Finite Group Databasebeta

← #15834777

Subgroups — #15834777

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125431C211yesmaximal, characteristic
2#13123840C211yesmaximal, characteristic, complemented
3#13123582C211yesmaximal, characteristic, complemented
4#13113751C211yesmaximal, characteristic, complemented
5#13113728C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113702C211yesmaximal, characteristic, complemented
8#13113674C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113650C211yesmaximal, characteristic, complemented
11C8×D104C211yesmaximal, characteristic, complemented
12#13113588C211yesmaximal, characteristic, complemented
13#13113254C211yesmaximal, characteristic, complemented
14#13113250C211yesmaximal, characteristic, complemented
15C13×#1455C211yesmaximal, characteristic, complemented
16C2×#88161—21no—
17#11719184C2211yescharacteristic
18#11719182C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21C4×C13×M16C2211yescharacteristic
22#11718796C411yescharacteristic
23#11718796C411yescharacteristic
24#11718795C411yescharacteristic
25#11718795C411yescharacteristic
26#11718790—21no—
27#11718789—21no—
28#11718788—21no—
29#11718586C2211yescharacteristic
30C2×C4⋊#1055C2211yescharacteristic
31#11718375C411yescharacteristic
32#11718374C411yescharacteristic
33#11718373C411yescharacteristic
34#11718370—21no—
35#11718369—21no—
36#11718367—21no—
37#11718367—21no—
38#11718363C411yescharacteristic
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic
46C8×D52C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
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×C13×M16—21no—
69C2×C13×M16C2×C411yescharacteristic
70C2×C13×M16C2×C411yescharacteristic
71C2×C13×M16D411yescharacteristic
72C2×C13×M16D411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74#88184—21no—
75#88184C2×C411yescharacteristic
76#88184C2×C411yescharacteristic
77#88184C2×C411yescharacteristic
78#88183—21no—
79C4×C22⋊D13—21no—
80#88178C2×C411yescharacteristic
81C22×#1055—21no—
82#88161—44no—
83C2×D104C2×C411yescharacteristic
84C2×D104C2×C411yescharacteristic
85C2×#6095C2×C411yescharacteristic
86C2×#6095C2×C411yescharacteristic
87C2×#6094—21no—
88C2×#6094—21no—
89C2×#6094—21no—
90C2×C8×D13—21no—
91C2×C8×D13—21no—
92C2×C8×D13—21no—
93#88130—21no—
94#88129—21no—
95#88129C2×C411yescharacteristic
96#88128C2×C411yescharacteristic
97C4×D52—21no—
98C4×D52C2311yescharacteristic
99C4×D52C2311yescharacteristic
100C4×D52C2311yescharacteristic
101#88126—21no—
102#88124C2×C411yescharacteristic
103#88123C2×C411yescharacteristic
104C4×Dic26C2311yescharacteristic
105C13×#97—21no—
106C13×#97C2×C411yescharacteristic
107C13×#97C2×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#88055—21no—
136#88054—21no—
137#88054—21no—
138C8×Dic13—21no—
139C4⋊#1055—21no—
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4⋊#1055C2311yescharacteristic
144C4×#1055—21no—
145#18076—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—42no—
153#6127—42no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52C22×C411yescharacteristic
157C2×D52C22×C411yescharacteristic
158C2×D52C22×C411yescharacteristic
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×Dic26—21no—
163C2×Dic26C22×C411yescharacteristic
164C13×M16—22no—
165C13×M16—22no—
166C13×M16—41no—
167C13×M16—41no—
168C13×M16—42no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C2×C8×C13C2×D411yescharacteristic
179C42×C13C22×C411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13#4111yescharacteristic
182C42×C13C2411yescharacteristic
183C22⋊Dic13—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13C22×C411yescharacteristic
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6101—21no—
198#6101—21no—
199#6101—21no—
200#6101—21no—
201C4×Dic13—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—42no—
207D104—22no—
208D104—41no—
209#6095—22no—
210#6095—41no—
211#6094—42no—
212#6094—42no—
213#6094—42no—
214C8×D13—42no—
215C8×D13—42no—
216C8×D13—42no—
217#3171—131no—
218#2969—131no—
219#2935—131no—
220#1594—131no—
221#1590—131no—
222#1588—131no—
223#1586—131no—
224#1582—131no—
225#1581—131no—
226SD16⋊C8—131no—
227C8×D8—131no—
228#1565—131no—
229#1484—131no—
230#1483—131no—
231#1455D1311yescharacteristic, complemented
232C23×C13C4×D411yescharacteristic
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C22⋊D13—42no—
248C22⋊D13—42no—
249C22⋊D13—81no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255D52—21no—
256D52—21no—
257D52—21no—
258D52—21no—
259D52—21no—
260D52—21no—
261D52—42no—
262D52—81no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
269Dic26—21no—
270Dic26—21no—
271Dic26—42no—
272C8×C13—22no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—21no—
279C8×C13—41no—
280C8×C13#13112yescomplemented
281C8×C13AGL(1,ℤ/8)12yes—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286C2×#131—261no—
287#532—131no—
288#529—131no—
289#501—131no—
290#496—131no—
291#490—131no—
292#489—131no—
293#469—131no—
294#469—131no—
295#468—131no—
296#468—131no—
297#446—131no—
298C8×Q8—131no—
299C4×SD16—131no—
300C4×SD16—131no—
301C4×D8—131no—
302C4×D8—131no—
303#436—131no—
304#436—131no—
305#436—131no—
306#436—261no—
307#435—261no—
308#435—261no—
309#435—261no—
310C8×D4—131no—
311C8×D4—131no—
312C8×D4—131no—
313#433—261no—
314#431—131no—
315C2×C4⋊C8—131no—
316#408—261no—
317#405—261no—
318C4×M16C2×D1311yescharacteristic
319C4×M16C2×D1311yescharacteristic
320C4×M16C2×D1311yescharacteristic
321#335—131no—
322#335—131no—
323#334—131no—
324#334—131no—
325Q8⋊C8—131no—
326Q8⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333#322C2×D1311yescharacteristic
334#322C2×D1311yescharacteristic
335#322C2×D1311yescharacteristic
336C82C2×D1311yescharacteristic
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13C2×C4×D411yescharacteristic
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13C2×#13111yescharacteristic
355C4×C13#56811yescharacteristic
356C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
357C4×C13#57511yescharacteristic
358Dic13—41no—
359Dic13—41no—
360Dic13—41no—
361Dic13—41no—
362Dic13—41no—
363C2×#41—261no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×D8—131no—
367C2×D8—131no—
368#131—524no—
369C2×M16—21no—
370C2×M16—261no—
371C2×M16—261no—
372C2×M16—261no—
373C2×M16C4×D1311yescharacteristic
374C2×M16C4×D1311yescharacteristic
375C2×M16D5211yescharacteristic
376C2×M16D5211yescharacteristic
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381C4⋊Q8—131no—
382#127—131no—
383#126—261no—
384#125—131no—
385#124—131no—
386#124—261no—
387#123—261no—
388C22⋊Q8—131no—
389#121—131no—
390#121—131no—
391#121—131no—
392#121—261no—
393C4×Q8—131no—
394C4×D4—131no—
395C4×D4—131no—
396C4×D4—131no—
397C4×D4—261no—
398C4×D4—261no—
399#117—261no—
400C2×C42C22×D1311yescharacteristic
401#107—131no—
402#107—131no—
403#106—131no—
404#106—131no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412#103—131no—
413#103—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427#97—21no—
428#97—261no—
429#97C4×D1311yescharacteristic
430#97C4×D1311yescharacteristic
431#97D5211yescharacteristic
432#97D5211yescharacteristic
433C4×C8—261no—
434C4×C8—261no—
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C4×C8C22×D1311yescharacteristic
441C2×C13—41no—
442C2×C13#293511yescharacteristic
443C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
444C2×C13#295611yescharacteristic
445D13—81no—
446D13—81no—
447D13—81no—
448#41—522no—
449#41—522no—
450C2×Q8—131no—
451C2×Q8—261no—
452C2×D4—131no—
453C2×D4—131no—
454C2×D4—131no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4C2×D5211yescharacteristic
465C22×C4#612711yescharacteristic
466SD16—262no—
467SD16—521no—
468D8—262no—
469D8—521no—
470M16—22no—
471M16—22no—
472M16—41no—
473M16—41no—
474M16—42no—
475M16—522no—
476M16—522no—
477M16—522no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—522no—
485C2×C8—522no—
486C2×C8—522no—
487C2×C8—522no—
488C2×C8C2×C4×D1311yescharacteristic
489C2×C8C2×C4×D1311yescharacteristic
490C2×C8C2×C4×D1311yescharacteristic
491C2×C8C2×C4×D1311yescharacteristic
492C2×C8C2×D5211yescharacteristic
493C2×C8C2×D5211yescharacteristic
494C2×C8C2×D5211yescharacteristic
495C2×C8C2×D5211yescharacteristic
496C4⋊C4—131no—
497C4⋊C4—131no—
498C4⋊C4—131no—
499C4⋊C4—131no—
500C4⋊C4—261no—
501C4⋊C4—261no—
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—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C42—261no—
515C42C2×C4×D1311yescharacteristic
516C42C2×D5211yescharacteristic
517C42#612711yescharacteristic
518C42C23×D1311yescharacteristic
519C13#1807611yescharacteristic, complemented, Sylow
520C23—261no—
521C23—261no—
522C23—261no—
523C23C4×D5211yescharacteristic
524Q8—261no—
525Q8—261no—
526Q8—522no—
527D4—261no—
528D4—261no—
529D4—261no—
530D4—261no—
531D4—261no—
532D4—261no—
533D4—522no—
534D4—522no—
535D4—522no—
536D4—1041no—
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—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4C4×D5211yescharacteristic
555C2×C4C4×D5211yescharacteristic
556C2×C4C4×D5211yescharacteristic
557C2×C4C22×C4×D1311yescharacteristic
558C2×C4C22×D5211yescharacteristic
559C2×C4C2×#612711yescharacteristic
560C8—22no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—521no—
569C8—521no—
570C8—521no—
571C8—521no—
572C8#8816112yescomplemented
573C8#8816212yes—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22—521no—
586C22C2×C4×D5211yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—521no—
592C4—521no—
593C4—521no—
594C4—521no—
595C4—521no—
596C4C2×#8816111yescharacteristic
597C4#1171945011yescharacteristic
598C4C2×#8816211yescharacteristic
599C4#1171945311yescharacteristic
600C2—41no—
601C2—1041no—
602C2—1041no—
603C2—1041no—
604C2#1312358211yescharacteristic
605C2C4×#8816211yescharacteristic
606C2#1312374711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1455C2
socleC22×C13C2×C4×D4
prime radical#13125431C2
cosocleC42×C13C24
hypercenter#1455D13
hypocenterC13#18076
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1455

Complements

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

NH ≅ G/Ntype
2. #13123840C2semidirect
3. #13123582C2semidirect
4. #13113751C2semidirect
5. #13113728C2semidirect
6. #13113716C2semidirect
7. #13113702C2semidirect
8. #13113674C2semidirect
9. #13113667C2semidirect
10. #13113650C2semidirect
11. C8×D104C2semidirect
12. #13113588C2semidirect
13. #13113254C2semidirect
14. #13113250C2semidirect
15. C13×#1455C2semidirect
231. #1455D13semidirect
280. C8×C13#131semidirect
519. C13#18076semidirect
572. C8#88161semidirect

Maximal subgroups

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

subgroupindex
#131254312
#131238402
#131235822
#131137512
#131137282
#131137162
#131137022
#131136742
#131136672
#131136502
C8×D1042
#131135882
#131132542
#131132502
C13×#14552
#1807613