Finite Group Databasebeta

← #14912761

Subgroups — #14912761

Order 2816.

2094 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
1C2×#10623259C211yesmaximal, characteristic
2#13071416C214yesmaximal, complemented
3#13071368C214yesmaximal
4#13071364C211yesmaximal, characteristic, complemented
5#13071362C211yesmaximal, characteristic, complemented
6#13071336C211yesmaximal, characteristic, complemented
7#13071301C212yesmaximal
8#13071292C212yesmaximal
9#13071108C214yesmaximal
10#13071091C212yesmaximal, complemented
11#13071089C214yesmaximal, complemented
12#13071009C211yesmaximal, characteristic
13C4×Q8×Dic11C212yesmaximal, complemented
14#13070955C211yesmaximal, characteristic
15C11×#2327C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×#66999C2212yes—
19C2×Q8×Dic11C2212yes—
20C2×Q8×Dic11C2212yes—
21#10623259C4116yescomplemented
22C2×#66950C2212yes—
23C2×#66945C2212yes—
24C2×#66943C2212yes—
25C2×#66940C2212yes—
26C2×#66925C2211yescharacteristic
27C2×#66925C2211yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C11×#391C2212yes—
31C11×#387C2214yes—
32C11×#387C2214yes—
33C11×#382C2211yescharacteristic
34C11×#376C2211yescharacteristic
35#10622843C2212yes—
36#10622603C2214yes—
37#10622600C2212yes—
38#10622594C2214yes—
39#10622594C2214yes—
40C4⋊C4×Dic11C2212yes—
41C4⋊C4×Dic11C2214yes—
42C4⋊C4×Dic11C2214yes—
43C4⋊C4×Dic11C2212yes—
44#10622586C2212yes—
45#10622585C2214yes—
46#10622553C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49C4×C4⋊Dic11C2214yes—
50#10622546C2214yes—
51#10622545C2211yescharacteristic
52C42×Dic11C2214yes—
53C42×Dic11C2211yescharacteristic
54C42×Dic11C2211yescharacteristic
55#10622541C2212yes—
56#10622283C2214yes—
57#10622282C2214yes—
58#10622279C2212yes—
59#10622279C2212yes—
60#10622279C2212yes—
61#10622277C2212yes—
62#10622267C2214yes—
63#10622267C2214yes—
64#10622266C2214yes—
65#10622266C2214yes—
66#10622265C2214yes—
67#10622264C2212yes—
68#10622262C2214yes—
69#10622262C2212yes—
70#10622262C2212yes—
71#10622261C2214yes—
72#10622261C2212yes—
73#10622260C2214yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×Dic22C2312yes—
81C11×C4⋊Q8C2×C418yes—
82C4×Q8×C11—28no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2314yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#66999C2×C4116yes—
92Q8×Dic11—28no—
93Q8×Dic11C2×C4116yes—
94C2×(C2×D11)⋊C4C2312yes—
95C2×(C2×D11)⋊C4C2312yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2314yes—
103C2×Dic11⋊C4C2312yes—
104C2×Dic11⋊C4C2312yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2312yes—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2311yescharacteristic
122#66950C2×C4116yes—
123#66945C2×C4116yes—
124#66943C2×C4116yes—
125#66940C2×C4116yes—
126#66925—24no—
127#66925—24no—
128C42×D11C2×C418yes—
129#66922C2×C418yes—
130C11×#95C2312yes—
131C11×#95C2312yes—
132C11×#95C2314yes—
133C11×#95C2314yes—
134C11×#95C2312yes—
135C11×#95C2312yes—
136C11⋊#95C2312yes—
137C11⋊#95C2312yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2312yes—
148#34085—111nomaximal, Sylow
149C23×D11C2411yescharacteristic
150C2×Q8×C11—24no—
151C2×Q8×C11—24no—
152C2×Q8×C11C22×C418yes—
153C22×C4×C11C2414yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11C2412yes—
161C22×Dic11C2414yes—
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2414yes—
164C22×Dic11C2411yescharacteristic
165C22×Dic11C2412yes—
166C22×Dic11C2411yescharacteristic
167C2×C4×D11—24no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—42no—
171C2×C4×D11C22×C414yes—
172C2×C4×D11C22×C414yes—
173C2×C4×D11C22×C414yes—
174C2×Dic22—44no—
175C2×Dic22C22×C418yes—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4C22×C418yes—
179C11×C4⋊C4C22×C418yes—
180C42×C11—22no—
181C42×C11—28no—
182C42×C11C22×C414yes—
183C42×C11#4114yes—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—44no—
187(C2×D11)⋊C4C22×C4116yes—
188C4⋊Dic11—28no—
189C4⋊Dic11—24no—
190C4⋊Dic11C22×C418yes—
191C4⋊Dic11C22×C418yes—
192C4⋊Dic11C22×C4116yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197Dic11⋊C4C22×C4116yes—
198C4×Dic11—28no—
199C4×Dic11—24no—
200C4×Dic11—24no—
201C4×Dic11—28no—
202C4×Dic11—22no—
203C4×Dic11—42no—
204C4×Dic11—44no—
205C4×Dic11—42no—
206C4×Dic11—44no—
207C4×Dic11C22×C414yes—
208C4×Dic11C22×C414yes—
209C4×Dic11C22×C414yes—
210C4×Dic11C22×C4116yes—
211C4×Dic11#4114yes—
212C2×#533—111no—
213#2336—114no—
214#2332—114no—
215#2331—111no—
216#2331—111no—
217#2327—111no—
218#2327D1111yescharacteristic, complemented
219#2323—112no—
220#2323—112no—
221#2298—114no—
222#2295—112no—
223#2295—114no—
224#2283—111no—
225C42×Q8—112no—
226C4×#117—111no—
227C23×C11C2511yescharacteristic
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11C23×C412yes—
233Q8×C11—216no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11C23×C418yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C412yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C11C2×#4114yes—
251C2×C4×C11C2×#4112yes—
252C2×C4×C11C2×#4112yes—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11C23×C412yes—
267C2×Dic11C23×C412yes—
268C2×Dic11C23×C418yes—
269C2×Dic11C23×C412yes—
270C2×Dic11C2×#4114yes—
271C2×Dic112−1+414yes—
272C4×D11—28no—
273C4×D11—28no—
274C4×D11—44no—
275Dic22—48no—
276#533—1116no—
277C2×C4⋊Q8—111no—
278C2×C4⋊Q8C2×D1111yescharacteristic
279C2×#125—112no—
280C2×C22⋊Q8—112no—
281C2×C22⋊Q8—112no—
282C2×C4×Q8—112no—
283C2×C4×Q8—112no—
284C2×C4×Q8—112no—
285C2×C4×Q8C2×D1112yes—
286C2×#117—112no—
287C2×#117—111no—
288C2×#117—111no—
289C22×C42—111no—
290#391—112no—
291#391—114no—
292#391—114no—
293#391C2×D1112yes—
294#389—112no—
295#389—114no—
296#389—112no—
297#389—114no—
298#388—114no—
299#388—114no—
300#388—114no—
301#388—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#387—114no—
306#387—114no—
307#387—114no—
308#387—114no—
309#387—114no—
310#387C2×D1114yes—
311#387C2×D1114yes—
312#383—112no—
313#382—111no—
314#382C2×D1111yescharacteristic
315#381—112no—
316#380—112no—
317C4×C4⋊C4—112no—
318C4×C4⋊C4—114no—
319C4×C4⋊C4—112no—
320C4×C4⋊C4—114no—
321C4×C4⋊C4—112no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4—112no—
324C4×C4⋊C4—112no—
325C4×C4⋊C4—114no—
326C4×C22⋊C4—112no—
327C4×C22⋊C4—112no—
328C4×C22⋊C4—112no—
329#376—111no—
330#376—112no—
331#376—114no—
332#376C2×D1111yescharacteristic
333C43—111no—
334C43—111no—
335C43—114no—
336C22×C11C24×C411yescharacteristic
337C22×C11C22×#4111yescharacteristic
338C22×C11C22×#4111yescharacteristic
339C22×C11C2×2−1+412yes—
340C22×C11#58512yes—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—42no—
345C2×D11—42no—
346C4×C11—28no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—24no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11C4×#4114yes—
353Dic11—22no—
354Dic11—28no—
355Dic11—22no—
356Dic11—24no—
357Dic11—42no—
358Dic11—44no—
359Dic11#51914yes—
360C22×Q8—112no—
361C22×Q8C22×D1112yes—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—111no—
365C4⋊Q8—118no—
366C4⋊Q8C4×D1118yes—
367#125—1116no—
368C22⋊Q8—1116no—
369C22⋊Q8—1116no—
370C4×Q8—28no—
371C4×Q8—1116no—
372C4×Q8—1116no—
373C4×Q8—228no—
374#117—1116no—
375#117—224no—
376#117—224no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4C22×D1112yes—
388C2×C4⋊C4C22×D1114yes—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1112yes—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—114no—
395C2×C42—114no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—118no—
401C2×C42—111no—
402C2×C42—114no—
403C2×C42—112no—
404C2×C42—114no—
405C2×C42—112no—
406C2×C42—112no—
407C2×C42—112no—
408C2×C42—114no—
409C2×C42—114no—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1114yes—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414#95—112no—
415#95—112no—
416#95—114no—
417#95—112no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95—112no—
422#95—114no—
423#95—114no—
424#95—114no—
425#95—114no—
426#95C22×D1112yes—
427#95C22×D1114yes—
428#95C22×D1112yes—
429#95C22×D1112yes—
430#95C22×D1112yes—
431#95C22×D1114yes—
432C2×C11C2×C4×#4111yescharacteristic
433C2×C11C2×#51911yescharacteristic
434C2×C11#342811yescharacteristic
435C2×C11#346112yes—
436C2×C11#346112yes—
437D11—42no—
438C24—111no—
439C2×Q8—24no—
440C2×Q8—24no—
441C2×Q8—118no—
442C2×Q8—444no—
443C2×Q8C2×C4×D1118yes—
444C22×C4—111no—
445C22×C4—112no—
446C22×C4—111no—
447C22×C4—114no—
448C22×C4—111no—
449C22×C4—114no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—112no—
453C22×C4—114no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—442no—
458C22×C4C23×D1114yes—
459C22×C4C23×D1112yes—
460C22×C4C23×D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C22×C4C23×D1114yes—
463C22×C4C23×D1112yes—
464C22×C4C23×D1111yescharacteristic
465C4⋊C4—28no—
466C4⋊C4—24no—
467C4⋊C4—118no—
468C4⋊C4—1116no—
469C4⋊C4—1116no—
470C4⋊C4—118no—
471C4⋊C4—224no—
472C4⋊C4—228no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—444no—
476C4⋊C4—444no—
477C4⋊C4C2×C4×D1118yes—
478C4⋊C4C2×C4×D1118yes—
479C22⋊C4—1116no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—444no—
483C42—28no—
484C42—22no—
485C42—114no—
486C42—114no—
487C42—114no—
488C42—1116no—
489C42—114no—
490C42—228no—
491C42—224no—
492C42—228no—
493C42—224no—
494C42—222no—
495C42—442no—
496C42—444no—
497C42—444no—
498C42—442no—
499C42C2×C4×D1114yes—
500C42#434114yes—
501C11#3408511yescharacteristic, complemented, Sylow
502C23—112no—
503C23—221no—
504C23—221no—
505C23—222no—
506C23—222no—
507C23C24×D1111yescharacteristic
508Q8—216no—
509Q8—448no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—22no—
522C2×C4—112no—
523C2×C4—114no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—118no—
527C2×C4—114no—
528C2×C4—228no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—228no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—444no—
544C2×C4C22×C4×D1112yes—
545C2×C4C22×C4×D1112yes—
546C2×C4C22×C4×D1118yes—
547C2×C4C22×C4×D1112yes—
548C2×C4C2×#434114yes—
549C2×C4C2×#434112yes—
550C2×C4#41×D1112yes—
551C22—222no—
552C22—222no—
553C22—222no—
554C22—442no—
555C22—442no—
556C22C23×C4×D1111yescharacteristic
557C22C22×#434111yescharacteristic
558C22C2×#41×D1111yescharacteristic
559C22D11×2−1+412yes—
560C22#1062345712yes—
561C4—24no—
562C4—28no—
563C4—22no—
564C4—22no—
565C4—44no—
566C4—42no—
567C4—114no—
568C4—224no—
569C4—222no—
570C4—222no—
571C4—228no—
572C4—442no—
573C4—444no—
574C4C4×#434114yes—
575C2—442no—
576C2C2×C4×#434111yescharacteristic
577C2D11×#51911yescharacteristic
578C2#1308181811yescharacteristic
579C2#1308204012yes—
580C2#1308204812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2327C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2327D11
hypocenterC11#34085
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2327

Complements

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

NH ≅ G/Ntype
2. #13071416C2semidirect
4. #13071364C2semidirect
5. #13071362C2semidirect
6. #13071336C2semidirect
10. #13071091C2semidirect
11. #13071089C2semidirect
13. C4×Q8×Dic11C2semidirect
15. C11×#2327C2semidirect
21. #10623259C4semidirect
218. #2327D11semidirect
501. C11#34085semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130714162
#130713682
#130713642
#130713622
#130713362
#130713012
#130712922
#130711082
#130710912
#130710892
#130710092
C4×Q8×Dic112
#130709552
C11×#23272
#3408511