Finite Group Databasebeta

← #14684737

Subgroups — #14684737

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#13066877C212yesmaximal, complemented
3#13066865C211yesmaximal, characteristic, complemented
4#13066864C212yesmaximal, complemented
5#13066856C212yesmaximal, complemented
6#13066855C212yesmaximal, complemented
7#13066855C212yesmaximal, complemented
8#13066854C212yesmaximal, complemented
9C11×#1437C211yesmaximal, characteristic, complemented
10C23×C22⋊D11C2212yes—
11C23×D44C2211yescharacteristic
12C22×C11×C22⋊C4C2212yes—
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C22⋊Dic11C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622573C418yescomplemented
32C25×C11C2311yescharacteristic
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
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—24no—
54C2×C11×C22⋊C4—41no—
55C2×C11×C22⋊C4—41no—
56C2×C11×C22⋊C4—42no—
57C2×C11×C22⋊C4—42no—
58C2×C11×C22⋊C4C2×C414yes—
59C2×C42×C11—42no—
60C2×C42×C11—41no—
61C2×C22⋊Dic11—42no—
62C2×C22⋊Dic11—42no—
63C2×C22⋊Dic11—41no—
64C2×C22⋊Dic11—41no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
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)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4C2×C418yes—
80C11×#95—42no—
81C11×#95—41no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95C2×C414yes—
89#14651—111nomaximal, Sylow
90C24×C11—22no—
91C24×C11—21no—
92C24×C11—21no—
93C24×C11—22no—
94C24×C11—22no—
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—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
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×C11C22×C412yes—
137C22×C4×C11C22×C412yes—
138C22×C4×C11#4114yes—
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×Dic11—22no—
166C22×Dic11C22×C414yes—
167C2×D44—44no—
168C2×D44—48no—
169C2×D44—44no—
170C2×D44—48no—
171C2×D44—44no—
172C11×C22⋊C4—44no—
173C11×C22⋊C4—48no—
174C42×C11—44no—
175C22⋊Dic11—44no—
176C22⋊Dic11—44no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180(C2×D11)⋊C4—48no—
181(C2×D11)⋊C4—48no—
182C2×#392—111no—
183#1443—112no—
184#1440—112no—
185#1440—111no—
186#1438—112no—
187#1438—112no—
188#1438—112no—
189#1437—112no—
190#1437D1111yescharacteristic, complemented
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—41no—
207C23×C11—41no—
208C23×C11—42no—
209C23×C11—42no—
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)12yes—
217C23×C11H(5,𝔽2)11yescharacteristic
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—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
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—41no—
272C2×C4×C11—41no—
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—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
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—111no—
309C22×C22⋊C4—111no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4C2×D1112yes—
313C22×C22⋊C4C2×D1111yescharacteristic
314C22×C42C2×D1111yescharacteristic
315#392—118no—
316C2×#95—111no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95C2×D1112yes—
324C2×#95C2×D1111yescharacteristic
325C22×C11—44no—
326C22×C11—42no—
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#56011yescharacteristic
348C22×C11#56012yes—
349C22×C11#56012yes—
350C22×C11#56012yes—
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—44no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—82no—
374Dic11—44no—
375Dic11—82no—
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×D1111yescharacteristic
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1112yes—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—442no—
407C2×C22⋊C4—442no—
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—441no—
419C2×C22⋊C4—441no—
420C2×C22⋊C4—442no—
421C2×C22⋊C4—442no—
422C2×C22⋊C4C4×D1114yes—
423C2×C42—41no—
424C2×C42—42no—
425#95—42no—
426#95—41no—
427#95—114no—
428#95—442no—
429#95—442no—
430#95—442no—
431#95—442no—
432#95—442no—
433#95—442no—
434C2×C11—82no—
435C2×C11#233312yes—
436C2×C11#233311yescharacteristic
437C2×C11#237511yescharacteristic
438C2×C11#237512yes—
439C2×C11#238011yescharacteristic
440C2×C11#282512yes—
441C2×C11#282812yes—
442C2×C11#282812yes—
443C2×C11#282812yes—
444D11—84no—
445C24—22no—
446C24—21no—
447C24—21no—
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—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
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—114no—
504C22×C4—222no—
505C22×C4—222no—
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×C4C2×C4×D1112yes—
525C22×C4C2×C4×D1112yes—
526C22×C4#433914yes—
527C22⋊C4—44no—
528C22⋊C4—48no—
529C22⋊C4—448no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C22⋊C4—448no—
534C22⋊C4—444no—
535C22⋊C4—444no—
536C42—44no—
537C11#1465111yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—22no—
541C23—24no—
542C23—24no—
543C23—42no—
544C23—41no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—41no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—42no—
557C23—41no—
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
595C23C2×#433912yes—
596C23#6703711yescharacteristic
597C23#6703712yes—
598C23#6703711yescharacteristic
599C23#6703712yes—
600C23#6704212yes—
601C23#6704212yes—
602C23#6704212yes—
603D4—4416no—
604D4—4432no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—41no—
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—442no—
633C2×C4—442no—
634C2×C4—442no—
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—44no—
651C22—42no—
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—
674C22C4×#433911yescharacteristic
675C22#1062301711yescharacteristic
676C22#1062302512yes—
677C22#1062305211yescharacteristic
678C22#1062306612yes—
679C22#1062307612yes—
680C22#1062307612yes—
681C22#1062309112yes—
682C22#1062309112yes—
683C22#1062309312yes—
684C22#1062309312yes—
685C22#1062312611yescharacteristic
686C22#1062315112yes—
687C22#1062315112yes—
688C22#1062315112yes—
689C22#1062319712yes—
690C22#1062319711yescharacteristic
691C22#1062321411yescharacteristic
692C22#1062321412yes—
693C22#1062324212yes—
694C22#1062325111yescharacteristic
695C4—42no—
696C4—42no—
697C4—44no—
698C4—82no—
699C4—444no—
700C4—882no—
701C4—882no—
702C2—82no—
703C2—884no—
704C2#1307137612yes—
705C2#1307138111yescharacteristic
706C2#1307175311yescharacteristic
707C2#1307175612yes—
708C2#1307179111yescharacteristic
709C2#1307670212yes—
710C2#1307673312yes—
711C2#1307673312yes—
712C2#1307673512yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1437D11
hypocenterC11#14651
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066865C2semidirect
4. #13066864C2semidirect
5. #13066856C2semidirect
6. #13066855C2semidirect
7. #13066855C2semidirect
8. #13066854C2semidirect
9. C11×#1437C2semidirect
31. #10622573C4semidirect
190. #1437D11semidirect
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
#130668772
#130668652
#130668642
#130668562
#130668552
#130668542
C11×#14372
#1465111