Finite Group Databasebeta

← #14755194

Subgroups — #14755194

Order 2816.

1926 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4#13071196C211yesmaximal, characteristic, complemented
5#13068969C214yesmaximal, complemented
6#13068962C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C2×C11×#416C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623358—24no—
15#10623358—24no—
16C2×#67002—24no—
17C2×#67002—24no—
18C2×#67002C418yescomplemented
19C2×Q8×Dic11C2212yescomplemented
20C22×#4325C2212yes—
21C2×D4×Dic11—22no—
22C2×D4×Dic11C2212yescomplemented
23C22×#4323C2212yes—
24C2×#66979—21no—
25C2×#66979C2211yescharacteristic
26C22×C4⋊Dic11—21no—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C11×#416—24no—
30C2×C11×#103C2212yescomplemented
31C2×C11×#102C2212yescomplemented
32C2×#66885—24no—
33C2×#66885C2214yes—
34#10622601C2214yes—
35#10622568—22no—
36#10622552—21no—
37#10622552—21no—
38#10622188C2214yescomplemented
39#10622167C2214yescomplemented
40C24×D11—21no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41C2×C414yes—
45C2×C11×#41D414yes—
46C2×C11×#41D414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C23×Dic11—21no—
53C23×Dic11—22no—
54C22×D44—22no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—21no—
59C22×D44—22no—
60C22×D44C2×C414yescomplemented
61C22×D44C2312yes—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2312yes—
66C11×#117—22no—
67C11×#117—22no—
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11D412yes—
73#67002—232no—
74Q8×Dic11—24no—
75Q8×Dic11—24no—
76C2×#4325—24no—
77C2×#4325—24no—
78C2×#4325C2×C418yescomplemented
79D4×Dic11—216no—
80D4×Dic11—24no—
81D4×Dic11—24no—
82C2×#4323—24no—
83C2×#4323—24no—
84C2×#4323C2×C418yescomplemented
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87#66979—28no—
88#66979—22no—
89#66979—22no—
90C2×C4⋊Dic11—28no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11D414yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4×Dic11—22no—
99C2×C4×Dic11C2312yes—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318C2×C414yescomplemented
103C22×C11⋊C8C2312yes—
104C11×#103—24no—
105C11×#102—24no—
106#66885—28no—
107#20932—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11C2×D411yescharacteristic
110C23×D11—22no—
111C23×D11—24no—
112C23×D11—42no—
113C23×D11—42no—
114C23×D11—82no—
115C23×D11—82no—
116C11×#41—28no—
117C11×#41—28no—
118C11×#41—28no—
119C11×#41C22⋊C4116yescomplemented
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11C22×C412yes—
124C2×Q8×C11C2×D412yes—
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C22×C412yes—
133C2×D4×C11C2×D412yes—
134C2×D4×C11C2×D412yes—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11#4112yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—28no—
149C22×Dic11—24no—
150C22×Dic11—22no—
151C22×Dic11—82no—
152C22×Dic11—84no—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C2×D44—28no—
156C2×D44—24no—
157C2×D44—28no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—22no—
163C2×D44—42no—
164C2×D44—44no—
165C2×D44—42no—
166C2×D44—44no—
167C2×D44C22×C414yes—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—44no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C22⋊C4—42no—
175C42×C11—42no—
176C22⋊Dic11—28no—
177C22⋊Dic11—24no—
178#4325—216no—
179#4323—216no—
180(C2×D11)⋊C4—84no—
181(C2×D11)⋊C4—84no—
182C4⋊Dic11—28no—
183C4⋊Dic11—22no—
184C4⋊Dic11—24no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11C2×D414yes—
188C4×Dic11—28no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191#4318—28no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8C22×C414yes—
195C22×AGL(1,ℤ/8)—111no—
196C2×#520—111no—
197C2×#416D1111yescharacteristic, complemented
198C22×#102—111no—
199#2309—111no—
200#1880—114no—
201#1879—114no—
202#1736—111no—
203#1729—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C4×D412yes—
212C23×C11#12012yes—
213C23×C11#12112yes—
214C23×C11C22×D411yescharacteristic
215C22×D11—24no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—48no—
221C22×D11—88no—
222C22×D11—84no—
223C22×D11—84no—
224C22×D11—88no—
225Q8×C11—22no—
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11C2×C22⋊C414yes—
229D4×C11—216no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11C2×C22⋊C414yes—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—216no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11C2×C22⋊C414yes—
242C2×C4×C11C4×D414yes—
243C2×C4×C11C4×D412yes—
244C2×C4×C11#12012yes—
245C2×C4×C11#12114yes—
246C2×C4×C11#12112yes—
247C2×C4×C11#12314yes—
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—44no—
260C2×Dic11—84no—
261C2×Dic11—88no—
262D44—24no—
263D44—24no—
264D44—42no—
265D44—42no—
266D44—48no—
267C8×C11—42no—
268C11⋊C8—24no—
269C22×#41C2×D1111yescharacteristic
270C23×D4—111no—
271C2×AGL(1,ℤ/8)—118no—
272C2×AGL(1,ℤ/8)—224no—
273C2×AGL(1,ℤ/8)—224no—
274C22×SD16—112no—
275C22×D8—112no—
276C22×M16—111no—
277C23×C8C2×D1111yescharacteristic
278#520—224no—
279#520—224no—
280C2×C4×Q8—112no—
281C2×C4×D4—112no—
282C2×C4×D4—222no—
283C2×#117—111no—
284C2×#117—221no—
285C2×#117C2×D1111yescharacteristic
286C22×C4⋊C4—111no—
287C22×C4⋊C4—221no—
288#416—24no—
289C2×#103C2×D1112yescomplemented
290C2×#102—114no—
291C2×#102—224no—
292C2×#102C2×D1112yescomplemented
293#390—114no—
294#390—221no—
295#390—221no—
296#379—222no—
297#340—114no—
298#336—114no—
299C22×C11—24no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—44no—
308C22×C11#38614yes—
309C22×C11C2×C4×D411yescharacteristic
310C22×C11C2×#12011yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11#57612yes—
313C22×C11#57712yes—
314C2×D11—48no—
315C2×D11—44no—
316C2×D11—816no—
317C2×D11—82no—
318C2×D11—82no—
319C2×D11—84no—
320C4×C11—24no—
321C4×C11—82no—
322C4×C11#38614yes—
323C4×C11C22×C22⋊C411yescharacteristic
324C4×C11C2×C4×D411yescharacteristic
325C4×C11C2×#12111yescharacteristic
326C4×C11C2×#12311yescharacteristic
327Dic11—42no—
328Dic11—44no—
329Dic11—42no—
330C25—221no—
331C2×#41—22no—
332C2×#41—22no—
333C2×#41—22no—
334C2×#41C4×D1114yes—
335C2×#41D4414yes—
336C2×#41C22⋊D1114yes—
337C22×Q8C22×D1111yescharacteristic
338C22×D4—21no—
339C22×D4—114no—
340C22×D4—112no—
341C22×D4—222no—
342C22×D4—222no—
343C22×D4—221no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—222no—
347C22×D4C22×D1111yescharacteristic
348C23×C4—21no—
349C23×C4—222no—
350C23×C4—221no—
351C23×C4C22×D1111yescharacteristic
352AGL(1,ℤ/8)—2232no—
353C2×SD16—118no—
354C2×SD16—224no—
355C2×SD16—224no—
356C2×D8—118no—
357C2×D8—224no—
358C2×D8—224no—
359C2×M16—114no—
360C2×M16—222no—
361C2×M16—222no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—22no—
365C22×C8—112no—
366C22×C8C22×D1112yes—
367C4×Q8—224no—
368C4×Q8—224no—
369C4×D4—224no—
370C4×D4—2216no—
371C4×D4—224no—
372#117—22no—
373#117—22no—
374#117—228no—
375#117—222no—
376#117—222no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—228no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1112yes—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—112no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C42—21no—
392C2×C42—112no—
393C2×C42—222no—
394#103—24no—
395#102—24no—
396#102—228no—
397C2×C11—24no—
398C2×C11—44no—
399C2×C11C2×#38611yescharacteristic
400C2×C11#294612yes—
401C2×C11#300811yescharacteristic
402C2×C11#301011yescharacteristic
403C2×C11#304512yes—
404D11—84no—
405C24—21no—
406C24—222no—
407C24—224no—
408C24—442no—
409C24—442no—
410C24—882no—
411C24—882no—
412C24D4×D1111yescharacteristic
413#41—28no—
414#41—28no—
415#41—28no—
416#41(C2×D11)⋊C4116yescomplemented
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8C2×C4×D1112yes—
421C2×Q8C2×D4412yes—
422C2×Q8C2×C22⋊D1112yes—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—114no—
430C2×D4—228no—
431C2×D4—224no—
432C2×D4—228no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—442no—
439C2×D4—444no—
440C2×D4—444no—
441C2×D4—442no—
442C2×D4C2×C4×D1112yes—
443C2×D4C2×D4412yes—
444C2×D4C2×C22⋊D1112yes—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—222no—
453C22×C4—228no—
454C22×C4—224no—
455C22×C4—884no—
456C22×C4—882no—
457C22×C4C2×C4×D1112yes—
458C22×C4C2×D4412yes—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1112yes—
461C22×C4#434112yes—
462C22×C4#434112yes—
463C22×C4C2×C22⋊D1112yes—
464C22×C4C23×D1111yescharacteristic
465SD16—2216no—
466D8—2216no—
467M16—228no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—44no—
472C2×C8—114no—
473C2×C8—222no—
474C2×C8—222no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—114no—
478C4⋊C4—228no—
479C4⋊C4—224no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C22⋊C4—42no—
484C22⋊C4—228no—
485C22⋊C4—224no—
486C22⋊C4—884no—
487C22⋊C4—884no—
488C42—42no—
489C42—228no—
490C42—222no—
491C42—222no—
492C11#2093211yescharacteristic, complemented, Sylow
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—42no—
499C23—42no—
500C23—224no—
501C23—442no—
502C23—444no—
503C23—444no—
504C23—442no—
505C23—448no—
506C23—888no—
507C23—884no—
508C23—888no—
509C23—884no—
510C23(C22⋊D11)⋊C412yes—
511C23#6693512yes—
512C23#6699212yes—
513C23C2×D4×D1111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—22no—
517Q8C2×(C2×D11)⋊C414yes—
518D4—216no—
519D4—22no—
520D4—22no—
521D4—22no—
522D4—224no—
523D4—224no—
524D4—442no—
525D4—442no—
526D4—448no—
527D4C2×(C2×D11)⋊C414yes—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—216no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—444no—
541C2×C4—884no—
542C2×C4—888no—
543C2×C4(C22⋊D11)⋊C414yes—
544C2×C4(C22⋊D11)⋊C412yes—
545C2×C4#6693512yes—
546C2×C4#6693914yes—
547C2×C4C2×(C2×D11)⋊C414yes—
548C2×C4#6699214yes—
549C2×C4#6699212yes—
550C2×C4C22×C4×D1111yescharacteristic
551C2×C4C22×D4411yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4C2×#434111yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—42no—
557C8—224no—
558C22—22no—
559C22—24no—
560C22—22no—
561C22—24no—
562C22—24no—
563C22—42no—
564C22—44no—
565C22—42no—
566C22—44no—
567C22—444no—
568C22—448no—
569C22—8816no—
570C22—882no—
571C22—884no—
572C22—882no—
573C22#1062257114yes—
574C22C2×(C22⋊D11)⋊C411yescharacteristic
575C22C2×#6693511yescharacteristic
576C22#1062330012yes—
577C22#1062330112yes—
578C22C2×#6699211yescharacteristic
579C4—24no—
580C4—82no—
581C4—442no—
582C4—444no—
583C4—442no—
584C4#1062257114yes—
585C4C2×(C22⋊D11)⋊C411yescharacteristic
586C4C2×#6693911yescharacteristic
587C4C22×(C2×D11)⋊C411yescharacteristic
588C4C2×#6699211yescharacteristic
589C2—24no—
590C2—44no—
591C2—884no—
592C2C2×#1062257111yescharacteristic
593C2#1307745112yes—
594C2#1307788711yescharacteristic
595C2#1307790511yescharacteristic
596C2#1307815312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#20932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#10623358C2semidirect
3. C22×#66885C2semidirect
4. #13071196C2semidirect
5. #13068969C2semidirect
6. #13068962C2semidirect
7. #13068337C2semidirect
8. #13068312C2semidirect
9. C2×C11×#416C2semidirect
18. C2×#67002C4semidirect
19. C2×Q8×Dic11C22semidirect
22. C2×D4×Dic11C22semidirect
30. C2×C11×#103C22semidirect
31. C2×C11×#102C22semidirect
38. #10622188C22semidirect
39. #10622167C22semidirect
60. C22×D44C2×C4semidirect
78. C2×#4325C2×C4semidirect
84. C2×#4323C2×C4semidirect
102. C2×#4318C2×C4semidirect
119. C11×#41C22⋊C4semidirect
197. C2×#416D11semidirect
289. C2×#103C2×D11semidirect
292. C2×#102C2×D11semidirect
416. #41(C2×D11)⋊C4semidirect
492. C11#20932semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106233582
C22×#668852
#130711962
#130689692
#130689622
#130683372
#130683122
C2×C11×#4162
#2093211