Finite Group Databasebeta

← #15834034

Subgroups — #15834034

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124897C211yesmaximal, characteristic
2#13123854C211yesmaximal, characteristic, complemented
3#13123582C211yesmaximal, characteristic, complemented
4#13113751C211yesmaximal, characteristic, complemented
5#13113722C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113702C211yesmaximal, characteristic, complemented
8#13113681C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113650C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113621C211yesmaximal, characteristic, complemented
13#13113306C211yesmaximal, characteristic, complemented
14#13113224C211yesmaximal, characteristic, complemented
15C13×#1453C211yesmaximal, characteristic, complemented
16C2×#88161—21no—
17#11719182C2211yescharacteristic
18C4×#6127C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21C4×C13×M16C2211yescharacteristic
22#11718790—21no—
23#11718789—21no—
24#11718789—21no—
25#11718587C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27#11718511C411yescharacteristic
28#11718509C411yescharacteristic
29#11718504C411yescharacteristic
30#11718503C411yescharacteristic
31#11718398C411yescharacteristic
32#11718398C411yescharacteristic
33#11718395C411yescharacteristic
34#11718395C411yescharacteristic
35#11718368—21no—
36#11718367—21no—
37#11718367—21no—
38#11718366—21no—
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic
46#11718349C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718049C2211yescharacteristic
64#11718049C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×#6127—21no—
68C2×#6127C2×C411yescharacteristic
69C2×C13×M16D411yescharacteristic
70C2×C13×M16D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72#88184—21no—
73#88184C2×C411yescharacteristic
74#88184C2×C411yescharacteristic
75C4×C22⋊D13—21no—
76C4×C22⋊D13—21no—
77#88180C2×C411yescharacteristic
78C22×#1055—21no—
79#88161—44no—
80C2×D104C2×C411yescharacteristic
81C2×D104C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6095C2×C411yescharacteristic
84C2×#6094—21no—
85C2×#6094—21no—
86C2×#6094—21no—
87C2×#6094—21no—
88C2×C8×D13—21no—
89C2×C8×D13—21no—
90#88129—21no—
91#88128C2×C411yescharacteristic
92C4×D52—21no—
93C4×D52C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95C4×D52C2311yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98C42×D13—21no—
99#88123C2×C411yescharacteristic
100C4×Dic26C2×C411yescharacteristic
101C4×Dic26C2311yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2×C411yescharacteristic
104C13×C4⋊C8C2×C411yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8C2×C411yescharacteristic
107C13×C22⋊C8C2×C411yescharacteristic
108C13×#97D411yescharacteristic
109C13×#97D411yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C22⋊#1055—21no—
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88060—21no—
129#88058C2×C411yescharacteristic
130#88058C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88057C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88056C2×C411yescharacteristic
135#88054—21no—
136#88054—21no—
137C8×Dic13—21no—
138C8×Dic13—21no—
139C4⋊#1055—21no—
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4⋊#1055C2311yescharacteristic
144#88043—21no—
145#18011—131nomaximal, Sylow
146C22×C4×C13C22×C411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13#4111yescharacteristic
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C2×C22⋊D13—21no—
152#6127—22no—
153#6127—41no—
154#6127—42no—
155#6127—42no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52C22×C411yescharacteristic
159C2×D52C22×C411yescharacteristic
160C2×D52C22×C411yescharacteristic
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×Dic26—21no—
167C2×Dic26C22×C411yescharacteristic
168C13×M16—22no—
169C13×M16—41no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C22×C411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C42×C13C22×C411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13#4111yescharacteristic
183C42×C13C2411yescharacteristic
184C22⋊Dic13—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196#6101—21no—
197#6101—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—42no—
206D104—41no—
207D104—41no—
208#6095—22no—
209#6095—22no—
210#6094—42no—
211#6094—42no—
212#6094—42no—
213#6094—42no—
214C8×D13—42no—
215C8×D13—42no—
216#3106—131no—
217#2971—131no—
218#2935—131no—
219#1594—131no—
220#1589—131no—
221#1588—131no—
222#1586—131no—
223#1583—131no—
224#1581—131no—
225SD16⋊C8—131no—
226C8×SD16—131no—
227#1573—131no—
228#1496—131no—
229#1477—131no—
230#1453D1311yescharacteristic, complemented
231C23×C13C4×D411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—41no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—42no—
247C22⋊D13—42no—
248C22⋊D13—42no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254D52—21no—
255D52—21no—
256D52—21no—
257D52—21no—
258D52—21no—
259D52—21no—
260D52—42no—
261D52—81no—
262C4×D13—42no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
269C4×D13—81no—
270Dic26—21no—
271Dic26—42no—
272Dic26#13112yescomplemented
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—21no—
279C8×C13—21no—
280C8×C13—41no—
281C8×C13—41no—
282C8×C13AGL(1,ℤ/8)12yes—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C2×#131—261no—
288#532—131no—
289C4×#41—131no—
290#482—131no—
291#482—131no—
292#477—131no—
293#476—131no—
294#460—131no—
295#459—131no—
296#449—131no—
297#449—131no—
298C8×Q8—131no—
299C8×Q8—131no—
300C4×SD16—131no—
301C4×SD16—131no—
302C4×D8—131no—
303C4×D8—131no—
304#436—131no—
305#436—131no—
306#436—131no—
307#436—131no—
308#436—261no—
309#436—261no—
310#435—261no—
311#435—261no—
312C8×D4—131no—
313C8×D4—131no—
314#432—131no—
315#432—261no—
316#431C2×D1311yescharacteristic
317#431C2×D1311yescharacteristic
318C2×C4⋊C8—131no—
319#408—261no—
320C4×M16—261no—
321C4×M16C2×D1311yescharacteristic
322#335—131no—
323#335—131no—
324#334—131no—
325#334—131no—
326Q8⋊C8—131no—
327Q8⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334#322C2×D1311yescharacteristic
335#322C2×D1311yescharacteristic
336#322C2×D1311yescharacteristic
337C82C2×D1311yescharacteristic
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13C2×C4×D411yescharacteristic
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13C2×#13111yescharacteristic
356C4×C13#56811yescharacteristic
357C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
358C4×C13#57511yescharacteristic
359Dic13—22no—
360Dic13—41no—
361Dic13—41no—
362Dic13—41no—
363Dic13—41no—
364C2×#41—131no—
365C2×#41—261no—
366C2×SD16—131no—
367C2×SD16—131no—
368C2×D8—131no—
369C2×D8—131no—
370#131—524no—
371C2×M16—261no—
372C2×M16—261no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16D5211yescharacteristic
376C2×M16D5211yescharacteristic
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C4⋊Q8—131no—
381#127—131no—
382#124—261no—
383#121—131no—
384#121—131no—
385#121—261no—
386C4×Q8—131no—
387C4×Q8—131no—
388C4×D4—131no—
389C4×D4—131no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—261no—
393C4×D4—261no—
394C4×D4—261no—
395#117—131no—
396#117—261no—
397C2×C42—261no—
398C2×C42C22×D1311yescharacteristic
399#107—131no—
400#107—131no—
401#106—131no—
402#106—131no—
403C4⋊C8—21no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—261no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8C4×D1311yescharacteristic
412C4⋊C8C4×D1311yescharacteristic
413#103—131no—
414#103—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421C22⋊C8—21no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8C4×D1311yescharacteristic
430C22⋊C8C4×D1311yescharacteristic
431#97—261no—
432#97D5211yescharacteristic
433#97D5211yescharacteristic
434C4×C8—261no—
435C4×C8—261no—
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C4×C8C22×D1311yescharacteristic
441C4×C8C22×D1311yescharacteristic
442C2×C13—41no—
443C2×C13#293311yescharacteristic
444C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
445C2×C13#295711yescharacteristic
446D13—81no—
447D13—81no—
448D13—81no—
449#41—262no—
450#41—521no—
451#41—522no—
452#41—522no—
453C2×Q8—131no—
454C2×Q8—261no—
455C2×D4—131no—
456C2×D4—131no—
457C2×D4—131no—
458C2×D4—261no—
459C2×D4—261no—
460C2×D4—261no—
461C2×D4—261no—
462C2×D4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4C2×C4×D1311yescharacteristic
469C22×C4C2×D5211yescharacteristic
470C22×C4#612711yescharacteristic
471SD16—262no—
472SD16—262no—
473D8—521no—
474D8—521no—
475M16—22no—
476M16—41no—
477M16—522no—
478M16—522no—
479M16—522no—
480M16—522no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—522no—
488C2×C8—522no—
489C2×C8—522no—
490C2×C8C2×C4×D1311yescharacteristic
491C2×C8C2×C4×D1311yescharacteristic
492C2×C8C2×C4×D1311yescharacteristic
493C2×C8C2×C4×D1311yescharacteristic
494C2×C8C2×D5211yescharacteristic
495C2×C8C2×D5211yescharacteristic
496C2×C8C2×D5211yescharacteristic
497C2×C8C2×D5211yescharacteristic
498C4⋊C4—131no—
499C4⋊C4—131no—
500C4⋊C4—131no—
501C4⋊C4—131no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C42—261no—
513C42—261no—
514C42—261no—
515C42C2×C4×D1311yescharacteristic
516C42C2×D5211yescharacteristic
517C42#612711yescharacteristic
518C42C23×D1311yescharacteristic
519C13#1801111yescharacteristic, complemented, Sylow
520C23—261no—
521C23—261no—
522C23—261no—
523C23C4×D5211yescharacteristic
524Q8—132no—
525Q8—261no—
526Q8—522no—
527D4—261no—
528D4—261no—
529D4—261no—
530D4—261no—
531D4—261no—
532D4—261no—
533D4—522no—
534D4—522no—
535D4—522no—
536D4—522no—
537D4—1041no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—522no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—1041no—
556C2×C4C4×D5211yescharacteristic
557C2×C4C4×D5211yescharacteristic
558C2×C4C4×D5211yescharacteristic
559C2×C4C22×C4×D1311yescharacteristic
560C2×C4C22×D5211yescharacteristic
561C2×C4C2×#612711yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—521no—
572C8—521no—
573C8—521no—
574C8—521no—
575C8#8816212yes—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22—521no—
586C22—521no—
587C22—521no—
588C22C2×C4×D5211yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—262no—
594C4—521no—
595C4—521no—
596C4—521no—
597C4—521no—
598C4C2×#8816211yescharacteristic
599C4#1171945311yescharacteristic
600C4D13×#13111yescharacteristic
601C4#1171945511yescharacteristic
602C2—41no—
603C2—1041no—
604C2—1041no—
605C2—1041no—
606C2#1312356411yescharacteristic
607C2C4×#8816211yescharacteristic
608C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1453C2
socleC22×C13C2×C4×D4
prime radical#13124897C2
cosocleC42×C13C24
hypercenter#1453D13
hypocenterC13#18011
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #13123854C2semidirect
3. #13123582C2semidirect
4. #13113751C2semidirect
5. #13113722C2semidirect
6. #13113716C2semidirect
7. #13113702C2semidirect
8. #13113681C2semidirect
9. #13113667C2semidirect
10. #13113650C2semidirect
11. C8×#6095C2semidirect
12. #13113621C2semidirect
13. #13113306C2semidirect
14. #13113224C2semidirect
15. C13×#1453C2semidirect
230. #1453D13semidirect
272. Dic26#131semidirect
519. C13#18011semidirect

Maximal subgroups

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

subgroupindex
#131248972
#131238542
#131235822
#131137512
#131137222
#131137162
#131137022
#131136812
#131136672
#131136502
C8×#60952
#131136212
#131133062
#131132242
C13×#14532
#1801113