Finite Group Databasebeta

← #15834253

Subgroups — #15834253

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#13124844C211yesmaximal, characteristic
2#13123937C211yesmaximal, characteristic, complemented
3#13113738C211yesmaximal, characteristic, complemented
4#13113724C211yesmaximal, characteristic, complemented
5#13113712C211yesmaximal, characteristic, complemented
6#13113693C211yesmaximal, characteristic, complemented
7#13113677C211yesmaximal, characteristic, complemented
8#13113672C211yesmaximal, characteristic, complemented
9#13113648C211yesmaximal, characteristic, complemented
10C8×#6105C211yesmaximal, characteristic, complemented
11#13113617C211yesmaximal, characteristic, complemented
12#13113308C211yesmaximal, characteristic, complemented
13#13113227C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2974C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#436C2211yescharacteristic
19C13×#436C2211yescharacteristic
20C13×#435—21no—
21C13×#435—21no—
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#432C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#407—21no—
27C2×C13×C22⋊C8—21no—
28#11718879C411yescharacteristic
29#11718879C411yescharacteristic
30#11718680C411yescharacteristic
31#11718680C411yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6105C2211yescharacteristic
34C4×#6105C2211yescharacteristic
35C4×#6105C2211yescharacteristic
36#11718669C411yescharacteristic
37#11718669C411yescharacteristic
38#11718632C411yescharacteristic
39#11718632C411yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718492—21no—
44#11718491—21no—
45#11718381—21no—
46#11718381—21no—
47#11718340C2211yescharacteristic, complemented
48#11718340C2211yescharacteristic, complemented
49C8×Dic26C2211yescharacteristic, complemented
50C8×Dic26C2211yescharacteristic, complemented
51D4⋊#1055C2211yescharacteristic
52D4⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic, complemented
56#11718076C2211yescharacteristic, complemented
57#11718076C2211yescharacteristic, complemented
58#11718076C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718071C2211yescharacteristic, complemented
62#11718071C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C2×C13×M16—21no—
70C2×C13×M16—21no—
71C22×C8×C13—21no—
72C22×C8×C13—21no—
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13C2×C411yescharacteristic
76C4×D4×C13C2×C411yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C4×D4×C13C2311yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6105C2×C411yescharacteristic
83C2×#6105C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6105C2×C411yescharacteristic
86#88180—21no—
87#88178—21no—
88#88178C2×C411yescharacteristic
89#88178C2×C411yescharacteristic
90#88124—21no—
91#88123C2×C411yescharacteristic
92#88123C2×C411yescharacteristic
93C4×Dic26—21no—
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8D411yescharacteristic
97C13×C4⋊C8D411yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C22⋊C8—21no—
101C13×C22⋊C8—21no—
102C13×C22⋊C8—21no—
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C13×C22⋊C8D411yescharacteristic
106C13×C22⋊C8D411yescharacteristic
107C13×#97—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055C2×C411yescharacteristic
117C22⋊#1055C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88048C2×C411yescharacteristic
133#88048C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18028—131nomaximal, Sylow
145C24×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—41no—
149C2×D4×C13C22×C411yescharacteristic
150C2×D4×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—81no—
157C22×C4×C13—81no—
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C2×Dic26C22×C411yescharacteristic
164C13×M16—81no—
165C13×M16—81no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—81no—
169C2×C8×C13—81no—
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C42×C13C22×C411yescharacteristic
182C42×C13C2×D411yescharacteristic
183C42×C13#4111yescharacteristic
184C42×C13C2411yescharacteristic
185C22⋊Dic13—21no—
186C22⋊Dic13—21no—
187#6105—22no—
188#6105—22no—
189#6105—41no—
190#6105—41no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196#6101—21no—
197#6101—21no—
198#6101—21no—
199#6101—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210#3101—131no—
211#2986—131no—
212#2974D1311yescharacteristic
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#1454—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—42no—
228C23×C13—42no—
229C23×C13—81no—
230C23×C13C4×D411yescharacteristic
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—21no—
234D4×C13—42no—
235D4×C13#13112yes—
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—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—81no—
248C2×C4×C13—81no—
249C2×C4×C13—81no—
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260Dic26—21no—
261Dic26—21no—
262Dic26—21no—
263Dic26—21no—
264Dic26—42no—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—21no—
269C8×C13—41no—
270C8×C13—41no—
271#1055—21no—
272#1055—21no—
273#1055—21no—
274#1055—21no—
275#1055—41no—
276#1055—41no—
277#1055—41no—
278#1055—41no—
279#533—131no—
280C2×C4×D4C2×D1311yescharacteristic
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#436C2×D1311yescharacteristic
300#436C2×D1311yescharacteristic
301#435—21no—
302#435—21no—
303C8×D4C2×D1311yescharacteristic
304C8×D4C2×D1311yescharacteristic
305#433—261no—
306#433—261no—
307#432C2×D1311yescharacteristic
308#431—131no—
309#431—131no—
310#431—131no—
311#431C2×D1311yescharacteristic
312#407—21no—
313C2×C22⋊C8—21no—
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#322—131no—
327#322—131no—
328#322—131no—
329C82—131no—
330C22×C13—21no—
331C22×C13—22no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—84no—
340C22×C13C2×C4×D411yescharacteristic
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13C2×#13111yescharacteristic
348C4×C13#56811yescharacteristic
349C4×C13#57711yescharacteristic
350C4×C13#57711yescharacteristic
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354Dic13—41no—
355C22×D4C4×D1311yescharacteristic
356C23×C4—21no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×M16—21no—
362C2×M16—21no—
363C22×C8—21no—
364C22×C8—21no—
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—21no—
375C4×D4—21no—
376C4×D4C4×D1311yescharacteristic
377C4×D4C4×D1311yescharacteristic
378C4×D4C22×D1311yescharacteristic
379C4×D4C22×D1311yescharacteristic
380#117—261no—
381C2×C4⋊C4C4×D1311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C42C22×D1311yescharacteristic
384#106—131no—
385#106—131no—
386#106—131no—
387#106—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8C22⋊D1311yescharacteristic
398C4⋊C8C22⋊D1311yescharacteristic
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—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—131no—
415C22⋊C8—131no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8C22⋊D1311yescharacteristic
419C22⋊C8C22⋊D1311yescharacteristic
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—42no—
434C2×C13—81no—
435C2×C13#293311yescharacteristic
436C2×C13#294911yescharacteristic
437C2×C13#295511yescharacteristic
438C24—21no—
439C2×Q8—131no—
440C2×Q8—131no—
441C2×Q8—261no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×C4×D1311yescharacteristic
446C2×D4C2×C4×D1311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4C2×C4×D1311yescharacteristic
455C22×C4#612711yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457SD16—262no—
458SD16—262no—
459SD16—521no—
460SD16—521no—
461M16—81no—
462M16—81no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—81no—
466C2×C8—81no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8C2×C22⋊D1311yescharacteristic
476C2×C8C2×C22⋊D1311yescharacteristic
477C2×C8C2×C22⋊D1311yescharacteristic
478C2×C8C2×C22⋊D1311yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—131no—
481C4⋊C4—131no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4C2×C4×D1311yescharacteristic
490C4⋊C4C2×C4×D1311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C42—261no—
498C42—261no—
499C42C2×C4×D1311yescharacteristic
500C42#612711yescharacteristic
501C42C2×C22⋊D1311yescharacteristic
502C42C23×D1311yescharacteristic
503C13#1802811yescharacteristic, complemented, Sylow
504C23—21no—
505C23—21no—
506C23—42no—
507C23—42no—
508C23—81no—
509C23C4×C22⋊D1311yescharacteristic
510Q8—261no—
511Q8—261no—
512Q8—261no—
513Q8—261no—
514Q8—522no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—42no—
519D4#8816112yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4C4×C22⋊D1311yescharacteristic
539C2×C4C4×C22⋊D1311yescharacteristic
540C2×C4C4×C22⋊D1311yescharacteristic
541C2×C4C22×C4×D1311yescharacteristic
542C2×C4C2×#612711yescharacteristic
543C2×C4C22×C22⋊D1311yescharacteristic
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—261no—
551C8—261no—
552C8—261no—
553C8—261no—
554C8—521no—
555C8—521no—
556C8—521no—
557C8—521no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—84no—
568C22C2×C4×C22⋊D1311yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—41no—
574C4—41no—
575C4—521no—
576C4—521no—
577C4—521no—
578C4—521no—
579C4C2×#8816111yescharacteristic
580C4#1171945011yescharacteristic
581C4#1171954111yescharacteristic
582C4#1171954111yescharacteristic
583C2—41no—
584C2—42no—
585C2—81no—
586C2#1312356111yescharacteristic
587C2#1312369311yescharacteristic
588C2#1312373711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2974C2
socleC22×C13C2×C4×D4
prime radicalC22×D4×C13C2×C4
cosocleC42×C13C24
hypercenter#2974D13
hypocenterC13#18028
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13123937C2semidirect
3. #13113738C2semidirect
4. #13113724C2semidirect
5. #13113712C2semidirect
6. #13113693C2semidirect
7. #13113677C2semidirect
8. #13113672C2semidirect
9. #13113648C2semidirect
10. C8×#6105C2semidirect
11. #13113617C2semidirect
12. #13113308C2semidirect
14. #13113136C2semidirect
47. #11718340C22semidirect
48. #11718340C22semidirect
49. C8×Dic26C22semidirect
50. C8×Dic26C22semidirect
55. #11718076C22semidirect
56. #11718076C22semidirect
57. #11718076C22semidirect
58. #11718076C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
61. #11718071C22semidirect
62. #11718071C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
503. C13#18028semidirect

Maximal subgroups

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

subgroupindex
#131248442
#131239372
#131137382
#131137242
#131137122
#131136932
#131136772
#131136722
#131136482
C8×#61052
#131136172
#131133082
#131132272
#131131362
C13×#29742
#1802813