Finite Group Databasebeta

← #15833124

Subgroups — #15833124

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124842C211yesmaximal, characteristic
2#13123765C211yesmaximal, characteristic, complemented
3D13×#436C211yesmaximal, characteristic
4#13113729C211yesmaximal, characteristic, complemented
5#13113727C211yesmaximal, characteristic, complemented
6#13113725C211yesmaximal, characteristic, complemented
7#13113723C211yesmaximal, characteristic, complemented
8#13113681C211yesmaximal, characteristic, complemented
9#13113679C211yesmaximal, characteristic, complemented
10#13113677C211yesmaximal, characteristic, complemented
11#13113605C211yesmaximal, characteristic, complemented
12#13113259C211yesmaximal, characteristic
13#13113237C211yesmaximal, characteristic, complemented
14#13113121C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16C2×M16×D13—21no—
17#11719283C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic, complemented
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22#11718830C411yescharacteristic
23#11718823C411yescharacteristic
24#11718789—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718531C411yescharacteristic
30#11718523C411yescharacteristic
31#11718500—21no—
32#11718499C2211yescharacteristic
33#11718498C2211yescharacteristic
34D13×C4⋊C8C2211yescharacteristic
35#11718492C2211yescharacteristic, complemented
36#11718489—21no—
37#11718479C411yescharacteristic
38#11718466C411yescharacteristic
39#11718437C411yescharacteristic
40#11718422C411yescharacteristic
41#11718390—21no—
42D13×C22⋊C8—21no—
43C4×#6095C2211yescharacteristic
44#11718350—21no—
45#11718349C2211yescharacteristic
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic, complemented
51C13×#334C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65C8×#1055C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×M16—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73#88200C2×C411yescharacteristic
74#88198C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C2×#6099—21no—
80M16×D13—44no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094—21no—
85C2×C8×D13—21no—
86C2×C8×D13D411yescharacteristic
87C2×C8×D13D411yescharacteristic
88#88151C2×C411yescharacteristic
89#88150—21no—
90#88147C2×C411yescharacteristic
91C4⋊C4×D13C2×C411yescharacteristic
92#88143—21no—
93#88142C2×C411yescharacteristic
94#88135—21no—
95C22⋊C4×D13—21no—
96C4×D52C2311yescharacteristic
97#88126—21no—
98C42×D13C2311yescharacteristic
99C4×Dic26—21no—
100C4×Dic26C2311yescharacteristic
101C13×#106C2×C411yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×C22⋊C8—21no—
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115#88061C2×C411yescharacteristic
116#88060—21no—
117#88060—21no—
118#88060—21no—
119#88060C2×C411yescharacteristic
120#88060C2×C411yescharacteristic
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054C2×C411yescharacteristic
130#88054C2×C411yescharacteristic
131C8×Dic13—21no—
132C8×Dic13D411yescharacteristic
133C8×Dic13D411yescharacteristic
134#88050C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141#88043—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17930—131nomaximal, Sylow
146C23×D13—21no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152D4×D13—41no—
153D4×D13—41no—
154C2×D52C22×C411yescharacteristic
155C2×C4×D13—21no—
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C2×C4×D13C22×C411yescharacteristic
161C2×C4×D13C2×D411yescharacteristic
162C2×C4×D13#4111yescharacteristic
163C2×Dic26—21no—
164C2×Dic26C22×C411yescharacteristic
165C13×SD16—41no—
166C13×M16—42no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
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#6106—41no—
182#6105—41no—
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—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13C22×C411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199C4×Dic13#4111yescharacteristic
200#6099—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6095—41no—
209#6094—42no—
210#6094—42no—
211#6094—42no—
212C8×D13—22no—
213C8×D13—42no—
214C8×D13SD1614yescomplemented
215#3101—131no—
216#2960—131no—
217C2×#436—131no—
218#1590—131no—
219#1590—131no—
220#1590—131no—
221#1590—131no—
222#1583—131no—
223#1583—131no—
224#1583—131no—
225#1583D1311yescharacteristic, complemented
226#1570—131no—
227#1486—131no—
228#1481—131no—
229#1450—131no—
230C23×C13—21no—
231C22×D13—21no—
232C22×D13—42no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13C4×D411yescharacteristic
236Q8×C13—21no—
237Q8×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13C23×C411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C22⋊D13—42no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—42no—
253C2×Dic13C4×D411yescharacteristic
254C2×Dic13C4×D411yescharacteristic
255C2×Dic13C4×D411yescharacteristic
256D52—21no—
257D52—21no—
258C4×D13—21no—
259C4×D13—21no—
260C4×D13—41no—
261C4×D13—42no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—42no—
265C4×D13C2×SD1612yes—
266C4×D13#13512yes—
267Dic26—21no—
268Dic26—21no—
269Dic26—42no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13C2×SD1612yes—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055C2×SD1612yes—
284C22×M16—261no—
285#533—131no—
286C2×C4×D4—131no—
287#483—131no—
288#483—131no—
289#476—131no—
290#476—131no—
291#461—131no—
292#461—131no—
293#450—131no—
294#450—131no—
295#446—131no—
296#446—131no—
297#446—261no—
298C8×Q8—131no—
299C8×Q8—261no—
300C8×Q8C2×D1311yescharacteristic, complemented
301C4×SD16—131no—
302C4×SD16—131no—
303C4×SD16—131no—
304C4×SD16C2×D1311yescharacteristic
305#436—131no—
306#436—131no—
307#436—131no—
308#436—261no—
309#436—261no—
310#436C2×D1311yescharacteristic
311#431—131no—
312#431—131no—
313#424—261no—
314#423—131no—
315C2×C4⋊C8—131no—
316C2×C22⋊C8—261no—
317#405—261no—
318C2×C4×C8—131no—
319#334—131no—
320#334—131no—
321#334—131no—
322#334C2×D1311yescharacteristic, complemented
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326Q8⋊C8C2×D1311yescharacteristic, complemented
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8C2×D1311yescharacteristic
331#322—131no—
332#322C2×D1311yescharacteristic, complemented
333C82—131no—
334C82—131no—
335C22×C13—41no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13C2×C4×D411yescharacteristic
339C2×D13—21no—
340C2×D13—21no—
341C2×D13—41no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—84no—
345C2×D13C4×SD1612yes—
346C4×C13—21no—
347C4×C13—41no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13#56811yescharacteristic
351C4×C13#56811yescharacteristic
352C4×C13C22×SD1611yescharacteristic
353C4×C13C2×#13511yescharacteristic
354Dic13—21no—
355Dic13—21no—
356Dic13—41no—
357Dic13—41no—
358Dic13—41no—
359Dic13C4×SD1612yes—
360C22×D4—131no—
361C23×C4—261no—
362C2×SD16—131no—
363C2×SD16—131no—
364C2×SD16—131no—
365C2×SD16C4×D1311yescharacteristic
366C2×M16—21no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—524no—
372C22×C8—131no—
373C22×C8—131no—
374C22×C8—261no—
375C4⋊Q8—131no—
376C4⋊Q8—131no—
377#125—261no—
378C22⋊Q8—131no—
379C22⋊Q8—131no—
380C22⋊Q8—261no—
381C4×Q8—131no—
382C4×Q8—261no—
383C4×Q8C22×D1311yescharacteristic
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—261no—
388C4×D4—261no—
389C4×D4C22×D1311yescharacteristic
390#117—261no—
391C2×C4⋊C4—131no—
392C2×C22⋊C4—261no—
393C2×C42—131no—
394#106—131no—
395#106—131no—
396#106—131no—
397#106C4×D1311yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8C22×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411#103—131no—
412#103—131no—
413#103—131no—
414#103C4×D1311yescharacteristic
415#102—131no—
416#102—131no—
417#102—131no—
418#102C4×D1311yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426#97—261no—
427#97—261no—
428C4×C8—21no—
429C4×C8—131no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C2×C13—81no—
439C2×C13#293011yescharacteristic
440C2×C13C2×C4×SD1611yescharacteristic
441C2×C13#295511yescharacteristic
442D13—22no—
443D13—81no—
444C24—261no—
445C2×Q8—131no—
446C2×Q8—261no—
447C2×Q8C2×C4×D1311yescharacteristic
448C2×D4—131no—
449C2×D4—261no—
450C2×D4—521no—
451C2×D4—521no—
452C2×D4C2×C4×D1311yescharacteristic
453C22×C4—21no—
454C22×C4—131no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—522no—
462C22×C4—522no—
463SD16—41no—
464SD16—521no—
465SD16—521no—
466SD16—521no—
467M16—42no—
468M16—522no—
469M16—522no—
470M16—522no—
471M16—522no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—131no—
476C2×C8—134no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—262no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—522no—
485C2×C8C2×C4×D1311yescharacteristic
486C2×C8C2×C4×D1311yescharacteristic
487C2×C8D4×D1311yescharacteristic
488C2×C8D4×D1311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—131no—
491C4⋊C4—131no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4C2×C4×D1311yescharacteristic
500C4⋊C4C2×C4×D1311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C42—21no—
508C42—131no—
509C42—131no—
510C42—131no—
511C42—261no—
512C42C23×D1311yescharacteristic
513C13#1793011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—131no—
516C23—261no—
517C23—522no—
518C23—522no—
519C23—522no—
520Q8—21no—
521Q8—21no—
522Q8—261no—
523Q8—261no—
524Q8—522no—
525D4—21no—
526D4—21no—
527D4—261no—
528D4—261no—
529D4—522no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—131no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—131no—
539C2×C4—131no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—521no—
546C2×C4—522no—
547C2×C4—522no—
548C2×C4—522no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4C22×C4×D1311yescharacteristic
552C2×C4C2×D4×D1311yescharacteristic
553C2×C4#41×D1311yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—132no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—521no—
565C8—521no—
566C8—521no—
567C8SD16×D1312yes—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—132no—
572C22—261no—
573C22—261no—
574C22—521no—
575C22—521no—
576C22—521no—
577C22—1044no—
578C22C4×D4×D1311yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—132no—
584C4—261no—
585C4—261no—
586C4—521no—
587C4—521no—
588C4—521no—
589C4#1171945011yescharacteristic
590C4#1171945511yescharacteristic
591C4C2×SD16×D1311yescharacteristic
592C4D13×#13511yescharacteristic
593C2—81no—
594C2—262no—
595C2—1041no—
596C2#1312353411yescharacteristic
597C2C4×SD16×D1311yescharacteristic
598C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C2×C4
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#17930
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #13123765C2semidirect
4. #13113729C2semidirect
5. #13113727C2semidirect
6. #13113725C2semidirect
7. #13113723C2semidirect
8. #13113681C2semidirect
9. #13113679C2semidirect
10. #13113677C2semidirect
11. #13113605C2semidirect
13. #13113237C2semidirect
14. #13113121C2semidirect
15. C13×#1583C2semidirect
19. C8×Q8×C13C22semidirect
26. #11718685C22semidirect
35. #11718492C22semidirect
50. C8×Dic26C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
62. #11718049C22semidirect
63. #11718048C22semidirect
64. #11718047C22semidirect
65. C8×#1055C22semidirect
66. C8×#1055C22semidirect
214. C8×D13SD16semidirect
225. #1583D13semidirect
300. C8×Q8C2×D13semidirect
322. #334C2×D13semidirect
326. Q8⋊C8C2×D13semidirect
332. #322C2×D13semidirect
513. C13#17930semidirect

Maximal subgroups

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

subgroupindex
#131248422
#131237652
D13×#4362
#131137292
#131137272
#131137252
#131137232
#131136812
#131136792
#131136772
#131136052
#131132592
#131132372
#131131212
C13×#15832
#1793013