Finite Group Databasebeta

← #15832978

Subgroups — #15832978

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124887C211yesmaximal, characteristic
2#13123988C211yesmaximal, characteristic, complemented
3#13123857C211yesmaximal, characteristic, complemented
4#13113702C211yesmaximal, characteristic, complemented
5#13113670C211yesmaximal, characteristic, complemented
6#13113665C211yesmaximal, characteristic, complemented
7#13113657C211yesmaximal, characteristic, complemented
8#13113651C211yesmaximal, characteristic, complemented
9SD16×#1055C211yesmaximal, characteristic, complemented
10#13113630C211yesmaximal, characteristic, complemented
11#13113626C211yesmaximal, characteristic, complemented
12#13113259C211yesmaximal, characteristic, complemented
13#13113243C211yesmaximal, characteristic, complemented
14#13113137C211yesmaximal, characteristic, complemented
15C13×#1585C211yesmaximal, characteristic, complemented
16#11719285C2211yescharacteristic
17C4×D4×D13C2211yescharacteristic
18C13×#446C2211yescharacteristic, complemented
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718830C411yescharacteristic
22#11718826C411yescharacteristic
23C8×C22⋊D13—21no—
24C2×#88060—21no—
25C4×#6106C2211yescharacteristic
26Q8×#1055C2211yescharacteristic, complemented
27C4×#6104C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718532C411yescharacteristic
30#11718524C411yescharacteristic
31#11718500—21no—
32#11718499—21no—
33#11718498C2211yescharacteristic
34#11718495C2211yescharacteristic
35#11718495C2211yescharacteristic, complemented
36#11718494C2211yescharacteristic
37#11718480C411yescharacteristic
38#11718470C411yescharacteristic
39#11718434C411yescharacteristic
40#11718427C411yescharacteristic
41#11718386—21no—
42D13×C22⋊C8—21no—
43#11718370—21no—
44#11718367—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic, complemented
47C8×D52C2211yescharacteristic
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
50#11718346C2211yescharacteristic
51C13×#335C2211yescharacteristic, complemented
52C13×Q8⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic, complemented
55Q8⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C22×C8×C13—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73#88201C2×C411yescharacteristic
74#88200C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6104C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C22×#1055—21no—
80C2×D104C2×C411yescharacteristic
81C2×#6094—21no—
82C2×#6094—21no—
83C2×C8×D13—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86#88152—21no—
87#88149C2×C411yescharacteristic
88#88148—21no—
89#88147C2×C411yescharacteristic
90C4⋊C4×D13C2×C411yescharacteristic
91#88144C2×C411yescharacteristic
92#88135—21no—
93C22⋊C4×D13—21no—
94C4×D52—21no—
95C4×D52C2311yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98C42×D13C2311yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#102C2×C411yescharacteristic
105C13×C22⋊C8—21no—
106C13×#97—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88075C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113#88061C2×C411yescharacteristic
114#88061C2×C411yescharacteristic
115#88060—21no—
116#88060—21no—
117#88060—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060C2×C411yescharacteristic
122#88060C2×C411yescharacteristic
123#88060D411yescharacteristic
124#88060D411yescharacteristic
125#88058C2×C411yescharacteristic
126#88054—21no—
127#88054—21no—
128#88054C2×C411yescharacteristic
129#88054C2×C411yescharacteristic
130#88054D411yescharacteristic
131#88054D411yescharacteristic
132C8×Dic13—21no—
133#88049C2×C411yescharacteristic
134#88049C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17918—131nomaximal, Sylow
145C23×D13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C22×Dic13—21no—
151D4×D13—22no—
152D4×D13—22no—
153C2×D52—21no—
154C2×D52C22×C411yescharacteristic
155C2×D52C22×C411yescharacteristic
156C2×C4×D13—21no—
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—81no—
161C2×C4×D13—81no—
162C2×C4×D13C22×C411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13#4111yescharacteristic
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#6106—22no—
182#6104—22no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13C22×C411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13#4111yescharacteristic
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207D104—22no—
208#6094—81no—
209#6094—81no—
210C8×D13—81no—
211C8×D13—81no—
212C8×D13—81no—
213#3105—131no—
214#2993—131no—
215#2972—131no—
216#1586—131no—
217#1585D1311yescharacteristic, complemented
218#1582—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1574—131no—
225#1486—131no—
226#1482—131no—
227#1454—131no—
228C23×C13—21no—
229C22×D13—21no—
230C22×D13—24no—
231C22×D13—21no—
232C22×D13—81no—
233C22×D13—81no—
234C22×D13C4×D411yescharacteristic
235Q8×C13—21no—
236Q8×C13—21no—
237D4×C13—21no—
238D4×C13#13112yes—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C22⋊D13—24no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—81no—
251C2×Dic13C4×D411yescharacteristic
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254D52—21no—
255D52—21no—
256D52—21no—
257D52—81no—
258D52#13112yes—
259C4×D13—21no—
260C4×D13—21no—
261C4×D13—21no—
262C4×D13—21no—
263C4×D13—41no—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—81no—
269C4×D13—81no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#529—131no—
285C2×C4×D4—131no—
286#484—131no—
287#481—131no—
288#478—131no—
289#478—131no—
290#463—131no—
291#463—131no—
292#450—131no—
293#447—131no—
294#446C2×D1311yescharacteristic, complemented
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16C2×D1311yescharacteristic
298C4×D8—131no—
299C4×D8—131no—
300#436—131no—
301#436—261no—
302#435—261no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—261no—
308C8×D4—261no—
309C8×D4C2×D1311yescharacteristic
310#433—261no—
311#431—131no—
312#431—131no—
313#431—131no—
314#431—131no—
315#424—261no—
316#423—131no—
317C2×C22⋊C8—261no—
318C2×C22⋊C8—261no—
319#335—131no—
320#335C2×D1311yescharacteristic, complemented
321#334—131no—
322#334—131no—
323Q8⋊C8—131no—
324Q8⋊C8C2×D1311yescharacteristic, complemented
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8C2×D1311yescharacteristic
331#322—131no—
332#322—131no—
333#322C2×D1311yescharacteristic, complemented
334C82—131no—
335C22×C13—22no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13C2×C4×D411yescharacteristic
339C2×D13—21no—
340C2×D13—22no—
341C2×D13—21no—
342C2×D13—21no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—84no—
349C4×C13—21no—
350C4×C13—41no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13C2×#13111yescharacteristic
354C4×C13C2×#13111yescharacteristic
355C4×C13#57611yescharacteristic
356C4×C13#57711yescharacteristic
357Dic13—21no—
358Dic13—21no—
359Dic13—21no—
360Dic13—41no—
361Dic13—41no—
362C22×D4—131no—
363C23×C4—261no—
364C2×SD16—131no—
365C2×SD16C4×D1311yescharacteristic
366C2×D8—131no—
367C2×D8—131no—
368C2×M16—261no—
369C2×M16—261no—
370C22×C8—21no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375#126—261no—
376#125—131no—
377#124—131no—
378#123—261no—
379C22⋊Q8—131no—
380#121—131no—
381C4×Q8C22×D1311yescharacteristic
382C4×D4—131no—
383C4×D4—131no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—261no—
387C4×D4—261no—
388C4×D4—261no—
389C4×D4C22×D1311yescharacteristic
390#117—261no—
391C2×C4⋊C4—131no—
392C2×C22⋊C4—261no—
393C2×C42—131no—
394#107—131no—
395#107—131no—
396#106—131no—
397#106C4×D1311yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8C22×D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410#103—131no—
411#103C4×D1311yescharacteristic
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102C4×D1311yescharacteristic
418C22⋊C8—21no—
419C22⋊C8—131no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—131no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430#97—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#292911yescharacteristic
441C2×C13#294611yescharacteristic
442C2×C13#295711yescharacteristic
443D13—41no—
444D13—42no—
445D13—81no—
446C24—261no—
447C2×Q8C2×C4×D1311yescharacteristic
448C2×D4—131no—
449C2×D4—131no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—262no—
453C2×D4—262no—
454C2×D4C2×C4×D1311yescharacteristic
455C22×C4—21no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—1041no—
465C22×C4—1041no—
466SD16—22no—
467SD16—262no—
468D8—262no—
469D8—262no—
470M16—1041no—
471M16—1041no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—1041no—
484C2×C8—1041no—
485C2×C8—1041no—
486C2×C8—1041no—
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⋊C4C2×C4×D1311yescharacteristic
499C4⋊C4C2×C4×D1311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—261no—
502C22⋊C4—261no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—21no—
510C42—131no—
511C42—131no—
512C42—131no—
513C42C23×D1311yescharacteristic
514C13#1791811yescharacteristic, complemented, Sylow
515C23—21no—
516C23—131no—
517C23—264no—
518C23—261no—
519C23—261no—
520C23—1041no—
521C23—1041no—
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—132no—
526D4—264no—
527D4—261no—
528D4—261no—
529D4—261no—
530D4—1041no—
531D4#8816112yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—131no—
538C2×C4—131no—
539C2×C4—131no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1041no—
552C2×C4—1041no—
553C2×C4—1041no—
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4C2×D4×D1311yescharacteristic
556C2×C4#41×D1311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—521no—
569C8—521no—
570C8—521no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—261no—
575C22—261no—
576C22—261no—
577C22—262no—
578C22—521no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—1044no—
584C22C4×D4×D1311yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—261no—
590C4—261no—
591C4—261no—
592C4—521no—
593C4—521no—
594C4C2×#8816111yescharacteristic
595C4D13×#13111yescharacteristic
596C4#1171947911yescharacteristic
597C4#1171948311yescharacteristic
598C2—42no—
599C2—521no—
600C2—522no—
601C2—1041no—
602C2#1312352711yescharacteristic
603C2#1312366711yescharacteristic
604C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1585C2
socleC22×C13C2×C4×D4
prime radical#11718434C4
cosocleC42×C13C24
hypercenter#1585D13
hypocenterC13#17918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #13123988C2semidirect
3. #13123857C2semidirect
4. #13113702C2semidirect
5. #13113670C2semidirect
6. #13113665C2semidirect
7. #13113657C2semidirect
8. #13113651C2semidirect
9. SD16×#1055C2semidirect
10. #13113630C2semidirect
11. #13113626C2semidirect
12. #13113259C2semidirect
13. #13113243C2semidirect
14. #13113137C2semidirect
15. C13×#1585C2semidirect
18. C13×#446C22semidirect
26. Q8×#1055C22semidirect
35. #11718495C22semidirect
46. #11718349C22semidirect
51. C13×#335C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718049C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
217. #1585D13semidirect
294. #446C2×D13semidirect
320. #335C2×D13semidirect
324. Q8⋊C8C2×D13semidirect
333. #322C2×D13semidirect
514. C13#17918semidirect

Maximal subgroups

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

subgroupindex
#131248872
#131239882
#131238572
#131137022
#131136702
#131136652
#131136572
#131136512
SD16×#10552
#131136302
#131136262
#131132592
#131132432
#131131372
C13×#15852
#1791813