Finite Group Databasebeta

← #15833874

Subgroups — #15833874

Order 3328.

672 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124842C211yesmaximal, characteristic
2#13123778C211yesmaximal, characteristic, complemented
3D4×#6094C211yesmaximal, characteristic
4#13113741C211yesmaximal, characteristic, complemented
5#13113740C211yesmaximal, characteristic, complemented
6#13113714C211yesmaximal, characteristic, complemented
7#13113713C211yesmaximal, characteristic, complemented
8#13113694C211yesmaximal, characteristic, complemented
9#13113693C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113609C211yesmaximal, characteristic, complemented
12#13113289C211yesmaximal, characteristic, complemented
13D13×D4⋊C8C211yesmaximal, characteristic
14#13113124C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16C22×#6094—21no—
17#11719283C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic, complemented
20C4×C13×SD16C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22#11718830C411yescharacteristic
23#11718823C411yescharacteristic
24#11718772—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718531C411yescharacteristic
30#11718523C411yescharacteristic
31#11718500—21no—
32#11718499C2211yescharacteristic
33#11718498C2211yescharacteristic
34D13×C4⋊C8C2211yescharacteristic
35#11718491C2211yescharacteristic, complemented
36#11718489—21no—
37#11718479C411yescharacteristic
38#11718466C411yescharacteristic
39#11718437C411yescharacteristic
40#11718422C411yescharacteristic
41#11718391—21no—
42#11718387—21no—
43C4×#6095C2211yescharacteristic
44#11718350—21no—
45#11718349C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49#11718340—21no—
50#11718340C2211yescharacteristic, complemented
51C13×#335C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718071C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718050C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C22×C8×C13—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—
79C22×#1055—21no—
80C2×#6095C2×C411yescharacteristic
81C2×#6094—21no—
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094—44no—
85C2×#6094D411yescharacteristic
86C2×#6094D411yescharacteristic
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89#88151C2×C411yescharacteristic
90#88150—21no—
91#88147C2×C411yescharacteristic
92C4⋊C4×D13C2×C411yescharacteristic
93#88143—21no—
94#88142C2×C411yescharacteristic
95#88135—21no—
96C22⋊C4×D13—21no—
97C4×D52C2311yescharacteristic
98#88126—21no—
99C42×D13C2311yescharacteristic
100C4×Dic26—21no—
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—
109C4×C8×C13—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#88060C2×C411yescharacteristic
120#88060C2×C411yescharacteristic
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055D411yescharacteristic
125#88055D411yescharacteristic
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132C8×Dic13—21no—
133C8×Dic13—21no—
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#18000—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—22no—
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—22no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—42no—
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—22no—
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
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—42no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6095—41no—
209#6094—22no—
210#6094—22no—
211#6094—42no—
212#6094—42no—
213#6094—42no—
214C8×D13—42no—
215C8×D13—42no—
216#3101—131no—
217#2962—131no—
218D4×M16—131no—
219#1592—131no—
220#1592—131no—
221#1588—131no—
222#1588—131no—
223#1585—131no—
224#1585—131no—
225SD16⋊C8—131no—
226SD16⋊C8D1311yescharacteristic, complemented
227#1571—131no—
228#1493—131no—
229C2×D4⋊C8—131no—
230#1451—131no—
231C23×C13—21no—
232C22×D13—21no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13—81no—
236C22×D13C4×D411yescharacteristic
237Q8×C13—21no—
238Q8×C13—21no—
239D4×C13—21no—
240D4×C13#13112yes—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—42no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—42no—
254C2×Dic13C4×D411yescharacteristic
255C2×Dic13C4×D411yescharacteristic
256C2×Dic13C4×D411yescharacteristic
257D52—21no—
258D52—21no—
259C4×D13—21no—
260C4×D13—21no—
261C4×D13—41no—
262C4×D13—42no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—42no—
266C4×D13AGL(1,ℤ/8)12yes—
267C4×D13#13712yes—
268Dic26—21no—
269Dic26—21no—
270Dic26—81no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13—41no—
278#1055—22no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—41no—
284#1055—41no—
285C22×M16—261no—
286#533—131no—
287C2×C4×D4—131no—
288#483—131no—
289#483—131no—
290#476—131no—
291#476—131no—
292#461—131no—
293#461—131no—
294#450—131no—
295#450—131no—
296#446—131no—
297#446—131no—
298#446—261no—
299#446—261no—
300C8×Q8—131no—
301C8×Q8C2×D1311yescharacteristic, complemented
302C4×SD16—131no—
303C4×SD16—131no—
304C4×SD16—131no—
305C4×SD16C2×D1311yescharacteristic
306#436—131no—
307#436—131no—
308#435—261no—
309#435—261no—
310C8×D4—131no—
311C8×D4C2×D1311yescharacteristic
312#431—131no—
313#424—261no—
314#423—131no—
315C2×C4⋊C8—131no—
316#407—261no—
317#405—261no—
318C4×M16—131no—
319C2×C4×C8—131no—
320#335—131no—
321#335—131no—
322#335—131no—
323#335C2×D1311yescharacteristic, complemented
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326Q8⋊C8—131no—
327Q8⋊C8C2×D1311yescharacteristic, complemented
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8C2×D1311yescharacteristic
332#322—131no—
333#322—131no—
334#322—131no—
335#322C2×D1311yescharacteristic, complemented
336C22×C13—22no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C4×D411yescharacteristic
340C2×D13—21no—
341C2×D13—21no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—84no—
346C2×D13#44012yes—
347C4×C13—21no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—41no—
351C4×C13C2×#13111yescharacteristic
352C4×C13#56811yescharacteristic
353C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
354C4×C13C2×#13711yescharacteristic
355Dic13—21no—
356Dic13—21no—
357Dic13—41no—
358Dic13—41no—
359Dic13—41no—
360Dic13#44012yes—
361C22×D4—131no—
362C23×C4—261no—
363C2×SD16—131no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×SD16C4×D1311yescharacteristic
367C2×M16—131no—
368C2×M16—131no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C2×M16—524no—
373C22×C8—21no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377C4⋊Q8—131no—
378C4⋊Q8—131no—
379#125—261no—
380C22⋊Q8—131no—
381C22⋊Q8—131no—
382C22⋊Q8—261no—
383C4×Q8—131no—
384C4×Q8—261no—
385C4×Q8C22×D1311yescharacteristic
386C4×D4—131no—
387C4×D4—131no—
388C4×D4—131no—
389C4×D4—261no—
390C4×D4—261no—
391C4×D4C22×D1311yescharacteristic
392#117—261no—
393C2×C4⋊C4—131no—
394C2×C22⋊C4—261no—
395C2×C42—131no—
396#106—131no—
397#106—131no—
398#106—131no—
399#106C4×D1311yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8—261no—
410C4⋊C8C22×D1311yescharacteristic
411C4⋊C8C22×D1311yescharacteristic
412#103—131no—
413#103—131no—
414#103—131no—
415#103C4×D1311yescharacteristic
416#102—131no—
417#102—131no—
418#102—131no—
419#102C4×D1311yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—131no—
422C22⋊C8—131no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426#97—131no—
427#97—131no—
428#97—261no—
429#97—261no—
430C4×C8—21no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8—261no—
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C2×C13—42no—
440C2×C13#293311yescharacteristic
441C2×C13C2×#44011yescharacteristic
442C2×C13#295611yescharacteristic
443D13—22no—
444D13—81no—
445C24—261no—
446C2×Q8—131no—
447C2×Q8—261no—
448C2×Q8C2×C4×D1311yescharacteristic
449C2×D4—131no—
450C2×D4—261no—
451C2×D4—262no—
452C2×D4—521no—
453C2×D4C2×C4×D1311yescharacteristic
454C22×C4—21no—
455C22×C4—131no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—522no—
463C22×C4—522no—
464SD16—22no—
465SD16—262no—
466SD16—521no—
467SD16—521no—
468M16—262no—
469M16—262no—
470M16—522no—
471M16—522no—
472M16—522no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—522no—
485C2×C8—522no—
486C2×C8—522no—
487C2×C8C2×C4×D1311yescharacteristic
488C2×C8C2×C4×D1311yescharacteristic
489C2×C8D4×D1311yescharacteristic
490C2×C8D4×D1311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—131no—
493C4⋊C4—131no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4C2×C4×D1311yescharacteristic
502C4⋊C4C2×C4×D1311yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—21no—
510C42—131no—
511C42—131no—
512C42—131no—
513C42—261no—
514C42C23×D1311yescharacteristic
515C13#1800011yescharacteristic, complemented, Sylow
516C23—21no—
517C23—131no—
518C23—261no—
519C23—522no—
520C23—522no—
521C23—1041no—
522Q8—21no—
523Q8—21no—
524Q8—261no—
525Q8—261no—
526Q8—1041no—
527D4—21no—
528D4—261no—
529D4—261no—
530D4—522no—
531D4#8815512yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—131no—
538C2×C4—132no—
539C2×C4—132no—
540C2×C4—131no—
541C2×C4—131no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—521no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4C22×C4×D1311yescharacteristic
554C2×C4C2×D4×D1311yescharacteristic
555C2×C4#41×D1311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—262no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—521no—
569C8—521no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—132no—
574C22—261no—
575C22—261no—
576C22—521no—
577C22—521no—
578C22—521no—
579C22—1044no—
580C22C4×D4×D1311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—132no—
586C4—261no—
587C4—261no—
588C4—521no—
589C4—521no—
590C4—521no—
591C4C2×#8815511yescharacteristic
592C4#1171945511yescharacteristic
593C4D13×AGL(1,ℤ/8)11yescharacteristic
594C4D13×#13711yescharacteristic
595C2—42no—
596C2—262no—
597C2—1041no—
598C2#1312355611yescharacteristic
599C2D13×#44011yescharacteristic
600C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×SD16⋊C8C2
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C2×C4
cosocleC42×C13C24
hypercenterSD16⋊C8D13
hypocenterC13#18000
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
2. #13123778C2semidirect
4. #13113741C2semidirect
5. #13113740C2semidirect
6. #13113714C2semidirect
7. #13113713C2semidirect
8. #13113694C2semidirect
9. #13113693C2semidirect
10. #13113645C2semidirect
11. #13113609C2semidirect
12. #13113289C2semidirect
14. #13113124C2semidirect
15. C13×SD16⋊C8C2semidirect
19. C8×Q8×C13C22semidirect
26. #11718685C22semidirect
35. #11718491C22semidirect
50. #11718340C22semidirect
51. C13×#335C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718071C22semidirect
60. #11718071C22semidirect
62. #11718050C22semidirect
63. #11718048C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
226. SD16⋊C8D13semidirect
301. C8×Q8C2×D13semidirect
323. #335C2×D13semidirect
327. Q8⋊C8C2×D13semidirect
335. #322C2×D13semidirect
515. C13#18000semidirect

Maximal subgroups

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

subgroupindex
#131248422
#131237782
D4×#60942
#131137412
#131137402
#131137142
#131137132
#131136942
#131136932
#131136452
#131136092
#131132892
D13×D4⋊C82
#131131242
C13×SD16⋊C82
#1800013