Finite Group Databasebeta

← #15834666

Subgroups — #15834666

Order 3328.

652 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123960C211yesmaximal, characteristic, complemented
2#13123959C211yesmaximal, characteristic, complemented
3C4×#88170C211yesmaximal, characteristic
4#13113743C211yesmaximal, characteristic, complemented
5#13113742C211yesmaximal, characteristic, complemented
6#13113674C211yesmaximal, characteristic, complemented
7#13113673C211yesmaximal, characteristic, complemented
8#13113671C211yesmaximal, characteristic, complemented
9#13113658C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113590C211yesmaximal, characteristic, complemented
12#13113274C211yesmaximal, characteristic, complemented
13#13113272C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1582C211yesmaximal, characteristic, complemented
16C2×#88170C411yescharacteristic
17C4×#6131C2211yescharacteristic
18C4×#6129C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22SD16×Dic13C411yescharacteristic
23#11718772—21no—
24C2×#88054—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6104C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718521C411yescharacteristic
30#11718513C411yescharacteristic
31#11718498C2211yescharacteristic
32#11718498C2211yescharacteristic
33#11718497—21no—
34#11718495C2211yescharacteristic
35D13×C4⋊C8—21no—
36#11718492C2211yescharacteristic
37#11718465C411yescharacteristic
38#11718451C411yescharacteristic
39#11718433C411yescharacteristic
40#11718417C411yescharacteristic
41#11718391—21no—
42#11718380—21no—
43#11718367—21no—
44#11718366—21no—
45C4×#6095C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47C8×D52C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×#6129C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C22×C8×C13—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75D4×Dic13C2×C411yescharacteristic
76C2×#6104C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78C2×C4×Dic13—21no—
79C22×#1055—21no—
80#88170—24no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87C2×C8×D13C2×C411yescharacteristic
88C2×C8×D13C2×C411yescharacteristic
89#88147—21no—
90#88147C2×C411yescharacteristic
91#88146—21no—
92#88146C2×C411yescharacteristic
93#88146C2×C411yescharacteristic
94#88141C2×C411yescharacteristic
95#88135—21no—
96#88131—21no—
97C4×D52—21no—
98C4×D52C2311yescharacteristic
99C42×D13—21no—
100C42×D13C2311yescharacteristic
101C4×Dic26C2311yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×C4⋊C8—21no—
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×C22⋊C8—21no—
109C13×#97—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88075C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060D411yescharacteristic
120#88060D411yescharacteristic
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055—21no—
125#88055—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054D411yescharacteristic
131#88054D411yescharacteristic
132C8×Dic13C2×C411yescharacteristic
133C8×Dic13C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141#88043—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18065—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152#6131—22no—
153#6131—41no—
154#6129—22no—
155#6129—41no—
156C2×D52—21no—
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13C22×C411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13#4111yescharacteristic
164C2×Dic26C22×C411yescharacteristic
165C13×SD16—22no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—81no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C22⋊C4—21no—
178C42×C13—21no—
179C42×C13C2411yescharacteristic
180C22⋊Dic13—21no—
181#6107—22no—
182#6104M1614yescomplemented
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13C22×C411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199C4×Dic13#4111yescharacteristic
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—81no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6095—22no—
209#6094—42no—
210#6094—81no—
211#6094—81no—
212C8×D13—22no—
213C8×D13—41no—
214C8×D13—81no—
215C8×D13—81no—
216#2990—131no—
217#2990—131no—
218C4×#135—131no—
219#1593—131no—
220#1593—131no—
221#1582—131no—
222#1582—131no—
223#1582—131no—
224#1582D1311yescharacteristic, complemented
225#1580—131no—
226#1580—131no—
227#1566—131no—
228#1489—131no—
229#1489—131no—
230#1451—131no—
231C23×C13—21no—
232C22×D13—21no—
233C22×D13C4×D411yescharacteristic
234Q8×C13—21no—
235Q8×C13—21no—
236D4×C13—21no—
237D4×C13C2×M1612yes—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—42no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254C2×Dic13C4×D411yescharacteristic
255D52—21no—
256D52—42no—
257D52C2×M1612yes—
258C4×D13—21no—
259C4×D13—21no—
260C4×D13—21no—
261C4×D13—21no—
262C4×D13—22no—
263C4×D13—42no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—42no—
267Dic26—21no—
268Dic26—21no—
269C8×C13—21no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282#1055C2×M1612yes—
283C2×#135—131no—
284C4×#41—131no—
285C4×#41—131no—
286#446—131no—
287#446—131no—
288#446—131no—
289#446C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294C4×SD16—131no—
295C4×SD16C2×D1311yescharacteristic
296C4×D8—131no—
297C4×D8—131no—
298#435—261no—
299#435—261no—
300#435—261no—
301#435—261no—
302C8×D4—131no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4C2×D1311yescharacteristic
306#432—261no—
307#432—261no—
308#431—131no—
309#427—131no—
310#423—131no—
311#423—131no—
312C2×C4⋊C8—261no—
313C2×C4⋊C8—261no—
314#416—131no—
315#416—131no—
316C4×M16—131no—
317C2×C4×C8—131no—
318#334—131no—
319#334—131no—
320#334—131no—
321#334C2×D1311yescharacteristic
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325Q8⋊C8C2×D1311yescharacteristic
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8C2×D1311yescharacteristic
330#322—131no—
331#322—131no—
332#322—131no—
333#322C2×D1311yescharacteristic
334C22×C13—22no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13C2×C4×D411yescharacteristic
338C2×D13—21no—
339C2×D13—22no—
340C2×D13—21no—
341C2×D13—21no—
342C2×D13—41no—
343C2×D13—41no—
344C4×C13—21no—
345C4×C13—41no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13C22×M1611yescharacteristic
349C4×C13#56811yescharacteristic
350C4×C13#57711yescharacteristic
351C4×C13#57711yescharacteristic
352Dic13—21no—
353Dic13—21no—
354Dic13—41no—
355Dic13—41no—
356Dic13—41no—
357Dic13#44412yes—
358C2×#41—131no—
359C2×#41—131no—
360#135—264no—
361C2×Q16—131no—
362C2×SD16—131no—
363C2×SD16C4×D1311yescharacteristic
364C2×D8—131no—
365C2×M16—261no—
366C2×M16—261no—
367C2×M16—261no—
368C22×C8—21no—
369C22×C8—131no—
370C22×C8—131no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C4×Q8—131no—
375C4×Q8—131no—
376C4×Q8—131no—
377C4×Q8C22×D1311yescharacteristic
378C4×D4—131no—
379C4×D4—131no—
380C4×D4—131no—
381C4×D4—261no—
382C4×D4—261no—
383C4×D4—261no—
384C4×D4—261no—
385C4×D4C22×D1311yescharacteristic
386#117—131no—
387#117—131no—
388#117—261no—
389#117—261no—
390C2×C42—131no—
391C2×C42—261no—
392C2×C42—261no—
393#107—131no—
394#107—131no—
395#106—131no—
396#106C4×D1311yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8C22×D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409#103—131no—
410#103—131no—
411#103—131no—
412#103C4×D1311yescharacteristic
413#102—131no—
414#102—131no—
415#102—131no—
416#102C4×D1311yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—131no—
419C22⋊C8—131no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423#97—21no—
424#97—261no—
425#97—261no—
426#97—261no—
427#97—261no—
428C4×C8—131no—
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8C22×D1311yescharacteristic
434C4×C8C22×D1311yescharacteristic
435C4×C8C22×D1311yescharacteristic
436C2×C13—42no—
437C2×C13D4×M1611yescharacteristic
438C2×C13#295211yescharacteristic
439C2×C13C2×#44411yescharacteristic
440D13—41no—
441D13—42no—
442#41—262no—
443#41—262no—
444#41—521no—
445#41—521no—
446C2×Q8—131no—
447C2×Q8C2×C4×D1311yescharacteristic
448C2×D4—131no—
449C2×D4—261no—
450C2×D4—261no—
451C2×D4C2×C4×D1311yescharacteristic
452C22×C4—21no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461Q16—262no—
462SD16—22no—
463SD16—262no—
464D8—134no—
465M16—522no—
466M16—1041no—
467M16—1041no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—81no—
472C2×C8—131no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—262no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—521no—
481C2×C8—1041no—
482C2×C8—1041no—
483C2×C8—1041no—
484C2×C8C2×C4×D1311yescharacteristic
485C2×C8C2×C4×D1311yescharacteristic
486C2×C8D4×D1311yescharacteristic
487C2×C8D4×D1311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—131no—
490C4⋊C4—131no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4C2×C4×D1311yescharacteristic
495C4⋊C4C2×C4×D1311yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—261no—
498C22⋊C4—261no—
499C22⋊C4—261no—
500C22⋊C4—261no—
501C22⋊C4—261no—
502C42—21no—
503C42—131no—
504C42—131no—
505C42—131no—
506C42—261no—
507C42—261no—
508C42—261no—
509C42—261no—
510C42—261no—
511C42C23×D1311yescharacteristic
512C13#1806511yescharacteristic, complemented, Sylow
513C23—21no—
514C23—131no—
515C23—261no—
516Q8—21no—
517Q8—21no—
518Q8—261no—
519Q8—261no—
520D4—21no—
521D4—132no—
522D4—261no—
523D4—522no—
524D4—522no—
525D4M16×D1312yes—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—131no—
532C2×C4—131no—
533C2×C4—131no—
534C2×C4—262no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—522no—
543C2×C4—522no—
544C2×C4—522no—
545C2×C4—522no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4C2×D4×D1311yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—132no—
559C8—261no—
560C8—261no—
561C8—261no—
562C8—521no—
563C8—521no—
564C8—521no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—261no—
569C22—261no—
570C22—261no—
571C22—262no—
572C22—521no—
573C22—521no—
574C22C4×D4×D1311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—132no—
580C4—261no—
581C4—261no—
582C4—521no—
583C4—521no—
584C4—521no—
585C4C2×M16×D1311yescharacteristic
586C4#1171945511yescharacteristic
587C4#1171946711yescharacteristic
588C4#1171947511yescharacteristic
589C2—42no—
590C2—521no—
591C2—522no—
592C2#1312356911yescharacteristic
593C2#1312371411yescharacteristic
594C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1582C2
socleC22×C13C2×C4×D4
prime radicalC2×#88170C4
cosocleC42×C13C24
hypercenter#1582D13
hypocenterC13#18065
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
1. #13123960C2semidirect
2. #13123959C2semidirect
4. #13113743C2semidirect
5. #13113742C2semidirect
6. #13113674C2semidirect
7. #13113673C2semidirect
8. #13113671C2semidirect
9. #13113658C2semidirect
10. #13113657C2semidirect
11. #13113590C2semidirect
12. #13113274C2semidirect
13. #13113272C2semidirect
14. #13113124C2semidirect
15. C13×#1582C2semidirect
182. #6104M16semidirect
224. #1582D13semidirect
512. C13#18065semidirect

Maximal subgroups

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

subgroupindex
#131239602
#131239592
C4×#881702
#131137432
#131137422
#131136742
#131136732
#131136712
#131136582
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