Finite Group Databasebeta

← #15833989

Subgroups — #15833989

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124885C211yesmaximal, characteristic
2#13123840C211yesmaximal, characteristic, complemented
3M16×D52C211yesmaximal, characteristic, complemented
4#13113740C211yesmaximal, characteristic, complemented
5#13113722C211yesmaximal, characteristic, complemented
6#13113702C211yesmaximal, characteristic, complemented
7#13113695C211yesmaximal, characteristic, complemented
8#13113681C211yesmaximal, characteristic, complemented
9#13113667C211yesmaximal, characteristic, complemented
10#13113661C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113625C211yesmaximal, characteristic, complemented
13#13113302C211yesmaximal, characteristic, complemented
14#13113228C211yesmaximal, characteristic, complemented
15C13×#1453C211yesmaximal, characteristic, complemented
16C2×M16×D13—21no—
17#11719184C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21C4×C13×M16C2211yescharacteristic
22#11718789—21no—
23#11718788—21no—
24#11718787—21no—
25#11718586C2211yescharacteristic
26#11718585C2211yescharacteristic
27#11718508C411yescharacteristic
28#11718508C411yescharacteristic
29#11718505C411yescharacteristic
30#11718505C411yescharacteristic
31#11718396C411yescharacteristic
32#11718393C411yescharacteristic
33#11718392C411yescharacteristic
34#11718383C411yescharacteristic
35#11718370—21no—
36#11718369—21no—
37#11718367—21no—
38#11718367—21no—
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44#11718349C2211yescharacteristic
45#11718349C2211yescharacteristic, complemented
46C8×D52C2211yescharacteristic
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic, complemented
49#11718340C2211yescharacteristic, complemented
50C8×Dic26C2211yescharacteristic, complemented
51C13×#322C2211yescharacteristic, complemented
52C13×#322C2211yescharacteristic, complemented
53C13×#322C2211yescharacteristic, complemented
54C82×C13C2211yescharacteristic, complemented
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718051C2211yescharacteristic
58#11718051C2211yescharacteristic
59#11718051C2211yescharacteristic, complemented
60#11718051C2211yescharacteristic, complemented
61#11718050C2211yescharacteristic, complemented
62#11718050C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718049C2211yescharacteristic, complemented
65#11718048C2211yescharacteristic, complemented
66#11718048C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×M16D411yescharacteristic
70C2×C13×M16D411yescharacteristic
71C2×C42×C13C2311yescharacteristic
72#88184C2×C411yescharacteristic
73#88183—21no—
74C4×C22⋊D13—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13C2×C411yescharacteristic
77#88178C2×C411yescharacteristic
78C2×#6099—21no—
79M16×D13—44no—
80C2×D104C2×C411yescharacteristic
81C2×D104C2×C411yescharacteristic
82C2×#6095C2×C411yescharacteristic
83C2×#6095C2×C411yescharacteristic
84C2×#6094—21no—
85C2×#6094—21no—
86C2×#6094—21no—
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89C2×C8×D13—21no—
90#88130—21no—
91#88129C2×C411yescharacteristic
92C4×D52—21no—
93C4×D52—21no—
94C4×D52C2×C411yescharacteristic
95C4×D52C2×C411yescharacteristic
96C4×D52C2311yescharacteristic
97C4×D52C2311yescharacteristic
98C4×D52C2311yescharacteristic
99#88126—21no—
100#88124C2×C411yescharacteristic
101C4×Dic26C2311yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2×C411yescharacteristic
104C13×C4⋊C8C2×C411yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8C2×C411yescharacteristic
107C13×C22⋊C8C2×C411yescharacteristic
108C13×#97D411yescharacteristic
109C13×#97D411yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C22⋊#1055—21no—
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88060—21no—
129#88058C2×C411yescharacteristic
130#88058C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88057C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88056C2×C411yescharacteristic
135#88055—21no—
136#88054—21no—
137#88054—21no—
138C8×Dic13—21no—
139C4⋊#1055—21no—
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4⋊#1055C2311yescharacteristic
144C4×#1055—21no—
145#18008—131nomaximal, Sylow
146C23×D13—21no—
147C22×C4×C13C22×C411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13#4111yescharacteristic
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152C2×D52—22no—
153C2×D52—21no—
154C2×D52—41no—
155C2×D52C22×C411yescharacteristic
156C2×D52C22×C411yescharacteristic
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—42no—
164C2×C4×D13—42no—
165C2×Dic26C22×C411yescharacteristic
166C13×M16—22no—
167C13×M16—41no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C2×C8×C13C2×D411yescharacteristic
178C42×C13C22×C411yescharacteristic
179C42×C13C2×D411yescharacteristic
180C42×C13#4111yescharacteristic
181C42×C13C2411yescharacteristic
182C22⋊Dic13—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194C4⋊Dic13C22×C411yescharacteristic
195C4⋊Dic13C22×C411yescharacteristic
196#6101—21no—
197#6101—21no—
198#6101—21no—
199#6101—21no—
200C4×Dic13—21no—
201#6099—42no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206D104—22no—
207D104—41no—
208#6095—22no—
209#6095—41no—
210#6094—42no—
211#6094—42no—
212#6094—42no—
213C8×D13—42no—
214C8×D13—42no—
215C8×D13—42no—
216#3105—131no—
217#2969—131no—
218D4×M16—131no—
219#1592—131no—
220#1589—131no—
221#1586—131no—
222#1585—131no—
223#1583—131no—
224#1581—131no—
225#1580—131no—
226C8×SD16—131no—
227#1574—131no—
228#1495—131no—
229#1478—131no—
230#1453D1311yescharacteristic, complemented
231C23×C13C4×D411yescharacteristic
232C22×D13—21no—
233C22×D13—21no—
234C22×D13—21no—
235C22×D13—42no—
236C22×D13—42no—
237C22×D13—81no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—41no—
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—81no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—42no—
256D52—21no—
257D52—21no—
258D52—21no—
259D52—21no—
260D52—21no—
261D52—42no—
262D52#13112yes—
263C4×D13—42no—
264C4×D13—42no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—41no—
271Dic26—21no—
272Dic26—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—21no—
279C8×C13—21no—
280C8×C13—41no—
281C8×C13—41no—
282C8×C13AGL(1,ℤ/8)12yes—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286#1055—41no—
287C22×M16—261no—
288#529—131no—
289C2×C4×D4—131no—
290#484—131no—
291#481—131no—
292#478—131no—
293#478—131no—
294#463—131no—
295#463—131no—
296#450—131no—
297#447—131no—
298#446—131no—
299C8×Q8—131no—
300C4×SD16—131no—
301C4×SD16—131no—
302C4×D8—131no—
303C4×D8—131no—
304#436—131no—
305#436—131no—
306#436—131no—
307#436—261no—
308#435—261no—
309#435—261no—
310#435—261no—
311C8×D4—131no—
312C8×D4—131no—
313C8×D4—131no—
314#433—261no—
315#431—131no—
316#431C2×D1311yescharacteristic
317#431C2×D1311yescharacteristic
318#423—131no—
319#407—261no—
320#405—261no—
321C4×M16C2×D1311yescharacteristic
322#335—131no—
323#335—131no—
324#334—131no—
325#334—131no—
326Q8⋊C8—131no—
327Q8⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334#322C2×D1311yescharacteristic, complemented
335#322C2×D1311yescharacteristic, complemented
336#322C2×D1311yescharacteristic, complemented
337C82C2×D1311yescharacteristic, complemented
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13C2×C4×D411yescharacteristic
342C2×D13—22no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C2×D13—84no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13C2×#13111yescharacteristic
357C4×C13#56811yescharacteristic
358C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C13#57511yescharacteristic
360Dic13—41no—
361Dic13—41no—
362Dic13—41no—
363Dic13—41no—
364Dic13—41no—
365C22×D4—131no—
366C23×C4—261no—
367C2×SD16—131no—
368C2×SD16—131no—
369C2×D8—131no—
370C2×D8—131no—
371C2×M16—261no—
372C2×M16—261no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16—524no—
376C2×M16D5211yescharacteristic
377C2×M16D5211yescharacteristic
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381#126—261no—
382#125—131no—
383#124—131no—
384#123—261no—
385C22⋊Q8—131no—
386#121—131no—
387C4×Q8—131no—
388C4×D4—131no—
389C4×D4—131no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—131no—
393C4×D4—261no—
394C4×D4—261no—
395C4×D4—261no—
396#117—261no—
397C2×C4⋊C4—131no—
398C2×C22⋊C4—261no—
399C2×C42C22×D1311yescharacteristic
400#107—131no—
401#107—131no—
402#106—131no—
403#106—131no—
404C4⋊C8—21no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412C4⋊C8C4×D1311yescharacteristic
413C4⋊C8C4×D1311yescharacteristic
414#103—131no—
415#103—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421#102—131no—
422C22⋊C8—21no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8C4×D1311yescharacteristic
431C22⋊C8C4×D1311yescharacteristic
432#97—261no—
433#97D5211yescharacteristic
434#97D5211yescharacteristic
435C4×C8—261no—
436C4×C8—261no—
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C4×C8C22×D1311yescharacteristic
441C4×C8C22×D1311yescharacteristic
442C4×C8C22×D1311yescharacteristic
443C2×C13—41no—
444C2×C13#293311yescharacteristic
445C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C13#295711yescharacteristic
447D13—42no—
448D13—81no—
449D13—81no—
450C24—261no—
451C2×Q8—131no—
452C2×D4—131no—
453C2×D4—131no—
454C2×D4—131no—
455C2×D4—262no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—521no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465C22×C4—522no—
466C22×C4—522no—
467C22×C4C2×C4×D1311yescharacteristic
468C22×C4C2×D5211yescharacteristic
469C22×C4#612711yescharacteristic
470SD16—262no—
471SD16—521no—
472D8—262no—
473D8—521no—
474M16—22no—
475M16—41no—
476M16—522no—
477M16—522no—
478M16—522no—
479M16—522no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—522no—
487C2×C8—522no—
488C2×C8—522no—
489C2×C8C2×C4×D1311yescharacteristic
490C2×C8C2×C4×D1311yescharacteristic
491C2×C8C2×C4×D1311yescharacteristic
492C2×C8C2×C4×D1311yescharacteristic
493C2×C8C2×D5211yescharacteristic
494C2×C8C2×D5211yescharacteristic
495C2×C8C2×D5211yescharacteristic
496C2×C8C2×D5211yescharacteristic
497C4⋊C4—131no—
498C4⋊C4—131no—
499C4⋊C4—131no—
500C4⋊C4—131no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C22⋊C4—261no—
515C42—261no—
516C42C2×C4×D1311yescharacteristic
517C42C2×D5211yescharacteristic
518C42#612711yescharacteristic
519C42C23×D1311yescharacteristic
520C13#1800811yescharacteristic, complemented, Sylow
521C23—261no—
522C23—261no—
523C23—261no—
524C23—522no—
525C23—522no—
526C23—1041no—
527C23C4×D5211yescharacteristic
528Q8—261no—
529Q8—261no—
530D4—132no—
531D4—261no—
532D4—261no—
533D4—261no—
534D4—261no—
535D4—261no—
536D4—522no—
537D4—1041no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—522no—
549C2×C4—522no—
550C2×C4—522no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4C4×D5211yescharacteristic
558C2×C4C4×D5211yescharacteristic
559C2×C4C4×D5211yescharacteristic
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C22×D5211yescharacteristic
562C2×C4C2×#612711yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—521no—
573C8—521no—
574C8—521no—
575C8—521no—
576C8#8816212yes—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—262no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22—521no—
586C22—521no—
587C22—521no—
588C22—521no—
589C22—1044no—
590C22C2×C4×D5211yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—521no—
596C4—521no—
597C4—521no—
598C4—521no—
599C4—521no—
600C4C2×#8816211yescharacteristic
601C4#1171945311yescharacteristic
602C4D13×#13111yescharacteristic
603C4#1171945511yescharacteristic
604C2—41no—
605C2—522no—
606C2—1041no—
607C2—1041no—
608C2#1312356411yescharacteristic
609C2C4×#8816211yescharacteristic
610C2#1312375411yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1453C2
socleC22×C13C2×C4×D4
prime radical#11718393C4
cosocleC42×C13C24
hypercenter#1453D13
hypocenterC13#18008
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1453

Complements

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

NH ≅ G/Ntype
2. #13123840C2semidirect
3. M16×D52C2semidirect
4. #13113740C2semidirect
5. #13113722C2semidirect
6. #13113702C2semidirect
7. #13113695C2semidirect
8. #13113681C2semidirect
9. #13113667C2semidirect
10. #13113661C2semidirect
11. C8×#6095C2semidirect
12. #13113625C2semidirect
13. #13113302C2semidirect
14. #13113228C2semidirect
15. C13×#1453C2semidirect
45. #11718349C22semidirect
48. C8×D52C22semidirect
49. #11718340C22semidirect
50. C8×Dic26C22semidirect
51. C13×#322C22semidirect
52. C13×#322C22semidirect
53. C13×#322C22semidirect
54. C82×C13C22semidirect
59. #11718051C22semidirect
60. #11718051C22semidirect
61. #11718050C22semidirect
62. #11718050C22semidirect
63. #11718049C22semidirect
64. #11718049C22semidirect
65. #11718048C22semidirect
66. #11718048C22semidirect
230. #1453D13semidirect
334. #322C2×D13semidirect
335. #322C2×D13semidirect
336. #322C2×D13semidirect
337. C82C2×D13semidirect
520. C13#18008semidirect

Maximal subgroups

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

subgroupindex
#131248852
#131238402
M16×D522
#131137402
#131137222
#131137022
#131136952
#131136812
#131136672
#131136612
C8×#60952
#131136252
#131133022
#131132282
C13×#14532
#1800813