Finite Group Databasebeta

← #15834680

Subgroups — #15834680

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125392C211yesmaximal, characteristic
2#13123778C211yesmaximal, characteristic, complemented
3#13123575C211yesmaximal, characteristic
4#13113728C211yesmaximal, characteristic, complemented
5#13113727C211yesmaximal, characteristic, complemented
6#13113682C211yesmaximal, characteristic, complemented
7#13113679C211yesmaximal, characteristic, complemented
8#13113675C211yesmaximal, characteristic, complemented
9#13113672C211yesmaximal, characteristic, complemented
10#13113635C211yesmaximal, characteristic, complemented
11D13×#334C211yesmaximal, characteristic, complemented
12#13113237C211yesmaximal, characteristic, complemented
13#13113233C211yesmaximal, characteristic
14C8×#6094C211yesmaximal, characteristic, complemented
15C8×C13×SD16C211yesmaximal, characteristic, complemented
16C2×#88155—21no—
17#11719283C2211yescharacteristic
18#11719253C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22#11718836C411yescharacteristic
23#11718832C411yescharacteristic
24#11718772—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718525C411yescharacteristic
30#11718516C411yescharacteristic
31#11718500—21no—
32#11718495C2211yescharacteristic
33D13×C4⋊C8C2211yescharacteristic
34D13×C4⋊C8C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718468C411yescharacteristic
38#11718453C411yescharacteristic
39#11718439C411yescharacteristic
40#11718421C411yescharacteristic
41#11718389—21no—
42#11718388—21no—
43C4×#6095C2211yescharacteristic
44#11718350—21no—
45#11718349C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49#11718340—21no—
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127—21no—
68C2×C13×SD16C2×C411yescharacteristic
69C22×C8×C13—21no—
70C4×Q8×C13C2311yescharacteristic
71C4×D4×C13C2311yescharacteristic
72#88200C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6106C2×C411yescharacteristic
75#88194C2×C411yescharacteristic
76#88192C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C2×#6099—21no—
80C2×#6095C2×C411yescharacteristic
81#88155—44no—
82C2×#6094—21no—
83C2×#6094D411yescharacteristic
84C2×#6094D411yescharacteristic
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88C2×C8×D13C2×C411yescharacteristic
89C2×C8×D13C2×C411yescharacteristic
90#88151C2×C411yescharacteristic
91#88150—21no—
92#88149C2×C411yescharacteristic
93#88143—21no—
94#88142C2×C411yescharacteristic
95#88142C2×C411yescharacteristic
96#88139—21no—
97#88138—21no—
98C4×D52C2311yescharacteristic
99#88126—21no—
100C42×D13C2311yescharacteristic
101C4×Dic26—21no—
102C4×Dic26C2311yescharacteristic
103C13×#106C2×C411yescharacteristic
104C13×C4⋊C8—21no—
105C13×C4⋊C8C2311yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×C22⋊C8—21no—
110C4×C8×C13—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88075C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116C22⋊#1055—21no—
117#88061C2×C411yescharacteristic
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055D411yescharacteristic
125#88055D411yescharacteristic
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—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#18067—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C2×C22⋊D13—21no—
152#6127—42no—
153#6127—42no—
154C2×D52—21no—
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13C22×C411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13#4111yescharacteristic
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26C22×C411yescharacteristic
163C13×SD16—22no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—42no—
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6106—41no—
180#6105—41no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13C22×C411yescharacteristic
196C4×Dic13C2×D411yescharacteristic
197C4×Dic13#4111yescharacteristic
198#6099—42no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206#6095—22no—
207#6094—22no—
208#6094—42no—
209#6094SD1614yescomplemented
210C8×D13—22no—
211C8×D13—41no—
212C8×D13—42no—
213C8×D13—42no—
214C8×D13—42no—
215#3167—131no—
216#2962—131no—
217#2935—131no—
218#1590—131no—
219#1590—131no—
220#1583—131no—
221#1583—131no—
222#1582—131no—
223#1582—131no—
224C8×SD16—131no—
225C8×SD16D1311yescharacteristic, complemented
226C2×#334—131no—
227#1481—131no—
228#1480—131no—
229C8×M16—131no—
230C23×C13—21no—
231C22×D13—21no—
232C22×D13C4×D411yescharacteristic
233Q8×C13—21no—
234Q8×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13C23×C411yescharacteristic
243C2×C4×C13C22×D411yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C22⋊D13—42no—
246C22⋊D13—42no—
247C22⋊D13—81no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13C4×D411yescharacteristic
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254D52—21no—
255D52—21no—
256D52—42no—
257C4×D13—21no—
258C4×D13—21no—
259C4×D13—41no—
260C4×D13—41no—
261C4×D13—41no—
262C4×D13C2×SD1612yes—
263C4×D13#13512yes—
264Dic26—21no—
265Dic26—21no—
266Dic26—42no—
267Dic26—81no—
268C8×C13—21no—
269C8×C13—21no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273C8×C13#13112yescomplemented
274C8×C13C2×SD1612yes—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—41no—
279#1055—41no—
280#1055—41no—
281#1055C2×SD1612yes—
282C2×#131—261no—
283#533—131no—
284#532—131no—
285#498—131no—
286#492—131no—
287#487—131no—
288#486—131no—
289#465—131no—
290#465—131no—
291#465—131no—
292#465—131no—
293#446—131no—
294#446—131no—
295#446—261no—
296#446—261no—
297C8×Q8—131no—
298C8×Q8C2×D1311yescharacteristic
299C4×SD16—131no—
300C4×SD16—131no—
301C4×SD16—131no—
302C4×SD16C2×D1311yescharacteristic
303#436—131no—
304#436—131no—
305#435—261no—
306#435—261no—
307C8×D4—131no—
308C8×D4C2×D1311yescharacteristic
309#431—131no—
310#424—261no—
311C2×C4⋊C8—131no—
312C2×C4⋊C8—131no—
313#408—261no—
314#405—261no—
315C4×M16—131no—
316C2×C4×C8—131no—
317#334—131no—
318#334—131no—
319#334—131no—
320#334C2×D1311yescharacteristic
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324Q8⋊C8C2×D1311yescharacteristic
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8C2×D1311yescharacteristic
329#322—131no—
330#322—131no—
331C82—131no—
332C82C2×D1311yescharacteristic
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×C4×D411yescharacteristic
337C2×D13—21no—
338C2×D13—21no—
339C2×D13—41no—
340C2×D13—41no—
341C2×D13—41no—
342C2×D13C4×SD1612yes—
343C4×C13—21no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13C2×#13111yescharacteristic
348C4×C13#56811yescharacteristic
349C4×C13C22×SD1611yescharacteristic
350C4×C13C2×#13511yescharacteristic
351Dic13—21no—
352Dic13—21no—
353Dic13—41no—
354Dic13—41no—
355Dic13—41no—
356Dic13C4×SD1612yes—
357C2×#41—261no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×SD16—131no—
361C2×SD16C4×D1311yescharacteristic
362#131—524no—
363C2×M16—131no—
364C2×M16—131no—
365C2×M16—261no—
366C2×M16—261no—
367C22×C8—21no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C4⋊Q8—131no—
374C4⋊Q8—131no—
375C4⋊Q8—131no—
376#127—131no—
377#125—261no—
378#124—261no—
379C22⋊Q8—131no—
380C22⋊Q8—131no—
381C22⋊Q8—261no—
382#121—131no—
383#121—131no—
384#121—261no—
385C4×Q8—131no—
386C4×Q8—261no—
387C4×Q8C22×D1311yescharacteristic
388C4×D4—131no—
389C4×D4—261no—
390C4×D4C22×D1311yescharacteristic
391#117—261no—
392C2×C42—131no—
393#106—131no—
394#106—131no—
395#106—131no—
396#106C4×D1311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8C22×D1311yescharacteristic
407C4⋊C8C22×D1311yescharacteristic
408#103—131no—
409#103—131no—
410#103—131no—
411#103C4×D1311yescharacteristic
412#102—131no—
413#102—131no—
414#102—131no—
415#102C4×D1311yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—261no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421#97—131no—
422#97—131no—
423#97—261no—
424#97—261no—
425C4×C8—21no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—261no—
432C4×C8C22×D1311yescharacteristic
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C2×C13—81no—
436C2×C13#293511yescharacteristic
437C2×C13C2×C4×SD1611yescharacteristic
438C2×C13#295711yescharacteristic
439D13—22no—
440D13—81no—
441#41—522no—
442#41—522no—
443C2×Q8—131no—
444C2×Q8—261no—
445C2×Q8—261no—
446C2×Q8C2×C4×D1311yescharacteristic
447C2×D4—131no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4C2×C4×D1311yescharacteristic
453C22×C4—21no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—261no—
458SD16—22no—
459SD16—262no—
460SD16—521no—
461SD16—521no—
462M16—134no—
463M16—262no—
464M16—522no—
465M16—522no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—42no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—262no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—521no—
479C2×C8—522no—
480C2×C8—522no—
481C2×C8—522no—
482C2×C8C2×C4×D1311yescharacteristic
483C2×C8C2×C4×D1311yescharacteristic
484C2×C8D4×D1311yescharacteristic
485C2×C8D4×D1311yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—131no—
488C4⋊C4—131no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4C2×C4×D1311yescharacteristic
497C4⋊C4C2×C4×D1311yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—261no—
500C22⋊C4—261no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C42—21no—
505C42—131no—
506C42—131no—
507C42—131no—
508C42—261no—
509C42C23×D1311yescharacteristic
510C13#1806711yescharacteristic, complemented, Sylow
511C23—21no—
512C23—131no—
513C23—261no—
514Q8—21no—
515Q8—21no—
516Q8—261no—
517Q8—261no—
518Q8—522no—
519Q8—1041no—
520D4—21no—
521D4—21no—
522D4—261no—
523D4—261no—
524D4—522no—
525D4—522no—
526D4—522no—
527D4—1041no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—131no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—131no—
537C2×C4—131no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4C22×C4×D1311yescharacteristic
547C2×C4C2×D4×D1311yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—132no—
555C8—261no—
556C8—261no—
557C8—261no—
558C8—521no—
559C8—521no—
560C8—521no—
561C8#8815512yescomplemented
562C8SD16×D1312yes—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—132no—
567C22—261no—
568C22—261no—
569C22—521no—
570C22—521no—
571C22—521no—
572C22C4×D4×D1311yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—132no—
578C4—261no—
579C4—261no—
580C4—521no—
581C4—521no—
582C4—521no—
583C4C2×#8815511yescharacteristic
584C4#1171945511yescharacteristic
585C4C2×SD16×D1311yescharacteristic
586C4D13×#13511yescharacteristic
587C2—81no—
588C2—262no—
589C2—1041no—
590C2#1312357511yescharacteristic
591C2C4×SD16×D1311yescharacteristic
592C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×SD16C2
socleC22×C13C2×C4×D4
prime radical#11719253C22
cosocleC42×C13C24
hypercenterC8×SD16D13
hypocenterC13#18067
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #13123778C2semidirect
4. #13113728C2semidirect
5. #13113727C2semidirect
6. #13113682C2semidirect
7. #13113679C2semidirect
8. #13113675C2semidirect
9. #13113672C2semidirect
10. #13113635C2semidirect
11. D13×#334C2semidirect
12. #13113237C2semidirect
14. C8×#6094C2semidirect
15. C8×C13×SD16C2semidirect
209. #6094SD16semidirect
225. C8×SD16D13semidirect
273. C8×C13#131semidirect
510. C13#18067semidirect
561. C8#88155semidirect

Maximal subgroups

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

subgroupindex
#131253922
#131237782
#131235752
#131137282
#131137272
#131136822
#131136792
#131136752
#131136722
#131136352
D13×#3342
#131132372
#131132332
C8×#60942
C8×C13×SD162
#1806713