Finite Group Databasebeta

← #14764061

Subgroups — #14764061

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622339C211yesmaximal, characteristic
2#13070998C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4#13068818C212yesmaximal, complemented
5#13068814C212yesmaximal, complemented
6#13068808C211yesmaximal, characteristic, complemented
7#13068806C211yesmaximal, characteristic, complemented
8#13068804C211yesmaximal, characteristic, complemented
9#13068648C212yesmaximal, complemented
10#13068646C212yesmaximal, complemented
11C11×#1853C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×C4⋊Dic11C2211yescharacteristic
16C22×#4313C2212yes—
17C2×#66945C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×C11×#106C2212yescomplemented
20C2×C11×C22⋊C8C2211yescharacteristic
21C11×#380C2211yescharacteristic
22#10622825C2211yescharacteristic
23C2×C11⋊#95—21no—
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66882C2212yescomplemented
27#10622600—21no—
28#10622600—21no—
29#10622600C2212yes—
30#10622600C2211yescharacteristic
31#10622600C2212yes—
32#10622600C2211yescharacteristic
33C2×#66872C2212yescomplemented
34C2×#66871C2212yescomplemented
35#10622568—21no—
36C22⋊C4×Dic11—21no—
37#10622339C418yescomplemented
38#10622279—21no—
39#10622277—21no—
40C11×#340C2212yescomplemented
41#10622189C2212yescomplemented
42#10622167C2212yescomplemented
43#10622167C2212yescomplemented
44C24×D11D411yescharacteristic
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C22×C4×D11—42no—
50C22×C4×D11—42no—
51C22×C4×D11C2×C414yes—
52C22×C4×D11D411yescharacteristic
53C22×C4×D11D411yescharacteristic
54C22×C4×D11Q814yes—
55C22×C4×D11C2311yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—42no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C22⋊Dic11—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—44no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—42no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C22×C11⋊C8C2312yes—
80C2×#4313—42no—
81C2×#4313—42no—
82C2×#4313C2×C418yescomplemented
83#66945—42no—
84#66945—42no—
85C11×#106—42no—
86C11×C22⋊C8C2×C414yes—
87C11×#95—21no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C22⋊(C11⋊C8)C2×C414yes—
94(C2×D11)⋊C8C2×C418yescomplemented
95#66882—42no—
96#66872—42no—
97#66871—42no—
98#21944—111nomaximal, Sylow
99C24×C11C2×D411yescharacteristic
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—41no—
103C23×D11—41no—
104C23×D11—41no—
105C23×D11—41no—
106C23×D11C4⋊C414yes—
107C23×D11C2×D411yescharacteristic
108C23×D11C2×D411yescharacteristic
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×Q812yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128C22×Dic11—42no—
129C22×Dic11C4⋊C414yes—
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—48no—
141C2×C4×D11—48no—
142C2×C4×D11C4⋊C414yes—
143C2×C4×D11C4⋊C414yes—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C22×C412yes—
146C2×C4×D11C2×Q812yes—
147C2×C4×D11C2×Q812yes—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C2×C8×C11C22×C414yes—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—42no—
156C11×C22⋊C4—42no—
157C22⋊Dic11—42no—
158(C2×D11)⋊C4—42no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—44no—
163(C2×D11)⋊C4—44no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—42no—
169C4×Dic11—42no—
170C4×Dic11—42no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8C22×C414yes—
174#4313—48no—
175C2×#407—111no—
176#2280—111no—
177C2×#380—111no—
178#1854—112no—
179#1854—112no—
180#1853—111no—
181#1853D1111yescharacteristic, complemented
182#1852—111no—
183#1852—111no—
184#1809—112no—
185#1809—112no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11C2×C4⋊C412yes—
191C23×C11AGL(1,ℤ/8)12yes—
192C23×C11#13712yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—21no—
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—28no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11C2×C4⋊C412yes—
214C22×D11C2×C4⋊C412yes—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—84no—
229C2×C4×C11C2×C4⋊C412yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×Q811yescharacteristic
232C2×C4×C11H(5,𝔽2)12yes—
233C2×C4×C11H(5,𝔽2)12yes—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—44no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—42no—
248C2×Dic11—84no—
249C2×Dic11C2×C4⋊C412yes—
250C2×Dic11C2×C4⋊C412yes—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—24no—
255C4×D11—44no—
256C4×D11—44no—
257C8×C11—24no—
258C11⋊C8—24no—
259C24×C4—111no—
260C22×M16—112no—
261C2×#117—111no—
262C2×#117—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4C2×D1111yescharacteristic
265C22×C22⋊C4—221no—
266C2×#107—112no—
267C2×#107—112no—
268C2×#106—112no—
269C2×#106C2×D1112yescomplemented
270#407—118no—
271C2×C22⋊C8—111no—
272C2×C22⋊C8—112no—
273C2×C22⋊C8C2×D1111yescharacteristic
274#381—221no—
275#380—111no—
276#380—112no—
277#380—111no—
278#380—111no—
279#380—112no—
280#380—221no—
281#380—221no—
282#380C2×D1111yescharacteristic
283#379—221no—
284C4×C22⋊C4—221no—
285C4×C22⋊C4—221no—
286C2×#95—221no—
287#340—112no—
288#340—112no—
289#340—112no—
290#340C2×D1112yescomplemented
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11#42814yes—
298C22×C11C22×C4⋊C411yescharacteristic
299C22×C11#53411yescharacteristic
300C22×C11#53411yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11#57511yescharacteristic
304C22×C11#57511yescharacteristic
305C2×D11—22no—
306C2×D11—22no—
307C2×D11—22no—
308C2×D11—22no—
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—416no—
312C2×D11—41no—
313C2×D11—41no—
314C2×D11—41no—
315C2×D11—41no—
316C2×D11—41no—
317C2×D11—41no—
318C2×D11—41no—
319C2×D11—41no—
320C4×C11—22no—
321C4×C11—82no—
322C4×C11—81no—
323C4×C11—81no—
324C4×C11#51812yes—
325C4×C11#54312yes—
326Dic11—22no—
327Dic11—22no—
328Dic11—81no—
329Dic11—81no—
330Dic11—82no—
331C25—111no—
332C23×C4—21no—
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—114no—
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—114no—
340C23×C4—221no—
341C23×C4—442no—
342C23×C4—442no—
343C23×C4C22×D1111yescharacteristic
344C2×M16—118no—
345C2×M16—442no—
346C2×M16—442no—
347C22×C8—112no—
348C22×C8C22×D1112yes—
349#117—442no—
350#117—442no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—442no—
358C2×C4⋊C4C22×D1112yes—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—444no—
370C2×C42—221no—
371C2×C42—221no—
372#107—442no—
373#107—442no—
374#106—42no—
375#106—442no—
376C22⋊C8—114no—
377C22⋊C8—118no—
378C22⋊C8C4×D1114yes—
379#95—21no—
380#95—222no—
381#95—222no—
382#95—221no—
383#95—221no—
384#95—221no—
385C2×C11—24no—
386C2×C11#231511yescharacteristic
387C2×C11C2×#42811yescharacteristic
388C2×C11#291111yescharacteristic
389C2×C11#319411yescharacteristic
390C2×C11#319411yescharacteristic
391C2×C11#319611yescharacteristic
392C2×C11#319611yescharacteristic
393D11—42no—
394D11—42no—
395C24—111no—
396C24—111no—
397C24—114no—
398C24—222no—
399C24—222no—
400C24—441no—
401C24—441no—
402C24—441no—
403C24—441no—
404C24D4×D1111yescharacteristic
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—114no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—448no—
430C22×C4—448no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4—441no—
434C22×C4—441no—
435C22×C4—441no—
436C22×C4—441no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4C2×C4×D1112yes—
441C22×C4D4×D1111yescharacteristic
442C22×C4Q8×D1112yes—
443C22×C4C23×D1111yescharacteristic
444M16—448no—
445C2×C8—22no—
446C2×C8—22no—
447C2×C8—114no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8C2×C4×D1114yes—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C4⋊C4—442no—
461C22⋊C4—42no—
462C22⋊C4—444no—
463C22⋊C4—444no—
464C22⋊C4—442no—
465C22⋊C4—442no—
466C22⋊C4—442no—
467C22⋊C4—442no—
468C22⋊C4—442no—
469C42—442no—
470C42—442no—
471C11#2194411yescharacteristic, complemented, Sylow
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—112no—
477C23—112no—
478C23—228no—
479C23—221no—
480C23—221no—
481C23—221no—
482C23—221no—
483C23—221no—
484C23—221no—
485C23—221no—
486C23—221no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23—444no—
492C23—444no—
493C23—444no—
494C23—444no—
495C23—444no—
496C23—444no—
497C23C4⋊C4×D1112yes—
498C23#6696712yes—
499C23#6696812yes—
500C23C2×D4×D1111yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—84no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—221no—
518C2×C4—221no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—444no—
526C2×C4—444no—
527C2×C4—444no—
528C2×C4—442no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—442no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—442no—
537C2×C4—884no—
538C2×C4C4⋊C4×D1112yes—
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4#6703712yes—
541C2×C4C2×Q8×D1111yescharacteristic
542C2×C4#6704212yes—
543C8—24no—
544C8—224no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—222no—
552C22—222no—
553C22—222no—
554C22—222no—
555C22—222no—
556C22—222no—
557C22—4416no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22#1062247414yes—
567C22C2×C4⋊C4×D1111yescharacteristic
568C22#1062312011yescharacteristic
569C22#1062318411yescharacteristic
570C22C2×#6696711yescharacteristic
571C22C2×#6696811yescharacteristic
572C22#1062330411yescharacteristic
573C22#1062330811yescharacteristic
574C4—22no—
575C4—82no—
576C4—81no—
577C4—81no—
578C4—222no—
579C4—222no—
580C4—881no—
581C4—882no—
582C4—881no—
583C4#1062307612yes—
584C4#1062316512yes—
585C2—24no—
586C2—442no—
587C2—442no—
588C2#1307122711yescharacteristic
589C2C2×#1062247411yescharacteristic
590C2#1307720311yescharacteristic
591C2#1307943311yescharacteristic
592C2#1307943511yescharacteristic
593C2#1307944311yescharacteristic
594C2#1307944511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11#21944
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #13068818C2semidirect
5. #13068814C2semidirect
6. #13068808C2semidirect
7. #13068806C2semidirect
8. #13068804C2semidirect
9. #13068648C2semidirect
10. #13068646C2semidirect
11. C11×#1853C2semidirect
19. C2×C11×#106C22semidirect
26. C2×#66882C22semidirect
33. C2×#66872C22semidirect
34. C2×#66871C22semidirect
37. #10622339C4semidirect
40. C11×#340C22semidirect
41. #10622189C22semidirect
42. #10622167C22semidirect
43. #10622167C22semidirect
82. C2×#4313C2×C4semidirect
94. (C2×D11)⋊C8C2×C4semidirect
181. #1853D11semidirect
269. C2×#106C2×D11semidirect
290. #340C2×D11semidirect
471. C11#21944semidirect

Maximal subgroups

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

subgroupindex
C2×#106223392
#130709982
C2×#106226002
#130688182
#130688142
#130688082
#130688062
#130688042
#130686482
#130686462
C11×#18532
#2194411