Finite Group Databasebeta

← #14725348

Subgroups — #14725348

Order 2816.

640 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077633C211yesmaximal, characteristic
2#13077567C211yesmaximal, characteristic, complemented
3C4×#66962C211yesmaximal, characteristic
4#13067517C211yesmaximal, characteristic, complemented
5#13067505C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067486C211yesmaximal, characteristic, complemented
8#13067465C211yesmaximal, characteristic, complemented
9#13067458C211yesmaximal, characteristic, complemented
10#13067434C211yesmaximal, characteristic, complemented
11#13067422C211yesmaximal, characteristic, complemented
12#13067062C211yesmaximal, characteristic, complemented
13#13067053C211yesmaximal, characteristic
14#13066919C211yesmaximal, characteristic, complemented
15C11×#1569C211yesmaximal, characteristic, complemented
16C2×#66962C411yescharacteristic
17C4×#4339C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#432C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622746C411yescharacteristic
23#10622734C411yescharacteristic
24#10622733C411yescharacteristic
25#10622731—21no—
26M16×Dic11—21no—
27C4×#4318C2211yescharacteristic
28C4×#4318C2211yescharacteristic
29#10622451C2211yescharacteristic
30#10622451C2211yescharacteristic
31#10622444C2211yescharacteristic
32#10622444C2211yescharacteristic
33#10622443C2211yescharacteristic
34#10622443C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622441—21no—
38#10622441—21no—
39#10622342—21no—
40#10622342—21no—
41#10622329C411yescharacteristic
42#10622329C411yescharacteristic
43#10622323C411yescharacteristic
44#10622323C411yescharacteristic
45#10622320—21no—
46#10622318—21no—
47C4×Dic44C2211yescharacteristic
48C4×Dic44C2211yescharacteristic
49C4×#4314C2211yescharacteristic
50C4×#4314C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×#335C2211yescharacteristic
53C11×#334C2211yescharacteristic
54C11×#334C2211yescharacteristic
55#10622122C2211yescharacteristic
56#10622122C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622122C2211yescharacteristic
60#10622122C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339C2×C411yescharacteristic
68C22×Dic22C2×C411yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16C2×C411yescharacteristic
71C2×C11×M16C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75#66979C2×C411yescharacteristic
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—21no—
79C2×#4318—21no—
80C2×#4318D411yescharacteristic
81C2×#4318D411yescharacteristic
82#66962—24no—
83C2×Dic44C2×C411yescharacteristic
84C2×Dic44C2×C411yescharacteristic
85C2×#4314C2×C411yescharacteristic
86C2×#4314C2×C411yescharacteristic
87C2×#4313—21no—
88C2×#4313—21no—
89C4×D44C2×C411yescharacteristic
90C4×D44C2311yescharacteristic
91#66925—21no—
92C42×D11—21no—
93C4×Dic22—21no—
94C4×Dic22—21no—
95C4×Dic22C2×C411yescharacteristic
96C4×Dic22C2×C411yescharacteristic
97C4×Dic22C2×C411yescharacteristic
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C11×#97C2×C411yescharacteristic
109C11×#97C2×C411yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66885C2×C411yescharacteristic
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116#66882C2×C411yescharacteristic
117#66882C2×C411yescharacteristic
118#66881C2×C411yescharacteristic
119#66881C2×C411yescharacteristic
120#66880C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66879—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134C8×Dic11—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C8×Dic11—21no—
138#66867—21no—
139#66867D411yescharacteristic
140#66867D411yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18049—111nomaximal, Sylow
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152#4339—22no—
153#4339—41no—
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×Dic22—22no—
159C2×Dic22—21no—
160C2×Dic22—41no—
161C2×Dic22C22×C411yescharacteristic
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—41no—
166C11×M16—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C42×C11C22×C411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11#4111yescharacteristic
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C411yescharacteristic
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186C4⋊Dic11C22×C411yescharacteristic
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200#4318—22no—
201#4318—41no—
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209Dic44—22no—
210Dic44M1614yescomplemented
211#4314—22no—
212#4314—22no—
213#4313—42no—
214#4313—42no—
215#2971—111no—
216Q8×M16—111no—
217C4×#137—111no—
218#1592—111no—
219#1590—111no—
220#1588—111no—
221#1587—111no—
222#1584—111no—
223#1583—111no—
224#1579—111no—
225C8×Q16—111no—
226#1569D1111yescharacteristic, complemented
227#1491—111no—
228#1489—111no—
229#1455—111no—
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—41no—
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C4×D411yescharacteristic
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C22⋊D11—42no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—42no—
252C2×Dic11—81no—
253D44—21no—
254D44—21no—
255C4×D11—42no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—81no—
259Dic22—21no—
260Dic22—21no—
261Dic22—21no—
262Dic22—21no—
263Dic22—42no—
264Dic22C2×M1612yes—
265Dic22C2×M1612yes—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11C2×M1612yes—
274C11⋊C8—22no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8#13712yescomplemented
280C2×#137—111no—
281C4×#41—111no—
282C2×C4×Q8—111no—
283#446—111no—
284#446—111no—
285#446—221no—
286#446—221no—
287C8×Q8—111no—
288C8×Q8—111no—
289C8×Q8—111no—
290C8×Q8—111no—
291#441—111no—
292#441—111no—
293#440—111no—
294#440—111no—
295C4×Q16—111no—
296C4×Q16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#436—111no—
300#436—111no—
301#436—221no—
302#436—221no—
303#432—221no—
304#432C2×D1111yescharacteristic
305#428—111no—
306#423—221no—
307#423C2×D1111yescharacteristic
308#419—111no—
309#417—111no—
310C4×M16—111no—
311C4×M16—111no—
312C4×M16—221no—
313C4×M16—221no—
314C4×M16C2×D1111yescharacteristic
315#335C2×D1111yescharacteristic
316#335C2×D1111yescharacteristic
317#334C2×D1111yescharacteristic
318#334C2×D1111yescharacteristic
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327#322—111no—
328#322—111no—
329#322—111no—
330C82—111no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×C4×D411yescharacteristic
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11C22×M1611yescharacteristic
343C4×C11#56811yescharacteristic
344C4×C11C2×#13711yescharacteristic
345C4×C11#57511yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353C2×#41—111no—
354C22×Q8—111no—
355#137—224no—
356C2×Q16—111no—
357C2×Q16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×M16—21no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—221no—
366C2×M16C4×D1111yescharacteristic
367C2×M16C4×D1111yescharacteristic
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—111no—
372C4×Q8—111no—
373C4×Q8—111no—
374C4×Q8—221no—
375C4×Q8—221no—
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C4×D4—221no—
380#117—111no—
381#117—221no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387#107—111no—
388#107—111no—
389#106—111no—
390#106—111no—
391C4⋊C8—21no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401C4⋊C8C22×D1111yescharacteristic
402#103—111no—
403#103—111no—
404#103—111no—
405#103—111no—
406#103—111no—
407#103—111no—
408#102—111no—
409#102—111no—
410C22⋊C8—21no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413#97—21no—
414#97—111no—
415#97—111no—
416#97—221no—
417#97—221no—
418#97—221no—
419#97C4×D1111yescharacteristic
420#97C4×D1111yescharacteristic
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C2×C11—41no—
432C2×C11D4×M1611yescharacteristic
433C2×C11C4×#13711yescharacteristic
434C2×C11#295611yescharacteristic
435D11—81no—
436#41—222no—
437#41—441no—
438C2×Q8—111no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—222no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×D4—111no—
445C2×D4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4#434311yescharacteristic
454Q16—114no—
455Q16—222no—
456SD16—222no—
457SD16—222no—
458M16—22no—
459M16—41no—
460M16—42no—
461M16—222no—
462M16—442no—
463M16—442no—
464M16—441no—
465M16—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8C2×C4×D1111yescharacteristic
477C2×C8C2×C4×D1111yescharacteristic
478C2×C8C2×C4×D1111yescharacteristic
479C2×C8C2×C4×D1111yescharacteristic
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—111no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42C2×C4×D1111yescharacteristic
502C42D4×D1111yescharacteristic
503C42#434311yescharacteristic
504C42C23×D1111yescharacteristic
505C11#1804911yescharacteristic, complemented, Sylow
506C23—221no—
507C23#6694611yescharacteristic
508Q8—112no—
509Q8—112no—
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—221no—
514Q8—442no—
515D4—221no—
516D4—221no—
517D4—442no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—881no—
535C2×C4—881no—
536C2×C4#6694611yescharacteristic
537C2×C4#6694611yescharacteristic
538C2×C4#6694611yescharacteristic
539C2×C4C22×C4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434311yescharacteristic
542C8—21no—
543C8—21no—
544C8—21no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—112no—
550C8—222no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—441no—
555C8M16×D1112yes—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22C2×#6694611yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—222no—
568C4—222no—
569C4—441no—
570C4—441no—
571C4—441no—
572C4—441no—
573C4—441no—
574C4C2×M16×D1111yescharacteristic
575C4#1062327611yescharacteristic
576C4#1062330411yescharacteristic
577C4D11×#13711yescharacteristic
578C2—41no—
579C2—881no—
580C2#1307735111yescharacteristic
581C2#1307743411yescharacteristic
582C2#1307752511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1569C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1569D11
hypocenterC11#18049
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #13077567C2semidirect
4. #13067517C2semidirect
5. #13067505C2semidirect
6. #13067493C2semidirect
7. #13067486C2semidirect
8. #13067465C2semidirect
9. #13067458C2semidirect
10. #13067434C2semidirect
11. #13067422C2semidirect
12. #13067062C2semidirect
14. #13066919C2semidirect
15. C11×#1569C2semidirect
210. Dic44M16semidirect
226. #1569D11semidirect
279. C11⋊C8#137semidirect
505. C11#18049semidirect

Maximal subgroups

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

subgroupindex
#130776332
#130775672
C4×#669622
#130675172
#130675052
#130674932
#130674862
#130674652
#130674582
#130674342
#130674222
#130670622
#130670532
#130669192
C11×#15692
#1804911