11#282812yes—
442C2×C11#282812yes—
443C2×C11#282812yes—
444D11—84no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—114no—
454C24—222no—
455C24—222no—
456C24—222no—
457C24—222no—
458C24—222no—
459C24—222no—
460C24—222no—
461C24—222no—
462C24—222no—
463C24—222no—
464C24—222no—
465C24—222no—
466C24—222no—
467C24—222no—
468C24C2×C4×D1112yes—
469C24C23×D1111yescharacteristic
470C2×D4—444no—
471C2×D4—448no—
472C2×D4—444no—
473C2×D4—448no—
474C2×D4—444no—
475C2×D4—448no—
476C2×D4—448no—
477C2×D4—448no—
478C2×D4—448no—
479C2×D4—448no—
480C2×D4—448no—
481C2×D4—448no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—114no—
505C22×C4—114no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4C2×C4×D1112yes—
526C22×C4C2×C4×D1112yes—
527C22⋊C4—44no—
528C22⋊C4—44no—
529C22⋊C4—44no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C22⋊C4—448no—
534C22⋊C4—448no—
535C22⋊C4—448no—
536C42—444no—
537C11#1465111yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—42no—
558C23—42no—
559C23—224no—
560C23—224no—
561C23—224no—
562C23—224no—
563C23—224no—
564C23—224no—
565C23—224no—
566C23—442no—
567C23—442no—
568C23—442no—
569C23—442no—
570C23—442no—
571C23—442no—
572C23—442no—
573C23—442no—
574C23—442no—
575C23—442no—
576C23—442no—
577C23—442no—
578C23—442no—
579C23—442no—
580C23—442no—
581C23—442no—
582C23—442no—
583C23—442no—
584C23—442no—
585C23—442no—
586C23—442no—
587C23—442no—
588C23—442no—
589C23—442no—
590C23—442no—
591C23—442no—
592C23—442no—
593C23—442no—
594C23C22×C4×D1111yescharacteristic
595C23#6703711yescharacteristic
596C23#6703711yescharacteristic
597C23#6703712yes—
598C23#6703712yes—
599C23#41×D1112yes—
600C23#6704212yes—
601C23#6704212yes—
602C23#6704212yes—
603D4—4416no—
604D4—4432no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—224no—
630C2×C4—224no—
631C2×C4—224no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—224no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4—442no—
641C2×C4—442no—
642C2×C4—442no—
643C2×C4—442no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4—442no—
650C22—42no—
651C22—44no—
652C22—42no—
653C22—44no—
654C22—42no—
655C22—82no—
656C22—82no—
657C22—82no—
658C22—82no—
659C22—444no—
660C22—444no—
661C22—444no—
662C22—444no—
663C22—444no—
664C22—444no—
665C22—444no—
666C22—882no—
667C22—882no—
668C22—882no—
669C22—882no—
670C22—882no—
671C22—882no—
672C22—882no—
673C22—882no—
674C22#1062301711yescharacteristic
675C22#1062305211yescharacteristic
676C22#1062305311yescharacteristic
677C22#1062307612yes—
678C22#1062307612yes—
679C22#1062312511yescharacteristic
680C22#1062312611yescharacteristic
681C22#1062314612yes—
682C22#1062315112yes—
683C22#1062315112yes—
684C22#1062315112yes—
685C22#1062318812yes—
686C22#1062319412yes—
687C22#1062319412yes—
688C22#1062319712yes—
689C22#1062319711yescharacteristic
690C22#1062319711yescharacteristic
691C22#1062320912yes—
692C22#1062321412yes—
693C22#1062323512yes—
694C22#1062324212yes—
695C4—42no—
696C4—42no—
697C4—82no—
698C4—82no—
699C4—444no—
700C4—444no—
701C4—882no—
702C2—82no—
703C2—884no—
704C2#1307137811yescharacteristic
705C2#1307137912yes—
706C2#1307175411yescharacteristic
707C2#1307175612yes—
708C2#1307179111yescharacteristic
709C2#1307670612yes—
710C2#1307673212yes—
711C2#1307673612yes—
712C2#1307673712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1440D11
hypocenterC11#14651
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #13066876C2semidirect
3. #13066864C2semidirect
4. #13066856C2semidirect
5. #13066855C2semidirect
6. #13066855C2semidirect
7. #13066853C2semidirect
8. #13066852C2semidirect
9. C11×#1440C2semidirect
31. #10622573C4semidirect
185. #1440D11semidirect
537. C11#14651semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
#130668762
#130668642
#130668562
#130668552
#130668532
#130668522
C11×#14402
#1465111