Finite Group Databasebeta

← #14786412

Subgroups — #14786412

Order 2816.

1500 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2C2×#10622418C212yesmaximal, complemented
3D11×#380C211yesmaximal, characteristic
4#13069811C212yesmaximal, complemented
5#13069810C212yesmaximal, complemented
6#13068920C212yesmaximal, complemented
7#13068811C211yesmaximal, characteristic, complemented
8#13068808C211yesmaximal, characteristic, complemented
9#13068551C211yesmaximal, characteristic, complemented
10#13068525C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×#66999—21no—
15C2×#66999—21no—
16C2×#66999—28no—
17C2×#66999C2212yes—
18C2×#66999C2212yes—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4—21no—
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×C22⋊C4×D11—21no—
25C2×C11×#103C2212yescomplemented
26C2×C11×#103C2212yescomplemented
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C2×#66899C2212yescomplemented
30C2×#66899C2212yescomplemented
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×#66881C2212yescomplemented
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38C2×#66872C2212yescomplemented
39#10622555—21no—
40#10622418—28no—
41#10622280—21no—
42D11×#95—21no—
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45C24×D11D411yescharacteristic
46C22×Q8×C11—24no—
47C22×Q8×C11—21no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—42no—
51C22×Q8×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C23×Dic11D411yescharacteristic
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11—24no—
59C22×C4×D11—21no—
60C22×C4×D11—21no—
61C22×C4×D11—42no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2312yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C22⋊Dic11—21no—
71#66999—28no—
72#66999—28no—
73#66999—24no—
74#66999—24no—
75#66999—24no—
76#66999D418yes—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C22×C11⋊C8C2312yes—
93C4⋊C4×D11—24no—
94C4⋊C4×D11—42no—
95C22⋊C4×D11—44no—
96C11×#103—24no—
97C11×#103—42no—
98C11×C22⋊C8—22no—
99C11×#95—21no—
100#66899—24no—
101#66899—42no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C22⋊(C11⋊C8)—22no—
106(C2×D11)⋊C8—24no—
107(C2×D11)⋊C8—42no—
108#66881—24no—
109#66872—24no—
110#24003—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—41no—
117C23×D11—41no—
118C23×D11SD1614yes—
119C23×D11C2×D411yescharacteristic
120C23×D11C2×D411yescharacteristic
121C2×Q8×C11—24no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—48no—
128C2×Q8×C11—48no—
129C2×Q8×C11—42no—
130C2×Q8×C11—42no—
131C2×Q8×C11C2×D414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—41no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—41no—
167C2×C4×D11—41no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11C2×D414yes—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C22⋊C4—42no—
183C22⋊Dic11—42no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188C4⋊Dic11—24no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11C2×D414yes—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C22×C22⋊Q8—111no—
201C2×#483—112no—
202C2×#380—111no—
203#2035—112no—
204#2035—112no—
205#1872—112no—
206#1853—111no—
207#1853—111no—
208#1787—111no—
209#1787D1111yescharacteristic, complemented
210#1779—111no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11#12312yes—
216C23×C11C2×SD1612yes—
217C23×C11#13712yes—
218C23×C11C22×D411yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—28no—
230C22×D11—28no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11#12012yes—
237C22×D11C2×SD1612yes—
238C22×D11C2×SD1612yes—
239C22×D11#13712yes—
240Q8×C11—24no—
241Q8×C11—24no—
242Q8×C11—48no—
243Q8×C11—42no—
244Q8×C11—42no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—48no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11#12312yes—
260C2×C4×C11C22×D412yes—
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)12yes—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—24no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—44no—
271C2×Dic11—48no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11#12012yes—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—44no—
284C4×D11—44no—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—84no—
288C4×D11—84no—
289C8×C11—42no—
290C11⋊C8—42no—
291C23×Q8C2×D1111yescharacteristic
292C24×C4—111no—
293C2×C22⋊Q8—112no—
294C2×C22⋊Q8—112no—
295C2×C22⋊Q8—228no—
296C2×C22⋊Q8—221no—
297C2×C22⋊Q8—221no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—221no—
302C22×C22⋊C4—221no—
303C22×C22⋊C4—221no—
304#483—228no—
305C2×#106—112no—
306C2×#106—112no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#103C2×D1112yescomplemented
310C2×#103C2×D1112yescomplemented
311C2×C22⋊C8—111no—
312C2×C22⋊C8—112no—
313C2×C22⋊C8—112no—
314C2×C22⋊C8C2×D1111yescharacteristic
315#380—111no—
316#380—111no—
317#380—111no—
318#380—221no—
319#380—221no—
320#380C2×D1111yescharacteristic
321C2×#95—221no—
322#340—112no—
323#340—112no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11#48314yescomplemented
331C22×C11C2×#12011yescharacteristic
332C22×C11C2×#12311yescharacteristic
333C22×C11#53411yescharacteristic
334C22×C11C22×SD1611yescharacteristic
335C22×C11C2×#13711yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57511yescharacteristic
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—416no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11#44814yes—
353C4×C11—22no—
354C4×C11—44no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11#54612yes—
358C4×C11#54612yes—
359Dic11—22no—
360Dic11—41no—
361Dic11—44no—
362Dic11—81no—
363Dic11—81no—
364C25—111no—
365C22×Q8—24no—
366C22×Q8—21no—
367C22×Q8—22no—
368C22×Q8—22no—
369C22×Q8—42no—
370C22×Q8C22×D1112yes—
371C23×C4—21no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—224no—
378C23×C4—221no—
379C23×C4—221no—
380C23×C4—221no—
381C23×C4—222no—
382C23×C4—222no—
383C23×C4—442no—
384C23×C4C22×D1111yescharacteristic
385C22×C8—112no—
386C22×C8C22×D1112yes—
387C22⋊Q8—118no—
388C22⋊Q8—224no—
389C22⋊Q8—224no—
390C22⋊Q8—228no—
391C22⋊Q8—228no—
392C22⋊Q8—224no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4—224no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—228no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—442no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—222no—
410C2×C22⋊C4—228no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—444no—
415#106—224no—
416#106—224no—
417#103—24no—
418#103—42no—
419#103—224no—
420#103—442no—
421C22⋊C8—22no—
422C22⋊C8—224no—
423C22⋊C8—222no—
424C22⋊C8—442no—
425#95—21no—
426#95—221no—
427#95—221no—
428#95—221no—
429C2×C11—24no—
430C2×C11#240511yescharacteristic
431C2×C11C2×#44811yescharacteristic
432C2×C11#300711yescharacteristic
433C2×C11C2×#48311yescharacteristic
434C2×C11#309511yescharacteristic
435C2×C11#318711yescharacteristic
436C2×C11#319511yescharacteristic
437D11—24no—
438D11—42no—
439C24—111no—
440C24—111no—
441C24—114no—
442C24—222no—
443C24—222no—
444C24—222no—
445C24—222no—
446C24—441no—
447C24—441no—
448C24D4×D1111yescharacteristic
449C2×Q8—24no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—48no—
456C2×Q8—48no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8D4×D1114yes—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—111no—
469C22×C4—114no—
470C22×C4—111no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—222no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—221no—
483C22×C4—222no—
484C22×C4—221no—
485C22×C4—222no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—441no—
489C22×C4—441no—
490C22×C4—448no—
491C22×C4—448no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—441no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4#433912yes—
502C22×C4D4×D1111yescharacteristic
503C22×C4#434112yes—
504C22×C4C23×D1111yescharacteristic
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—114no—
514C4⋊C4—228no—
515C4⋊C4—228no—
516C4⋊C4—224no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C22⋊C4—42no—
523C22⋊C4—228no—
524C22⋊C4—228no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C11#2400311yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—112no—
534C23—112no—
535C23—112no—
536C23—112no—
537C23—228no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—228no—
549C23—444no—
550C23—444no—
551C23—444no—
552C23—444no—
553C23—444no—
554C23#6693612yes—
555C23SD16×D1112yes—
556C23#6697112yes—
557C23C2×D4×D1111yescharacteristic
558Q8—24no—
559Q8—24no—
560Q8—48no—
561Q8—42no—
562Q8—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—48no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—112no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—221no—
583C2×C4—224no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—444no—
587C2×C4—444no—
588C2×C4—444no—
589C2×C4—448no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—884no—
601C2×C4—884no—
602C2×C4#6693612yes—
603C2×C4C2×#433911yescharacteristic
604C2×C4C2×D4×D1112yes—
605C2×C4C2×#434111yescharacteristic
606C2×C4#6703712yes—
607C8—42no—
608C8—442no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—114no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—222no—
621C22—222no—
622C22—222no—
623C22—222no—
624C22—222no—
625C22—4416no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22#1062241814yescomplemented
631C22C2×#6693611yescharacteristic
632C22D11×#12011yescharacteristic
633C22#1062312011yescharacteristic
634C22C2×SD16×D1111yescharacteristic
635C22C2×#6697111yescharacteristic
636C22D11×#13711yescharacteristic
637C22#1062330811yescharacteristic
638C4—22no—
639C4—44no—
640C4—81no—
641C4—81no—
642C4—222no—
643C4—441no—
644C4—444no—
645C4—881no—
646C4—881no—
647C4#1062302112yes—
648C4#1062312212yes—
649C2—24no—
650C2—224no—
651C2—442no—
652C2#1307194111yescharacteristic
653C2D11×#44811yescharacteristic
654C2#1307787511yescharacteristic
655C2C2×#1062241811yescharacteristic
656C2#1307856211yescharacteristic
657C2#1307937111yescharacteristic
658C2#1307943811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenter#1787D11
hypocenterC11#24003
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#10622418C2semidirect
4. #13069811C2semidirect
5. #13069810C2semidirect
6. #13068920C2semidirect
7. #13068811C2semidirect
8. #13068808C2semidirect
9. #13068551C2semidirect
11. C11×#1787C2semidirect
25. C2×C11×#103C22semidirect
26. C2×C11×#103C22semidirect
29. C2×#66899C22semidirect
30. C2×#66899C22semidirect
35. C2×#66881C22semidirect
38. C2×#66872C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
209. #1787D11semidirect
309. C2×#103C2×D11semidirect
310. C2×#103C2×D11semidirect
330. C22×C11#483semidirect
528. C11#24003semidirect
630. C22#10622418semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
C2×#106224182
D11×#3802
#130698112
#130698102
#130689202
#130688112
#130688082
#130685512
#130685252
C11×#17872
#2400311