Finite Group Databasebeta

← #14676532

Subgroups — #14676532

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622600C211yesmaximal, characteristic
2C2×#10622279C211yesmaximal, characteristic
3C2×D11×#95C211yesmaximal, characteristic
4#13066875C211yesmaximal, characteristic, complemented
5#13066873C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066841C212yesmaximal, complemented
8#13066840C212yesmaximal, complemented
9(C2×D11)⋊#95C212yesmaximal
10(C2×D11)⋊#95C212yesmaximal
11C11×#1442C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C2×C11×#95C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622600—24no—
36#10622279C418yescomplemented
37D11×#95—24no—
38C24×D11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—24no—
56C22×C4×D11—24no—
57C22×C4×D11—42no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11—42no—
61C22×C4×D11C2×C414yes—
62C22×C4×D11D414yes—
63C22×C4×D11Q814yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—42no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4C2×C418yes—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—42no—
74C2×C4×Dic11—42no—
75C2×C4×Dic11—42no—
76C2×C4×Dic11C2×C418yescomplemented
77C11×#95—22no—
78C11×#95—24no—
79C11×#95—42no—
80C11×#95C2×C414yescomplemented
81C11⋊#95—22no—
82C11⋊#95—24no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—42no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91C11⋊#95C2×C414yescomplemented
92#13966—111nomaximal, Sylow
93C24×C11C2411yescharacteristic
94C23×D11—21no—
95C23×D11—21no—
96C23×D11—21no—
97C23×D11—21no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11C22×C412yes—
101C23×D11C2×D412yes—
102C23×D11C2×Q812yes—
103C23×D11#4114yes—
104C23×D11#4114yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×Q812yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—22no—
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—22no—
156C22×Dic11—22no—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×Q812yes—
161C22×Dic11#4112yes—
162C22×Dic11#4112yes—
163C2×C4×D11—28no—
164C2×C4×D11—28no—
165C2×C4×D11—48no—
166C2×C4×D11—44no—
167C2×C4×D11—44no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—48no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C2×C4×D11—44no—
174C2×C4×D11—44no—
175C2×C4×D11—44no—
176C2×C4×D11—44no—
177C2×C4×D11C4⋊C4116yes—
178C11×C4⋊C4—44no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—48no—
181C4⋊Dic11—44no—
182C4×Dic11—48no—
183C2×#380—111no—
184C2×C4×C22⋊C4—111no—
185C22×#95—111no—
186#1442—111no—
187#1442—111no—
188#1442—111no—
189#1442D1111yescharacteristic, complemented
190#1434—112no—
191#1434—112no—
192C22⋊#95—112no—
193C22⋊#95—112no—
194C23×C11C23×C411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C22×Q811yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C11C2×#4111yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C23×C11H(5,𝔽2)12yes—
204C23×C11H(5,𝔽2)12yes—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—24no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11C2×C4⋊C414yes—
224C22×D11#11718yes—
225C22×D11#12414yes—
226C22×D11#12414yes—
227C22×D11#12518yes—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11C2×C4⋊C414yes—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11C2×C4⋊C414yes—
286C4×D11—416no—
287C4×D11—416no—
288C4×D11—416no—
289C24×C4—111no—
290C24×C4—111no—
291C24×C4—111no—
292C22×C4⋊C4—111no—
293C22×C4⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C42—112no—
297#380—224no—
298C4×C22⋊C4—118no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—111no—
304C2×#95—111no—
305C2×#95—112no—
306C2×#95—111no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—224no—
311C2×#95C2×D1112yes—
312C2×#95C2×D1111yescharacteristic
313C2×#95C2×D1112yes—
314C2×#95C2×D1111yescharacteristic
315C22×C11C22×C4⋊C411yescharacteristic
316C22×C11C2×#11712yes—
317C22×C11C4×#4111yescharacteristic
318C22×C11C4×#4111yescharacteristic
319C22×C11#51812yes—
320C22×C11#52511yescharacteristic
321C22×C11#52511yescharacteristic
322C22×C11C2×#12411yescharacteristic
323C22×C11C2×#12411yescharacteristic
324C22×C11C2×#12512yes—
325C22×C11#53311yescharacteristic
326C22×C11#53311yescharacteristic
327C22×C11#53411yescharacteristic
328C22×C11#53411yescharacteristic
329C22×C11#54312yes—
330C22×C11#55112yes—
331C22×C11#55112yes—
332C22×C11#55112yes—
333C22×C11#55112yes—
334C22×C11#55312yes—
335C22×C11#55312yes—
336C22×C11#55312yes—
337C22×C11#55312yes—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—28no—
341C2×D11—28no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—24no—
345C2×D11—28no—
346C2×D11—28no—
347C2×D11—24no—
348C2×D11#38218yes—
349C4×C11—24no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—44no—
353C4×C11—82no—
354Dic11—24no—
355Dic11—42no—
356Dic11—42no—
357Dic11—44no—
358Dic11—82no—
359C25—111no—
360C23×C4—111no—
361C23×C4—114no—
362C23×C4—114no—
363C23×C4—114no—
364C23×C4—112no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—112no—
368C23×C4—222no—
369C23×C4—222no—
370C23×C4—222no—
371C23×C4—222no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4—222no—
375C23×C4—222no—
376C23×C4—442no—
377C23×C4—442no—
378C23×C4—442no—
379C23×C4—442no—
380C23×C4C22×D1112yes—
381C23×C4C22×D1112yes—
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—442no—
389C2×C22⋊C4—118no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C42—118no—
396C2×C42—442no—
397C2×C42—442no—
398#95—22no—
399#95—24no—
400#95—42no—
401#95—114no—
402#95—224no—
403#95—224no—
404#95—222no—
405#95—222no—
406#95—224no—
407#95—222no—
408#95—224no—
409#95—442no—
410#95—442no—
411#95—442no—
412#95C4×D1114yescomplemented
413C2×C11C2×#38211yescharacteristic
414C2×C11#229611yescharacteristic
415C2×C11#231511yescharacteristic
416C2×C11#235312yes—
417C2×C11#235312yes—
418C2×C11#256111yescharacteristic
419C2×C11#256111yescharacteristic
420C2×C11#256912yes—
421C2×C11#256912yes—
422C2×C11#259111yescharacteristic
423C2×C11#259111yescharacteristic
424D11—28no—
425C24—112no—
426C24—112no—
427C24—112no—
428C24—114no—
429C24—114no—
430C24—221no—
431C24—222no—
432C24—221no—
433C24—221no—
434C24—221no—
435C24—222no—
436C24C23×D1111yescharacteristic
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—1116no—
464C22×C4—114no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—228no—
468C22×C4—228no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—448no—
493C22×C4—444no—
494C22×C4—448no—
495C22×C4—444no—
496C22×C4—448no—
497C22×C4—448no—
498C22×C4—448no—
499C22×C4—448no—
500C22×C4—444no—
501C22×C4—444no—
502C22×C4—444no—
503C22×C4—444no—
504C22×C4C2×C4×D1114yes—
505C22×C4C2×C4×D1112yes—
506C22×C4D4×D1112yes—
507C22×C4#434112yes—
508C22×C4Q8×D1112yes—
509C22×C4#434312yes—
510C4⋊C4—44no—
511C4⋊C4—444no—
512C22⋊C4—2216no—
513C22⋊C4—448no—
514C42—448no—
515C11#1396611yescharacteristic, complemented, Sylow
516C23—114no—
517C23—118no—
518C23—114no—
519C23—114no—
520C23—118no—
521C23—224no—
522C23—224no—
523C23—222no—
524C23—222no—
525C23—224no—
526C23—222no—
527C23—222no—
528C23—222no—
529C23—224no—
530C23—222no—
531C23—224no—
532C23—224no—
533C23—222no—
534C23—224no—
535C23—224no—
536C23—224no—
537C23—222no—
538C23—224no—
539C23C22×C4×D1111yescharacteristic
540C23C2×D4×D1111yescharacteristic
541C23C2×#434111yescharacteristic
542C23#6703712yes—
543C23C2×Q8×D1111yescharacteristic
544C23C2×#434311yescharacteristic
545C23#41×D1111yescharacteristic
546C23#41×D1112yes—
547C23#41×D1111yescharacteristic
548C23#41×D1112yes—
549C23#6704212yes—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—114no—
579C2×C4—224no—
580C2×C4—222no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—4416no—
591C2×C4—4416no—
592C2×C4—4416no—
593C2×C4—442no—
594C2×C4—441no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—441no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4C4⋊C4×D1114yes—
611C22—118no—
612C22—224no—
613C22—224no—
614C22—224no—
615C22—228no—
616C22—224no—
617C22—228no—
618C22—224no—
619C22—228no—
620C22—228no—
621C22—224no—
622C22C2×C4⋊C4×D1111yescharacteristic
623C22D11×#11712yes—
624C22C4×#434111yescharacteristic
625C22#1062307612yes—
626C22C4×#434311yescharacteristic
627C22#1062312011yescharacteristic
628C22#1062313711yescharacteristic
629C22#1062314512yes—
630C22#1062315811yescharacteristic
631C22#1062316512yes—
632C22#1062316812yes—
633C22#1062318411yescharacteristic
634C22#1062318912yes—
635C22#1062319212yes—
636C22D11×#12411yescharacteristic
637C22D11×#12411yescharacteristic
638C22#1062321012yes—
639C22D11×#12512yes—
640C22#1062321911yescharacteristic
641C22#1062322612yes—
642C22#1062323612yes—
643C22#1062324012yes—
644C22#1062325911yescharacteristic
645C4—24no—
646C4—42no—
647C4—42no—
648C4—44no—
649C4—82no—
650C4—224no—
651C4—442no—
652C4—442no—
653C4—444no—
654C4—882no—
655C2—228no—
656C2D11×#38211yescharacteristic
657C2#1307109711yescharacteristic
658C2#1307122711yescharacteristic
659C2#1307155112yes—
660C2#1307155512yes—
661C2#1307376811yescharacteristic
662C2#1307377011yescharacteristic
663C2#1307383412yes—
664C2#1307383612yes—
665C2#1307409011yescharacteristic
666C2#1307409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1442C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1442D11
hypocenterC11#13966
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
4. #13066875C2semidirect
5. #13066873C2semidirect
6. #13066872C2semidirect
7. #13066841C2semidirect
8. #13066840C2semidirect
11. C11×#1442C2semidirect
36. #10622279C4semidirect
76. C2×C4×Dic11C2×C4semidirect
80. C11×#95C2×C4semidirect
91. C11⋊#95C2×C4semidirect
189. #1442D11semidirect
412. #95C4×D11semidirect
515. C11#13966semidirect

Maximal subgroups

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

subgroupindex
C2×#106226002
C2×#106222792
C2×D11×#952
#130668752
#130668732
#130668722
#130668412
#130668402
(C2×D11)⋊#952
C11×#14422
#1396611