Finite Group Databasebeta

← #15834257

Subgroups — #15834257

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#13124845C211yesmaximal, characteristic
2#13123937C211yesmaximal, characteristic, complemented
3#13123870C211yesmaximal, characteristic
4#13113740C211yesmaximal, characteristic, complemented
5#13113728C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113695C211yesmaximal, characteristic, complemented
8#13113681C211yesmaximal, characteristic, complemented
9#13113674C211yesmaximal, characteristic, complemented
10#13113650C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113616C211yesmaximal, characteristic, complemented
13#13113310C211yesmaximal, characteristic, complemented
14#13113228C211yesmaximal, characteristic
15C13×#1454C211yesmaximal, characteristic, complemented
16C2×C4×D52C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718587C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718503C411yescharacteristic
24#11718503C411yescharacteristic
25#11718502C411yescharacteristic
26#11718502C411yescharacteristic
27#11718497—21no—
28#11718497—21no—
29#11718492—21no—
30#11718491—21no—
31#11718392C411yescharacteristic
32#11718392C411yescharacteristic
33#11718387—21no—
34D13×C22⋊C8—21no—
35#11718382C411yescharacteristic
36#11718382C411yescharacteristic
37#11718381—21no—
38#11718381—21no—
39C4×#6095C2211yescharacteristic
40C4×#6095C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45C8×D52C2211yescharacteristic
46C8×D52C2211yescharacteristic
47#11718340C2211yescharacteristic, complemented
48#11718340C2211yescharacteristic, complemented
49C8×Dic26C2211yescharacteristic, complemented
50C8×Dic26C2211yescharacteristic, complemented
51C13×#322C2211yescharacteristic, complemented
52C13×#322C2211yescharacteristic, complemented
53C13×#322C2211yescharacteristic, complemented
54C82×C13C2211yescharacteristic, complemented
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718050C2211yescharacteristic, complemented
60#11718050C2211yescharacteristic, complemented
61#11718049C2211yescharacteristic, complemented
62#11718049C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718048C2211yescharacteristic, complemented
65#11718048C2211yescharacteristic, complemented
66#11718048C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71#88180—21no—
72C2×C4⋊Dic13C2×C411yescharacteristic
73#88178—21no—
74#88178C2×C411yescharacteristic
75#88178C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6095C2×C411yescharacteristic
78C2×#6095C2×C411yescharacteristic
79C2×#6095C2×C411yescharacteristic
80C2×#6094—21no—
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84C4×D52—21no—
85C4×D52—21no—
86C4×D52C2×C411yescharacteristic
87C4×D52C2×C411yescharacteristic
88C4×D52C2311yescharacteristic
89C4×D52C2311yescharacteristic
90#88124—21no—
91#88123C2×C411yescharacteristic
92#88123C2×C411yescharacteristic
93C4×Dic26—21no—
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8C2×C411yescharacteristic
98C13×C4⋊C8C2×C411yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C22⋊C8—21no—
102C13×C22⋊C8C2×C411yescharacteristic
103C13×C22⋊C8C2×C411yescharacteristic
104C13×C22⋊C8D411yescharacteristic
105C13×C22⋊C8D411yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055—21no—
114#88061C2×C411yescharacteristic
115#88061C2×C411yescharacteristic
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88057C2×C411yescharacteristic
123#88057C2×C411yescharacteristic
124#88057C2×C411yescharacteristic
125#88057C2×C411yescharacteristic
126#88056C2×C411yescharacteristic
127#88056C2×C411yescharacteristic
128#88056C2×C411yescharacteristic
129#88056C2×C411yescharacteristic
130#88055—21no—
131#88055—21no—
132#88054—21no—
133#88054—21no—
134#88054—21no—
135#88054—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142#88043—21no—
143C4×#1055—21no—
144#18028—131nomaximal, Sylow
145C23×D13—21no—
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C22×Dic13—21no—
150C2×D52—22no—
151C2×D52—21no—
152C2×D52—41no—
153C2×D52C22×C411yescharacteristic
154C2×D52C22×C411yescharacteristic
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—81no—
160C2×C4×D13—81no—
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C2×Dic26C22×C411yescharacteristic
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C22×C411yescharacteristic
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179C22⋊Dic13—21no—
180#6103—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202#6095—22no—
203#6095—22no—
204#6095—41no—
205#6095—41no—
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#1497—131no—
223#1478—131no—
224#1454D1311yescharacteristic, complemented
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228C22×D13—42no—
229C22×D13—42no—
230C22×D13—81no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C4×D411yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—81no—
249D52—21no—
250D52—21no—
251D52—21no—
252D52—42no—
253D52#13112yes—
254C4×D13—41no—
255C4×D13—41no—
256C4×D13—41no—
257C4×D13—41no—
258C4×D13—81no—
259C4×D13—81no—
260Dic26—21no—
261Dic26—21no—
262Dic26—21no—
263Dic26—21no—
264Dic26—42no—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—41no—
274C8×C13—41no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279#533—131no—
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#432—131no—
308#431—131no—
309#431C2×D1311yescharacteristic
310#431C2×D1311yescharacteristic
311#431C2×D1311yescharacteristic
312#407—261no—
313C2×C22⋊C8—261no—
314#335—131no—
315#335—131no—
316#334—131no—
317#334—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322D4⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326#322C2×D1311yescharacteristic, complemented
327#322C2×D1311yescharacteristic, complemented
328#322C2×D1311yescharacteristic, complemented
329C82C2×D1311yescharacteristic, complemented
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×C13C2×#13111yescharacteristic
346C4×C13#56811yescharacteristic
347C4×C13#57711yescharacteristic
348C4×C13#57711yescharacteristic
349Dic13—41no—
350Dic13—41no—
351Dic13—41no—
352Dic13—41no—
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⋊Q8—131no—
366C4⋊Q8—131no—
367#125—261no—
368C22⋊Q8—131no—
369C22⋊Q8—131no—
370C22⋊Q8—261no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—261no—
374C4×D4—131no—
375C4×D4—131no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4—261no—
380#117—261no—
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—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8C4×D1311yescharacteristic
398C4⋊C8C4×D1311yescharacteristic
399C4⋊C8D5211yescharacteristic
400C4⋊C8D5211yescharacteristic
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—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8C4×D1311yescharacteristic
417C22⋊C8C4×D1311yescharacteristic
418C22⋊C8D5211yescharacteristic
419C22⋊C8D5211yescharacteristic
420#97—261no—
421#97—261no—
422#97—261no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C4×C8C22×D1311yescharacteristic
429C4×C8C22×D1311yescharacteristic
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—131no—
440C2×Q8—131no—
441C2×Q8—261no—
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×C4C2×D5211yescharacteristic
456C22×C4#612711yescharacteristic
457SD16—262no—
458SD16—262no—
459SD16—521no—
460SD16—521no—
461M16—1041no—
462M16—1041no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—1041no—
470C2×C8—1041no—
471C2×C8C2×C4×D1311yescharacteristic
472C2×C8C2×C4×D1311yescharacteristic
473C2×C8C2×C4×D1311yescharacteristic
474C2×C8C2×C4×D1311yescharacteristic
475C2×C8C2×D5211yescharacteristic
476C2×C8C2×D5211yescharacteristic
477C2×C8C2×D5211yescharacteristic
478C2×C8C2×D5211yescharacteristic
479C4⋊C4—131no—
480C4⋊C4—131no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C42—261no—
498C42—261no—
499C42C2×C4×D1311yescharacteristic
500C42C2×D5211yescharacteristic
501C42#612711yescharacteristic
502C42C23×D1311yescharacteristic
503C13#1802811yescharacteristic, complemented, Sylow
504C23—261no—
505C23—261no—
506C23—522no—
507C23—522no—
508C23—1041no—
509C23C4×D5211yescharacteristic
510Q8—261no—
511Q8—261no—
512Q8—261no—
513Q8—261no—
514Q8—522no—
515D4—132no—
516D4—261no—
517D4—261no—
518D4—261no—
519D4—522no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
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×C4C4×D5211yescharacteristic
539C2×C4C4×D5211yescharacteristic
540C2×C4C4×D5211yescharacteristic
541C2×C4C22×C4×D1311yescharacteristic
542C2×C4C22×D5211yescharacteristic
543C2×C4C2×#612711yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—521no—
555C8—521no—
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×C4×D5211yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4—521no—
578C4—521no—
579C4D13×#13111yescharacteristic
580C4#1171945511yescharacteristic
581C4#1171945611yescharacteristic
582C4#1171945611yescharacteristic
583C2—41no—
584C2—522no—
585C2—1041no—
586C2#1312356411yescharacteristic
587C2#1312369711yescharacteristic
588C2#1312374011yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1454C2
socleC22×C13C2×C4×D4
prime radicalC22×D52C2×C4
cosocleC42×C13C24
hypercenter#1454D13
hypocenterC13#18028
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
2. #13123937C2semidirect
4. #13113740C2semidirect
5. #13113728C2semidirect
6. #13113716C2semidirect
7. #13113695C2semidirect
8. #13113681C2semidirect
9. #13113674C2semidirect
10. #13113650C2semidirect
11. C8×#6095C2semidirect
12. #13113616C2semidirect
13. #13113310C2semidirect
15. C13×#1454C2semidirect
47. #11718340C22semidirect
48. #11718340C22semidirect
49. C8×Dic26C22semidirect
50. C8×Dic26C22semidirect
51. C13×#322C22semidirect
52. C13×#322C22semidirect
53. C13×#322C22semidirect
54. C82×C13C22semidirect
59. #11718050C22semidirect
60. #11718050C22semidirect
61. #11718049C22semidirect
62. #11718049C22semidirect
63. #11718048C22semidirect
64. #11718048C22semidirect
65. #11718048C22semidirect
66. #11718048C22semidirect
224. #1454D13semidirect
326. #322C2×D13semidirect
327. #322C2×D13semidirect
328. #322C2×D13semidirect
329. C82C2×D13semidirect
503. C13#18028semidirect

Maximal subgroups

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

subgroupindex
#131248452
#131239372
#131238702
#131137402
#131137282
#131137162
#131136952
#131136812
#131136742
#131136502
C8×#60952
#131136162
#131133102
#131132282
C13×#14542
#1802813