Finite Group Databasebeta

← #15833870

Subgroups — #15833870

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#13124856C211yesmaximal, characteristic
2#13123854C211yesmaximal, characteristic, complemented
3#13123840C211yesmaximal, characteristic, complemented
4#13113728C211yesmaximal, characteristic, complemented
5#13113722C211yesmaximal, characteristic, complemented
6#13113688C211yesmaximal, characteristic, complemented
7#13113681C211yesmaximal, characteristic, complemented
8#13113681C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10C8×Dic52C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113616C211yesmaximal, characteristic, complemented
13#13113297C211yesmaximal, characteristic, complemented
14#13113219C211yesmaximal, characteristic, complemented
15C8×C13×M16C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C4×#6127C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21#11718789—21no—
22#11718789—21no—
23#11718789—21no—
24#11718788—21no—
25#11718587C2211yescharacteristic
26#11718586C2211yescharacteristic
27#11718508C411yescharacteristic
28#11718506C411yescharacteristic
29#11718505C411yescharacteristic
30#11718490C411yescharacteristic
31#11718398C411yescharacteristic
32#11718395C411yescharacteristic
33#11718394C411yescharacteristic
34#11718384C411yescharacteristic
35#11718370—21no—
36#11718369—21no—
37#11718368—21no—
38#11718366—21no—
39C4×Dic52C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic
46C8×D52C2211yescharacteristic
47#11718340C2211yescharacteristic
48C8×Dic26C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C82×C13C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C2×#6127C2×C411yescharacteristic
68C2×C13×M16D411yescharacteristic
69C2×C13×M16D411yescharacteristic
70C22×C8×C13—21no—
71C2×C42×C13C2311yescharacteristic
72#88184C2×C411yescharacteristic
73#88183—21no—
74C4×C22⋊D13—21no—
75C4×C22⋊D13—21no—
76C4×C22⋊D13—21no—
77#88180C2×C411yescharacteristic
78#88178C2×C411yescharacteristic
79C2×Dic52C2×C411yescharacteristic
80C2×D104C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6094—21no—
84C2×#6094—21no—
85C2×#6094—21no—
86C2×C8×D13—21no—
87#88130—21no—
88#88129C2×C411yescharacteristic
89C4×D52C2×C411yescharacteristic
90C4×D52C2311yescharacteristic
91C4×D52C2311yescharacteristic
92#88126—21no—
93#88126—21no—
94C42×D13—21no—
95#88124C2×C411yescharacteristic
96C4×Dic26C2×C411yescharacteristic
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8C2×C411yescharacteristic
100C13×C4⋊C8C2×C411yescharacteristic
101C13×C22⋊C8C2×C411yescharacteristic
102C13×C22⋊C8C2×C411yescharacteristic
103C13×#97D411yescharacteristic
104C13×#97D411yescharacteristic
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055—21no—
114#88061C2×C411yescharacteristic
115#88061C2×C411yescharacteristic
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88058C2×C411yescharacteristic
123#88058C2×C411yescharacteristic
124#88057C2×C411yescharacteristic
125#88057C2×C411yescharacteristic
126#88056C2×C411yescharacteristic
127#88056C2×C411yescharacteristic
128#88056C2×C411yescharacteristic
129#88056C2×C411yescharacteristic
130#88055—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134#88054—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142#88043—21no—
143C4×#1055—21no—
144#17999—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×C22⋊D13—21no—
150#6127—22no—
151#6127—41no—
152C2×D52C22×C411yescharacteristic
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×Dic26C22×C411yescharacteristic
159C2×Dic26C22×C411yescharacteristic
160C13×M16—22no—
161C13×M16—22no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—42no—
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C22×C411yescharacteristic
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C42×C13C22×C411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C42×C13#4111yescharacteristic
176C42×C13C2411yescharacteristic
177C22⋊Dic13—21no—
178C22⋊Dic13—21no—
179#6103—21no—
180#6103—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203Dic52—22no—
204D104—41no—
205#6095—22no—
206#6095—41no—
207#6094—42no—
208#6094—42no—
209#6094—42no—
210C8×D13—42no—
211#3102—131no—
212#2971—131no—
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×M16D1311yescharacteristic, complemented
226C23×C13C4×D411yescharacteristic
227C22×D13—21no—
228C22×D13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C23×C411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C22⋊D13—42no—
241C22⋊D13—81no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248D52—21no—
249D52—21no—
250D52—21no—
251D52—21no—
252C4×D13—42no—
253C4×D13—41no—
254C4×D13—41no—
255C4×D13—41no—
256C4×D13—41no—
257C4×D13—81no—
258Dic26—21no—
259Dic26—21no—
260Dic26—21no—
261Dic26#13112yes—
262C8×C13—22no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—21no—
266C8×C13—21no—
267C8×C13—21no—
268C8×C13—21no—
269C8×C13—41no—
270C8×C13#13512yes—
271C8×C13#13512yes—
272#1055—41no—
273#1055—41no—
274#1055—41no—
275#1055—41no—
276#529—131no—
277C4×#41—131no—
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×Q8—131no—
289C8×Q8—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293C4×D8—131no—
294#436—131no—
295#436—131no—
296#436—131no—
297#436—261no—
298#436—261no—
299#436—261no—
300#435—261no—
301C8×D4—131no—
302#433—261no—
303#432—131no—
304#432—261no—
305#431—131no—
306#431C2×D1311yescharacteristic
307#405—261no—
308C4×M16—261no—
309C4×M16C2×D1311yescharacteristic
310C2×C4×C8C2×D1311yescharacteristic
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#322C2×D1311yescharacteristic
324#322C2×D1311yescharacteristic
325C82C2×D1311yescharacteristic
326C82C2×D1311yescharacteristic
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—21no—
330C22×C13C2×C4×D411yescharacteristic
331C2×D13—41no—
332C2×D13—41no—
333C2×D13—41no—
334C2×D13—41no—
335C2×D13—41no—
336C2×D13—41no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13C2×#13111yescharacteristic
342C4×C13#56811yescharacteristic
343C4×C13C2×#13511yescharacteristic
344C4×C13C2×#13511yescharacteristic
345Dic13—22no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351C2×#41—131no—
352C2×Q16—131no—
353C2×SD16—131no—
354C2×SD16—131no—
355C2×D8—131no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16D5211yescharacteristic
360C2×M16D5211yescharacteristic
361C22×C8—21no—
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×Q8—131no—
371C4×Q8—131no—
372C4×D4—131no—
373C4×D4—131no—
374C4×D4—131no—
375C4×D4—261no—
376C4×D4—261no—
377C4×D4—261no—
378#117—131no—
379#117—261no—
380#117—261no—
381C2×C42—261no—
382C2×C42C22×D1311yescharacteristic
383#107—131no—
384#107—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
390C4⋊C8—131no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8C4×D1311yescharacteristic
396C4⋊C8C4×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—261no—
406C22⋊C8—261no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8C4×D1311yescharacteristic
412C22⋊C8C4×D1311yescharacteristic
413#97—261no—
414#97—261no—
415#97D5211yescharacteristic
416#97D5211yescharacteristic
417C4×C8—21no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8—261no—
421C4×C8—261no—
422C4×C8C22×D1311yescharacteristic
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C4×C8C22×D1311yescharacteristic
427C4×C8C22×D1311yescharacteristic
428C2×C13—41no—
429C2×C13#293311yescharacteristic
430C2×C13C4×#13511yescharacteristic
431C2×C13#295611yescharacteristic
432D13—81no—
433D13—81no—
434#41—262no—
435#41—521no—
436C2×Q8—131no—
437C2×Q8—131no—
438C2×D4—131no—
439C2×D4—131no—
440C2×D4—261no—
441C2×D4—261no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4C2×C4×D1311yescharacteristic
447C22×C4C2×D5211yescharacteristic
448C22×C4#612711yescharacteristic
449Q16—262no—
450SD16—262no—
451SD16—521no—
452D8—521no—
453M16—22no—
454M16—22no—
455M16—522no—
456M16—522no—
457M16—522no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—42no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—522no—
466C2×C8C2×C4×D1311yescharacteristic
467C2×C8C2×C4×D1311yescharacteristic
468C2×C8C2×C4×D1311yescharacteristic
469C2×C8C2×C4×D1311yescharacteristic
470C2×C8C2×D5211yescharacteristic
471C2×C8C2×D5211yescharacteristic
472C2×C8C2×D5211yescharacteristic
473C2×C8C2×D5211yescharacteristic
474C4⋊C4—131no—
475C4⋊C4—131no—
476C4⋊C4—131no—
477C4⋊C4—131no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C22⋊C4—261no—
485C22⋊C4—261no—
486C22⋊C4—261no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—261no—
493C42—261no—
494C42—261no—
495C42—261no—
496C42C2×C4×D1311yescharacteristic
497C42C2×D5211yescharacteristic
498C42#612711yescharacteristic
499C42C23×D1311yescharacteristic
500C13#1799911yescharacteristic, complemented, Sylow
501C23—261no—
502C23—261no—
503C23C4×D5211yescharacteristic
504Q8—132no—
505Q8—261no—
506Q8—261no—
507Q8—261no—
508D4—261no—
509D4—261no—
510D4—261no—
511D4—261no—
512D4—522no—
513D4—1041no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—522no—
526C2×C4—521no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—1041no—
531C2×C4C4×D5211yescharacteristic
532C2×C4C4×D5211yescharacteristic
533C2×C4C4×D5211yescharacteristic
534C2×C4C22×C4×D1311yescharacteristic
535C2×C4C22×D5211yescharacteristic
536C2×C4C2×#612711yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—41no—
545C8—521no—
546C8—521no—
547C8—521no—
548C8—521no—
549C8#8815812yes—
550C8#8815812yes—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—521no—
555C22—521no—
556C22—521no—
557C22—521no—
558C22—521no—
559C22—521no—
560C22C2×C4×D5211yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—262no—
566C4—521no—
567C4—521no—
568C4—521no—
569C4—521no—
570C4—521no—
571C4C2×#8815811yescharacteristic
572C4C2×#8815811yescharacteristic
573C4D13×#13111yescharacteristic
574C4#1171945511yescharacteristic
575C2—41no—
576C2—1041no—
577C2—1041no—
578C2#1312356411yescharacteristic
579C2C4×#8815811yescharacteristic
580C2#1312374711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×M16C2
socleC22×C13C2×C4×D4
prime radical#11718395C4
cosocleC42×C13C24
hypercenterC8×M16D13
hypocenterC13#17999
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #13123854C2semidirect
3. #13123840C2semidirect
4. #13113728C2semidirect
5. #13113722C2semidirect
6. #13113688C2semidirect
7. #13113681C2semidirect
8. #13113681C2semidirect
9. #13113667C2semidirect
10. C8×Dic52C2semidirect
11. C8×#6095C2semidirect
12. #13113616C2semidirect
13. #13113297C2semidirect
14. #13113219C2semidirect
15. C8×C13×M16C2semidirect
225. C8×M16D13semidirect
500. C13#17999semidirect

Maximal subgroups

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

subgroupindex
#131248562
#131238542
#131238402
#131137282
#131137222
#131136882
#131136812
#131136672
C8×Dic522
C8×#60952
#131136162
#131132972
#131132192
C8×C13×M162
#1799913