Finite Group Databasebeta

← #14676476

Subgroups — #14676476

Order 2816.

2078 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic
3C2×D11×#95C211yesmaximal, characteristic
4#13066882C212yesmaximal, complemented
5#13066882C212yesmaximal, complemented
6#13066843C211yesmaximal, characteristic, complemented
7#13066840C211yesmaximal, characteristic, complemented
8#13066840C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C212yesmaximal
10(C2×D11)⋊#95C212yesmaximal
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×#66925—24no—
22C2×#66925—24no—
23C2×#66925C418yescomplemented
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622277—24no—
39D11×#95—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—24no—
54C22×C4×D11—24no—
55C22×C4×D11—24no—
56C22×C4×D11—24no—
57C22×C4×D11—24no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11C2×C414yes—
61C22×C4×D11D414yes—
62C22×C4×D11D414yes—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11C2×C414yescomplemented
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4C2×C414yes—
74C2×(C2×D11)⋊C4C2×C414yes—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4C2×C414yescomplemented
80C2×Dic11⋊C4C2×C414yescomplemented
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11C2×C414yescomplemented
84#66925—232no—
85C11×#95—22no—
86C11×#95—22no—
87C11×#95—24no—
88C11×#95—42no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99#13958—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—21no—
104C23×D11—21no—
105C23×D11—21no—
106C23×D11—21no—
107C23×D11C22×C412yes—
108C23×D11C2×D412yes—
109C23×D11C2×D412yes—
110C23×D11#4114yes—
111C23×D11#4114yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
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—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4114yes—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
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—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11C22×C412yes—
169C22×Dic11C22×C412yes—
170C22×Dic11C22×C412yes—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D412yes—
173C22×Dic11#4114yes—
174C2×C4×D11—216no—
175C2×C4×D11—28no—
176C2×C4×D11—28no—
177C2×C4×D11—216no—
178C2×C4×D11—216no—
179C2×C4×D11—48no—
180C2×C4×D11—48no—
181C2×C4×D11—48no—
182C2×C4×D11—48no—
183C2×C4×D11—48no—
184C2×C4×D11—48no—
185C2×C4×D11C22⋊C4116yes—
186C42×C11—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—48no—
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192C4×Dic11—28no—
193C22×#117—111no—
194C2×#381—111no—
195C22×#95—111no—
196#1445—112no—
197#1445—112no—
198#1434—111no—
199#1434—111no—
200#1434—111no—
201#1434D1111yescharacteristic, complemented
202C22⋊#95—112no—
203C22⋊#95—112no—
204C23×C11C23×C411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11C2×#4112yes—
211C23×C11H(5,𝔽2)11yescharacteristic
212C23×C11H(5,𝔽2)11yescharacteristic
213C23×C112−1+411yescharacteristic
214C23×C112−1+411yescharacteristic
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11C2×C22⋊C414yes—
234C22×D11#11714yes—
235C22×D11#11714yes—
236C22×D11#12318yes—
237C22×D11#12318yes—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11C2×C22⋊C414yes—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
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×Dic11C2×C22⋊C414yes—
300C4×D11—232no—
301C4×D11—432no—
302C24×C4—111no—
303C24×C4—112no—
304C2×#117—118no—
305C2×#117—224no—
306C2×#117—224no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—111no—
309C22×C22⋊C4—111no—
310C22×C22⋊C4—111no—
311C22×C22⋊C4—112no—
312C22×C42—111no—
313C22×C42C2×D1111yescharacteristic
314#381—224no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—111no—
319C2×#95—111no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—224no—
326C2×#95C2×D1112yes—
327C2×#95C2×D1111yescharacteristic
328C2×#95C2×D1111yescharacteristic
329C2×#95C2×D1112yes—
330C22×C11C22×C22⋊C411yescharacteristic
331C22×C11C2×#11711yescharacteristic
332C22×C11C2×#11711yescharacteristic
333C22×C11C4×#4111yescharacteristic
334C22×C11C4×#4111yescharacteristic
335C22×C11#52011yescharacteristic
336C22×C11#52011yescharacteristic
337C22×C11C2×#12312yes—
338C22×C11C2×#12312yes—
339C22×C11#52512yes—
340C22×C11#53212yes—
341C22×C11#53511yescharacteristic
342C22×C11#53611yescharacteristic
343C22×C11#53711yescharacteristic
344C22×C11#53711yescharacteristic
345C22×C11#55112yes—
346C22×C11#55112yes—
347C22×C11#55112yes—
348C22×C11#55112yes—
349C22×C11#55212yes—
350C22×C11#55212yes—
351C22×C11#55212yes—
352C22×C11#55212yes—
353C2×D11—24no—
354C2×D11—24no—
355C2×D11—24no—
356C2×D11—24no—
357C2×D11—24no—
358C2×D11—28no—
359C2×D11—28no—
360C2×D11—28no—
361C2×D11—28no—
362C2×D11—24no—
363C2×D11#38118yes—
364C4×C11—24no—
365C4×C11—42no—
366C4×C11—44no—
367C4×C11—42no—
368C4×C11—82no—
369Dic11—24no—
370Dic11—42no—
371Dic11—44no—
372Dic11—42no—
373Dic11—82no—
374C25—111no—
375C23×C4—111no—
376C23×C4—114no—
377C23×C4—114no—
378C23×C4—114no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—112no—
382C23×C4—112no—
383C23×C4—224no—
384C23×C4—224no—
385C23×C4—224no—
386C23×C4—224no—
387C23×C4—224no—
388C23×C4—224no—
389C23×C4—224no—
390C23×C4—442no—
391C23×C4—442no—
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397#117—2232no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—222no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—224no—
412C2×C22⋊C4—224no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—114no—
416C2×C42—222no—
417C2×C42—222no—
418C2×C42C4×D1114yescomplemented
419#95—24no—
420#95—22no—
421#95—22no—
422#95—42no—
423#95—224no—
424#95—224no—
425#95—224no—
426#95—224no—
427#95—224no—
428#95—222no—
429#95—222no—
430#95—442no—
431#95—442no—
432#95—442no—
433C2×C11C2×#38111yescharacteristic
434C2×C11#229711yescharacteristic
435C2×C11#231111yescharacteristic
436C2×C11#234311yescharacteristic
437C2×C11#234311yescharacteristic
438C2×C11#234311yescharacteristic
439C2×C11#234311yescharacteristic
440C2×C11#248212yes—
441C2×C11#248412yes—
442C2×C11#249812yes—
443C2×C11#249812yes—
444D11—28no—
445C24—112no—
446C24—112no—
447C24—112no—
448C24—114no—
449C24—114no—
450C24—222no—
451C24—221no—
452C24—221no—
453C24—222no—
454C24—221no—
455C24—221no—
456C24C23×D1111yescharacteristic
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—1116no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—114no—
489C22×C4—228no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—2216no—
493C22×C4—2216no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—222no—
511C22×C4—221no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—448no—
520C22×C4—448no—
521C22×C4—448no—
522C22×C4—448no—
523C22×C4—448no—
524C22×C4—448no—
525C22×C4C2×C4×D1112yes—
526C22×C4C2×C4×D1112yes—
527C22×C4C2×C4×D1112yes—
528C22×C4#433914yes—
529C22×C4D4×D1112yes—
530C22×C4D4×D1112yes—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—448no—
536C42—28no—
537C42—228no—
538C11#1395811yescharacteristic, complemented, Sylow
539C23—114no—
540C23—114no—
541C23—114no—
542C23—118no—
543C23—118no—
544C23—224no—
545C23—224no—
546C23—222no—
547C23—222no—
548C23—222no—
549C23—222no—
550C23—224no—
551C23—224no—
552C23—224no—
553C23—224no—
554C23—224no—
555C23—224no—
556C23—222no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23—224no—
561C23—224no—
562C23C22×C4×D1111yescharacteristic
563C23C2×#433912yes—
564C23C2×D4×D1111yescharacteristic
565C23C2×D4×D1111yescharacteristic
566C23#6703711yescharacteristic
567C23#6704011yescharacteristic
568C23#41×D1112yes—
569C23#41×D1112yes—
570C23#41×D1112yes—
571C23#6704211yescharacteristic
572C23#6704311yescharacteristic
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—114no—
604C2×C4—2232no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—4432no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—442no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4C22⋊C4×D1114yes—
637C22—118no—
638C22—228no—
639C22—224no—
640C22—224no—
641C22—224no—
642C22—224no—
643C22—224no—
644C22—228no—
645C22—228no—
646C22—228no—
647C22—224no—
648C22C4×#433911yescharacteristic
649C22C2×C22⋊C4×D1111yescharacteristic
650C22#1062303511yescharacteristic
651C22D11×#11711yescharacteristic
652C22D11×#11711yescharacteristic
653C22#1062305311yescharacteristic
654C22#1062305411yescharacteristic
655C22#1062305812yes—
656C22#1062306012yes—
657C22#1062307812yes—
658C22#1062307912yes—
659C22#1062308712yes—
660C22#1062311212yes—
661C22#1062313811yescharacteristic
662C22#1062313911yescharacteristic
663C22#1062315911yescharacteristic
664C22#1062316011yescharacteristic
665C22D11×#12312yes—
666C22D11×#12312yes—
667C22#1062321012yes—
668C22#1062322412yes—
669C22#1062323612yes—
670C22#1062323912yes—
671C4—24no—
672C4—42no—
673C4—44no—
674C4—42no—
675C4—82no—
676C4—224no—
677C4—442no—
678C4—444no—
679C4—442no—
680C4—882no—
681C2—228no—
682C2D11×#38111yescharacteristic
683C2#1307110211yescharacteristic
684C2#1307120511yescharacteristic
685C2#1307146911yescharacteristic
686C2#1307147311yescharacteristic
687C2#1307147711yescharacteristic
688C2#1307147911yescharacteristic
689C2#1307288812yes—
690C2#1307290112yes—
691C2#1307305712yes—
692C2#1307305912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13958
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
4. #13066882C2semidirect
5. #13066882C2semidirect
6. #13066843C2semidirect
7. #13066840C2semidirect
8. #13066840C2semidirect
11. C11×#1434C2semidirect
23. C2×#66925C4semidirect
65. C2×C42×C11C2×C4semidirect
79. C2×Dic11⋊C4C2×C4semidirect
80. C2×Dic11⋊C4C2×C4semidirect
83. C2×C4×Dic11C2×C4semidirect
201. #1434D11semidirect
418. C2×C42C4×D11semidirect
538. C11#13958semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106222772
C2×D11×#952
#130668822
#130668432
#130668402
(C2×D11)⋊#952
C11×#14342
#1395811