Finite Group Databasebeta

← #15833555

Subgroups — #15833555

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125432C211yesmaximal, characteristic
2#13123985C211yesmaximal, characteristic, complemented
3#13123914C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113741C211yesmaximal, characteristic, complemented
6#13113723C211yesmaximal, characteristic, complemented
7#13113718C211yesmaximal, characteristic, complemented
8#13113657C211yesmaximal, characteristic, complemented
9#13113651C211yesmaximal, characteristic, complemented
10#13113633C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113604C211yesmaximal, characteristic, complemented
13#13113288C211yesmaximal, characteristic, complemented
14C8×#6099C211yesmaximal, characteristic, complemented
15C13×#1494C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17#11719182C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20#11718728C411yescharacteristic
21#11718726C411yescharacteristic
22#11718719C411yescharacteristic
23#11718716C411yescharacteristic
24#11718710C411yescharacteristic
25#11718710C411yescharacteristic
26#11718700C411yescharacteristic
27#11718700C411yescharacteristic
28C4×#6106C2211yescharacteristic
29C4×#6106C2211yescharacteristic
30#11718685C2211yescharacteristic
31Q8×#1055C2211yescharacteristic
32C4×#6104C2211yescharacteristic
33C4×#6104C2211yescharacteristic
34#11718673—21no—
35#11718673C2211yescharacteristic
36#11718672—21no—
37D4×#1055C2211yescharacteristic
38#11718661—21no—
39#11718660—21no—
40#11718586C2211yescharacteristic
41#11718585C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718495C2211yescharacteristic
46#11718495C2211yescharacteristic
47#11718388—21no—
48#11718388—21no—
49#11718367—21no—
50#11718367—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127—21no—
68C22×C8×C13—21no—
69C13×#126—21no—
70C13×#125C2×C411yescharacteristic
71C13×#124C2×C411yescharacteristic
72C13×#123—21no—
73C13×C22⋊Q8C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×Q8×C13C2311yescharacteristic
76C4×D4×C13—21no—
77C4×D4×C13C2311yescharacteristic
78C13×#117—21no—
79C2×C42×C13C2311yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6104C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84#88184—21no—
85#88184C2×C411yescharacteristic
86#88184C2×C411yescharacteristic
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099C2×C411yescharacteristic
90C2×#6099C2×C411yescharacteristic
91C22×#1055—21no—
92C2×#6094—21no—
93C2×#6094—21no—
94C2×C8×D13—21no—
95C2×C8×D13—21no—
96#88129—21no—
97#88128C2×C411yescharacteristic
98C4×D52—21no—
99C4×D52C2311yescharacteristic
100C4×D52C2311yescharacteristic
101#88123C2×C411yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C22⋊C8—21no—
105C13×#97—21no—
106C4×C8×C13—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109#88075C2×C411yescharacteristic
110#88075C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115C22⋊#1055D411yescharacteristic
116C22⋊#1055D411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88049C2×C411yescharacteristic
122#88049C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055D411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137#88043C2×C411yescharacteristic
138#88043C2×C411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17968—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×C22⋊D13—21no—
153C2×C22⋊D13—21no—
154#6127—81no—
155#6127—81no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52C22×C411yescharacteristic
159C2×D52C22×C411yescharacteristic
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×Dic26—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—42no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C42×C13—21no—
180C42×C13C22×C411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13#4111yescharacteristic
183C42×C13C2411yescharacteristic
184#6106—22no—
185#6106—22no—
186#6104—22no—
187#6104—22no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13C22×C411yescharacteristic
194C4⋊Dic13C22×C411yescharacteristic
195#6099—22no—
196#6099—22no—
197#6099—81no—
198#6099—81no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—81no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#6094—81no—
211#6094—81no—
212C8×D13—81no—
213C8×D13—81no—
214#3171—131no—
215#2993—131no—
216#2981—131no—
217#1594—131no—
218#1592—131no—
219#1590—131no—
220#1589—131no—
221#1580—131no—
222SD16⋊C8—131no—
223C8×SD16—131no—
224C8×D8—131no—
225#1569—131no—
226#1494D1311yescharacteristic, complemented
227#1492—131no—
228C8×M16—131no—
229C23×C13—21no—
230C23×C13C4×D411yescharacteristic
231C22×D13—21no—
232C22×D13—21no—
233Q8×C13—21no—
234Q8×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—81no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
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
254C22⋊D13—81no—
255C22⋊D13—81no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258D52—21no—
259D52—21no—
260D52—21no—
261D52—21no—
262D52—81no—
263D52—81no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268Dic26—81no—
269C8×C13—22no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—41no—
280#1055—41no—
281#1055#13112yes—
282#1055#13112yes—
283#532—131no—
284#529C2×D1311yescharacteristic
285#501—131no—
286#496—131no—
287#490—131no—
288#489—131no—
289#469—131no—
290#469—131no—
291#468—131no—
292#468—131no—
293#446—131no—
294C8×Q8—131no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×D8—131no—
298C4×D8—131no—
299#436—131no—
300#436—131no—
301#436—131no—
302#436—261no—
303#435—261no—
304#435—261no—
305#435—261no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—131no—
309#433—261no—
310#432C2×D1311yescharacteristic
311#431—131no—
312#424—261no—
313#423—131no—
314#408—261no—
315#408—261no—
316C4×M16—131no—
317C2×C4×C8C2×D1311yescharacteristic
318#335—131no—
319#335—131no—
320#334—131no—
321#334—131no—
322Q8⋊C8C2×D1311yescharacteristic
323Q8⋊C8C2×D1311yescharacteristic
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8C2×D1311yescharacteristic
329D4⋊C8C2×D1311yescharacteristic
330#322—131no—
331#322—131no—
332C82—131no—
333C82—131no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13C2×C4×D411yescharacteristic
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13C2×#13111yescharacteristic
355C4×C13C2×#13111yescharacteristic
356C4×C13#57611yescharacteristic
357C4×C13#57711yescharacteristic
358Dic13—41no—
359Dic13—41no—
360C2×#41—261no—
361C2×SD16—131no—
362C2×SD16—131no—
363C2×D8—131no—
364C2×D8—131no—
365C2×M16—131no—
366C2×M16—131no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16—261no—
371C22×C8—21no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C4⋊Q8—131no—
376#127—131no—
377#126—21no—
378#125C4×D1311yescharacteristic
379#124—261no—
380#124C4×D1311yescharacteristic
381#123—21no—
382C22⋊Q8C4×D1311yescharacteristic
383#121—131no—
384#121—131no—
385#121—261no—
386#121C4×D1311yescharacteristic
387C4×Q8C22×D1311yescharacteristic
388C4×D4—21no—
389C4×D4—131no—
390C4×D4—131no—
391C4×D4—261no—
392C4×D4C22×D1311yescharacteristic
393#117—21no—
394C2×C42C22×D1311yescharacteristic
395#107—131no—
396#107—131no—
397#106—131no—
398#106—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8C22×D1311yescharacteristic
407C4⋊C8C22×D1311yescharacteristic
408#103—131no—
409#103—131no—
410#102—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416C22⋊C8—21no—
417C22⋊C8—131no—
418C22⋊C8—131no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425#97—21no—
426#97—131no—
427#97—131no—
428#97—261no—
429C4×C8—21no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C2×C13—41no—
438C2×C13—81no—
439C2×C13#293111yescharacteristic
440C2×C13#294611yescharacteristic
441C2×C13#295611yescharacteristic
442D13—81no—
443D13—81no—
444#41—1041no—
445#41—1041no—
446C2×Q8—261no—
447C2×Q8C2×C4×D1311yescharacteristic
448C2×D4—21no—
449C2×D4—131no—
450C2×D4—131no—
451C2×D4—261no—
452C2×D4—261no—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4C2×C4×D1311yescharacteristic
456C22×C4—21no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4D4×D1311yescharacteristic
461C22×C4#612911yescharacteristic
462SD16—262no—
463SD16—262no—
464D8—262no—
465D8—262no—
466M16—262no—
467M16—262no—
468M16—1041no—
469M16—1041no—
470M16—1041no—
471M16—1041no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8—1041no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—131no—
495C4⋊C4—131no—
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—21no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C42—21no—
509C42C2×C4×D1311yescharacteristic
510C42D4×D1311yescharacteristic
511C42#612911yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1796811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—261no—
516C23—261no—
517C23#8813511yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—1041no—
521D4—21no—
522D4—21no—
523D4—81no—
524D4—261no—
525D4—261no—
526D4—261no—
527D4—261no—
528D4—1041no—
529D4—1041no—
530D4—1041no—
531D4—1041no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4#8813511yescharacteristic
549C2×C4#8813511yescharacteristic
550C2×C4#8813511yescharacteristic
551C2×C4C22×C4×D1311yescharacteristic
552C2×C4C2×D4×D1311yescharacteristic
553C2×C4C2×#612911yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—132no—
559C8—132no—
560C8—261no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—521no—
567C8—521no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—521no—
575C22—521no—
576C22—521no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22C2×#8813511yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—521no—
589C4—521no—
590C4D13×#13111yescharacteristic
591C4D13×#13111yescharacteristic
592C4#1171947411yescharacteristic
593C4#1171947511yescharacteristic
594C2—41no—
595C2—81no—
596C2—1041no—
597C2—1041no—
598C2#1312354411yescharacteristic
599C2#1312367111yescharacteristic
600C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1494C2
socleC22×C13C2×C4×D4
prime radical#13125432C2
cosocleC42×C13C24
hypercenter#1494D13
hypocenterC13#17968
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #13123985C2semidirect
3. #13123914C2semidirect
4. #13113747C2semidirect
5. #13113741C2semidirect
6. #13113723C2semidirect
7. #13113718C2semidirect
8. #13113657C2semidirect
9. #13113651C2semidirect
10. #13113633C2semidirect
11. #13113628C2semidirect
12. #13113604C2semidirect
13. #13113288C2semidirect
14. C8×#6099C2semidirect
15. C13×#1494C2semidirect
226. #1494D13semidirect
513. C13#17968semidirect

Maximal subgroups

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

subgroupindex
#131254322
#131239852
#131239142
#131137472
#131137412
#131137232
#131137182
#131136572
#131136512
#131136332
#131136282
#131136042
#131132882
C8×#60992
C13×#14942
#1796813