Finite Group Databasebeta

← #14755464

Subgroups — #14755464

Order 2816.

1914 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4313C211yesmaximal, characteristic, complemented
2C2×#10623359C211yesmaximal, characteristic
3C2×#10622846C211yesmaximal, characteristic, complemented
4#13070995C211yesmaximal, characteristic, complemented
5#13069051C214yesmaximal, complemented
6#13069046C214yesmaximal, complemented
7#13068333C211yesmaximal, characteristic, complemented
8#13068332C211yesmaximal, characteristic, complemented
9C2×C11×#416C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623359—24no—
15#10623359C418yescomplemented
16C2×#66999C2212yes—
17C2×#66991C2212yes—
18C2×#66990—21no—
19C2×#66988—21no—
20C2×C4×C22⋊D11—22no—
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C22×#4313—24no—
25C22×#4313—24no—
26C22×#4313—24no—
27C22×#4313C2214yes—
28C11×#416—24no—
29C2×C11×#103C2212yescomplemented
30C2×C11×#102C2212yescomplemented
31#10622846—24no—
32C2×#66899C2212yescomplemented
33C2×#66896C2212yescomplemented
34#10622600C2214yes—
35#10622568—21no—
36#10622556—21no—
37C4×(C2×D11)⋊C4—22no—
38#10622189C2214yescomplemented
39#10622167C2214yescomplemented
40C24×D11D411yescharacteristic
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41C2×C414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—22no—
53C23×Dic11D411yescharacteristic
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11C2×C414yes—
59C22×C4×D11D412yes—
60C22×C4×D11D414yes—
61C22×C4×D11C2312yes—
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11D414yescomplemented
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—21no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—21no—
74#66999—24no—
75#66999C2×C418yes—
76#66991—24no—
77#66991C2×C418yes—
78#66990—28no—
79#66988—28no—
80C4×C22⋊D11—216no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—24no—
83#66979—22no—
84#66979—22no—
85#66979—22no—
86#66979C2×C414yes—
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2312yes—
89C2×Dic11⋊C4—22no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8—22no—
93C22×C11⋊C8—22no—
94C22×C11⋊C8D414yescomplemented
95C22×C11⋊C8C2312yes—
96C2×#4313—232no—
97C2×#4313—28no—
98C2×#4313—28no—
99C2×#4313—28no—
100C11×#103—24no—
101C11×#102—24no—
102#66899—24no—
103#66896—24no—
104C11⋊#95—24no—
105#20970—111nomaximal, Sylow
106C24×C11—21no—
107C24×C11C2×D411yescharacteristic
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—44no—
111C23×D11C22⋊C414yes—
112C23×D11C2×D412yes—
113C11×#41—28no—
114C11×#41—28no—
115C11×#41—44no—
116C11×#41—44no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11C22×C412yes—
123C2×D4×C11—24no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—42no—
130C2×D4×C11—42no—
131C2×D4×C11C22×C412yes—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—28no—
146C2×C22⋊D11—48no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11C22⋊C414yes—
152C22×Dic11C2×D412yes—
153C2×C4×D11—28no—
154C2×C4×D11—28no—
155C2×C4×D11—28no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—28no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11C22⋊C418yes—
164C2×C4×D11C22×C414yes—
165C2×C4×D11C2×D414yes—
166C2×C8×C11—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11C2×D414yes—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C22⋊C4—42no—
173C42×C11—42no—
174C22⋊Dic11—28no—
175C22⋊Dic11—24no—
176C22⋊Dic11—42no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—48no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11C22×C414yes—
183Dic11⋊C4—28no—
184C4×Dic11—24no—
185C4×Dic11—42no—
186C2×C11⋊C8—28no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C2×D414yes—
190#4313—232no—
191C23×M16—111no—
192C2×#525—111no—
193C2×#416—111no—
194C2×#416D1111yescharacteristic, complemented
195#2280—111no—
196#1895—114no—
197#1894—114no—
198#1735—111no—
199#1735—111no—
200C23×C11—24no—
201C23×C11—22no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—44no—
205C23×C11C2×C22⋊C412yes—
206C23×C11#12112yes—
207C23×C11#12112yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—28no—
214C22×D11—48no—
215C22×D11—48no—
216C22×D11—48no—
217C22×D11C2×C22⋊C414yes—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—48no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C4×D414yes—
235C2×C4×C11C4×D414yes—
236C2×C4×C11#12014yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12314yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—416no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—28no—
250C2×Dic11—24no—
251C2×Dic11—44no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11C2×C22⋊C414yes—
255C4×D11—24no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—216no—
260C8×C11—24no—
261C11⋊C8—24no—
262C22×#41C2×D1111yescharacteristic
263C24×C4—111no—
264C22×M16—114no—
265C22×M16—224no—
266C22×M16—224no—
267C22×M16—224no—
268C23×C8—111no—
269C23×C8C2×D1111yescharacteristic
270#525—118no—
271#525—224no—
272C2×#123—221no—
273C2×C22⋊Q8—112no—
274C2×#121—112no—
275C2×#120—221no—
276C2×C4×D4—222no—
277C2×#117—111no—
278C2×#117—111no—
279C2×#117C2×D1111yescharacteristic
280#416—24no—
281#416—224no—
282C2×#103—112no—
283C2×#103C2×D1112yescomplemented
284C2×#102—112no—
285C2×#102C2×D1112yescomplemented
286#381—221no—
287#380—114no—
288#379—221no—
289C4×C22⋊C4—222no—
290#340—114no—
291#340—114no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—24no—
295C22×C11—44no—
296C22×C11—42no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11#38614yes—
300C22×C11C22×C22⋊C411yescharacteristic
301C22×C11C2×#12111yescharacteristic
302C22×C11C2×#12111yescharacteristic
303C22×C11#57514yes—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—416no—
308C2×D11—44no—
309C2×D11—44no—
310C4×C11—42no—
311C4×C11—82no—
312C4×C11#38614yes—
313C4×C11C2×C4×D411yescharacteristic
314C4×C11C2×C4×D411yescharacteristic
315C4×C11C2×#12011yescharacteristic
316C4×C11C2×#12311yescharacteristic
317Dic11—24no—
318Dic11—44no—
319Dic11—82no—
320C25—111no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41C4×D1114yes—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—21no—
329C22×D4—222no—
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4—111no—
333C23×C4—114no—
334C23×C4—114no—
335C23×C4—112no—
336C23×C4—112no—
337C23×C4—222no—
338C23×C4—222no—
339C23×C4—222no—
340C23×C4—222no—
341C23×C4C22×D1111yescharacteristic
342C2×M16—228no—
343C2×M16—228no—
344C2×M16—2232no—
345C2×M16—228no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—114no—
349C22×C8—112no—
350C22×C8—222no—
351C22×C8—222no—
352C22×C8C22⋊D1114yescomplemented
353C22×C8C22×D1112yes—
354#123—228no—
355C22⋊Q8—118no—
356C22⋊Q8—224no—
357#121—118no—
358#121—224no—
359#120—228no—
360C4×D4—2216no—
361#117—22no—
362#117—22no—
363#117—114no—
364#117—222no—
365#117—222no—
366#117—222no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4C22×D1112yes—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—221no—
379C2×C42—221no—
380#103—24no—
381#103—224no—
382#102—24no—
383#102—224no—
384#95—224no—
385C2×C11—24no—
386C2×C11—82no—
387C2×C11C2×#38611yescharacteristic
388C2×C11#289612yes—
389C2×C11#305412yes—
390C2×C11#305412yes—
391D11—44no—
392C24—21no—
393C24—112no—
394C24—114no—
395C24—222no—
396C24—222no—
397C24—444no—
398C24D4×D1111yescharacteristic
399#41—28no—
400#41—28no—
401#41—44no—
402#41—44no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×C4×D1112yes—
409C2×D4—24no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—42no—
416C2×D4—42no—
417C2×D4—228no—
418C2×D4—448no—
419C2×D4C2×C4×D1112yes—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—114no—
426C22×C4—112no—
427C22×C4—118no—
428C22×C4—114no—
429C22×C4—114no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—228no—
433C22×C4—228no—
434C22×C4—224no—
435C22×C4—228no—
436C22×C4—228no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4C2×C4×D1112yes—
445C22×C4#433912yes—
446C22×C4D4×D1112yes—
447C22×C4D4×D1112yes—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434112yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C23×D1111yescharacteristic
452M16—2232no—
453C2×C8—28no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—114no—
457C2×C8—228no—
458C2×C8—222no—
459C2×C8—222no—
460C2×C8C2×C22⋊D1114yes—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—114no—
464C4⋊C4—228no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C22⋊C4—42no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C22⋊C4—448no—
473C22⋊C4—442no—
474C42—42no—
475C42—224no—
476C42—442no—
477C11#2097011yescharacteristic, complemented, Sylow
478C23—24no—
479C23—22no—
480C23—41no—
481C23—44no—
482C23—41no—
483C23—114no—
484C23—222no—
485C23—224no—
486C23—224no—
487C23—222no—
488C23—228no—
489C23—448no—
490C23—448no—
491C23—448no—
492C23C22⋊C4×D1112yes—
493C23#6693712yes—
494C23#6699112yes—
495C23C2×D4×D1111yescharacteristic
496Q8—22no—
497Q8—22no—
498Q8—41no—
499Q8—41no—
500D4—22no—
501D4—22no—
502D4—48no—
503D4—41no—
504D4—41no—
505D4—4416no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—48no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—114no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—228no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—2216no—
521C2×C4—224no—
522C2×C4—444no—
523C2×C4—442no—
524C2×C4—444no—
525C2×C4C22⋊C4×D1112yes—
526C2×C4(C22⋊D11)⋊C414yes—
527C2×C4#6693614yes—
528C2×C4#6693712yes—
529C2×C4C4×C22⋊D1114yes—
530C2×C4#6699014yes—
531C2×C4#6699112yes—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×#433911yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4C2×D4×D1111yescharacteristic
536C2×C4C2×#434111yescharacteristic
537C2×C4C22×C22⋊D1111yescharacteristic
538C8—24no—
539C8—224no—
540C22—24no—
541C22—24no—
542C22—24no—
543C22—44no—
544C22—42no—
545C22—82no—
546C22—82no—
547C22—224no—
548C22—224no—
549C22—224no—
550C22—4416no—
551C22—444no—
552C22—444no—
553C22#1062256914yes—
554C22C2×C22⋊C4×D1111yescharacteristic
555C22C2×#6693711yescharacteristic
556C22#1062329914yes—
557C22C2×#6699111yescharacteristic
558C4—42no—
559C4—82no—
560C4—224no—
561C4—444no—
562C4—882no—
563C4#1062256914yes—
564C4C2×(C22⋊D11)⋊C411yescharacteristic
565C4C2×#6693611yescharacteristic
566C4C2×C4×C22⋊D1111yescharacteristic
567C4C2×#6699011yescharacteristic
568C2—24no—
569C2—82no—
570C2—444no—
571C2C2×#1062256911yescharacteristic
572C2#1307713112yes—
573C2#1307822112yes—
574C2#1307822412yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#20970
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C23×#4313C2semidirect
3. C2×#10622846C2semidirect
4. #13070995C2semidirect
5. #13069051C2semidirect
6. #13069046C2semidirect
7. #13068333C2semidirect
8. #13068332C2semidirect
9. C2×C11×#416C2semidirect
15. #10623359C4semidirect
29. C2×C11×#103C22semidirect
30. C2×C11×#102C22semidirect
32. C2×#66899C22semidirect
33. C2×#66896C22semidirect
38. #10622189C22semidirect
39. #10622167C22semidirect
64. C22×C8×C11D4semidirect
94. C22×C11⋊C8D4semidirect
194. C2×#416D11semidirect
283. C2×#103C2×D11semidirect
285. C2×#102C2×D11semidirect
352. C22×C8C22⋊D11semidirect
477. C11#20970semidirect

Maximal subgroups

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

subgroupindex
C23×#43132
C2×#106233592
C2×#106228462
#130709952
#130690512
#130690462
#130683332
#130683322
C2×C11×#4162
#2097011