Finite Group Databasebeta

← #15834259

Subgroups — #15834259

Order 3328.

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#13124840C211yesmaximal, characteristic
2#13123938C211yesmaximal, characteristic, complemented
3#13123873C211yesmaximal, characteristic
4#13113741C211yesmaximal, characteristic, complemented
5#13113723C211yesmaximal, characteristic, complemented
6#13113711C211yesmaximal, characteristic, complemented
7#13113696C211yesmaximal, characteristic, complemented
8#13113676C211yesmaximal, characteristic, complemented
9#13113675C211yesmaximal, characteristic, complemented
10#13113651C211yesmaximal, characteristic, complemented
11#13113633C211yesmaximal, characteristic, complemented
12#13113617C211yesmaximal, characteristic, complemented
13#13113228C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1497C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718745C411yescharacteristic
21#11718745C411yescharacteristic
22#11718744C411yescharacteristic
23#11718744C411yescharacteristic
24#11718707C411yescharacteristic
25#11718707C411yescharacteristic
26#11718704C411yescharacteristic
27#11718704C411yescharacteristic
28C4×#6106C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30C4×#6106C2211yescharacteristic
31C4×#6106C2211yescharacteristic
32#11718685—21no—
33#11718685C2211yescharacteristic, complemented
34#11718685C2211yescharacteristic, complemented
35Q8×#1055—21no—
36Q8×#1055C2211yescharacteristic, complemented
37Q8×#1055C2211yescharacteristic, complemented
38#11718661—21no—
39#11718661—21no—
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718495C2211yescharacteristic
46#11718495C2211yescharacteristic
47#11718387—21no—
48D13×C22⋊C8—21no—
49#11718367—21no—
50#11718367—21no—
51C13×Q8⋊C8C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×Q8⋊C8C2211yescharacteristic, complemented
54C13×Q8⋊C8C2211yescharacteristic, complemented
55#11718072C2211yescharacteristic, complemented
56#11718072C2211yescharacteristic, complemented
57#11718071C2211yescharacteristic, complemented
58#11718071C2211yescharacteristic, complemented
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×C4⋊Q8C2×C411yescharacteristic
71C13×#125—21no—
72C13×C22⋊Q8—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C13×C22⋊Q8C2×C411yescharacteristic
75C4×Q8×C13—21no—
76C4×Q8×C13C2311yescharacteristic
77C4×Q8×C13C2311yescharacteristic
78C13×#117—21no—
79C2×C42×C13C2311yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6103—21no—
85C2×C4⋊Dic13C2×C411yescharacteristic
86C2×#6094—21no—
87C2×#6094—21no—
88C2×C8×D13—21no—
89C2×C8×D13—21no—
90C4×D52—21no—
91C4×D52—21no—
92C4×D52C2×C411yescharacteristic
93C4×D52C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95C4×D52C2311yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C22⋊C8—21no—
100C13×C22⋊C8—21no—
101C13×#97—21no—
102C4×C8×C13C2311yescharacteristic
103C4×C8×C13C2311yescharacteristic
104#88075C2×C411yescharacteristic
105#88075C2×C411yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108C22⋊#1055—21no—
109C22⋊#1055C2×C411yescharacteristic
110C22⋊#1055C2×C411yescharacteristic
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88060—21no—
116#88060—21no—
117#88049C2×C411yescharacteristic
118#88049C2×C411yescharacteristic
119#88049C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88048C2×C411yescharacteristic
122#88048C2×C411yescharacteristic
123#88048C2×C411yescharacteristic
124#88048C2×C411yescharacteristic
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055C2×C411yescharacteristic
130C4⋊#1055C2×C411yescharacteristic
131C4⋊#1055D411yescharacteristic
132C4⋊#1055D411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18028—131nomaximal, Sylow
145C23×D13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×Q8×C13C22×C411yescharacteristic
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C22×Dic13—21no—
153C2×D52—22no—
154C2×D52—21no—
155C2×D52—41no—
156C2×D52C22×C411yescharacteristic
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—81no—
163C2×C4×D13—81no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185#6106—22no—
186#6106—22no—
187#6106—41no—
188#6106—41no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206#6094—81no—
207#6094—81no—
208C8×D13—81no—
209C8×D13—81no—
210#3101—131no—
211#2986—131no—
212#2974—131no—
213#1592—131no—
214#1590—131no—
215#1588—131no—
216#1585—131no—
217#1583—131no—
218#1582—131no—
219SD16⋊C8—131no—
220C8×SD16—131no—
221#1572—131no—
222#1497D1311yescharacteristic, complemented
223#1478—131no—
224#1454—131no—
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228C22×D13—42no—
229C22×D13—42no—
230C22×D13—81no—
231Q8×C13—21no—
232Q8×C13—21no—
233Q8×C13—21no—
234Q8×C13—21no—
235Q8×C13—42no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C4×D411yescharacteristic
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—81no—
254D52—21no—
255D52—21no—
256D52—21no—
257D52—42no—
258D52#13112yes—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13—41no—
263C4×D13—81no—
264C4×D13—81no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13—41no—
269#1055—21no—
270#1055—21no—
271#1055—21no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—41no—
278#1055—41no—
279#533C2×D1311yescharacteristic
280C2×C4×D4—131no—
281#483—131no—
282#483—131no—
283#476—131no—
284#476—131no—
285#461—131no—
286#461—131no—
287#450—131no—
288#450—131no—
289#446—131no—
290#446—131no—
291#446—261no—
292C8×Q8—131no—
293C8×Q8—131no—
294C8×Q8—261no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#436—131no—
300#436—131no—
301#435—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305#433—261no—
306#433—261no—
307#432C2×D1311yescharacteristic
308#431—131no—
309#431—131no—
310#431—131no—
311#431C2×D1311yescharacteristic
312#407—261no—
313C2×C22⋊C8—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334—131no—
318Q8⋊C8C2×D1311yescharacteristic, complemented
319Q8⋊C8C2×D1311yescharacteristic, complemented
320Q8⋊C8C2×D1311yescharacteristic, complemented
321Q8⋊C8C2×D1311yescharacteristic, complemented
322D4⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326#322—131no—
327#322—131no—
328#322—131no—
329C82—131no—
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—22no—
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C2×D13—84no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13C2×#13111yescharacteristic
350C4×C13#56811yescharacteristic
351C4×C13#57711yescharacteristic
352C4×C13#57711yescharacteristic
353Dic13—41no—
354Dic13—41no—
355C22×D4—131no—
356C23×C4—261no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×M16—261no—
362C2×M16—261no—
363C22×C8—261no—
364C22×C8—261no—
365C4⋊Q8C4×D1311yescharacteristic
366C4⋊Q8C4×D1311yescharacteristic
367#125—21no—
368C22⋊Q8—21no—
369C22⋊Q8C4×D1311yescharacteristic
370C22⋊Q8C4×D1311yescharacteristic
371C4×Q8—21no—
372C4×Q8C22×D1311yescharacteristic
373C4×Q8C22×D1311yescharacteristic
374C4×D4—131no—
375C4×D4—131no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4—261no—
380#117—21no—
381C2×C4⋊C4—131no—
382C2×C22⋊C4—261no—
383C2×C42C22×D1311yescharacteristic
384#106—131no—
385#106—131no—
386#106—131no—
387#106—131no—
388C4⋊C8—21no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8C22×D1311yescharacteristic
400C4⋊C8C22×D1311yescharacteristic
401#103—131no—
402#103—131no—
403#103—131no—
404#103—131no—
405#102—131no—
406#102—131no—
407#102—131no—
408#102—131no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—131no—
412C22⋊C8—131no—
413C22⋊C8—131no—
414C22⋊C8—131no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420#97—21no—
421#97—261no—
422#97—261no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—261no—
428C4×C8—261no—
429C4×C8—261no—
430C4×C8C22×D1311yescharacteristic
431C4×C8C22×D1311yescharacteristic
432C2×C13—41no—
433C2×C13#293311yescharacteristic
434C2×C13#294911yescharacteristic
435C2×C13#295511yescharacteristic
436D13—42no—
437D13—81no—
438C24—261no—
439C2×Q8—21no—
440C2×Q8C2×C4×D1311yescharacteristic
441C2×Q8C2×C4×D1311yescharacteristic
442C2×D4—131no—
443C2×D4—131no—
444C2×D4—262no—
445C2×D4—261no—
446C2×D4—521no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—1041no—
453C22×C4—1041no—
454C22×C4C2×C4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4#612911yescharacteristic
457SD16—262no—
458SD16—262no—
459SD16—521no—
460SD16—521no—
461M16—1041no—
462M16—1041no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—1041no—
478C2×C8—1041no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—131no—
487C4⋊C4—131no—
488C4⋊C4—261no—
489C4⋊C4C2×C4×D1311yescharacteristic
490C4⋊C4C2×C4×D1311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—261no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C42—21no—
498C42—21no—
499C42C2×C4×D1311yescharacteristic
500C42D4×D1311yescharacteristic
501C42#612911yescharacteristic
502C42C23×D1311yescharacteristic
503C13#1802811yescharacteristic, complemented, Sylow
504C23—261no—
505C23—261no—
506C23—522no—
507C23—522no—
508C23—1041no—
509C23#8813511yescharacteristic
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—42no—
515D4—132no—
516D4—261no—
517D4—261no—
518D4—261no—
519D4—522no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—1041no—
536C2×C4—1041no—
537C2×C4—1041no—
538C2×C4#8813511yescharacteristic
539C2×C4#8813511yescharacteristic
540C2×C4#8813511yescharacteristic
541C2×C4C22×C4×D1311yescharacteristic
542C2×C4C2×D4×D1311yescharacteristic
543C2×C4C2×#612911yescharacteristic
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—261no—
553C8—261no—
554C8—261no—
555C8—261no—
556C8—521no—
557C8—521no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—262no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22—521no—
567C22—1044no—
568C22C2×#8813511yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—521no—
578C4—521no—
579C4D13×#13111yescharacteristic
580C4#1171945511yescharacteristic
581C4#1171948311yescharacteristic
582C4#1171948311yescharacteristic
583C2—41no—
584C2—522no—
585C2—1041no—
586C2#1312356611yescharacteristic
587C2#1312369111yescharacteristic
588C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1497C2
socleC22×C13C2×C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenter#1497D13
hypocenterC13#18028
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
2. #13123938C2semidirect
4. #13113741C2semidirect
5. #13113723C2semidirect
6. #13113711C2semidirect
7. #13113696C2semidirect
8. #13113676C2semidirect
9. #13113675C2semidirect
10. #13113651C2semidirect
11. #13113633C2semidirect
12. #13113617C2semidirect
14. #13113136C2semidirect
15. C13×#1497C2semidirect
33. #11718685C22semidirect
34. #11718685C22semidirect
36. Q8×#1055C22semidirect
37. Q8×#1055C22semidirect
51. C13×Q8⋊C8C22semidirect
52. C13×Q8⋊C8C22semidirect
53. C13×Q8⋊C8C22semidirect
54. C13×Q8⋊C8C22semidirect
55. #11718072C22semidirect
56. #11718072C22semidirect
57. #11718071C22semidirect
58. #11718071C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
222. #1497D13semidirect
318. Q8⋊C8C2×D13semidirect
319. Q8⋊C8C2×D13semidirect
320. Q8⋊C8C2×D13semidirect
321. Q8⋊C8C2×D13semidirect
503. C13#18028semidirect

Maximal subgroups

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

subgroupindex
#131248402
#131239382
#131238732
#131137412
#131137232
#131137112
#131136962
#131136762
#131136752
#131136512
#131136332
#131136172
#131132282
#131131362
C13×#14972
#1802813