Finite Group Databasebeta

← #16795792

Subgroups — #16795792

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131740C211yesmaximal, characteristic, complemented
2#13131698C211yesmaximal, characteristic
3#13130479C211yesmaximal, characteristic, complemented
4#13130477C211yesmaximal, characteristic, complemented
5#13130473C211yesmaximal, characteristic, complemented
6#13130472C211yesmaximal, characteristic, complemented
7#13130466C211yesmaximal, characteristic, complemented
8#13130465C211yesmaximal, characteristic, complemented
9#13130446C211yesmaximal, characteristic, complemented
10#13130445C211yesmaximal, characteristic, complemented
11#13130407C211yesmaximal, characteristic, complemented
12#13130175C211yesmaximal, characteristic
13#13130158C211yesmaximal, characteristic, complemented
14#13130053C211yesmaximal, characteristic, complemented
15#13124839C211yesmaximal, characteristic
16C2×D4×Dic13C2211yescharacteristic
17#11719327C2211yescharacteristic
18#11719169—21no—
19#11719169—21no—
20#11719158C2211yescharacteristic, complemented
21Q8×#1057C2211yescharacteristic, complemented
22#11719145—21no—
23#11719145—21no—
24#11719145C2211yescharacteristic
25#11719145C2211yescharacteristic
26#11719145C2211yescharacteristic
27#11719145C2211yescharacteristic
28#11719130C2211yescharacteristic
29C4×#6122C2211yescharacteristic
30#11719119C2211yescharacteristic
31#11719119C2211yescharacteristic
32#11719080—21no—
33#11719080C2211yescharacteristic, complemented
34#11719078—21no—
35#11719074C2211yescharacteristic, complemented
36#11719068—21no—
37#11719068—21no—
38C13×#450C411yescharacteristic
39#11718879C411yescharacteristic
40#11718823C411yescharacteristic
41#11718823C411yescharacteristic
42SD16×Dic13C2211yescharacteristic
43SD16×Dic13C2211yescharacteristic
44#11718704C411yescharacteristic
45#11718422C411yescharacteristic
46#11718422C411yescharacteristic
47#11718419C2211yescharacteristic
48#11718419C2211yescharacteristic
49#11718382C411yescharacteristic
50#11718379C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic, complemented
52Q8⋊#1057C2211yescharacteristic, complemented
53D4⋊#1057C2211yescharacteristic
54D4⋊#1057C2211yescharacteristic
55D4⋊#1057C2211yescharacteristic
56D4⋊#1057C2211yescharacteristic
57#11718256C2211yescharacteristic, complemented
58#11718255C2211yescharacteristic, complemented
59#11718254C2211yescharacteristic, complemented
60#11718253C2211yescharacteristic, complemented
61#1057⋊C8C2211yescharacteristic, complemented
62#1057⋊C8C2211yescharacteristic, complemented
63#11718251C2211yescharacteristic, complemented
64C8×#1057C2211yescharacteristic, complemented
65#11718244C2211yescharacteristic, complemented
66#11718244C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×Dic13—21no—
69C2×#6122—21no—
70C2×#6122—21no—
71C2×#6122—21no—
72C2×#6122—21no—
73C2×#6122—21no—
74C2×C13×SD16C2×C411yescharacteristic
75C2×C13×SD16C2×C411yescharacteristic
76C13×C22⋊Q8C2×C411yescharacteristic
77C2×C22⋊Dic13—21no—
78Q8×Dic13C2311yescharacteristic
79#88198C2×C411yescharacteristic
80D4×Dic13—21no—
81D4×Dic13—21no—
82D4×Dic13C2×C411yescharacteristic
83D4×Dic13C2×C411yescharacteristic
84D4×Dic13C2311yescharacteristic
85D4×Dic13C2311yescharacteristic
86C2×#6105C2×C411yescharacteristic
87C2×#6105C2×C411yescharacteristic
88C2×C4⋊Dic13C2×C411yescharacteristic
89#88178C2×C411yescharacteristic
90C2×C4×Dic13C2311yescharacteristic
91#88143—21no—
92#88142C2×C411yescharacteristic
93#88141—21no—
94#88141C2311yescharacteristic
95#88132—21no—
96#88131—21no—
97C22⋊#1057—21no—
98C22⋊#1057—21no—
99C22⋊#1057—21no—
100C22⋊#1057—21no—
101C22⋊#1057—21no—
102C22⋊#1057—21no—
103C22⋊#1057D411yescharacteristic
104C22⋊#1057D411yescharacteristic
105#88112—21no—
106#88112—21no—
107#88110—21no—
108#88110—21no—
109#88110—21no—
110#88110—21no—
111C4⋊#1057—21no—
112C4⋊#1057—21no—
113C4⋊#1057D411yescharacteristic
114C4⋊#1057D411yescharacteristic
115C4⋊#1057C2311yescharacteristic
116C4⋊#1057C2311yescharacteristic
117C4⋊#1057C2311yescharacteristic
118C4⋊#1057C2311yescharacteristic
119C4×#1057—21no—
120C4×#1057—21no—
121C4×#1057—21no—
122C4×#1057C2311yescharacteristic
123C4×#1057C2311yescharacteristic
124C4×#1057C2311yescharacteristic
125C4×#1057C2311yescharacteristic
126C13×#102C2×C411yescharacteristic
127C13×#102C2×C411yescharacteristic
128C13×C22⋊C8C2×C411yescharacteristic
129#88075C2×C411yescharacteristic
130#88075C2×C411yescharacteristic
131#88072C2×C411yescharacteristic
132#88072C2×C411yescharacteristic
133C22⋊#1055C2×C411yescharacteristic
134#88057C2×C411yescharacteristic
135#88057C2×C411yescharacteristic
136#88056C2×C411yescharacteristic
137#88056C2×C411yescharacteristic
138#88054C2×C411yescharacteristic
139#88054C2×C411yescharacteristic
140C8×Dic13C2311yescharacteristic
141C8×Dic13C2311yescharacteristic
142#88048C2×C411yescharacteristic
143#88048C2×C411yescharacteristic
144#17952—131nomaximal, Sylow
145C24×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13—21no—
148C2×D4×C13—41no—
149C2×D4×C13—41no—
150C2×D4×C13C22×C411yescharacteristic
151C2×D4×C13C22×C411yescharacteristic
152C22×C4×C13C22×C411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—81no—
159C22×Dic13—81no—
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13#4111yescharacteristic
162C2×Dic26—21no—
163C2×Dic26C22×C411yescharacteristic
164#6122—42no—
165#6122—81no—
166#6122—81no—
167#6122—81no—
168#6122—81no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057C2×D411yescharacteristic
176C2×#1057C2×D411yescharacteristic
177C2×#1057C2×D411yescharacteristic
178C2×#1057C2×D411yescharacteristic
179C13×SD16—41no—
180C13×SD16—41no—
181C2×C8×C13C22×C411yescharacteristic
182C2×C8×C13C22×C411yescharacteristic
183C13×C4⋊C4—21no—
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C22⋊C4—21no—
186C22⋊Dic13—21no—
187C22⋊Dic13—21no—
188C22⋊Dic13—21no—
189C22⋊Dic13—21no—
190C22⋊Dic13—21no—
191#6105—41no—
192#6105—41no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197C4⋊Dic13C22×C411yescharacteristic
198#6101—21no—
199#6101—21no—
200#6101—21no—
201#6101—21no—
202#6101—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13C22×C411yescharacteristic
206C4×Dic13C2×D411yescharacteristic
207C4×Dic13#4111yescharacteristic
208C4×Dic13C2411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211#3101—131no—
212#2985—131no—
213#2975—131no—
214#1592—131no—
215#1592—131no—
216#1590—131no—
217#1590—131no—
218#1588—131no—
219#1588—131no—
220#1583—131no—
221#1583—131no—
222#1572—131no—
223#1490—131no—
224#1485—131no—
225#1453—131no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—42no—
229C23×C13—81no—
230C23×C13—81no—
231C23×C13C4×D411yescharacteristic
232Q8×C13—21no—
233Q8×C13—21no—
234D4×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—42no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—81no—
257C2×Dic13—81no—
258C2×Dic13—81no—
259C2×Dic13C4×D411yescharacteristic
260C2×Dic13C4×D411yescharacteristic
261C2×Dic13C22×D411yescharacteristic
262C2×Dic13C2×#4111yescharacteristic
263Dic26—21no—
264Dic26—21no—
265Dic26—81no—
266#1057—22no—
267#1057—21no—
268#1057—21no—
269#1057—21no—
270#1057—21no—
271#1057—41no—
272#1057—41no—
273#1057—41no—
274#1057—41no—
275#1057—41no—
276C8×C13—21no—
277C8×C13—21no—
278#1055—21no—
279#1055—21no—
280#533—131no—
281C2×C4×D4—131no—
282#483—131no—
283#483—131no—
284#476—131no—
285#476—131no—
286#461—131no—
287#461—131no—
288#450—131no—
289#450#26111yescharacteristic
290#446—131no—
291#446—131no—
292#446—261no—
293#446—261no—
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×SD16—131no—
300#436—131no—
301#436—131no—
302#436—131no—
303#436—131no—
304#436—261no—
305#436—261no—
306#433—261no—
307#433—261no—
308#432—131no—
309#431—131no—
310#431—131no—
311#431—131no—
312#407—261no—
313#407—261no—
314C4×M16—131no—
315#335—131no—
316#335—131no—
317#334—131no—
318#334—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323D4⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327#322—131no—
328#322—131no—
329#322—131no—
330C82—131no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13—21no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—84no—
341C22×C13C2×C4×D411yescharacteristic
342C4×C13—21no—
343C4×C13—41no—
344C4×C13—41no—
345C4×C13#56811yescharacteristic
346C4×C13#56811yescharacteristic
347Dic13—21no—
348Dic13—21no—
349Dic13—21no—
350Dic13—41no—
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354Dic13#57711yescharacteristic
355Dic13#57711yescharacteristic
356C22×D4C2×#26111yescharacteristic
357C23×C4—261no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16C2×#26111yescharacteristic
361C2×SD16C2×#26111yescharacteristic
362C2×M16—261no—
363C2×M16—261no—
364C2×M16—261no—
365C2×M16—261no—
366C2×M16—261no—
367C4⋊Q8—131no—
368C4⋊Q8—131no—
369#125—261no—
370C22⋊Q8—131no—
371C22⋊Q8—261no—
372C22⋊Q8C2×#26111yescharacteristic
373C4×Q8—131no—
374C4×Q8—131no—
375C4×Q8—261no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—131no—
379C4×D4—131no—
380C4×D4—261no—
381C4×D4—261no—
382#117—261no—
383C2×C4⋊C4—131no—
384C2×C22⋊C4—261no—
385C2×C42—131no—
386#106—131no—
387#106—131no—
388#106—131no—
389#106—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—131no—
396C4⋊C8—131no—
397C4⋊C8—131no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402#103—131no—
403#103—131no—
404#103—131no—
405#103—131no—
406#102—131no—
407#102—131no—
408#102C2×#26111yescharacteristic
409#102C2×#26111yescharacteristic
410C22⋊C8—131no—
411C22⋊C8—131no—
412C22⋊C8—131no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419C22⋊C8C2×#26111yescharacteristic
420#97—261no—
421#97—261no—
422#97—261no—
423#97—261no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—261no—
431C4×C8—261no—
432C4×C8—261no—
433C2×C13—41no—
434C2×C13—81no—
435C2×C13—81no—
436C2×C13#293011yescharacteristic
437C2×C13#294911yescharacteristic
438C2×C13#295611yescharacteristic
439C24—21no—
440C2×Q8—131no—
441C2×Q8—261no—
442C2×Q8C22×#26111yescharacteristic
443C2×D4—21no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4C22×#26111yescharacteristic
447C2×D4C22×#26111yescharacteristic
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—1041no—
456C22×C4—1041no—
457C22×C4C22×#26111yescharacteristic
458SD16—41no—
459SD16—41no—
460SD16—521no—
461SD16—521no—
462M16—522no—
463M16—1041no—
464M16—1041no—
465M16—1041no—
466M16—1041no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8C22×#26111yescharacteristic
480C2×C8C22×#26111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—131no—
483C4⋊C4—131no—
484C4⋊C4—131no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4C22×#26111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—261no—
495C22⋊C4—261no—
496C22⋊C4—261no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C42—131no—
500C42—131no—
501C42—131no—
502C42—131no—
503C42—261no—
504C42—261no—
505C13#1795211yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508C23—42no—
509C23—81no—
510C23—81no—
511C23D4×#26111yescharacteristic
512Q8—21no—
513Q8—21no—
514Q8—261no—
515Q8—261no—
516Q8—1041no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—21no—
521D4—42no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—131no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—131no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—521no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—1041no—
542C2×C4—1041no—
543C2×C4—1041no—
544C2×C4D4×#26111yescharacteristic
545C2×C4C23×#26111yescharacteristic
546C8—21no—
547C8—21no—
548C8—261no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—262no—
553C8—261no—
554C8—261no—
555C8—521no—
556C8—521no—
557C8—521no—
558C8—521no—
559C8—521no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—84no—
570C22C2×D4×#26111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—131no—
575C4—131no—
576C4—261no—
577C4—261no—
578C4—261no—
579C4—521no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4#1171962111yescharacteristic
584C4#1171962111yescharacteristic
585C2—41no—
586C2—81no—
587C2—81no—
588C2#1313155511yescharacteristic
589C2#1313159611yescharacteristic
590C2#1313161011yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#450C4
socleC22×C13C2×C4×D4
prime radicalC22×D4×C13C2×C4
cosocleC4×Dic13C24
hypercenter#450#261
hypocenterC13#17952
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #13131740C2semidirect
3. #13130479C2semidirect
4. #13130477C2semidirect
5. #13130473C2semidirect
6. #13130472C2semidirect
7. #13130466C2semidirect
8. #13130465C2semidirect
9. #13130446C2semidirect
10. #13130445C2semidirect
11. #13130407C2semidirect
13. #13130158C2semidirect
14. #13130053C2semidirect
20. #11719158C22semidirect
21. Q8×#1057C22semidirect
33. #11719080C22semidirect
35. #11719074C22semidirect
51. Q8⋊#1057C22semidirect
52. Q8⋊#1057C22semidirect
57. #11718256C22semidirect
58. #11718255C22semidirect
59. #11718254C22semidirect
60. #11718253C22semidirect
61. #1057⋊C8C22semidirect
62. #1057⋊C8C22semidirect
63. #11718251C22semidirect
64. C8×#1057C22semidirect
65. #11718244C22semidirect
66. #11718244C22semidirect
505. C13#17952semidirect

Maximal subgroups

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

subgroupindex
#131317402
#131316982
#131304792
#131304772
#131304732
#131304722
#131304662
#131304652
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