Finite Group Databasebeta

← #15834624

Subgroups — #15834624

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123922C211yesmaximal, characteristic, complemented
2#13123868C211yesmaximal, characteristic
3C4×SD16×D13C211yesmaximal, characteristic
4#13113739C211yesmaximal, characteristic, complemented
5#13113682C211yesmaximal, characteristic, complemented
6#13113677C211yesmaximal, characteristic, complemented
7#13113675C211yesmaximal, characteristic, complemented
8#13113670C211yesmaximal, characteristic, complemented
9#13113650C211yesmaximal, characteristic, complemented
10#13113647C211yesmaximal, characteristic, complemented
11#13113598C211yesmaximal, characteristic, complemented
12#13113281C211yesmaximal, characteristic, complemented
13#13113277C211yesmaximal, characteristic
14#13113122C211yesmaximal, characteristic, complemented
15C13×#1592C211yesmaximal, characteristic, complemented
16C2×SD16×D13C411yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C13×#446C2211yescharacteristic, complemented
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22SD16×Dic13C411yescharacteristic
23#11718788—21no—
24#11718787—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29D13×#106C411yescharacteristic
30#11718513C411yescharacteristic
31#11718496C2211yescharacteristic
32#11718496C2211yescharacteristic
33#11718495C2211yescharacteristic
34#11718494—21no—
35#11718491C2211yescharacteristic, complemented
36#11718489—21no—
37D13×#103C411yescharacteristic
38#11718449C411yescharacteristic
39D13×#102C411yescharacteristic
40#11718419C411yescharacteristic
41#11718389—21no—
42D13×C22⋊C8—21no—
43#11718366—21no—
44#11718362—21no—
45C4×#6095C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47C8×D52C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50C8×Dic26C2211yescharacteristic, complemented
51C13×#335C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718050C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718047C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×Q8×D13C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×M16—21no—
72C4×Q8×C13C2311yescharacteristic
73C4×D4×C13C2311yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C2×#6099—21no—
80SD16×D13—24no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×C8×D13—21no—
84C2×C8×D13—21no—
85C2×C8×D13C2×C411yescharacteristic
86C2×C8×D13C2×C411yescharacteristic
87#88147C2×C411yescharacteristic
88C4⋊C4×D13—21no—
89C4⋊C4×D13C2×C411yescharacteristic
90C4⋊C4×D13C2×C411yescharacteristic
91#88141—21no—
92#88141C2×C411yescharacteristic
93#88135—21no—
94C22⋊C4×D13—21no—
95C4×D52C2311yescharacteristic
96C42×D13—21no—
97C42×D13C2311yescharacteristic
98C4×Dic26—21no—
99C4×Dic26C2311yescharacteristic
100C13×#106C2×C411yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#102C2×C411yescharacteristic
106C13×C22⋊C8—21no—
107C13×#97—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113C22⋊#1055—21no—
114#88061C2×C411yescharacteristic
115#88060—21no—
116#88060—21no—
117#88060—21no—
118#88060—21no—
119#88060D411yescharacteristic
120#88060D411yescharacteristic
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055—21no—
125#88055—21no—
126#88054—21no—
127#88054—21no—
128#88054D411yescharacteristic
129#88054D411yescharacteristic
130C8×Dic13—21no—
131C8×Dic13—21no—
132C8×Dic13C2×C411yescharacteristic
133C8×Dic13C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141#88043—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18060—131nomaximal, Sylow
146C23×D13—21no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152Q8×D13—22no—
153Q8×D13—41no—
154D4×D13—22no—
155D4×D13—41no—
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
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×C4×D13C22×C411yescharacteristic
165C2×C4×D13C2×D411yescharacteristic
166C2×C4×D13#4111yescharacteristic
167C2×Dic26—21no—
168C2×Dic26C22×C411yescharacteristic
169C13×SD16—22no—
170C13×M16—81no—
171C2×C8×C13—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C22×C411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C13×C4⋊C4—21no—
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C22⋊C4—21no—
182C42×C13—21no—
183C42×C13C2411yescharacteristic
184C22⋊Dic13—21no—
185#6106—22no—
186#6105—22no—
187#6103—21no—
188#6103—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13C22×C411yescharacteristic
200C4×Dic13C2×D411yescharacteristic
201C4×Dic13#4111yescharacteristic
202#6099—81no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#6095M1614yescomplemented
211#6094—42no—
212C8×D13—22no—
213C8×D13—41no—
214C8×D13—81no—
215C8×D13—81no—
216#2984—131no—
217#2974—131no—
218C2×C4×SD16—131no—
219#1592—131no—
220#1592D1311yescharacteristic, complemented
221#1583—131no—
222#1583—131no—
223#1582—131no—
224#1582—131no—
225SD16⋊C8—131no—
226SD16⋊C8—131no—
227#1568—131no—
228#1491—131no—
229#1490—131no—
230#1451—131no—
231C23×C13—21no—
232C22×D13—21no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13—81no—
236C22×D13C4×D411yescharacteristic
237Q8×C13—21no—
238Q8×C13—21no—
239D4×C13—21no—
240D4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—42no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—81no—
254C2×Dic13C4×D411yescharacteristic
255C2×Dic13C4×D411yescharacteristic
256C2×Dic13C4×D411yescharacteristic
257D52—21no—
258D52C2×M1612yes—
259C4×D13—22no—
260C4×D13—21no—
261C4×D13—21no—
262C4×D13—21no—
263C4×D13—21no—
264C4×D13—42no—
265C4×D13—42no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—81no—
269C4×D13—81no—
270Dic26—21no—
271Dic26—42no—
272Dic26C2×M1612yes—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—41no—
277C8×C13—41no—
278C8×C13—41no—
279C8×C13C2×M1612yes—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—21no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C22×SD16—131no—
288C2×C4×Q8—131no—
289C2×C4×D4—131no—
290#446—131no—
291#446—261no—
292#446—261no—
293#446C2×D1311yescharacteristic, complemented
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×SD16—131no—
300C4×SD16—131no—
301C4×SD16—131no—
302C4×SD16—131no—
303C4×SD16C2×D1311yescharacteristic
304#436—131no—
305#436C2×D1311yescharacteristic
306#435—261no—
307#435—261no—
308C8×D4—131no—
309C8×D4—131no—
310#432—131no—
311#432—131no—
312#432—261no—
313#431—131no—
314#431—261no—
315C2×#106—131no—
316C2×#103—131no—
317C2×#102—131no—
318#407—261no—
319C2×C22⋊C8—261no—
320C4×M16—131no—
321C2×C4×C8—131no—
322#335—131no—
323#335C2×D1311yescharacteristic, complemented
324#334—131no—
325#334—131no—
326Q8⋊C8—131no—
327Q8⋊C8—131no—
328Q8⋊C8—131no—
329Q8⋊C8C2×D1311yescharacteristic, complemented
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8C2×D1311yescharacteristic
334#322—131no—
335#322—131no—
336#322—131no—
337#322C2×D1311yescharacteristic, complemented
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13C2×C4×D411yescharacteristic
342C2×D13—21no—
343C2×D13—21no—
344C2×D13—22no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—84no—
348C2×D13#44412yes—
349C4×C13—21no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13C22×M1611yescharacteristic
354C4×C13#56811yescharacteristic
355C4×C13#57711yescharacteristic
356C4×C13#57711yescharacteristic
357Dic13—22no—
358Dic13—21no—
359Dic13—21no—
360Dic13—21no—
361Dic13—41no—
362Dic13—41no—
363C22×Q8—131no—
364C22×D4—131no—
365C23×C4—261no—
366C2×SD16—131no—
367C2×SD16—131no—
368C2×SD16—131no—
369C2×SD16—264no—
370C2×SD16C4×D1311yescharacteristic
371C2×M16—21no—
372C2×M16—261no—
373C2×M16—261no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—261no—
377C22×C8—261no—
378C4×Q8—131no—
379C4×Q8—131no—
380C4×Q8—131no—
381C4×Q8—261no—
382C4×Q8—261no—
383C4×Q8C22×D1311yescharacteristic
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—261no—
388C4×D4—261no—
389C4×D4C22×D1311yescharacteristic
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—131no—
395C2×C42—261no—
396#106—131no—
397#106—131no—
398#106—131no—
399#106C4×D1311yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8C22×D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410#103—131no—
411#103—131no—
412#103—131no—
413#103C4×D1311yescharacteristic
414#102—131no—
415#102—131no—
416#102—131no—
417#102C4×D1311yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—131no—
420C22⋊C8—131no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426#97—21no—
427#97—261no—
428#97—261no—
429#97—261no—
430#97—261no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8—261no—
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C4×C8C22×D1311yescharacteristic
441C2×C13—81no—
442C2×C13D4×M1611yescharacteristic
443C2×C13#294911yescharacteristic
444C2×C13C2×#44411yescharacteristic
445D13—22no—
446D13—42no—
447C24—261no—
448C2×Q8—131no—
449C2×Q8—261no—
450C2×Q8—262no—
451C2×Q8—521no—
452C2×Q8C2×C4×D1311yescharacteristic
453C2×D4—131no—
454C2×D4—261no—
455C2×D4—262no—
456C2×D4—521no—
457C2×D4C2×C4×D1311yescharacteristic
458C22×C4—21no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—1041no—
469C22×C4—1041no—
470SD16—22no—
471SD16—134no—
472SD16—262no—
473SD16—262no—
474M16—81no—
475M16—522no—
476M16—1041no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—262no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—521no—
489C2×C8—1041no—
490C2×C8—1041no—
491C2×C8C2×C4×D1311yescharacteristic
492C2×C8C2×C4×D1311yescharacteristic
493C2×C8D4×D1311yescharacteristic
494C2×C8D4×D1311yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—131no—
497C4⋊C4—131no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4C2×C4×D1311yescharacteristic
504C4⋊C4C2×C4×D1311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—21no—
510C42—131no—
511C42—131no—
512C42—131no—
513C42—261no—
514C42—261no—
515C42—261no—
516C42C23×D1311yescharacteristic
517C13#1806011yescharacteristic, complemented, Sylow
518C23—21no—
519C23—131no—
520C23—261no—
521C23—522no—
522C23—522no—
523C23—1041no—
524Q8—21no—
525Q8—21no—
526Q8—132no—
527Q8—261no—
528Q8—522no—
529D4—21no—
530D4—21no—
531D4—132no—
532D4—261no—
533D4—522no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—131no—
540C2×C4—131no—
541C2×C4—131no—
542C2×C4—262no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—522no—
551C2×C4—522no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—1041no—
555C2×C4—1041no—
556C2×C4—1041no—
557C2×C4C22×C4×D1311yescharacteristic
558C2×C4C2×D4×D1311yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—261no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—521no—
571C8—521no—
572C8—521no—
573C8M16×D1312yes—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—132no—
578C22—261no—
579C22—261no—
580C22—262no—
581C22—521no—
582C22—521no—
583C22—1044no—
584C22C4×D4×D1311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—261no—
590C4—261no—
591C4—261no—
592C4—262no—
593C4—521no—
594C4—521no—
595C4C2×M16×D1311yescharacteristic
596C4#1171945511yescharacteristic
597C4#1171948011yescharacteristic
598C4#1171948311yescharacteristic
599C2—81no—
600C2—262no—
601C2—522no—
602C2#1312357211yescharacteristic
603C2#1312369211yescharacteristic
604C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1592C2
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C2×C4
cosocleC42×C13C24
hypercenter#1592D13
hypocenterC13#18060
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
1. #13123922C2semidirect
4. #13113739C2semidirect
5. #13113682C2semidirect
6. #13113677C2semidirect
7. #13113675C2semidirect
8. #13113670C2semidirect
9. #13113650C2semidirect
10. #13113647C2semidirect
11. #13113598C2semidirect
12. #13113281C2semidirect
14. #13113122C2semidirect
15. C13×#1592C2semidirect
19. C13×#446C22semidirect
26. #11718685C22semidirect
35. #11718491C22semidirect
50. C8×Dic26C22semidirect
51. C13×#335C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
62. #11718050C22semidirect
63. #11718048C22semidirect
64. #11718047C22semidirect
65. #11718047C22semidirect
66. #11718046C22semidirect
210. #6095M16semidirect
220. #1592D13semidirect
293. #446C2×D13semidirect
323. #335C2×D13semidirect
329. Q8⋊C8C2×D13semidirect
337. #322C2×D13semidirect
517. C13#18060semidirect

Maximal subgroups

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

subgroupindex
#131239222
#131238682
C4×SD16×D132
#131137392
#131136822
#131136772
#131136752
#131136702
#131136502
#131136472
#131135982
#131132812
#131132772
#131131222
C13×#15922
#1806013