Finite Group Databasebeta

← #15833866

Subgroups — #15833866

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124854C211yesmaximal, characteristic
2#13123840C211yesmaximal, characteristic, complemented
3#13113724C211yesmaximal, characteristic, complemented
4#13113719C211yesmaximal, characteristic, complemented
5#13113686C211yesmaximal, characteristic, complemented
6#13113679C211yesmaximal, characteristic, complemented
7#13113677C211yesmaximal, characteristic, complemented
8#13113663C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113617C211yesmaximal, characteristic, complemented
12#13113294C211yesmaximal, characteristic, complemented
13#13113218C211yesmaximal, characteristic, complemented
14M16×#1055C211yesmaximal, characteristic, complemented
15C13×#2971C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719184C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436—21no—
21C13×#436—21no—
22C13×#436C2211yescharacteristic
23C13×#436C2211yescharacteristic
24C13×#432—21no—
25C13×#432C2211yescharacteristic
26C4×C13×M16—21no—
27C4×C13×M16C2211yescharacteristic
28#11718900C411yescharacteristic
29#11718899C411yescharacteristic
30#11718789—21no—
31#11718788—21no—
32C4×#6107C2211yescharacteristic
33#11718689C411yescharacteristic
34C4×#6106C2211yescharacteristic
35#11718683C411yescharacteristic
36C4×#6105C2211yescharacteristic
37#11718677C411yescharacteristic
38C4×#6104C2211yescharacteristic
39#11718670C411yescharacteristic
40#11718664C411yescharacteristic
41#11718657C411yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718370—21no—
46#11718369—21no—
47#11718349C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×C13×M16—21no—
69C2×C13×M16—21no—
70C2×C13×M16D411yescharacteristic
71C2×C13×M16D411yescharacteristic
72C4×Q8×C13C2×C411yescharacteristic
73C4×Q8×C13C2311yescharacteristic
74C4×D4×C13—21no—
75C4×D4×C13—21no—
76C4×D4×C13C2×C411yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C13×#117—21no—
79C13×#117C2×C411yescharacteristic
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86#88184C2×C411yescharacteristic
87#88183—21no—
88C4×C22⋊D13—21no—
89#88178C2×C411yescharacteristic
90C22×#1055—21no—
91C2×#6094—21no—
92C2×C8×D13—21no—
93#88130—21no—
94#88129C2×C411yescharacteristic
95C4×D52C2311yescharacteristic
96#88126—21no—
97#88124C2×C411yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×#97—21no—
107C13×#97D411yescharacteristic
108C13×#97D411yescharacteristic
109C4×C8×C13—21no—
110C4×C8×C13—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88075C2×C411yescharacteristic
114#88075C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—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⋊#1055C2×C411yescharacteristic
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17999—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—41no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13—21no—
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C2×C22⋊D13—21no—
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×Dic26C22×C411yescharacteristic
160C13×M16—22no—
161C13×M16—22no—
162C13×M16—42no—
163C13×M16—42no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
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—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13C22×C411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13#4111yescharacteristic
183C42×C13C2411yescharacteristic
184C22⋊Dic13—21no—
185#6107—22no—
186#6106—22no—
187#6105—41no—
188#6104—41no—
189#6103—21no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13C22×C411yescharacteristic
194C4⋊Dic13C22×C411yescharacteristic
195#6101—21no—
196#6101—21no—
197#6101—21no—
198#6101—21no—
199C4×Dic13—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—42no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209#6094—42no—
210C8×D13—42no—
211#3102—131no—
212#2971D1311yescharacteristic, complemented
213#2969—131no—
214#1590—131no—
215#1589—131no—
216#1584—131no—
217#1583—131no—
218#1583—131no—
219#1581—131no—
220C8×Q16—131no—
221C8×SD16—131no—
222#1572—131no—
223#1494—131no—
224#1476—131no—
225C8×M16—131no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228C22×D13—21no—
229Q8×C13—21no—
230Q8×C13#13112yes—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—42no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—81no—
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C4×D411yescharacteristic
248C2×C4×C13C4×D411yescharacteristic
249C2×C4×C13C23×C411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C22⋊D13—81no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256D52—21no—
257D52—21no—
258C4×D13—41no—
259C4×D13—41no—
260Dic26—21no—
261Dic26—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13#13512yes—
267C8×C13#13512yes—
268#1055—22no—
269#1055—21no—
270#1055—21no—
271#1055—21no—
272#1055—21no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276#529—131no—
277C4×#41C2×D1311yescharacteristic
278#485—131no—
279#482—131no—
280#479—131no—
281#478—131no—
282#464—131no—
283#463—131no—
284#452—131no—
285#449—131no—
286#446—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293C4×D8—131no—
294#436—21no—
295#436—21no—
296#436—131no—
297#436—261no—
298#436C2×D1311yescharacteristic
299#436C2×D1311yescharacteristic
300#435—261no—
301C8×D4—131no—
302#433—261no—
303#432—21no—
304#432C2×D1311yescharacteristic
305#431—131no—
306#431—131no—
307#405—261no—
308C4×M16—21no—
309C4×M16C2×D1311yescharacteristic
310C2×C4×C8—131no—
311#335—131no—
312#335—131no—
313#334—131no—
314#334—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8—131no—
318Q8⋊C8—131no—
319D4⋊C8—131no—
320D4⋊C8—131no—
321D4⋊C8—131no—
322D4⋊C8—131no—
323#322—131no—
324#322—131no—
325C82—131no—
326C82—131no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13C2×C4×D411yescharacteristic
334C2×D13—41no—
335C2×D13—41no—
336C2×D13—41no—
337C4×C13—21no—
338C4×C13—22no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—21no—
342C4×C13—41no—
343C4×C13—41no—
344C4×C13C2×#13111yescharacteristic
345C4×C13#56811yescharacteristic
346C4×C13C2×#13511yescharacteristic
347C4×C13C2×#13511yescharacteristic
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351C2×#41C4×D1311yescharacteristic
352C2×Q16—131no—
353C2×SD16—131no—
354C2×SD16—131no—
355C2×D8—131no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—261no—
359C2×M16C22⋊D1311yescharacteristic
360C2×M16C22⋊D1311yescharacteristic
361C22×C8—261no—
362C22×C8—261no—
363#126—261no—
364#125—131no—
365#124—131no—
366#123—261no—
367C22⋊Q8—131no—
368#121—131no—
369C4×Q8—131no—
370C4×Q8C4×D1311yescharacteristic
371C4×Q8C22×D1311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—131no—
375C4×D4—261no—
376C4×D4C4×D1311yescharacteristic
377C4×D4C22×D1311yescharacteristic
378#117—21no—
379#117—261no—
380#117C4×D1311yescharacteristic
381C2×C42—21no—
382C2×C42C22×D1311yescharacteristic
383#107—131no—
384#107—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8C22×D1311yescharacteristic
396C4⋊C8C22×D1311yescharacteristic
397#103—131no—
398#103—131no—
399#103—131no—
400#103—131no—
401#102—131no—
402#102—131no—
403#102—131no—
404#102—131no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—131no—
409C22⋊C8—131no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—21no—
414#97—261no—
415#97C22⋊D1311yescharacteristic
416#97C22⋊D1311yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—131no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8—261no—
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C2×C13—41no—
429C2×C13—81no—
430C2×C13#293311yescharacteristic
431C2×C13C4×#13511yescharacteristic
432C2×C13#295611yescharacteristic
433D13—81no—
434#41—22no—
435#41—41no—
436C2×Q8—131no—
437C2×Q8C2×C4×D1311yescharacteristic
438C2×D4—21no—
439C2×D4—131no—
440C2×D4—261no—
441C2×D4C2×C4×D1311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—261no—
446C22×C4C2×C4×D1311yescharacteristic
447C22×C4#612711yescharacteristic
448C22×C4C2×C22⋊D1311yescharacteristic
449Q16—262no—
450SD16—262no—
451SD16—521no—
452D8—521no—
453M16—22no—
454M16—22no—
455M16—42no—
456M16—42no—
457M16—522no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—131no—
463C2×C8—131no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—522no—
469C2×C8—522no—
470C2×C8C2×C22⋊D1311yescharacteristic
471C2×C8C2×C22⋊D1311yescharacteristic
472C2×C8C2×C22⋊D1311yescharacteristic
473C2×C8C2×C22⋊D1311yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—131no—
477C4⋊C4—131no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4C2×C4×D1311yescharacteristic
483C4⋊C4C2×C4×D1311yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—261no—
496C42C2×C4×D1311yescharacteristic
497C42#612711yescharacteristic
498C42C2×C22⋊D1311yescharacteristic
499C42C23×D1311yescharacteristic
500C13#1799911yescharacteristic, complemented, Sylow
501C23—21no—
502C23—261no—
503C23C4×C22⋊D1311yescharacteristic
504Q8—21no—
505Q8—261no—
506Q8—261no—
507Q8#8816112yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—261no—
512D4—261no—
513D4—1041no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4C4×C22⋊D1311yescharacteristic
532C2×C4C4×C22⋊D1311yescharacteristic
533C2×C4C4×C22⋊D1311yescharacteristic
534C2×C4C22×C4×D1311yescharacteristic
535C2×C4C2×#612711yescharacteristic
536C2×C4C22×C22⋊D1311yescharacteristic
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—262no—
542C8—261no—
543C8—261no—
544C8—261no—
545C8—261no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8#8820412yes—
550C8#8820412yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—521no—
558C22—521no—
559C22—521no—
560C22C2×C4×C22⋊D1311yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—521no—
569C4—521no—
570C4—521no—
571C4C2×#8816111yescharacteristic
572C4#1171945011yescharacteristic
573C4C2×#8820411yescharacteristic
574C4C2×#8820411yescharacteristic
575C2—41no—
576C2—81no—
577C2—1041no—
578C2#1312356111yescharacteristic
579C2C4×#8820411yescharacteristic
580C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2971C2
socleC22×C13C2×C4×D4
prime radical#11718899C4
cosocleC42×C13C24
hypercenter#2971D13
hypocenterC13#17999
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13123840C2semidirect
3. #13113724C2semidirect
4. #13113719C2semidirect
5. #13113686C2semidirect
6. #13113679C2semidirect
7. #13113677C2semidirect
8. #13113663C2semidirect
9. C8×#6107C2semidirect
10. C8×#6106C2semidirect
11. #13113617C2semidirect
12. #13113294C2semidirect
13. #13113218C2semidirect
14. M16×#1055C2semidirect
15. C13×#2971C2semidirect
212. #2971D13semidirect
500. C13#17999semidirect

Maximal subgroups

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

subgroupindex
#131248542
#131238402
#131137242
#131137192
#131136862
#131136792
#131136772
#131136632
C8×#61072
C8×#61062
#131136172
#131132942
#131132182
M16×#10552
C13×#29712
#1799913