Finite Group Databasebeta

← #14725105

Subgroups — #14725105

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#13078625C211yesmaximal, characteristic
2#13077717C211yesmaximal, characteristic, complemented
3#13077653C211yesmaximal, characteristic
4#13067517C211yesmaximal, characteristic, complemented
5#13067505C211yesmaximal, characteristic, complemented
6#13067493C211yesmaximal, characteristic, complemented
7#13067472C211yesmaximal, characteristic, complemented
8#13067458C211yesmaximal, characteristic, complemented
9#13067451C211yesmaximal, characteristic, complemented
10#13067427C211yesmaximal, characteristic, complemented
11#13067415C211yesmaximal, characteristic, complemented
12#13067088C211yesmaximal, characteristic, complemented
13#13067006C211yesmaximal, characteristic
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1572C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17#10623001C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C11×#431C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622455C411yescharacteristic
24#10622455C411yescharacteristic
25#10622454C411yescharacteristic
26#10622454C411yescharacteristic
27#10622451C2211yescharacteristic
28#10622451C2211yescharacteristic
29#10622447C2211yescharacteristic
30#10622447C2211yescharacteristic
31#10622444C2211yescharacteristic, complemented
32#10622444C2211yescharacteristic, complemented
33#10622443C2211yescharacteristic, complemented
34#10622443C2211yescharacteristic, complemented
35#10622344C411yescharacteristic
36#10622344C411yescharacteristic
37#10622339—21no—
38D11×C22⋊C8—21no—
39#10622334C411yescharacteristic
40#10622334C411yescharacteristic
41#10622333—21no—
42#10622333—21no—
43#10622319—21no—
44#10622319—21no—
45C4×#4314C2211yescharacteristic
46C4×#4314C2211yescharacteristic
47C4×#4314C2211yescharacteristic
48C4×#4314C2211yescharacteristic
49#10622292—21no—
50C8×Dic22—21no—
51C11×#335C2211yescharacteristic, complemented
52C11×#335C2211yescharacteristic, complemented
53C11×#334C2211yescharacteristic, complemented
54C11×#334C2211yescharacteristic, complemented
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622122C2211yescharacteristic, complemented
58#10622122C2211yescharacteristic, complemented
59#10622121C2211yescharacteristic
60#10622121C2211yescharacteristic
61#10622121C2211yescharacteristic
62#10622121C2211yescharacteristic
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71#66979—21no—
72C2×C4⋊Dic11C2×C411yescharacteristic
73#66977—21no—
74#66977C2×C411yescharacteristic
75#66977C2×C411yescharacteristic
76C2×#4314C2×C411yescharacteristic
77C2×#4314C2×C411yescharacteristic
78C2×#4314C2×C411yescharacteristic
79C2×#4314C2×C411yescharacteristic
80C2×#4313—21no—
81C2×#4313—21no—
82C2×C8×D11—21no—
83C2×C8×D11—21no—
84C4×D44—21no—
85C4×D44—21no—
86C4×D44C2×C411yescharacteristic
87C4×D44C2×C411yescharacteristic
88C4×D44C2311yescharacteristic
89C4×D44C2311yescharacteristic
90#66923—21no—
91#66922C2×C411yescharacteristic
92#66922C2×C411yescharacteristic
93C4×Dic22—21no—
94C4×Dic22C2311yescharacteristic
95C4×Dic22C2311yescharacteristic
96C11×C4⋊C8C2×C411yescharacteristic
97C11×C4⋊C8C2×C411yescharacteristic
98C11×C4⋊C8C2311yescharacteristic
99C11×C4⋊C8C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×C22⋊C8C2×C411yescharacteristic
105C11×C22⋊C8C2×C411yescharacteristic
106C11×#97—21no—
107C4×C8×C11—21no—
108C4×C8×C11C2311yescharacteristic
109C4×C8×C11C2311yescharacteristic
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)D411yescharacteristic
112C22⋊(C11⋊C8)D411yescharacteristic
113#66885C2×C411yescharacteristic
114#66885C2×C411yescharacteristic
115#66885C2×C411yescharacteristic
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66881C2×C411yescharacteristic
122#66881C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66881C2×C411yescharacteristic
125#66880C2×C411yescharacteristic
126#66880C2×C411yescharacteristic
127#66880C2×C411yescharacteristic
128#66880C2×C411yescharacteristic
129#66879—21no—
130#66879—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135C8×Dic11—21no—
136C8×Dic11—21no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)D411yescharacteristic
139C4⋊(C11⋊C8)D411yescharacteristic
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#18028—111nomaximal, Sylow
145C23×D11—21no—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C22×Dic11—21no—
150C2×D44—22no—
151C2×D44—21no—
152C2×D44—41no—
153C2×D44C22×C411yescharacteristic
154C2×D44C22×C411yescharacteristic
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C2×Dic22C22×C411yescharacteristic
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C22×C411yescharacteristic
171C2×C8×C11C22×C411yescharacteristic
172C42×C11C22×C411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11#4111yescharacteristic
175C42×C11C2411yescharacteristic
176C22⋊Dic11—21no—
177C22⋊Dic11—21no—
178(C2×D11)⋊C4—21no—
179(C2×D11)⋊C4—21no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×C11⋊C8C2×D411yescharacteristic
201C2×C11⋊C8C2×D411yescharacteristic
202#4314—22no—
203#4314—22no—
204#4314—41no—
205#4314—41no—
206#4313—81no—
207#4313—81no—
208C8×D11—81no—
209C8×D11—81no—
210#3101—111no—
211#2986—111no—
212#2974—111no—
213#1592—111no—
214#1590—111no—
215#1588—111no—
216#1585—111no—
217#1583—111no—
218#1582—111no—
219SD16⋊C8—111no—
220C8×SD16—111no—
221#1572D1111yescharacteristic, complemented
222#1497—111no—
223#1478—111no—
224#1454—111no—
225C23×C11C4×D411yescharacteristic
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—41no—
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11C4×D411yescharacteristic
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—81no—
249D44—21no—
250D44—21no—
251D44—21no—
252D44—42no—
253D44#13112yes—
254C4×D11—41no—
255C4×D11—41no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—81no—
259C4×D11—81no—
260Dic22—21no—
261Dic22—21no—
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—
272C8×C11—41no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
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—111no—
291#446—221no—
292C8×Q8—111no—
293C8×Q8—111no—
294C8×Q8—221no—
295C4×SD16—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299#436—111no—
300#436—111no—
301#435—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305#433—221no—
306#433—221no—
307#432C2×D1111yescharacteristic
308#431—111no—
309#431—111no—
310#431C2×D1111yescharacteristic
311#431C2×D1111yescharacteristic
312#407—221no—
313C2×C22⋊C8—221no—
314#335C2×D1111yescharacteristic, complemented
315#335C2×D1111yescharacteristic, complemented
316#334C2×D1111yescharacteristic, complemented
317#334C2×D1111yescharacteristic, complemented
318Q8⋊C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—111no—
321Q8⋊C8—111no—
322D4⋊C8—111no—
323D4⋊C8—111no—
324D4⋊C8—111no—
325D4⋊C8—111no—
326#322—111no—
327#322—111no—
328#322—111no—
329C82—111no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11C2×C4×D411yescharacteristic
334C2×D11—22no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—41no—
340C2×D11—84no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11C2×#13111yescharacteristic
346C4×C11#56811yescharacteristic
347C4×C11#57711yescharacteristic
348C4×C11#57711yescharacteristic
349Dic11—41no—
350Dic11—41no—
351Dic11—41no—
352Dic11—41no—
353Dic11—41no—
354Dic11—41no—
355C22×D4—111no—
356C23×C4—221no—
357C2×SD16—111no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×SD16—111no—
361C2×M16—221no—
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—111no—
373C4×Q8—221no—
374C4×D4—111no—
375C4×D4—111no—
376C4×D4—111no—
377C4×D4—111no—
378C4×D4—221no—
379C4×D4—221no—
380#117—221no—
381C2×C4⋊C4—111no—
382C2×C22⋊C4—221no—
383C2×C42C22×D1111yescharacteristic
384#106—111no—
385#106—111no—
386#106—111no—
387#106—111no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—221no—
391C4⋊C8—221no—
392C4⋊C8—221no—
393C4⋊C8—221no—
394C4⋊C8—221no—
395C4⋊C8C4×D1111yescharacteristic
396C4⋊C8C4×D1111yescharacteristic
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—111no—
402#103—111no—
403#103—111no—
404#103—111no—
405#102—111no—
406#102—111no—
407#102—111no—
408#102—111no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8C4×D1111yescharacteristic
419C22⋊C8C4×D1111yescharacteristic
420#97—21no—
421#97—221no—
422#97—221no—
423C4×C8—21no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—221no—
429C4×C8—221no—
430C4×C8C22×D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—41no—
433C2×C11#293311yescharacteristic
434C2×C11#294911yescharacteristic
435C2×C11#295511yescharacteristic
436D11—42no—
437D11—81no—
438C24—221no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—221no—
442C2×D4—111no—
443C2×D4—111no—
444C2×D4—222no—
445C2×D4—221no—
446C2×D4—441no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—881no—
453C22×C4—881no—
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4D4×D1111yescharacteristic
456C22×C4#434311yescharacteristic
457SD16—222no—
458SD16—222no—
459SD16—441no—
460SD16—441no—
461M16—881no—
462M16—881no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—881no—
474C2×C8—881no—
475C2×C8C2×C4×D1111yescharacteristic
476C2×C8C2×C4×D1111yescharacteristic
477C2×C8C2×C4×D1111yescharacteristic
478C2×C8C2×C4×D1111yescharacteristic
479C4⋊C4—111no—
480C4⋊C4—111no—
481C4⋊C4—111no—
482C4⋊C4—111no—
483C4⋊C4—221no—
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—
494C22⋊C4—221no—
495C22⋊C4—221no—
496C22⋊C4—221no—
497C42—221no—
498C42—221no—
499C42C2×C4×D1111yescharacteristic
500C42D4×D1111yescharacteristic
501C42#434311yescharacteristic
502C42C23×D1111yescharacteristic
503C11#1802811yescharacteristic, complemented, Sylow
504C23—221no—
505C23—221no—
506C23—442no—
507C23—442no—
508C23—881no—
509C23#6694611yescharacteristic
510Q8—221no—
511Q8—221no—
512Q8—221no—
513Q8—221no—
514Q8—442no—
515D4—112no—
516D4—221no—
517D4—221no—
518D4—221no—
519D4—442no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—881no—
536C2×C4—881no—
537C2×C4—881no—
538C2×C4#6694611yescharacteristic
539C2×C4#6694611yescharacteristic
540C2×C4#6694611yescharacteristic
541C2×C4C22×C4×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434311yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—221no—
553C8—221no—
554C8—221no—
555C8—221no—
556C8—441no—
557C8—441no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—222no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22—884no—
568C22C2×#6694611yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—441no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4—441no—
578C4—441no—
579C4D11×#13111yescharacteristic
580C4#1062328111yescharacteristic
581C4#1062330111yescharacteristic
582C4#1062330111yescharacteristic
583C2—41no—
584C2—442no—
585C2—881no—
586C2#1307734011yescharacteristic
587C2#1307747411yescharacteristic
588C2#1307751811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1572C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#1572D11
hypocenterC11#18028
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #13077717C2semidirect
4. #13067517C2semidirect
5. #13067505C2semidirect
6. #13067493C2semidirect
7. #13067472C2semidirect
8. #13067458C2semidirect
9. #13067451C2semidirect
10. #13067427C2semidirect
11. #13067415C2semidirect
12. #13067088C2semidirect
14. #13066916C2semidirect
15. C11×#1572C2semidirect
31. #10622444C22semidirect
32. #10622444C22semidirect
33. #10622443C22semidirect
34. #10622443C22semidirect
51. C11×#335C22semidirect
52. C11×#335C22semidirect
53. C11×#334C22semidirect
54. C11×#334C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
57. #10622122C22semidirect
58. #10622122C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
221. #1572D11semidirect
314. #335C2×D11semidirect
315. #335C2×D11semidirect
316. #334C2×D11semidirect
317. #334C2×D11semidirect
503. C11#18028semidirect

Maximal subgroups

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

subgroupindex
#130786252
#130777172
#130776532
#130675172
#130675052
#130674932
#130674722
#130674582
#130674512
#130674272
#130674152
#130670882
#130670062
#130669162
C11×#15722
#1802811