Finite Group Databasebeta

← #15834146

Subgroups — #15834146

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124887C211yesmaximal, characteristic
2#13123995C211yesmaximal, characteristic, complemented
3#13123868C211yesmaximal, characteristic, complemented
4#13113748C211yesmaximal, characteristic, complemented
5#13113739C211yesmaximal, characteristic, complemented
6#13113675C211yesmaximal, characteristic, complemented
7#13113668C211yesmaximal, characteristic, complemented
8#13113667C211yesmaximal, characteristic, complemented
9#13113659C211yesmaximal, characteristic, complemented
10#13113646C211yesmaximal, characteristic, complemented
11#13113618C211yesmaximal, characteristic, complemented
12#13113295C211yesmaximal, characteristic, complemented
13D13×D4⋊C8C211yesmaximal, characteristic, complemented
14#13113127C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16#11719285C2211yescharacteristic
17C4×D4×D13C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic, complemented
19C4×C13×SD16C2211yescharacteristic
20C13×#436C2211yescharacteristic
21#11718830C411yescharacteristic
22#11718826C411yescharacteristic
23#11718788—21no—
24#11718787—21no—
25C4×#6106C2211yescharacteristic
26#11718685C2211yescharacteristic, complemented
27C4×#6104C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718532C411yescharacteristic
30#11718524C411yescharacteristic
31#11718500—21no—
32#11718497—21no—
33#11718496C2211yescharacteristic
34#11718495C2211yescharacteristic
35#11718495C2211yescharacteristic, complemented
36D13×C4⋊C8C2211yescharacteristic
37#11718480C411yescharacteristic
38#11718470C411yescharacteristic
39#11718434C411yescharacteristic
40#11718427C411yescharacteristic
41#11718389—21no—
42D13×C22⋊C8—21no—
43C4×D104C2211yescharacteristic
44#11718351—21no—
45#11718349C2211yescharacteristic, complemented
46C8×D52—21no—
47C8×D52C2211yescharacteristic
48#11718346C2211yescharacteristic
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#334C2211yescharacteristic, 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#11718050C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×M16—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—
79C2×#6099—21no—
80C2×D104C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83C2×C8×D13—21no—
84C2×C8×D13—21no—
85C2×C8×D13—21no—
86C2×C8×D13—21no—
87#88152—21no—
88#88149C2×C411yescharacteristic
89#88148—21no—
90#88147C2×C411yescharacteristic
91C4⋊C4×D13C2×C411yescharacteristic
92#88144C2×C411yescharacteristic
93#88135—21no—
94C22⋊C4×D13—21no—
95C4×D52—21no—
96C4×D52C2311yescharacteristic
97C4×D52C2311yescharacteristic
98#88126—21no—
99C42×D13C2311yescharacteristic
100C13×#106C2×C411yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#102C2×C411yescharacteristic
106C13×C22⋊C8—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113C22⋊#1055—21no—
114#88061C2×C411yescharacteristic
115#88061C2×C411yescharacteristic
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#88055—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
140#88043—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18020—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—41no—
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—41no—
166C13×M16—81no—
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—22no—
182#6104—41no—
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
199#6099—81no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207D104—22no—
208#6094—81no—
209C8×D13—42no—
210C8×D13—81no—
211C8×D13—81no—
212C8×D13—81no—
213C8×D13—81no—
214#3105—131no—
215#2994—131no—
216#2974—131no—
217#1594—131no—
218#1592—131no—
219#1583D1311yescharacteristic, complemented
220#1582—131no—
221#1581—131no—
222#1581—131no—
223#1580—131no—
224SD16⋊C8—131no—
225#1573—131no—
226#1494—131no—
227C2×D4⋊C8—131no—
228#1452—131no—
229C23×C13—21no—
230C22×D13—21no—
231C22×D13—21no—
232C22×D13—42no—
233C22×D13—42no—
234C22×D13—81no—
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—81no—
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254C2×Dic13C4×D411yescharacteristic
255D52—21no—
256D52—21no—
257D52—21no—
258D52—42no—
259D52#13112yes—
260C4×D13—22no—
261C4×D13—21no—
262C4×D13—21no—
263C4×D13—21no—
264C4×D13—21no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
269C4×D13—81no—
270C4×D13—81no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13—41no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285#529—131no—
286C2×C4×D4—131no—
287#484—131no—
288#481—131no—
289#478—131no—
290#478—131no—
291#463—131no—
292#463—131no—
293#450—131no—
294#447—131no—
295#446—131no—
296C8×Q8C2×D1311yescharacteristic, complemented
297C4×SD16—131no—
298C4×SD16C2×D1311yescharacteristic
299C4×D8—131no—
300C4×D8—131no—
301#436—131no—
302#436—131no—
303#436C2×D1311yescharacteristic
304#435—261no—
305#435—261no—
306#435—261no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—261no—
311#433—261no—
312#432—131no—
313#431—131no—
314#431—131no—
315#424—261no—
316C2×C4⋊C8—131no—
317#407—261no—
318C2×C22⋊C8—261no—
319C2×C4×C8—131no—
320#335—131no—
321#335—131no—
322#334—131no—
323#334C2×D1311yescharacteristic, complemented
324Q8⋊C8—131no—
325Q8⋊C8C2×D1311yescharacteristic, complemented
326D4⋊C8—131no—
327D4⋊C8—131no—
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—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C4×D411yescharacteristic
340C2×D13—21no—
341C2×D13—21no—
342C2×D13—22no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—84no—
349C2×D13#44412yes—
350C4×C13—21no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13C2×#13111yescharacteristic
355C4×C13#56811yescharacteristic
356C4×C13#57611yescharacteristic
357C4×C13#57711yescharacteristic
358Dic13—21no—
359Dic13—21no—
360Dic13—21no—
361Dic13—41no—
362Dic13—41no—
363C22×D4—131no—
364C23×C4—261no—
365C2×SD16—131no—
366C2×SD16C4×D1311yescharacteristic
367C2×D8—131no—
368C2×D8—131no—
369C2×M16—21no—
370C2×M16—261no—
371C2×M16—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377#126—261no—
378#125—131no—
379#124—131no—
380#123—261no—
381C22⋊Q8—131no—
382#121—131no—
383C4×Q8C22×D1311yescharacteristic
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—131no—
388C4×D4—261no—
389C4×D4—261no—
390C4×D4—261no—
391C4×D4C22×D1311yescharacteristic
392#117—261no—
393C2×C4⋊C4—131no—
394C2×C22⋊C4—261no—
395C2×C42—131no—
396#107—131no—
397#107—131no—
398#106—131no—
399#106C4×D1311yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8C22×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411#103—131no—
412#103C4×D1311yescharacteristic
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102C4×D1311yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—131no—
423C22⋊C8—131no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430#97—261no—
431#97—261no—
432C4×C8—21no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C2×C13—81no—
441C2×C13#293311yescharacteristic
442C2×C13#294611yescharacteristic
443C2×C13C2×#44411yescharacteristic
444D13—22no—
445D13—42no—
446D13—81no—
447C24—261no—
448C2×Q8C2×C4×D1311yescharacteristic
449C2×D4—131no—
450C2×D4—131no—
451C2×D4—261no—
452C2×D4—261no—
453C2×D4—262no—
454C2×D4—521no—
455C2×D4C2×C4×D1311yescharacteristic
456C22×C4—21no—
457C22×C4—131no—
458C22×C4—131no—
459C22×C4—131no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—1041no—
466C22×C4—1041no—
467SD16—41no—
468SD16—262no—
469D8—262no—
470D8—521no—
471M16—81no—
472M16—1041no—
473M16—1041no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
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—1041no—
486C2×C8—1041no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8C2×C4×D1311yescharacteristic
490C2×C8C2×C4×D1311yescharacteristic
491C2×C8D4×D1311yescharacteristic
492C2×C8D4×D1311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—131no—
495C4⋊C4—131no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4C2×C4×D1311yescharacteristic
501C4⋊C4C2×C4×D1311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C42—21no—
512C42—131no—
513C42—131no—
514C42—131no—
515C42C23×D1311yescharacteristic
516C13#1802011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—131no—
519C23—261no—
520C23—261no—
521C23—522no—
522C23—522no—
523C23—1041no—
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—132no—
529D4—261no—
530D4—261no—
531D4—261no—
532D4—522no—
533D4—522no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—131no—
540C2×C4—131no—
541C2×C4—131no—
542C2×C4—262no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—1041no—
554C2×C4—1041no—
555C2×C4—1041no—
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×D4×D1311yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—261no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—521no—
571C8—521no—
572C8—521no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—132no—
577C22—261no—
578C22—261no—
579C22—262no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22—1044no—
586C22C4×D4×D1311yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—261no—
592C4—261no—
593C4—261no—
594C4—521no—
595C4—521no—
596C4#1171945011yescharacteristic
597C4D13×#13111yescharacteristic
598C4#1171946711yescharacteristic
599C4#1171947411yescharacteristic
600C2—81no—
601C2—262no—
602C2—522no—
603C2—1041no—
604C2#1312355911yescharacteristic
605C2#1312366311yescharacteristic
606C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radical#11718434C4
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#18020
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. #13123995C2semidirect
3. #13123868C2semidirect
4. #13113748C2semidirect
5. #13113739C2semidirect
6. #13113675C2semidirect
7. #13113668C2semidirect
8. #13113667C2semidirect
9. #13113659C2semidirect
10. #13113646C2semidirect
11. #13113618C2semidirect
12. #13113295C2semidirect
13. D13×D4⋊C8C2semidirect
14. #13113127C2semidirect
15. C13×#1583C2semidirect
18. C8×Q8×C13C22semidirect
26. #11718685C22semidirect
35. #11718495C22semidirect
45. #11718349C22semidirect
51. C13×#334C22semidirect
52. C13×Q8⋊C8C22semidirect
54. C13×#322C22semidirect
55. Q8⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718051C22semidirect
63. #11718050C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
219. #1583D13semidirect
296. C8×Q8C2×D13semidirect
323. #334C2×D13semidirect
325. Q8⋊C8C2×D13semidirect
335. #322C2×D13semidirect
516. C13#18020semidirect

Maximal subgroups

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

subgroupindex
#131248872
#131239952
#131238682
#131137482
#131137392
#131136752
#131136682
#131136672
#131136592
#131136462
#131136182
#131132952
D13×D4⋊C82
#131131272
C13×#15832
#1802013