Finite Group Databasebeta

← #15833005

Subgroups — #15833005

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124890C211yesmaximal, characteristic
2#13123944C211yesmaximal, characteristic, complemented
3#13113712C211yesmaximal, characteristic, complemented
4#13113698C211yesmaximal, characteristic, complemented
5#13113677C211yesmaximal, characteristic, complemented
6#13113663C211yesmaximal, characteristic, complemented
7#13113658C211yesmaximal, characteristic, complemented
8#13113648C211yesmaximal, characteristic, complemented
9C8×#6105C211yesmaximal, characteristic, complemented
10C8×#6104C211yesmaximal, characteristic, complemented
11#13113622C211yesmaximal, characteristic, complemented
12#13113268C211yesmaximal, characteristic, complemented
13#13113235C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2981C211yesmaximal, characteristic, complemented
16C13×#532C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#436C2211yescharacteristic
19C13×#436C2211yescharacteristic
20C13×#435—21no—
21C13×#435—21no—
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#432C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#408—21no—
27C13×#408—21no—
28#11718752C411yescharacteristic
29#11718745C411yescharacteristic
30#11718736C411yescharacteristic
31#11718733C411yescharacteristic
32#11718698C411yescharacteristic
33#11718698C411yescharacteristic
34#11718696C411yescharacteristic
35#11718696C411yescharacteristic
36C4×#6105C2211yescharacteristic
37C4×#6105C2211yescharacteristic
38C4×#6104C2211yescharacteristic
39C4×#6104C2211yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43#11718494—21no—
44D13×C4⋊C8—21no—
45#11718386—21no—
46#11718386—21no—
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51D4⋊#1055C2211yescharacteristic
52D4⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C2×#6127C2×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×#6104C2×C411yescharacteristic
86C2×#6104C2×C411yescharacteristic
87C4×C22⋊D13—21no—
88C4×C22⋊D13—21no—
89#88180C2×C411yescharacteristic
90C22×#1055—21no—
91C2×C8×D13—21no—
92C2×C8×D13—21no—
93C4×D52C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95#88126—21no—
96C42×D13—21no—
97C4×Dic26C2×C411yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8D411yescharacteristic
109C13×C22⋊C8D411yescharacteristic
110C13×#97—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17920—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
159C2×C22⋊D13—21no—
160#6127—22no—
161#6127—22no—
162C2×D52C22×C411yescharacteristic
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×Dic26C22×C411yescharacteristic
167C13×M16—81no—
168C13×M16—81no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—81no—
172C2×C8×C13—81no—
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C42×C13C22×C411yescharacteristic
185C42×C13C2×D411yescharacteristic
186C42×C13#4111yescharacteristic
187C42×C13C2411yescharacteristic
188C22⋊Dic13—21no—
189#6105—22no—
190#6105—22no—
191#6104—22no—
192#6104—22no—
193#6103—21no—
194#6103—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6101—21no—
198#6101—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—81no—
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C8×D13—81no—
212C8×D13—81no—
213#3106—131no—
214#2988—131no—
215#2981D1311yescharacteristic, complemented
216#1588—131no—
217#1586—131no—
218#1583—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1573—131no—
225#1488—131no—
226#1480—131no—
227#1454—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13C4×D411yescharacteristic
231C22×D13—21no—
232Q8×C13—81no—
233D4×C13—21no—
234D4×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—81no—
238D4×C13—81no—
239D4×C13—81no—
240D4×C13—81no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C22⋊D13—24no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262D52—21no—
263D52#13112yes—
264C4×D13—24no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—81no—
268Dic26—21no—
269Dic26#13112yes—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—41no—
275C8×C13—41no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#532C2×D1311yescharacteristic
285C4×#41—131no—
286#482—131no—
287#482—131no—
288#477—131no—
289#476—131no—
290#460—131no—
291#459—131no—
292#449—131no—
293#449—131no—
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436C2×D1311yescharacteristic
301#436C2×D1311yescharacteristic
302#435—21no—
303#435—21no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—261no—
307C8×D4—261no—
308C8×D4C2×D1311yescharacteristic
309C8×D4C2×D1311yescharacteristic
310#432C2×D1311yescharacteristic
311#431—131no—
312#431—131no—
313#431—261no—
314#431C2×D1311yescharacteristic
315C2×C4⋊C8—131no—
316C2×C4⋊C8—261no—
317#408—21no—
318#408—21no—
319#335—131no—
320#335—131no—
321#334—131no—
322#334—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331#322—131no—
332#322—131no—
333#322—131no—
334C82—131no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13C2×C4×D411yescharacteristic
345C2×D13—22no—
346C2×D13—41no—
347C2×D13—41no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13C2×#13111yescharacteristic
355C4×C13C2×#13111yescharacteristic
356C4×C13#57611yescharacteristic
357C4×C13#57711yescharacteristic
358Dic13—22no—
359Dic13—41no—
360Dic13—41no—
361C2×#41—21no—
362C2×#41—131no—
363C2×SD16—131no—
364C2×SD16—131no—
365C2×D8—131no—
366C2×D8—131no—
367C2×M16—21no—
368C2×M16—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C4⋊Q8C4×D1311yescharacteristic
375#127C4×D1311yescharacteristic
376#124—21no—
377#121—21no—
378#121C4×D1311yescharacteristic
379#121C4×D1311yescharacteristic
380C4×Q8—131no—
381C4×Q8—131no—
382C4×D4—21no—
383C4×D4—131no—
384C4×D4—131no—
385C4×D4—261no—
386C4×D4—261no—
387C4×D4C22×D1311yescharacteristic
388C4×D4C22×D1311yescharacteristic
389#117—131no—
390#117—261no—
391C2×C42—261no—
392C2×C42C22×D1311yescharacteristic
393#107—131no—
394#107—131no—
395#106—131no—
396#106—131no—
397C4⋊C8—131no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—261no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8C22⋊D1311yescharacteristic
406C4⋊C8C22⋊D1311yescharacteristic
407C4⋊C8C22×D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409#103—131no—
410#103—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—131no—
423C22⋊C8—131no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8C22⋊D1311yescharacteristic
428C22⋊C8C22⋊D1311yescharacteristic
429#97—21no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8—261no—
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C2×C13—41no—
439C2×C13—81no—
440C2×C13—81no—
441C2×C13#292911yescharacteristic
442C2×C13#294611yescharacteristic
443C2×C13#295711yescharacteristic
444D13—42no—
445#41—81no—
446#41—81no—
447#41—262no—
448#41—262no—
449C2×Q8—21no—
450C2×Q8—131no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—131no—
456C2×D4—261no—
457C2×D4C2×C4×D1311yescharacteristic
458C2×D4C2×C4×D1311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4#612711yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467SD16—262no—
468SD16—262no—
469D8—262no—
470D8—262no—
471M16—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—1041no—
486C2×C8—1041no—
487C2×C8—1041no—
488C2×C8C2×C22⋊D1311yescharacteristic
489C2×C8C2×C22⋊D1311yescharacteristic
490C2×C8C2×C22⋊D1311yescharacteristic
491C2×C8C2×C22⋊D1311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—131no—
494C4⋊C4—131no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4C2×C4×D1311yescharacteristic
498C4⋊C4C2×C4×D1311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42C2×C4×D1311yescharacteristic
510C42#612711yescharacteristic
511C42C2×C22⋊D1311yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1792011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—261no—
517C23C4×C22⋊D1311yescharacteristic
518Q8—81no—
519Q8—132no—
520Q8—261no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—132no—
530D4—264no—
531D4—261no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—264no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—1041no—
550C2×C4C4×C22⋊D1311yescharacteristic
551C2×C4C4×C22⋊D1311yescharacteristic
552C2×C4C4×C22⋊D1311yescharacteristic
553C2×C4C22×C4×D1311yescharacteristic
554C2×C4C2×#612711yescharacteristic
555C2×C4C22×C22⋊D1311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—261no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—521no—
567C8—521no—
568C8—521no—
569C8—521no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—262no—
580C22—521no—
581C22—521no—
582C22C2×C4×C22⋊D1311yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—262no—
590C4—521no—
591C4—521no—
592C4D13×#13111yescharacteristic
593C4D13×#13111yescharacteristic
594C4#1171954011yescharacteristic
595C4#1171954111yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—522no—
600C2#1312352811yescharacteristic
601C2#1312366811yescharacteristic
602C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2981C2
socleC22×C13C2×C4×D4
prime radical#13124890C2
cosocleC42×C13C24
hypercenter#2981D13
hypocenterC13#17920
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. #13123944C2semidirect
3. #13113712C2semidirect
4. #13113698C2semidirect
5. #13113677C2semidirect
6. #13113663C2semidirect
7. #13113658C2semidirect
8. #13113648C2semidirect
9. C8×#6105C2semidirect
10. C8×#6104C2semidirect
11. #13113622C2semidirect
12. #13113268C2semidirect
13. #13113235C2semidirect
14. #13113136C2semidirect
15. C13×#2981C2semidirect
215. #2981D13semidirect
513. C13#17920semidirect

Maximal subgroups

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

subgroupindex
#131248902
#131239442
#131137122
#131136982
#131136772
#131136632
#131136582
#131136482
C8×#61052
C8×#61042
#131136222
#131132682
#131132352
#131131362
C13×#29812
#1792013