Finite Group Databasebeta

← #14769478

Subgroups — #14769478

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D8×D11C211yesmaximal, characteristic
2C2×#10622765C211yesmaximal, characteristic, complemented
3D4×(C2×D11)⋊C4C212yesmaximal, complemented
4#13069492C211yesmaximal, characteristic, complemented
5#13069490C211yesmaximal, characteristic, complemented
6#13068964C212yesmaximal, complemented
7#13068962C212yesmaximal, complemented
8#13068638C211yesmaximal, characteristic, complemented
9#13068545C212yesmaximal, complemented
10#13068393C211yesmaximal, characteristic, complemented
11C2×C11×#442C211yesmaximal, characteristic, complemented
12C22×D4×D11C2212yes—
13C22×C11×D8C2211yescharacteristic
14C2×C4×D4×C11C2212yescomplemented
15C2×D4×Dic11C2212yescomplemented
16C22×#4323C2212yes—
17C22×(C2×D11)⋊C4—22no—
18C2×D8×D11—24no—
19C2×D8×D11—24no—
20C2×D8×D11C418yescomplemented
21C22×D88C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C11×#442—24no—
24C2×C11×#106C2211yescharacteristic, complemented
25C2×C11×#102C2212yescomplemented
26C2×C11×#97C2211yescharacteristic, complemented
27C2×#66896C2212yescomplemented
28#10622826—22no—
29#10622765—24no—
30C2×#66885C2212yescomplemented
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66881C2211yescharacteristic, complemented
33C2×#66879C2211yescharacteristic, complemented
34#10622601C2212yescomplemented
35#10622600C2212yes—
36C2×#66873C2212yescomplemented
37#10622571—22no—
38#10622568—22no—
39#10622552C2212yescomplemented
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622188C2211yescharacteristic, complemented
42#10622167C2212yescomplemented
43#10622162C2211yescharacteristic, complemented
44C24×D11—22no—
45C22×D4×C11C2312yes—
46C23×C4×C11—22no—
47C22×C22⋊D11—22no—
48C23×Dic11—22no—
49C2×D4×D11—24no—
50C2×D4×D11—24no—
51C2×D4×D11—24no—
52C2×D4×D11—42no—
53C2×D4×D11—42no—
54C2×D4×D11C2×C418yescomplemented
55C22×D44C2312yes—
56C22×C4×D11C2311yescharacteristic
57C2×C11×D8C2×C414yes—
58C2×C11×D8D414yes—
59C2×C11×D8D414yes—
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C4×D4×C11—24no—
63C4×D4×C11—42no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11C2311yescharacteristic
67C2×C22⋊Dic11—22no—
68D4×Dic11—24no—
69D4×Dic11—42no—
70C2×#4323—24no—
71C2×#4323—24no—
72C2×#4323C2×C418yescomplemented
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—48no—
79C2×(C2×D11)⋊C4D412yes—
80C2×C4⋊Dic11C2312yes—
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84D8×D11—232no—
85C2×D88—22no—
86C2×D88—22no—
87C2×D88C2×C414yescomplemented
88C2×C8×D11—22no—
89C2×C8×D11—22no—
90C2×C8×D11C2×C414yescomplemented
91C11×#106—22no—
92C11×#102—24no—
93C11×#97—22no—
94#66896—24no—
95C11⋊#95—22no—
96C11⋊#95D412yes—
97#66885—42no—
98(C2×D11)⋊C8—22no—
99#66881—22no—
100#66879—22no—
101#66873—42no—
102#22436—111nomaximal, Sylow
103C24×C11—22no—
104C23×D11—22no—
105C23×D11—28no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11—44no—
109C23×D11—44no—
110C23×D11—82no—
111C23×D11—82no—
112C23×D11C2×D411yescharacteristic
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11C22×C414yes—
117C2×D4×C11C2×D414yes—
118C2×D4×C11C2×D414yes—
119C22×C4×C11—22no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11—82no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—28no—
126C2×C22⋊D11—44no—
127C2×C22⋊D11—44no—
128C22×Dic11—22no—
129C22×Dic11—44no—
130C22×Dic11—44no—
131C22×Dic11—82no—
132C22×Dic11C2×D412yes—
133C22×Dic11C2×D411yescharacteristic
134D4×D11—216no—
135D4×D11—48no—
136D4×D11—48no—
137D4×D11—48no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—22no—
143C2×D44C22×C414yes—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11C22×C412yes—
149C2×C4×D11#4112yes—
150C11×D8C22⋊C4116yescomplemented
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C22×C412yes—
155C2×C8×C11C2×D412yes—
156C2×C8×C11C2×D412yes—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C22⋊C4—44no—
160C42×C11—21no—
161C42×C11—21no—
162C22⋊Dic11—44no—
163#4323—216no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—44no—
166(C2×D11)⋊C4—44no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—82no—
169(C2×D11)⋊C4—82no—
170C4⋊Dic11—22no—
171C4⋊Dic11—22no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8C22×C412yes—
180D88—28no—
181C8×D11—28no—
182C23×D8—111no—
183C2×#442—111no—
184C2×#442D1111yescharacteristic, complemented
185D4×C22⋊C4—112no—
186#1972—111no—
187#1972—111no—
188#1879—112no—
189#1879—112no—
190#1807—111no—
191#1786—112no—
192#1752—111no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11C22×D411yescharacteristic
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—416no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—416no—
213C22×D11—88no—
214C22×D11—88no—
215C22×D11—88no—
216C22×D11—88no—
217C22×D11—88no—
218C22×D11C4×D412yes—
219C22×D11AGL(1,ℤ/8)14yes—
220D4×C11—24no—
221D4×C11—24no—
222D4×C11—24no—
223D4×C11C2×C22⋊C418yescomplemented
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—88no—
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C22⋊D11—416no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—88no—
247C2×Dic11C4×D412yes—
248D44—24no—
249D44—24no—
250D44—42no—
251D44—42no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C8×C11—41no—
257C8×C11C2×C22⋊C414yescomplemented
258C11⋊C8—22no—
259C11⋊C8—41no—
260C23×D4—112no—
261C22×D8—112no—
262C22×D8—118no—
263C22×D8—111no—
264C22×D8—224no—
265C22×D8—224no—
266C22×D8C2×D1111yescharacteristic
267C23×C8—111no—
268C2×C4×D4—112no—
269C2×C4×D4C2×D1112yescomplemented
270C22×C22⋊C4—222no—
271#442—24no—
272#442—224no—
273C2×#106—111no—
274C2×#106C2×D1111yescharacteristic, complemented
275C2×#102—112no—
276C2×#102—112no—
277C2×#102—112no—
278C2×#102C2×D1112yescomplemented
279C2×C22⋊C8—111no—
280C2×#97—111no—
281C2×#97C2×D1111yescharacteristic, complemented
282#390—112no—
283#390—112no—
284#386—222no—
285#386—222no—
286#380—112no—
287#379—222no—
288C4×C22⋊C4—111no—
289#340—112no—
290#336—111no—
291#336—111no—
292C22×C11—28no—
293C22×C11—44no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11C2×C4×D411yescharacteristic
300C22×C11D4211yescharacteristic
301C22×C11D4211yescharacteristic
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C22×C11#57612yes—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—44no—
309C2×D11—44no—
310C2×D11—44no—
311C2×D11—832no—
312C2×D11—82no—
313C2×D11—82no—
314C2×D11—82no—
315C2×D11—82no—
316C2×D11#44214yescomplemented
317C4×C11—42no—
318C4×C11—82no—
319C4×C11C22×C22⋊C411yescharacteristic
320C4×C11#51811yescharacteristic
321C4×C11#54611yescharacteristic
322C4×C11#54611yescharacteristic
323Dic11—22no—
324Dic11—42no—
325Dic11—82no—
326C25—222no—
327C22×D4—118no—
328C22×D4—112no—
329C22×D4—224no—
330C22×D4—222no—
331C22×D4—224no—
332C22×D4—224no—
333C22×D4—442no—
334C22×D4—442no—
335C22×D4C22×D1112yes—
336C23×C4—22no—
337C23×C4—111no—
338C23×C4—222no—
339C2×D8—118no—
340C2×D8—114no—
341C2×D8—224no—
342C2×D8—224no—
343C2×D8—2232no—
344C2×D8—222no—
345C2×D8—222no—
346C2×D8C4×D1114yes—
347C2×D8D4414yes—
348C2×D8C22⋊D1114yes—
349C22×C8—111no—
350C22×C8—114no—
351C22×C8—111no—
352C22×C8—222no—
353C22×C8—222no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C4×D4—24no—
357C4×D4—42no—
358C4×D4—224no—
359C4×D4—442no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4C22×D1112yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—112no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4—222no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—448no—
371C2×C42—111no—
372C2×C42C22×D1111yescharacteristic
373#106—22no—
374#106—222no—
375#102—24no—
376#102—224no—
377#102—442no—
378#102—442no—
379C22⋊C8—222no—
380#97—22no—
381#97—222no—
382#95—112no—
383#95—222no—
384C2×C11—48no—
385C2×C11D4×C22⋊C411yescharacteristic
386C2×C11C2×#44211yescharacteristic
387C2×C11#294811yescharacteristic
388C2×C11#326412yes—
389C2×C11#326412yes—
390D11—24no—
391D11—84no—
392C24—22no—
393C24—111no—
394C24—228no—
395C24—222no—
396C24—444no—
397C24—444no—
398C24—444no—
399C24—444no—
400C24—882no—
401C24—882no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—114no—
406C2×D4—228no—
407C2×D4—2216no—
408C2×D4—222no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—448no—
414C2×D4—448no—
415C2×D4—448no—
416C2×D4—444no—
417C2×D4—444no—
418C2×D4C2×C4×D1114yes—
419C2×D4C2×D4414yes—
420C2×D4C2×C22⋊D1114yes—
421C22×C4—22no—
422C22×C4—44no—
423C22×C4—44no—
424C22×C4—82no—
425C22×C4—111no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—222no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4—882no—
437C22×C4D4×D1112yes—
438C22×C4C23×D1111yescharacteristic
439D8—2216no—
440D8—228no—
441D8(C2×D11)⋊C4116yescomplemented
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—112no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—228no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8C2×C4×D1112yes—
453C2×C8C2×D4412yes—
454C2×C8C2×C22⋊D1112yes—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C22⋊C4—44no—
460C22⋊C4—224no—
461C22⋊C4—444no—
462C22⋊C4—444no—
463C22⋊C4—444no—
464C22⋊C4—444no—
465C22⋊C4—882no—
466C22⋊C4—882no—
467C42—21no—
468C42—21no—
469C42—221no—
470C42—221no—
471C11#2243611yescharacteristic, complemented, Sylow
472C23—24no—
473C23—24no—
474C23—24no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—114no—
480C23—112no—
481C23—222no—
482C23—221no—
483C23—221no—
484C23—224no—
485C23—4416no—
486C23—4416no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23—888no—
494C23—888no—
495C23—888no—
496C23—888no—
497C23—888no—
498C23C2×D4×D1111yescharacteristic
499D4—24no—
500D4—24no—
501D4—24no—
502D4—224no—
503D4—224no—
504D4—4416no—
505D4—442no—
506D4—442no—
507D4C2×(C2×D11)⋊C418yescomplemented
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—88no—
515C2×C4—112no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—888no—
529C2×C4C22×C4×D1111yescharacteristic
530C2×C4C22×D4411yescharacteristic
531C2×C4#6703711yescharacteristic
532C2×C4#41×D1111yescharacteristic
533C2×C4#6704211yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—41no—
536C8—222no—
537C8—441no—
538C8C2×(C2×D11)⋊C414yescomplemented
539C22—28no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—44no—
544C22—44no—
545C22—44no—
546C22—114no—
547C22—224no—
548C22—224no—
549C22—222no—
550C22—222no—
551C22—444no—
552C22—444no—
553C22—444no—
554C22—8832no—
555C22—882no—
556C22—882no—
557C22—882no—
558C22—882no—
559C22C4×D4×D1111yescharacteristic
560C22D4×D4411yescharacteristic
561C22D11×AGL(1,ℤ/8)12yes—
562C22#1062330512yes—
563C22D4×C22⋊D1111yescharacteristic
564C4—42no—
565C4—82no—
566C4—222no—
567C4—442no—
568C4—882no—
569C4#1062307611yescharacteristic
570C4#1062308511yescharacteristic
571C4C22×(C2×D11)⋊C411yescharacteristic
572C4#1062336011yescharacteristic
573C2—48no—
574C2—224no—
575C2—884no—
576C2D4×(C2×D11)⋊C411yescharacteristic
577C2D11×#44211yescharacteristic
578C2#1307746511yescharacteristic
579C2#1308009012yes—
580C2#1308009812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC22×D8×D11C2
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#22436
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×#10622765C2semidirect
3. D4×(C2×D11)⋊C4C2semidirect
4. #13069492C2semidirect
5. #13069490C2semidirect
6. #13068964C2semidirect
7. #13068962C2semidirect
8. #13068638C2semidirect
9. #13068545C2semidirect
10. #13068393C2semidirect
11. C2×C11×#442C2semidirect
14. C2×C4×D4×C11C22semidirect
15. C2×D4×Dic11C22semidirect
20. C2×D8×D11C4semidirect
24. C2×C11×#106C22semidirect
25. C2×C11×#102C22semidirect
26. C2×C11×#97C22semidirect
27. C2×#66896C22semidirect
30. C2×#66885C22semidirect
32. C2×#66881C22semidirect
33. C2×#66879C22semidirect
34. #10622601C22semidirect
36. C2×#66873C22semidirect
39. #10622552C22semidirect
41. #10622188C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
54. C2×D4×D11C2×C4semidirect
72. C2×#4323C2×C4semidirect
87. C2×D88C2×C4semidirect
90. C2×C8×D11C2×C4semidirect
150. C11×D8C22⋊C4semidirect
184. C2×#442D11semidirect
223. D4×C11C2×C22⋊C4semidirect
257. C8×C11C2×C22⋊C4semidirect
269. C2×C4×D4C2×D11semidirect
274. C2×#106C2×D11semidirect
278. C2×#102C2×D11semidirect
281. C2×#97C2×D11semidirect
316. C2×D11#442semidirect
441. D8(C2×D11)⋊C4semidirect
471. C11#22436semidirect
507. D4C2×(C2×D11)⋊C4semidirect
538. C8C2×(C2×D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×D8×D112
C2×#106227652
D4×(C2×D11)⋊C42
#130694922
#130694902
#130689642
#130689622
#130686382
#130685452
#130683932
C2×C11×#4422
#2243611