Finite Group Databasebeta

← #15834287

Subgroups — #15834287

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124868C211yesmaximal, characteristic
2#13123923C211yesmaximal, characteristic, complemented
3#13123902C211yesmaximal, 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#13113306C211yesmaximal, characteristic
14#13113232C211yesmaximal, characteristic, complemented
15C13×#1454C211yesmaximal, characteristic, complemented
16#11719182C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718587C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718512C411yescharacteristic
24#11718512C411yescharacteristic
25#11718509C411yescharacteristic
26#11718509C411yescharacteristic
27#11718499—21no—
28#11718495—21no—
29#11718489—21no—
30#11718489—21no—
31#11718399C411yescharacteristic
32#11718399C411yescharacteristic
33#11718396C411yescharacteristic
34#11718396C411yescharacteristic
35#11718388—21no—
36#11718388—21no—
37#11718380—21no—
38#11718379—21no—
39C4×#6095C2211yescharacteristic
40C4×#6095C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45C8×D52C2211yescharacteristic
46C8×D52C2211yescharacteristic
47#11718340C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×#6127—21no—
68C22×Dic26C2×C411yescharacteristic
69C2×C42×C13C2311yescharacteristic
70#88184—21no—
71#88184C2×C411yescharacteristic
72#88184C2×C411yescharacteristic
73C2×C4⋊Dic13C2×C411yescharacteristic
74C2×#6101—21no—
75C2×C4×Dic13—21no—
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—
84#88129—21no—
85#88128C2×C411yescharacteristic
86C4×D52—21no—
87C4×D52C2311yescharacteristic
88C4×D52C2311yescharacteristic
89#88123C2×C411yescharacteristic
90C4×Dic26—21no—
91C4×Dic26—21no—
92C4×Dic26C2×C411yescharacteristic
93C4×Dic26C2×C411yescharacteristic
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#18030—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152#6127—81no—
153#6127—81no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52C22×C411yescharacteristic
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×Dic26—22no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—41no—
164C2×Dic26C22×C411yescharacteristic
165C2×Dic26C22×C411yescharacteristic
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C42×C13C22×C411yescharacteristic
177C42×C13C2×D411yescharacteristic
178C42×C13#4111yescharacteristic
179C42×C13C2411yescharacteristic
180#6103—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13—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#3103—131no—
211#2984—131no—
212#2979—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#1496—131no—
223#1479—131no—
224#1454D1311yescharacteristic, complemented
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C22×D13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—41no—
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C22⋊D13—81no—
240C22⋊D13—81no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249D52—21no—
250D52—21no—
251D52—21no—
252D52—21no—
253D52—42no—
254D52—81no—
255C4×D13—41no—
256C4×D13—41no—
257C4×D13—41no—
258C4×D13—41no—
259Dic26—21no—
260Dic26—21no—
261Dic26—21no—
262Dic26—42no—
263Dic26—81no—
264Dic26#13112yes—
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#532—131no—
280C2×C4×Q8—131no—
281#481—131no—
282#481—131no—
283#475—131no—
284#475—131no—
285#460—131no—
286#460—131no—
287#448—131no—
288#448—131no—
289#446—131no—
290#446—131no—
291#446—261no—
292#446—261no—
293C8×Q8—131no—
294C8×Q8—131no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#436—131no—
300#436—131no—
301#436—261no—
302C8×D4—131no—
303C8×D4—131no—
304C8×D4—261no—
305#432—131no—
306#432—261no—
307#431—131no—
308#431—261no—
309#431C2×D1311yescharacteristic
310#431C2×D1311yescharacteristic
311#431C2×D1311yescharacteristic
312#408—261no—
313#408—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
327#322C2×D1311yescharacteristic
328#322C2×D1311yescharacteristic
329C82C2×D1311yescharacteristic
330C22×C13—21no—
331C22×C13—21no—
332C22×C13—21no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—41no—
335C2×D13—41no—
336C2×D13—41no—
337C2×D13—41no—
338C2×D13—41no—
339C2×D13—41no—
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13C2×#13111yescharacteristic
345C4×C13#56811yescharacteristic
346C4×C13#57711yescharacteristic
347C4×C13#57711yescharacteristic
348Dic13—22no—
349Dic13—41no—
350Dic13—41no—
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354C2×#41—261no—
355C22×Q8—131no—
356C2×SD16—131no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×M16—261no—
361C2×M16—261no—
362C22×C8—261no—
363C22×C8—261no—
364C4⋊Q8—131no—
365#127—131no—
366#124—261no—
367#121—131no—
368#121—131no—
369#121—261no—
370C4×Q8—131no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8—261no—
375C4×Q8—261no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—261no—
381C2×C42—261no—
382C2×C42C22×D1311yescharacteristic
383#106—131no—
384#106—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—21no—
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⋊C8C4×D1311yescharacteristic
397C4⋊C8C4×D1311yescharacteristic
398C4⋊C8D5211yescharacteristic
399C4⋊C8D5211yescharacteristic
400#103—131no—
401#103—131no—
402#103—131no—
403#103—131no—
404#102—131no—
405#102—131no—
406#102—131no—
407#102—131no—
408C22⋊C8—21no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413C22⋊C8—261no—
414C22⋊C8—261no—
415C22⋊C8C4×D1311yescharacteristic
416C22⋊C8C4×D1311yescharacteristic
417C22⋊C8D5211yescharacteristic
418C22⋊C8D5211yescharacteristic
419#97—261no—
420#97—261no—
421#97—261no—
422C4×C8—261no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8C22×D1311yescharacteristic
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C4×C8C22×D1311yescharacteristic
429C4×C8C22×D1311yescharacteristic
430C4×C8C22×D1311yescharacteristic
431C2×C13—41no—
432C2×C13#293311yescharacteristic
433C2×C13#294911yescharacteristic
434C2×C13#295511yescharacteristic
435D13—81no—
436D13—81no—
437#41—1041no—
438#41—1041no—
439C2×Q8—131no—
440C2×Q8—131no—
441C2×Q8—262no—
442C2×Q8—261no—
443C2×Q8—261no—
444C2×Q8—521no—
445C2×D4—131no—
446C2×D4—131no—
447C2×D4—261no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4C2×D5211yescharacteristic
457C22×C4#612711yescharacteristic
458SD16—262no—
459SD16—262no—
460SD16—521no—
461SD16—521no—
462M16—1041no—
463M16—1041no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—1041no—
471C2×C8—1041no—
472C2×C8C2×C4×D1311yescharacteristic
473C2×C8C2×C4×D1311yescharacteristic
474C2×C8C2×C4×D1311yescharacteristic
475C2×C8C2×C4×D1311yescharacteristic
476C2×C8C2×D5211yescharacteristic
477C2×C8C2×D5211yescharacteristic
478C2×C8C2×D5211yescharacteristic
479C2×C8C2×D5211yescharacteristic
480C4⋊C4—131no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—131no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42C2×C4×D1311yescharacteristic
499C42C2×D5211yescharacteristic
500C42#612711yescharacteristic
501C42C23×D1311yescharacteristic
502C13#1803011yescharacteristic, complemented, Sylow
503C23—261no—
504C23—261no—
505C23C4×D5211yescharacteristic
506Q8—132no—
507Q8—261no—
508Q8—261no—
509Q8—261no—
510Q8—522no—
511Q8—1041no—
512D4—261no—
513D4—261no—
514D4—261no—
515D4—261no—
516D4—522no—
517D4—1041no—
518D4—1041no—
519D4—1041no—
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—522no—
532C2×C4—522no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4C4×D5211yescharacteristic
538C2×C4C4×D5211yescharacteristic
539C2×C4C4×D5211yescharacteristic
540C2×C4C22×C4×D1311yescharacteristic
541C2×C4C22×D5211yescharacteristic
542C2×C4C2×#612711yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—21no—
551C8—41no—
552C8—41no—
553C8—521no—
554C8—521no—
555C8—521no—
556C8—521no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—521no—
561C22—521no—
562C22—521no—
563C22—521no—
564C22—521no—
565C22—521no—
566C22C2×C4×D5211yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—262no—
572C4—521no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4D13×#13111yescharacteristic
578C4#1171945511yescharacteristic
579C4#1171945611yescharacteristic
580C4#1171945611yescharacteristic
581C2—41no—
582C2—1041no—
583C2—1041no—
584C2#1312356411yescharacteristic
585C2#1312369711yescharacteristic
586C2#1312374011yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1454C2
socleC22×C13C2×C4×D4
prime radical#11719182C22
cosocleC42×C13C24
hypercenter#1454D13
hypocenterC13#18030
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. #13123923C2semidirect
4. #13113740C2semidirect
5. #13113728C2semidirect
6. #13113716C2semidirect
7. #13113695C2semidirect
8. #13113681C2semidirect
9. #13113674C2semidirect
10. #13113650C2semidirect
11. C8×#6095C2semidirect
12. #13113616C2semidirect
14. #13113232C2semidirect
15. C13×#1454C2semidirect
224. #1454D13semidirect
502. C13#18030semidirect

Maximal subgroups

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

subgroupindex
#131248682
#131239232
#131239022
#131137402
#131137282
#131137162
#131136952
#131136812
#131136742
#131136502
C8×#60952
#131136162
#131133062
#131132322
C13×#14542
#1803013