Finite Group Databasebeta

← #14725114

Subgroups — #14725114

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078622C211yesmaximal, characteristic
2#13077714C211yesmaximal, characteristic, complemented
3#13077648C211yesmaximal, characteristic
4#13067509C211yesmaximal, characteristic, complemented
5#13067495C211yesmaximal, characteristic, complemented
6#13067472C211yesmaximal, characteristic, complemented
7#13067457C211yesmaximal, characteristic, complemented
8#13067450C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10#13067413C211yesmaximal, characteristic, complemented
11#13067395C211yesmaximal, characteristic, complemented
12#13067087C211yesmaximal, characteristic, complemented
13#13067005C211yesmaximal, characteristic
14#13066917C211yesmaximal, characteristic, complemented
15C11×#1592C211yesmaximal, characteristic, complemented
16#10623109C2211yescharacteristic
17C4×D4×D11C2211yescharacteristic
18C11×#446C2211yescharacteristic, complemented
19C4×C11×SD16C2211yescharacteristic
20C11×#436C2211yescharacteristic
21#10622782C411yescharacteristic
22#10622775C411yescharacteristic
23#10622740—21no—
24#10622739—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic, complemented
27C4×#4324C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622483C411yescharacteristic
30#10622475C411yescharacteristic
31#10622453—21no—
32#10622448C2211yescharacteristic
33#10622447C2211yescharacteristic
34#10622446C2211yescharacteristic
35#10622444C2211yescharacteristic, complemented
36#10622443—21no—
37#10622431C411yescharacteristic
38#10622418C411yescharacteristic
39#10622389C411yescharacteristic
40#10622374C411yescharacteristic
41#10622341—21no—
42D11×C22⋊C8—21no—
43#10622322—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46C8×D44C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C8×Dic22C2211yescharacteristic, complemented
51C11×#335C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic, complemented
63#10622094C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73#66999C2×C411yescharacteristic
74#66997C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80C2×#4314C2×C411yescharacteristic
81C2×C8×D11—21no—
82C2×C8×D11—21no—
83#66950C2×C411yescharacteristic
84#66949—21no—
85#66946C2×C411yescharacteristic
86C4⋊C4×D11C2×C411yescharacteristic
87#66942—21no—
88#66941C2×C411yescharacteristic
89(C22⋊D11)⋊C4—21no—
90C22⋊C4×D11—21no—
91C4×D44C2311yescharacteristic
92#66925—21no—
93C42×D11C2311yescharacteristic
94C4×Dic22—21no—
95C4×Dic22C2311yescharacteristic
96C11×#106C2×C411yescharacteristic
97C11×C4⋊C8—21no—
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×#103C2×C411yescharacteristic
101C11×#102C2×C411yescharacteristic
102C11×C22⋊C8—21no—
103C11×#97—21no—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109C22⋊(C11⋊C8)—21no—
110#66885C2×C411yescharacteristic
111(C2×D11)⋊C8—21no—
112(C2×D11)⋊C8—21no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8C2×C411yescharacteristic
117(C2×D11)⋊C8C2×C411yescharacteristic
118(C2×D11)⋊C8D411yescharacteristic
119(C2×D11)⋊C8D411yescharacteristic
120#66881C2×C411yescharacteristic
121#66880C2×C411yescharacteristic
122#66879—21no—
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8C2×C411yescharacteristic
128Dic11⋊C8C2×C411yescharacteristic
129Dic11⋊C8D411yescharacteristic
130Dic11⋊C8D411yescharacteristic
131C8×Dic11—21no—
132C8×Dic11—21no—
133#66874C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66872C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18028—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C22×Dic11—21no—
151D4×D11—22no—
152D4×D11—41no—
153C2×D44C22×C411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×C4×D11#4111yescharacteristic
162C2×Dic22—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×SD16—41no—
165C11×M16—81no—
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#4325—22no—
181#4324—41no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11#4111yescharacteristic
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207#4314—22no—
208C8×D11—81no—
209C8×D11—81no—
210#3101—111no—
211#2986—111no—
212#2974—111no—
213#1592D1111yescharacteristic, complemented
214#1590—111no—
215#1588—111no—
216#1585—111no—
217#1583—111no—
218#1582—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221#1572—111no—
222#1497—111no—
223#1478—111no—
224#1454—111no—
225C23×C11—21no—
226C22×D11—21no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—81no—
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—81no—
248C2×Dic11C4×D411yescharacteristic
249C2×Dic11C4×D411yescharacteristic
250C2×Dic11C4×D411yescharacteristic
251D44—21no—
252D44#13112yes—
253C4×D11—21no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—81no—
261C4×D11—81no—
262Dic22—21no—
263Dic22—21no—
264Dic22—42no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—41no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279#533—111no—
280C2×C4×D4—111no—
281#483—111no—
282#483—111no—
283#476—111no—
284#476—111no—
285#461—111no—
286#461—111no—
287#450—111no—
288#450—111no—
289#446—111no—
290#446—221no—
291#446C2×D1111yescharacteristic, complemented
292C8×Q8—111no—
293C8×Q8—111no—
294C8×Q8—221no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16C2×D1111yescharacteristic
299#436—111no—
300#436C2×D1111yescharacteristic
301#435—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305#433—221no—
306#433—221no—
307#432—111no—
308#431—111no—
309#431—111no—
310#431—111no—
311#431—111no—
312#407—221no—
313C2×C22⋊C8—221no—
314#335—111no—
315#335C2×D1111yescharacteristic, complemented
316#334—111no—
317#334—111no—
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8C2×D1111yescharacteristic, complemented
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8C2×D1111yescharacteristic
326#322—111no—
327#322—111no—
328#322C2×D1111yescharacteristic, complemented
329C82—111no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—22no—
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—84no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11C2×#13111yescharacteristic
346C4×C11#56811yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57711yescharacteristic
349Dic11—21no—
350Dic11—21no—
351Dic11—21no—
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355C22×D4—111no—
356C23×C4—221no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×SD16C4×D1111yescharacteristic
361C2×M16—21no—
362C2×M16—221no—
363C22×C8—221no—
364C22×C8—221no—
365C4⋊Q8—111no—
366C4⋊Q8—111no—
367#125—221no—
368C22⋊Q8—111no—
369C22⋊Q8—111no—
370C22⋊Q8—221no—
371C4×Q8—111no—
372C4×Q8—221no—
373C4×Q8C22×D1111yescharacteristic
374C4×D4—111no—
375C4×D4—111no—
376C4×D4—111no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4C22×D1111yescharacteristic
380#117—221no—
381C2×C4⋊C4—111no—
382C2×C22⋊C4—221no—
383C2×C42—111no—
384#106—111no—
385#106—111no—
386#106—111no—
387#106C4×D1111yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
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#103C4×D1111yescharacteristic
405#102—111no—
406#102—111no—
407#102—111no—
408#102C4×D1111yescharacteristic
409C22⋊C8—21no—
410C22⋊C8—111no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—111no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420#97—21no—
421#97—221no—
422#97—221no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—221no—
427C4×C8—221no—
428C4×C8—221no—
429C4×C8C22×D1111yescharacteristic
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—81no—
433C2×C11#293311yescharacteristic
434C2×C11#294911yescharacteristic
435C2×C11#295511yescharacteristic
436D11—41no—
437D11—42no—
438C24—221no—
439C2×Q8—111no—
440C2×Q8—221no—
441C2×Q8C2×C4×D1111yescharacteristic
442C2×D4—111no—
443C2×D4—221no—
444C2×D4—222no—
445C2×D4—441no—
446C2×D4C2×C4×D1111yescharacteristic
447C22×C4—21no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—881no—
456C22×C4—881no—
457SD16—41no—
458SD16—222no—
459SD16—222no—
460SD16—441no—
461M16—81no—
462M16—881no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—881no—
474C2×C8—881no—
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8C2×C4×D1111yescharacteristic
477C2×C8D4×D1111yescharacteristic
478C2×C8D4×D1111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4C2×C4×D1111yescharacteristic
490C4⋊C4C2×C4×D1111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C42—21no—
498C42—111no—
499C42—111no—
500C42—111no—
501C42—221no—
502C42C23×D1111yescharacteristic
503C11#1802811yescharacteristic, complemented, Sylow
504C23—21no—
505C23—111no—
506C23—221no—
507C23—442no—
508C23—442no—
509C23—881no—
510Q8—21no—
511Q8—21no—
512Q8—221no—
513Q8—221no—
514Q8—442no—
515D4—21no—
516D4—21no—
517D4—112no—
518D4—221no—
519D4—442no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—111no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—881no—
539C2×C4—881no—
540C2×C4—881no—
541C2×C4C22×C4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4#41×D1111yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—221no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—441no—
556C8—441no—
557C8—441no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—221no—
562C22—221no—
563C22—222no—
564C22—221no—
565C22—441no—
566C22—441no—
567C22—884no—
568C22C4×D4×D1111yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—221no—
574C4—221no—
575C4—221no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4#1062327611yescharacteristic
580C4D11×#13111yescharacteristic
581C4#1062330611yescharacteristic
582C4#1062330911yescharacteristic
583C2—81no—
584C2—441no—
585C2—442no—
586C2#1307734511yescharacteristic
587C2#1307747211yescharacteristic
588C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1592C2
socleC22×C11C2×C4×D4
prime radicalC2×D4×D11C2×C4
cosocleC42×C11C24
hypercenter#1592D11
hypocenterC11#18028
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #13077714C2semidirect
4. #13067509C2semidirect
5. #13067495C2semidirect
6. #13067472C2semidirect
7. #13067457C2semidirect
8. #13067450C2semidirect
9. #13067430C2semidirect
10. #13067413C2semidirect
11. #13067395C2semidirect
12. #13067087C2semidirect
14. #13066917C2semidirect
15. C11×#1592C2semidirect
18. C11×#446C22semidirect
26. Q8×C11⋊C8C22semidirect
35. #10622444C22semidirect
50. C8×Dic22C22semidirect
51. C11×#335C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C11×#322C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
57. #10622122C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622096C22semidirect
63. #10622094C22semidirect
64. #10622093C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
213. #1592D11semidirect
291. #446C2×D11semidirect
315. #335C2×D11semidirect
321. Q8⋊C8C2×D11semidirect
328. #322C2×D11semidirect
503. C11#18028semidirect

Maximal subgroups

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

subgroupindex
#130786222
#130777142
#130776482
#130675092
#130674952
#130674722
#130674572
#130674502
#130674302
#130674132
#130673952
#130670872
#130670052
#130669172
C11×#15922
#1802811