Finite Group Databasebeta

← #16796403

Subgroups — #16796403

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131673C211yesmaximal, characteristic
2Q8×#6122C211yesmaximal, characteristic, complemented
3#13130483C211yesmaximal, characteristic, complemented
4#13130476C211yesmaximal, characteristic, complemented
5#13130461C211yesmaximal, characteristic, complemented
6#13130453C211yesmaximal, characteristic, complemented
7#13130449C211yesmaximal, characteristic, complemented
8#13130441C211yesmaximal, characteristic, complemented
9SD16⋊#1057C211yesmaximal, characteristic, complemented
10SD16×#1057C211yesmaximal, characteristic, complemented
11#13130400C211yesmaximal, characteristic, complemented
12#13130178C211yesmaximal, characteristic, complemented
13#13130171C211yesmaximal, characteristic
14#13130059C211yesmaximal, characteristic, complemented
15#137×Dic13C211yesmaximal, characteristic
16C2×C13×#137C411yescharacteristic
17#41×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19#11719158—21no—
20#11719158—21no—
21#11719158C2211yescharacteristic
22#11719158C2211yescharacteristic
23#11719158C2211yescharacteristic
24#11719158C2211yescharacteristic
25Q8×#1057C2211yescharacteristic
26Q8×#1057C2211yescharacteristic
27#11719144—21no—
28#11719144—21no—
29D4×#1057C2211yescharacteristic
30D4×#1057C2211yescharacteristic
31#11719130C2211yescharacteristic
32#11719129—21no—
33#11719129C2211yescharacteristic
34#11719128—21no—
35C4×#6122—21no—
36C4×#6122C2211yescharacteristic
37C4×#6122C2211yescharacteristic
38C2×#88110—21no—
39#11718893C411yescharacteristic
40#11718886C411yescharacteristic
41#11718845C411yescharacteristic
42#11718845C411yescharacteristic
43Q16×Dic13C2211yescharacteristic
44Q16×Dic13C2211yescharacteristic
45#11718825C411yescharacteristic
46#11718825C411yescharacteristic
47SD16×Dic13C2211yescharacteristic
48SD16×Dic13C2211yescharacteristic
49#11718782C411yescharacteristic
50M16×Dic13C2211yescharacteristic
51Q8⋊#1057C2211yescharacteristic
52Q8⋊#1057C2211yescharacteristic
53Q8⋊#1057C2211yescharacteristic
54Q8⋊#1057C2211yescharacteristic
55Q8⋊#1057C2211yescharacteristic
56Q8⋊#1057C2211yescharacteristic
57D4⋊#1057C2211yescharacteristic
58D4⋊#1057C2211yescharacteristic
59#11718256C2211yescharacteristic
60#11718255C2211yescharacteristic
61#11718254C2211yescharacteristic
62#11718253C2211yescharacteristic
63#1057⋊C8C2211yescharacteristic
64#1057⋊C8C2211yescharacteristic
65#11718251C2211yescharacteristic
66C8×#1057C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C22×Q8×C13C2×C411yescharacteristic
69C2×#6122—21no—
70C2×#6122—21no—
71C2×#6122D411yescharacteristic
72C2×#6122D411yescharacteristic
73C22×#1057—21no—
74C22×#1057—21no—
75C13×#137—24no—
76C2×C13×Q16C2×C411yescharacteristic
77C2×C13×Q16C2×C411yescharacteristic
78C2×C13×SD16C2×C411yescharacteristic
79C2×C13×SD16C2×C411yescharacteristic
80C2×C13×M16C2×C411yescharacteristic
81Q8×Dic13—21no—
82Q8×Dic13—21no—
83Q8×Dic13C2×C411yescharacteristic
84Q8×Dic13C2×C411yescharacteristic
85Q8×Dic13C2×C411yescharacteristic
86Q8×Dic13C2311yescharacteristic
87Q8×Dic13C2311yescharacteristic
88Q8×Dic13C2311yescharacteristic
89D4×Dic13—21no—
90D4×Dic13—21no—
91D4×Dic13C2×C411yescharacteristic
92D4×Dic13C2311yescharacteristic
93#88180—21no—
94#88180C2×C411yescharacteristic
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2×C411yescharacteristic
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13C2311yescharacteristic
100C2×#6099C2×C411yescharacteristic
101C22⋊#1057—21no—
102C22⋊#1057—21no—
103C22⋊#1057—21no—
104#88112—21no—
105#88112—21no—
106#88112—21no—
107#88112—21no—
108#88112—21no—
109#88110—21no—
110#88110—21no—
111#88110—21no—
112#88110—21no—
113#88110—21no—
114#88110—21no—
115#88110D411yescharacteristic
116#88110D411yescharacteristic
117C4⋊#1057—21no—
118C4⋊#1057—21no—
119C4⋊#1057C2311yescharacteristic
120C4⋊#1057C2311yescharacteristic
121C4⋊#1057C2311yescharacteristic
122C4⋊#1057C2311yescharacteristic
123C4×#1057—21no—
124C4×#1057—21no—
125C4×#1057C2311yescharacteristic
126C4×#1057C2311yescharacteristic
127C4×#1057C2311yescharacteristic
128C4×#1057C2311yescharacteristic
129#88075C2×C411yescharacteristic
130#88075C2×C411yescharacteristic
131#88075C2×C411yescharacteristic
132#88075C2×C411yescharacteristic
133#88075C2×C411yescharacteristic
134#88075C2×C411yescharacteristic
135#88072C2×C411yescharacteristic
136#88072C2×C411yescharacteristic
137#88058C2×C411yescharacteristic
138#88058C2×C411yescharacteristic
139#88057C2×C411yescharacteristic
140#88057C2×C411yescharacteristic
141#88055C2×C411yescharacteristic
142#88055C2×C411yescharacteristic
143C8×Dic13C2311yescharacteristic
144C8×Dic13C2311yescharacteristic
145#18047—131nomaximal, Sylow
146C13×#41—22no—
147C13×#41—41no—
148C2×Q8×C13—21no—
149C2×Q8×C13—22no—
150C2×Q8×C13—41no—
151C2×Q8×C13C22×C411yescharacteristic
152C2×Q8×C13C22×C411yescharacteristic
153C2×Q8×C13C22×C411yescharacteristic
154C2×D4×C13—21no—
155C2×D4×C13C22×C411yescharacteristic
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13C22×C411yescharacteristic
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13C2×D411yescharacteristic
163C22×Dic13#4111yescharacteristic
164#6122—22no—
165#6122—41no—
166#6122—42no—
167#6122—42no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—42no—
175C2×#1057—42no—
176C2×#1057C2×D411yescharacteristic
177C2×#1057C2×D411yescharacteristic
178C2×#1057C2×D411yescharacteristic
179C2×#1057C2×D411yescharacteristic
180C13×Q16—22no—
181C13×Q16—22no—
182C13×SD16—22no—
183C13×SD16M1614yescomplemented
184C13×M16—22no—
185C2×C8×C13C22×C411yescharacteristic
186C2×C8×C13C22×C411yescharacteristic
187C22⋊Dic13—21no—
188C22⋊Dic13—21no—
189C22⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13C22×C411yescharacteristic
198C4⋊Dic13C22×C411yescharacteristic
199C4⋊Dic13C22×C411yescharacteristic
200C4⋊Dic13C22×C411yescharacteristic
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208C4×Dic13C22×C411yescharacteristic
209C4×Dic13C2×D411yescharacteristic
210C4×Dic13#4111yescharacteristic
211C4×Dic13C2411yescharacteristic
212#6099—41no—
213C2×#1055C22×C411yescharacteristic
214C2×#1055C22×C411yescharacteristic
215#2970—131no—
216Q8×M16—131no—
217C4×#137—131no—
218#1593—131no—
219#1591—131no—
220#1587—131no—
221#1585—131no—
222#1584—131no—
223#1582—131no—
224SD16⋊C8—131no—
225C8×SD16—131no—
226#1569—131no—
227#1491—131no—
228#1489—131no—
229#1455—131no—
230C23×C13—21no—
231C23×C13C4×D411yescharacteristic
232Q8×C13—21no—
233Q8×C13—21no—
234Q8×C13—21no—
235Q8×C13—21no—
236Q8×C13—21no—
237Q8×C13—42no—
238Q8×C13C2×M1612yes—
239D4×C13—21no—
240D4×C13—42no—
241D4×C13C2×M1612yes—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13C4×D411yescharacteristic
250C2×C4×C13C23×C411yescharacteristic
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—81no—
261C2×Dic13—81no—
262C2×Dic13C4×D411yescharacteristic
263C2×Dic13C4×D411yescharacteristic
264C2×Dic13C22×D411yescharacteristic
265C2×Dic13C2×#4111yescharacteristic
266#1057—22no—
267#1057—21no—
268#1057—21no—
269#1057—21no—
270#1057—41no—
271#1057—41no—
272#1057—41no—
273#1057—41no—
274#1057—41no—
275#1057#13712yescomplemented
276C8×C13—21no—
277C8×C13C2×M1612yes—
278#1055—21no—
279#1055—21no—
280C2×#137#26111yescharacteristic
281C4×#41—131no—
282C2×C4×Q8—131no—
283#446—131no—
284#446—131no—
285#446—131no—
286#446—131no—
287#446—261no—
288#446—261no—
289C8×Q8—131no—
290C8×Q8—131no—
291#441—131no—
292#441—131no—
293#440—131no—
294#440—131no—
295C4×Q16—131no—
296C4×Q16—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299#435—261no—
300#435—261no—
301C8×D4—131no—
302C8×D4—131no—
303#432—131no—
304#432—261no—
305#428—131no—
306#423—131no—
307#423—261no—
308#419—131no—
309#417—131no—
310C4×M16—131no—
311C4×M16—131no—
312C4×M16—131no—
313C4×M16—261no—
314C2×#97—261no—
315#335—131no—
316#335—131no—
317#334—131no—
318#334—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8—131no—
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327#322—131no—
328#322—131no—
329#322—131no—
330C82—131no—
331C22×C13—21no—
332C22×C13—22no—
333C22×C13—21no—
334C22×C13—21no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13C2×C4×D411yescharacteristic
338C4×C13—21no—
339C4×C13—22no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13C22×M1611yescharacteristic
343C4×C13#56811yescharacteristic
344Dic13—21no—
345Dic13—21no—
346Dic13—21no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350Dic13—41no—
351Dic13C2×#13711yescharacteristic
352Dic13#57511yescharacteristic
353C2×#41C2×#26111yescharacteristic
354C22×Q8C2×#26111yescharacteristic
355#137—24no—
356C2×Q16C2×#26111yescharacteristic
357C2×Q16C2×#26111yescharacteristic
358C2×SD16C2×#26111yescharacteristic
359C2×SD16C2×#26111yescharacteristic
360C2×M16—131no—
361C2×M16—131no—
362C2×M16—131no—
363C2×M16—261no—
364C2×M16—261no—
365C2×M16C2×#26111yescharacteristic
366C22×C8—261no—
367C22×C8—261no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—131no—
371C4×Q8—131no—
372C4×Q8—131no—
373C4×Q8—131no—
374C4×Q8—261no—
375C4×Q8—261no—
376C4×D4—131no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4—261no—
380#117—131no—
381#117—261no—
382C2×C4⋊C4—131no—
383C2×C4⋊C4—261no—
384C2×C42—131no—
385C2×C42—261no—
386C2×C42—261no—
387#107—131no—
388#107—131no—
389#106—131no—
390#106—131no—
391C4⋊C8—131no—
392C4⋊C8—131no—
393C4⋊C8—131no—
394C4⋊C8—131no—
395C4⋊C8—261no—
396C4⋊C8—261no—
397C4⋊C8—261no—
398C4⋊C8—261no—
399C4⋊C8—261no—
400C4⋊C8—261no—
401C4⋊C8—261no—
402#103—131no—
403#103—131no—
404#103—131no—
405#103—131no—
406#103—131no—
407#103—131no—
408#102—131no—
409#102—131no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—131no—
414#97—131no—
415#97—131no—
416#97—131no—
417#97—261no—
418#97—261no—
419#97—261no—
420#97—261no—
421#97—261no—
422#97—261no—
423C4×C8—131no—
424C4×C8—131no—
425C4×C8—131no—
426C4×C8—131no—
427C4×C8—131no—
428C4×C8—131no—
429C4×C8—261no—
430C4×C8—261no—
431C2×C13—41no—
432C2×C13—42no—
433C2×C13D4×M1611yescharacteristic
434C2×C13C4×#13711yescharacteristic
435C2×C13#295611yescharacteristic
436#41—22no—
437#41—41no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—41no—
441C2×Q8C22×#26111yescharacteristic
442C2×Q8C22×#26111yescharacteristic
443C2×Q8C22×#26111yescharacteristic
444C2×D4—21no—
445C2×D4C22×#26111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—131no—
449C22×C4—131no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—261no—
453C22×C4C22×#26111yescharacteristic
454Q16—22no—
455Q16—22no—
456SD16—22no—
457SD16#612214yescomplemented
458M16—22no—
459M16—262no—
460M16—521no—
461M16—521no—
462M16—522no—
463M16—522no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—131no—
468C2×C8—131no—
469C2×C8—131no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—522no—
477C2×C8—522no—
478C2×C8C22×#26111yescharacteristic
479C2×C8C22×#26111yescharacteristic
480C4⋊C4—131no—
481C4⋊C4—131no—
482C4⋊C4—131no—
483C4⋊C4—131no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C22⋊C4—261no—
492C22⋊C4—261no—
493C22⋊C4—261no—
494C42—131no—
495C42—131no—
496C42—131no—
497C42—131no—
498C42—261no—
499C42—261no—
500C42—261no—
501C42—261no—
502C42—261no—
503C42—261no—
504C42—261no—
505C13#1804711yescharacteristic, complemented, Sylow
506C23—21no—
507C23D4×#26111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—42no—
514Q8C2×#612212yes—
515D4—21no—
516D4—42no—
517D4C2×#612212yes—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—131no—
526C2×C4—131no—
527C2×C4—131no—
528C2×C4—131no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4—521no—
538C2×C4—1041no—
539C2×C4—1041no—
540C2×C4D4×#26111yescharacteristic
541C2×C4C23×#26111yescharacteristic
542C8—21no—
543C8—132no—
544C8—261no—
545C8—261no—
546C8—261no—
547C8—262no—
548C8—261no—
549C8—261no—
550C8—521no—
551C8—521no—
552C8—521no—
553C8—521no—
554C8—521no—
555C8C2×#612212yes—
556C22—21no—
557C22—22no—
558C22—21no—
559C22—21no—
560C22—41no—
561C22—41no—
562C22C2×D4×#26111yescharacteristic
563C4—21no—
564C4—22no—
565C4—41no—
566C4—41no—
567C4—131no—
568C4—131no—
569C4—261no—
570C4—261no—
571C4—261no—
572C4—521no—
573C4—521no—
574C4—521no—
575C4—521no—
576C4#1171962111yescharacteristic
577C4C22×#612211yescharacteristic
578C2—41no—
579C2—42no—
580C2D4×#612211yescharacteristic
581C2#137×#26111yescharacteristic
582C2#1313161111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC2×C13×#137C4
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC4×Dic13C24
hypercenterC2×#137#261
hypocenterC13#18047
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. Q8×#6122C2semidirect
3. #13130483C2semidirect
4. #13130476C2semidirect
5. #13130461C2semidirect
6. #13130453C2semidirect
7. #13130449C2semidirect
8. #13130441C2semidirect
9. SD16⋊#1057C2semidirect
10. SD16×#1057C2semidirect
11. #13130400C2semidirect
12. #13130178C2semidirect
14. #13130059C2semidirect
183. C13×SD16M16semidirect
275. #1057#137semidirect
457. SD16#6122semidirect
505. C13#18047semidirect

Maximal subgroups

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

subgroupindex
#131316732
Q8×#61222
#131304832
#131304762
#131304612
#131304532
#131304492
#131304412
SD16⋊#10572
SD16×#10572
#131304002
#131301782
#131301712
#131300592
#137×Dic132
#1804713