Finite Group Databasebeta

← #15834279

Subgroups — #15834279

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#13124863C211yesmaximal, characteristic
2#13123923C211yesmaximal, 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#13113614C211yesmaximal, characteristic, complemented
12#13113305C211yesmaximal, characteristic
13#13113230C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2979C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#436—21no—
19C13×#436C2211yescharacteristic
20C13×#436C2211yescharacteristic
21C8×D4×C13—21no—
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#408—21no—
27C13×#408—21no—
28#11718755C411yescharacteristic
29#11718755C411yescharacteristic
30#11718736C411yescharacteristic
31#11718736C411yescharacteristic
32#11718701C411yescharacteristic
33#11718701C411yescharacteristic
34#11718695C411yescharacteristic
35#11718695C411yescharacteristic
36C4×#6105C2211yescharacteristic
37C4×#6105C2211yescharacteristic
38C4×#6105C2211yescharacteristic
39C4×#6105C2211yescharacteristic
40#11718587C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718489—21no—
44#11718489—21no—
45#11718380—21no—
46#11718379—21no—
47#11718340C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51D4⋊#1055C2211yescharacteristic
52D4⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C22×Dic26C2×C411yescharacteristic
69C2×C13×M16—21no—
70C2×C13×M16—21no—
71C22×C8×C13—21no—
72C22×C8×C13—21no—
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×#127C2×C411yescharacteristic
75C13×#124—21no—
76C13×#121—21no—
77C13×#121C2×C411yescharacteristic
78C13×#121C2×C411yescharacteristic
79C4×D4×C13—21no—
80C4×D4×C13C2311yescharacteristic
81C4×D4×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×#6105C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6105C2×C411yescharacteristic
86C2×#6105C2×C411yescharacteristic
87C2×C4⋊Dic13C2×C411yescharacteristic
88C2×#6101—21no—
89C2×C4×Dic13—21no—
90C4×Dic26—21no—
91C4×Dic26—21no—
92C4×Dic26C2×C411yescharacteristic
93C4×Dic26C2×C411yescharacteristic
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
107C4×C8×C13—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
139#88043—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18030—131nomaximal, Sylow
145C13×#41—81no—
146C13×#41—81no—
147C2×Q8×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13C22×C411yescharacteristic
153C2×D4×C13C22×C411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C22×Dic13—21no—
160C22×Dic13—21no—
161C2×Dic26—22no—
162C2×Dic26—21no—
163C2×Dic26—41no—
164C2×Dic26C22×C411yescharacteristic
165C2×Dic26C22×C411yescharacteristic
166C13×M16—81no—
167C13×M16—81no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—81no—
171C2×C8×C13—81no—
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C13×C4⋊C4—21no—
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C42×C13C22×C411yescharacteristic
184C42×C13C2×D411yescharacteristic
185C42×C13#4111yescharacteristic
186C42×C13C2411yescharacteristic
187#6105—22no—
188#6105—22no—
189#6105—41no—
190#6105—41no—
191C4⋊Dic13—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197#6101—21no—
198C4×Dic13—21no—
199C4×Dic13—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#3103—131no—
211#2984—131no—
212#2979D1311yescharacteristic
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#1454—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228Q8×C13—81no—
229D4×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—42no—
234D4×C13—81no—
235D4×C13—81no—
236D4×C13—81no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C4×D411yescharacteristic
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C23×C411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260Dic26—21no—
261Dic26—21no—
262Dic26—21no—
263Dic26—42no—
264Dic26#13112yes—
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#532C2×D1311yescharacteristic
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—21no—
300#436C2×D1311yescharacteristic
301#436C2×D1311yescharacteristic
302C8×D4—21no—
303C8×D4C2×D1311yescharacteristic
304C8×D4C2×D1311yescharacteristic
305#432—131no—
306#432—261no—
307#431—131no—
308#431—131no—
309#431—261no—
310#431C2×D1311yescharacteristic
311#431C2×D1311yescharacteristic
312#408—21no—
313#408—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—21no—
332C22×C13—21no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C4×D411yescharacteristic
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—21no—
343C4×C13—21no—
344C4×C13—41no—
345C4×C13—41no—
346C4×C13C2×#13111yescharacteristic
347C4×C13#56811yescharacteristic
348C4×C13#57711yescharacteristic
349C4×C13#57711yescharacteristic
350Dic13—22no—
351Dic13—41no—
352Dic13—41no—
353Dic13—41no—
354C2×#41—21no—
355C22×Q8—131no—
356C2×SD16—131no—
357C2×SD16—131no—
358C2×SD16—131no—
359C2×SD16—131no—
360C2×M16—21no—
361C2×M16—21no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8C4×D1311yescharacteristic
365#127C4×D1311yescharacteristic
366#124—21no—
367#121—21no—
368#121C4×D1311yescharacteristic
369#121C4×D1311yescharacteristic
370C4×Q8—131no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8—261no—
375C4×Q8—261no—
376C4×D4—21no—
377C4×D4C22×D1311yescharacteristic
378C4×D4C22×D1311yescharacteristic
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—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8C22⋊D1311yescharacteristic
397C4⋊C8C22⋊D1311yescharacteristic
398C4⋊C8C22×D1311yescharacteristic
399C4⋊C8C22×D1311yescharacteristic
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—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—131no—
414C22⋊C8—131no—
415C22⋊C8—261no—
416C22⋊C8—261no—
417C22⋊C8C22⋊D1311yescharacteristic
418C22⋊C8C22⋊D1311yescharacteristic
419#97—261no—
420#97—261no—
421#97—261no—
422C4×C8—21no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—261no—
428C4×C8—261no—
429C4×C8C22×D1311yescharacteristic
430C4×C8C22×D1311yescharacteristic
431C2×C13—41no—
432C2×C13—81no—
433C2×C13—81no—
434C2×C13#293311yescharacteristic
435C2×C13#294911yescharacteristic
436C2×C13#295511yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—131no—
441C2×Q8—131no—
442C2×Q8—262no—
443C2×Q8—261no—
444C2×Q8—521no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×C4×D1311yescharacteristic
450C2×D4C2×C4×D1311yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4#612711yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458SD16—262no—
459SD16—262no—
460SD16—521no—
461SD16—521no—
462M16—81no—
463M16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—81no—
467C2×C8—81no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—131no—
471C2×C8—131no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8C2×C22⋊D1311yescharacteristic
477C2×C8C2×C22⋊D1311yescharacteristic
478C2×C8C2×C22⋊D1311yescharacteristic
479C2×C8C2×C22⋊D1311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4C2×C4×D1311yescharacteristic
489C4⋊C4C2×C4×D1311yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42—261no—
498C42C2×C4×D1311yescharacteristic
499C42#612711yescharacteristic
500C42C2×C22⋊D1311yescharacteristic
501C42C23×D1311yescharacteristic
502C13#1803011yescharacteristic, complemented, Sylow
503C23—21no—
504C23—21no—
505C23C4×C22⋊D1311yescharacteristic
506Q8—81no—
507Q8—132no—
508Q8—261no—
509Q8—261no—
510Q8—261no—
511Q8—522no—
512D4—21no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—42no—
517D4—81no—
518D4—81no—
519D4—81no—
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—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4C4×C22⋊D1311yescharacteristic
538C2×C4C4×C22⋊D1311yescharacteristic
539C2×C4C4×C22⋊D1311yescharacteristic
540C2×C4C22×C4×D1311yescharacteristic
541C2×C4C2×#612711yescharacteristic
542C2×C4C22×C22⋊D1311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—261no—
550C8—261no—
551C8—261no—
552C8—261no—
553C8—521no—
554C8—521no—
555C8—521no—
556C8—521no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×C4×C22⋊D1311yescharacteristic
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—262no—
574C4—521no—
575C4—521no—
576C4—521no—
577C4D13×#13111yescharacteristic
578C4#1171945511yescharacteristic
579C4#1171954111yescharacteristic
580C4#1171954111yescharacteristic
581C2—41no—
582C2—81no—
583C2—81no—
584C2#1312355811yescharacteristic
585C2#1312369311yescharacteristic
586C2#1312373711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2979C2
socleC22×C13C2×C4×D4
prime radicalC13×#532C22
cosocleC42×C13C24
hypercenter#2979D13
hypocenterC13#18030
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #13123923C2semidirect
3. #13113738C2semidirect
4. #13113724C2semidirect
5. #13113712C2semidirect
6. #13113693C2semidirect
7. #13113677C2semidirect
8. #13113672C2semidirect
9. #13113648C2semidirect
10. C8×#6105C2semidirect
11. #13113614C2semidirect
13. #13113230C2semidirect
14. #13113136C2semidirect
502. C13#18030semidirect

Maximal subgroups

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

subgroupindex
#131248632
#131239232
#131137382
#131137242
#131137122
#131136932
#131136772
#131136722
#131136482
C8×#61052
#131136142
#131133052
#131132302
#131131362
C13×#29792
#1803013