Finite Group Databasebeta

← #14680312

Subgroups — #14680312

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622602C212yesmaximal
2C2×#10622280C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4C2×D11×#95C211yesmaximal, characteristic
5#13066879C211yesmaximal, characteristic, complemented
6#13066873C211yesmaximal, characteristic, complemented
7#13066872C211yesmaximal, characteristic, complemented
8#13066867C212yesmaximal, complemented
9#13066866C212yesmaximal, complemented
10(C2×D11)⋊#95C212yesmaximal
11C11×#1444C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35#10622602—28no—
36#10622600—24no—
37#10622280C418yescomplemented
38D11×#95—24no—
39C24×D11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—42no—
55C22×C4×D11—42no—
56C22×C4×D11—42no—
57C22×C4×D11—42no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11C2×C414yes—
61C22×C4×D11D414yes—
62C22×C4×D11D414yes—
63C22×C4×D11Q814yes—
64C22×C4×D11Q814yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—42no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C4⋊C4—42no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4C2×C418yes—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—42no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—42no—
80C2×Dic11⋊C4—42no—
81C2×Dic11⋊C4—42no—
82C2×Dic11⋊C4—42no—
83C2×Dic11⋊C4C2×C418yescomplemented
84C11×#95—22no—
85C11×#95—42no—
86C11×#95C2×C414yescomplemented
87C11⋊#95—22no—
88C11⋊#95—24no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95C11⋊#95—42no—
96C11⋊#95C2×C414yescomplemented
97#14275—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11C22×C412yes—
104C23×D11C2×D412yes—
105C23×D11C2×D412yes—
106C23×D11C2×Q812yes—
107C23×D11C2×Q812yes—
108C23×D11#4112yes—
109C23×D11#4112yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
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×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11C2×Q812yes—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—21no—
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×Dic11C22×C414yes—
163C22×Dic11C22×C412yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D412yes—
166C22×Dic11C2×Q812yes—
167C22×Dic11C2×Q812yes—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—48no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11—48no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11—44no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×C4×D11—44no—
180C2×C4×D11—48no—
181C2×C4×D11—48no—
182C2×C4×D11C4⋊C4116yescomplemented
183C11×C4⋊C4—44no—
184C11×C4⋊C4—48no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—48no—
187C4⋊Dic11—44no—
188Dic11⋊C4—48no—
189Dic11⋊C4—48no—
190C2×#385—112no—
191C2×#380—111no—
192C2×#380—111no—
193C22×#95—111no—
194#1444—111no—
195#1444D1111yescharacteristic, complemented
196#1442—111no—
197#1442—111no—
198#1441—112no—
199#1441—112no—
200C22⋊#95—112no—
201C23×C11C23×C411yescharacteristic
202C23×C11C22×D411yescharacteristic
203C23×C11C22×D411yescharacteristic
204C23×C11C22×Q811yescharacteristic
205C23×C11C22×Q811yescharacteristic
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11H(5,𝔽2)12yes—
209C23×C11H(5,𝔽2)12yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C112−1+412yes—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11C2×C4⋊C414yes—
229C22×D11C4×D414yes—
230C22×D11C4×Q814yes—
231C22×D11#12114yes—
232C22×D11C22⋊Q814yes—
233C22×D11#12514yes—
234C22×D11C4⋊Q814yes—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11C2×C4⋊C414yes—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—42no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
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×Dic11C2×C4⋊C414yes—
293C4×D11—416no—
294C4×D11—416no—
295C4×D11—416no—
296C24×C4—111no—
297C24×C4—111no—
298C24×C4—111no—
299C22×C4⋊C4—112no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4C2×D1112yes—
303C22×C4⋊C4C2×D1111yescharacteristic
304C22×C22⋊C4—112no—
305C22×C22⋊C4—112no—
306#385—228no—
307#380—118no—
308#380—224no—
309C2×#95—111no—
310C2×#95—111no—
311C2×#95—111no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—111no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—224no—
320C2×#95C2×D1111yescharacteristic
321C2×#95C2×D1112yes—
322C2×#95C2×D1111yescharacteristic
323C22×C11C22×C4⋊C411yescharacteristic
324C22×C11C2×C4×D411yescharacteristic
325C22×C11C2×C4×Q811yescharacteristic
326C22×C11#51812yes—
327C22×C11#52012yes—
328C22×C11C2×#12111yescharacteristic
329C22×C11C2×C22⋊Q811yescharacteristic
330C22×C11C2×#12511yescharacteristic
331C22×C11C2×C4⋊Q811yescharacteristic
332C22×C11#53411yescharacteristic
333C22×C11#53412yes—
334C22×C11#53411yescharacteristic
335C22×C11#53511yescharacteristic
336C22×C11#53611yescharacteristic
337C22×C11#53712yes—
338C22×C11#53812yes—
339C22×C11#53812yes—
340C22×C11#53912yes—
341C22×C11#53912yes—
342C22×C11#54312yes—
343C22×C11#54312yes—
344C22×C11#54412yes—
345C22×C11#54412yes—
346C2×D11—24no—
347C2×D11—24no—
348C2×D11—28no—
349C2×D11—28no—
350C2×D11—24no—
351C2×D11—24no—
352C2×D11—24no—
353C2×D11—24no—
354C2×D11—28no—
355C2×D11—28no—
356C2×D11#38918yes—
357C4×C11—24no—
358C4×C11—44no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—82no—
362Dic11—24no—
363Dic11—44no—
364Dic11—42no—
365Dic11—42no—
366Dic11—82no—
367C25—111no—
368C23×C4—111no—
369C23×C4—114no—
370C23×C4—114no—
371C23×C4—114no—
372C23×C4—112no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—114no—
376C23×C4—114no—
377C23×C4—112no—
378C23×C4—222no—
379C23×C4—222no—
380C23×C4—222no—
381C23×C4—222no—
382C23×C4—442no—
383C23×C4—442no—
384C23×C4—442no—
385C23×C4—442no—
386C23×C4—442no—
387C23×C4—442no—
388C23×C4C22×D1112yes—
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1111yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—42no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—224no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—442no—
402C2×C4⋊C4—442no—
403C2×C4⋊C4—442no—
404C2×C4⋊C4—442no—
405C2×C4⋊C4—442no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—224no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—224no—
410C2×C22⋊C4—224no—
411C2×C22⋊C4—224no—
412#95—22no—
413#95—42no—
414#95—114no—
415#95—222no—
416#95—222no—
417#95—224no—
418#95—224no—
419#95—222no—
420#95—224no—
421#95—442no—
422#95—442no—
423#95—442no—
424#95C4×D1114yescomplemented
425C2×C11C2×#38911yescharacteristic
426C2×C11#231511yescharacteristic
427C2×C11#231711yescharacteristic
428C2×C11#232512yes—
429C2×C11#232912yes—
430C2×C11#261711yescharacteristic
431C2×C11#261811yescharacteristic
432C2×C11#262611yescharacteristic
433C2×C11#262711yescharacteristic
434C2×C11#264612yes—
435C2×C11#265912yes—
436D11—28no—
437C24—112no—
438C24—112no—
439C24—112no—
440C24—112no—
441C24—112no—
442C24—112no—
443C24—112no—
444C24—222no—
445C24—222no—
446C24—222no—
447C24—222no—
448C24C23×D1111yescharacteristic
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—112no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—1116no—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—228no—
480C22×C4—228no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—448no—
505C22×C4—444no—
506C22×C4—448no—
507C22×C4—444no—
508C22×C4—448no—
509C22×C4—448no—
510C22×C4—444no—
511C22×C4—444no—
512C22×C4—444no—
513C22×C4—448no—
514C22×C4—444no—
515C22×C4—448no—
516C22×C4C2×C4×D1114yes—
517C22×C4C2×C4×D1112yes—
518C22×C4D4×D1112yes—
519C22×C4D4×D1112yes—
520C22×C4Q8×D1112yes—
521C22×C4Q8×D1112yes—
522C4⋊C4—44no—
523C4⋊C4—48no—
524C4⋊C4—448no—
525C4⋊C4—444no—
526C4⋊C4—448no—
527C22⋊C4—2216no—
528C22⋊C4—448no—
529C11#1427511yescharacteristic, complemented, Sylow
530C23—114no—
531C23—114no—
532C23—114no—
533C23—114no—
534C23—114no—
535C23—114no—
536C23—114no—
537C23—222no—
538C23—222no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—222no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—224no—
549C23—224no—
550C23—222no—
551C23—224no—
552C23—224no—
553C23C22×C4×D1111yescharacteristic
554C23C2×D4×D1111yescharacteristic
555C23C2×D4×D1111yescharacteristic
556C23#6703712yes—
557C23#6703712yes—
558C23C2×Q8×D1111yescharacteristic
559C23C2×Q8×D1111yescharacteristic
560C23#6704012yes—
561C23#41×D1111yescharacteristic
562C23#41×D1111yescharacteristic
563C23#6704212yes—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—114no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—4416no—
605C2×C4—4416no—
606C2×C4—4416no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—442no—
610C2×C4—441no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—441no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4C4⋊C4×D1114yes—
625C22—118no—
626C22—228no—
627C22—224no—
628C22—224no—
629C22—228no—
630C22—224no—
631C22—224no—
632C22—228no—
633C22—228no—
634C22—224no—
635C22—224no—
636C22C2×C4⋊C4×D1111yescharacteristic
637C22#1062303512yes—
638C22C4×D4×D1111yescharacteristic
639C22#1062307612yes—
640C22C4×Q8×D1111yescharacteristic
641C22#1062312012yes—
642C22#1062312011yescharacteristic
643C22D11×#12111yescharacteristic
644C22#1062314412yes—
645C22D11×C22⋊Q811yescharacteristic
646C22#1062316012yes—
647C22#1062316512yes—
648C22#1062316512yes—
649C22#1062316912yes—
650C22#1062318411yescharacteristic
651C22#1062318812yes—
652C22D11×#12511yescharacteristic
653C22#1062322312yes—
654C22#1062324611yescharacteristic
655C22D11×C4⋊Q811yescharacteristic
656C22#1062325511yescharacteristic
657C22#1062326012yes—
658C22#1062326012yes—
659C4—24no—
660C4—42no—
661C4—44no—
662C4—42no—
663C4—82no—
664C4—224no—
665C4—442no—
666C4—444no—
667C4—442no—
668C4—882no—
669C2—228no—
670C2D11×#38911yescharacteristic
671C2#1307122711yescharacteristic
672C2#1307123711yescharacteristic
673C2#1307131312yes—
674C2#1307135012yes—
675C2#1307434911yescharacteristic
676C2#1307435911yescharacteristic
677C2#1307442211yescharacteristic
678C2#1307442811yescharacteristic
679C2#1307458512yes—
680C2#1307472912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1444D11
hypocenterC11#14275
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
5. #13066879C2semidirect
6. #13066873C2semidirect
7. #13066872C2semidirect
8. #13066867C2semidirect
9. #13066866C2semidirect
11. C11×#1444C2semidirect
37. #10622280C4semidirect
83. C2×Dic11⋊C4C2×C4semidirect
86. C11×#95C2×C4semidirect
96. C11⋊#95C2×C4semidirect
182. C2×C4×D11C4⋊C4semidirect
195. #1444D11semidirect
424. #95C4×D11semidirect
529. C11#14275semidirect

Maximal subgroups

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

subgroupindex
C2×#106226022
C2×#106222802
C2×#106226002
C2×D11×#952
#130668792
#130668732
#130668722
#130668672
#130668662
(C2×D11)⋊#952
C11×#14442
#1427511