Finite Group Databasebeta

← #14723564

Subgroups — #14723564

Order 2816.

648 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
1#13077579C211yesmaximal, characteristic
2D11×#446C211yesmaximal, characteristic, complemented
3C4×#66968C211yesmaximal, characteristic
4#13067524C211yesmaximal, characteristic, complemented
5#13067522C211yesmaximal, characteristic, complemented
6#13067519C211yesmaximal, characteristic, complemented
7#13067515C211yesmaximal, characteristic, complemented
8#13067514C211yesmaximal, characteristic, complemented
9#13067511C211yesmaximal, characteristic, complemented
10#13067504C211yesmaximal, characteristic, complemented
11#13067365C211yesmaximal, characteristic, complemented
12#13067009C211yesmaximal, characteristic, complemented
13#13067000C211yesmaximal, characteristic
14C8×#4313C211yesmaximal, characteristic, complemented
15C11×#1590C211yesmaximal, characteristic, complemented
16C2×#66968C411yescharacteristic
17C4×Q8×D11C2211yescharacteristic
18C4×#4341C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622777C411yescharacteristic
23#10622740—21no—
24M16×Dic11—21no—
25C4×#4326C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622474C411yescharacteristic
30#10622466C411yescharacteristic
31#10622446C2211yescharacteristic
32D11×C4⋊C8—21no—
33D11×C4⋊C8C2211yescharacteristic
34#10622444C2211yescharacteristic
35#10622444C2211yescharacteristic
36#10622441—21no—
37#10622415C411yescharacteristic
38#10622402C411yescharacteristic
39#10622384C411yescharacteristic
40#10622370C411yescharacteristic
41#10622341—21no—
42#10622331—21no—
43D11×#97—21no—
44#10622314—21no—
45C4×Dic44C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622122C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622094C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×Q8×D11C2×C411yescharacteristic
68C2×#4341C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4326C2×C411yescharacteristic
75D4×Dic11C2×C411yescharacteristic
76C2×#4324C2×C411yescharacteristic
77C4×C22⋊D11—21no—
78C2×C4×Dic11—21no—
79C2×#4318—21no—
80#66968—24no—
81C2×Dic44C2×C411yescharacteristic
82C2×#4313C2×C411yescharacteristic
83C2×#4313C2×C411yescharacteristic
84C2×C8×D11—21no—
85C2×C8×D11D411yescharacteristic
86C2×C8×D11D411yescharacteristic
87#66945C2×C411yescharacteristic
88C4⋊C4×D11—21no—
89C4⋊C4×D11C2×C411yescharacteristic
90#66940—21no—
91#66940C2×C411yescharacteristic
92#66940C2×C411yescharacteristic
93(C22⋊D11)⋊C4—21no—
94#66930—21no—
95C42×D11—21no—
96C42×D11C2311yescharacteristic
97C4×Dic22—21no—
98C4×Dic22C2311yescharacteristic
99C4×Dic22C2311yescharacteristic
100C11×#106C2×C411yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8C2311yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×#103C2×C411yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×C22⋊C8—21no—
107C11×#97—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111#66899C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116#66882C2×C411yescharacteristic
117#66880C2×C411yescharacteristic
118#66880C2×C411yescharacteristic
119#66879—21no—
120#66879—21no—
121#66879—21no—
122#66879—21no—
123#66879C2×C411yescharacteristic
124#66879C2×C411yescharacteristic
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131C8×Dic11—21no—
132C8×Dic11D411yescharacteristic
133C8×Dic11D411yescharacteristic
134#66874C2×C411yescharacteristic
135#66874C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17892—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152Q8×D11—22no—
153Q8×D11—22no—
154#4341—22no—
155#4341—22no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11C22×C411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×C4×D11#4111yescharacteristic
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C11×SD16—22no—
165C11×M16—42no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C42×C11—21no—
178C42×C11C2411yescharacteristic
179C22⋊Dic11—21no—
180#4326—22no—
181#4324—22no—
182(C2×D11)⋊C4—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11C22×C411yescharacteristic
185C4⋊Dic11C22×C411yescharacteristic
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208Dic44—22no—
209#4313—22no—
210#4313M1614yescomplemented
211C8×D11—22no—
212C8×D11—41no—
213C8×D11—42no—
214#2965—111no—
215C2×#446—111no—
216C4×#137—111no—
217#1593—111no—
218#1593—111no—
219#1592—111no—
220#1592—111no—
221#1591—111no—
222#1591—111no—
223#1590—111no—
224#1590D1111yescharacteristic, complemented
225#1565—111no—
226#1479—111no—
227#1477—111no—
228C8×M16—111no—
229C23×C11—21no—
230C22×D11C4×D411yescharacteristic
231Q8×C11—21no—
232Q8×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
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—42no—
249C2×Dic11—42no—
250C2×Dic11C4×D411yescharacteristic
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—41no—
256C4×D11—42no—
257C4×D11—42no—
258C4×D11C2×M1612yes—
259C4×D11#13112yes—
260Dic22—21no—
261Dic22—21no—
262Dic22—21no—
263Dic22—21no—
264Dic22—42no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11C2×M1612yes—
271C8×C11#13712yescomplemented
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8C2×M1612yes—
279C2×#137—111no—
280C4×#41—111no—
281C2×C4×Q8—111no—
282#446—111no—
283#446—111no—
284#446—111no—
285#446—111no—
286#446—111no—
287#446—221no—
288#446—221no—
289#446C2×D1111yescharacteristic
290#441—111no—
291#441—111no—
292#440—111no—
293#440—111no—
294C4×Q16—111no—
295C4×Q16—111no—
296C4×SD16—111no—
297C4×SD16C2×D1111yescharacteristic
298#436—111no—
299#436C2×D1111yescharacteristic
300#435—221no—
301#435—221no—
302#431—111no—
303#431—111no—
304#431—221no—
305#428—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—221no—
308#419—111no—
309#417—111no—
310C4×M16—111no—
311C4×M16—221no—
312C2×#97—221no—
313C2×C4×C8—111no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334C2×D1111yescharacteristic
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8C2×D1111yescharacteristic
324D4⋊C8—111no—
325D4⋊C8C2×D1111yescharacteristic
326#322—111no—
327#322—111no—
328C82—111no—
329C82C2×D1111yescharacteristic
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—21no—
335C2×D11—21no—
336C2×D11#43612yes—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C22×M1611yescharacteristic
342C4×C11C2×#13111yescharacteristic
343C4×C11C2×#13711yescharacteristic
344C4×C11#57511yescharacteristic
345Dic11—21no—
346Dic11—21no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350Dic11—41no—
351Dic11#43612yes—
352C2×#41—111no—
353C22×Q8—111no—
354#137—224no—
355C2×Q16—111no—
356C2×Q16—111no—
357C2×SD16—111no—
358C2×SD16C4×D1111yescharacteristic
359C2×M16—21no—
360C2×M16—111no—
361C2×M16—111no—
362C2×M16—221no—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—221no—
366C4×Q8—111no—
367C4×Q8—111no—
368C4×Q8—111no—
369C4×Q8—111no—
370C4×Q8—111no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8C22×D1111yescharacteristic
374C4×D4—111no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—111no—
379#117—221no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C42—111no—
383C2×C42—221no—
384C2×C42—221no—
385#107—111no—
386#107—111no—
387#106—111no—
388#106C4×D1111yescharacteristic
389C4⋊C8—21no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#103—111no—
406#103C4×D1111yescharacteristic
407#102—111no—
408#102C4×D1111yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—221no—
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#97—221no—
420#97—221no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—221no—
427C4×C8C22×D1111yescharacteristic
428C4×C8C22×D1111yescharacteristic
429C4×C8C22×D1111yescharacteristic
430C2×C11—81no—
431C2×C11C2×#43611yescharacteristic
432C2×C11C4×#13711yescharacteristic
433C2×C11#295511yescharacteristic
434D11—22no—
435#41—222no—
436#41—222no—
437C2×Q8—111no—
438C2×Q8—111no—
439C2×Q8—221no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8C2×C4×D1111yescharacteristic
443C2×D4—221no—
444C2×D4C2×C4×D1111yescharacteristic
445C22×C4—21no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453Q16—222no—
454Q16—222no—
455SD16—22no—
456SD16—222no—
457M16—42no—
458M16—114no—
459M16—222no—
460M16—442no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—222no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—441no—
473C2×C8—442no—
474C2×C8C2×C4×D1111yescharacteristic
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8D4×D1111yescharacteristic
477C2×C8D4×D1111yescharacteristic
478C4⋊C4—21no—
479C4⋊C4—111no—
480C4⋊C4—111no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4C2×C4×D1111yescharacteristic
488C4⋊C4C2×C4×D1111yescharacteristic
489C22⋊C4—21no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C42—21no—
493C42—111no—
494C42—111no—
495C42—111no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42C23×D1111yescharacteristic
503C11#1789211yescharacteristic, complemented, Sylow
504C23—21no—
505C23—111no—
506Q8—21no—
507Q8—21no—
508Q8—221no—
509Q8—221no—
510Q8—221no—
511Q8—221no—
512Q8—442no—
513D4—21no—
514D4—21no—
515D4—442no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—111no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—441no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4C22×C4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—112no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8M16×D1112yes—
553C8#6696812yescomplemented
554C22—41no—
555C22—41no—
556C22—41no—
557C22—112no—
558C22—221no—
559C22—221no—
560C22C4×D4×D1111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—112no—
566C4—221no—
567C4—221no—
568C4—441no—
569C4—441no—
570C4—441no—
571C4—441no—
572C4C2×M16×D1111yescharacteristic
573C4D11×#13111yescharacteristic
574C4C2×#6696811yescharacteristic
575C4#1062329911yescharacteristic
576C2—81no—
577C2—222no—
578C2D11×#43611yescharacteristic
579C2C4×#6696811yescharacteristic
580C2#1307751411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1590C2
socleC22×C11C2×C4×D4
prime radicalC2×#4341C2×C4
cosocleC42×C11C24
hypercenter#1590D11
hypocenterC11#17892
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. D11×#446C2semidirect
4. #13067524C2semidirect
5. #13067522C2semidirect
6. #13067519C2semidirect
7. #13067515C2semidirect
8. #13067514C2semidirect
9. #13067511C2semidirect
10. #13067504C2semidirect
11. #13067365C2semidirect
12. #13067009C2semidirect
14. C8×#4313C2semidirect
15. C11×#1590C2semidirect
210. #4313M16semidirect
224. #1590D11semidirect
271. C8×C11#137semidirect
503. C11#17892semidirect
553. C8#66968semidirect

Maximal subgroups

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

subgroupindex
#130775792
D11×#4462
C4×#669682
#130675242
#130675222
#130675192
#130675152
#130675142
#130675112
#130675042
#130673652
#130670092
#130670002
C8×#43132
C11×#15902
#1789211