Finite Group Databasebeta

← #15833953

Subgroups — #15833953

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#13123834C211yesmaximal, characteristic, complemented
3#13123571C211yesmaximal, characteristic, complemented
4#13113749C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113713C211yesmaximal, characteristic, complemented
7#13113699C211yesmaximal, characteristic, complemented
8#13113671C211yesmaximal, characteristic, complemented
9#13113664C211yesmaximal, characteristic, complemented
10#13113647C211yesmaximal, characteristic, complemented
11#13113630C211yesmaximal, characteristic, complemented
12#13113299C211yesmaximal, characteristic, complemented
13#13113226C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1574C211yesmaximal, characteristic, complemented
16C2×M16×D13—21no—
17#11719184C2211yescharacteristic
18C2×C4×D52C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21C13×#423C2211yescharacteristic
22#11718787—21no—
23#11718586C2211yescharacteristic
24C4×#6099C2211yescharacteristic
25#11718508C411yescharacteristic
26#11718508C411yescharacteristic
27#11718505C411yescharacteristic
28#11718505C411yescharacteristic
29#11718499C2211yescharacteristic
30#11718499C2211yescharacteristic
31#11718499C2211yescharacteristic, complemented
32#11718497—21no—
33#11718497—21no—
34#11718495C2211yescharacteristic
35#11718495C2211yescharacteristic
36#11718495C2211yescharacteristic, complemented
37#11718492C2211yescharacteristic, complemented
38#11718491C2211yescharacteristic, complemented
39#11718396C411yescharacteristic
40#11718393C411yescharacteristic
41#11718392C411yescharacteristic
42#11718390—21no—
43#11718389—21no—
44#11718383C411yescharacteristic
45C4×D104C2211yescharacteristic
46C4×D104C2211yescharacteristic
47C4×#6095C2211yescharacteristic
48C4×#6095C2211yescharacteristic
49#11718351—21no—
50#11718350—21no—
51C13×#335C2211yescharacteristic, complemented
52C13×#335C2211yescharacteristic, complemented
53C13×#334C2211yescharacteristic, complemented
54C13×#334C2211yescharacteristic, complemented
55#11718076C2211yescharacteristic, complemented
56#11718076C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718075C2211yescharacteristic
60#11718075C2211yescharacteristic
61#11718075C2211yescharacteristic, complemented
62#11718075C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×M16—21no—
70C2×C42×C13C2311yescharacteristic
71#88184C2×C411yescharacteristic
72#88183—21no—
73C4×C22⋊D13—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13C2×C411yescharacteristic
76#88178C2×C411yescharacteristic
77C2×#6099D411yescharacteristic
78C2×#6099D411yescharacteristic
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×C4⋊C8C2311yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×C4⋊C8C2311yescharacteristic
109C13×C22⋊C8—21no—
110C13×C22⋊C8C2×C411yescharacteristic
111C13×C22⋊C8C2×C411yescharacteristic
112C4×C8×C13—21no—
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88061C2×C411yescharacteristic
118#88061C2×C411yescharacteristic
119#88061C2×C411yescharacteristic
120#88061C2×C411yescharacteristic
121#88061C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88058C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88057C2×C411yescharacteristic
131#88057C2×C411yescharacteristic
132#88056C2×C411yescharacteristic
133#88056C2×C411yescharacteristic
134#88055—21no—
135#88054—21no—
136#88054—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139#88043D411yescharacteristic
140#88043D411yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18006—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—42no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C42×C13C22×C411yescharacteristic
176C42×C13C2×D411yescharacteristic
177C42×C13#4111yescharacteristic
178C42×C13C2411yescharacteristic
179C22⋊Dic13—21no—
180#6103—21no—
181#6103—21no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13—21no—
198#6099—22no—
199#6099—41no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
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#1594—131no—
220#1590—131no—
221#1588—131no—
222#1586—131no—
223#1582—131no—
224#1581—131no—
225SD16⋊C8—131no—
226C8×D8—131no—
227#1574D1311yescharacteristic, complemented
228#1495—131no—
229#1478—131no—
230#1453—131no—
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—41no—
278C8×C13—41no—
279C8×C13—41no—
280C8×C13—41no—
281#1055—21no—
282#1055—21no—
283#1055—21no—
284#1055—41no—
285#1055—41no—
286#1055AGL(1,ℤ/8)12yes—
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#423C2×D1311yescharacteristic
319#407—261no—
320#405—261no—
321C4×M16—131no—
322#335C2×D1311yescharacteristic, complemented
323#335C2×D1311yescharacteristic, complemented
324#334C2×D1311yescharacteristic, complemented
325#334C2×D1311yescharacteristic, complemented
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#322—131no—
335#322—131no—
336#322—131no—
337C82—131no—
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—21no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16—261no—
375C2×M16—261no—
376C2×M16—261no—
377C2×M16—524no—
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—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8C4×D1311yescharacteristic
409C4⋊C8C4×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411C4⋊C8C22×D1311yescharacteristic
412C4⋊C8C22×D1311yescharacteristic
413C4⋊C8C22×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—131no—
433#97—131no—
434#97—261no—
435C4×C8—21no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—131no—
440C4×C8—261no—
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×C4D4×D1311yescharacteristic
469C22×C4#613111yescharacteristic
470SD16—262no—
471SD16—521no—
472D8—262no—
473D8—521no—
474M16—42no—
475M16—262no—
476M16—522no—
477M16—522no—
478M16—522no—
479M16—521no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—131no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—522no—
491C2×C8—522no—
492C2×C8—522no—
493C2×C8C2×C4×D1311yescharacteristic
494C2×C8C2×C4×D1311yescharacteristic
495C2×C8C2×C4×D1311yescharacteristic
496C2×C8C2×C4×D1311yescharacteristic
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
517C42D4×D1311yescharacteristic
518C42#613111yescharacteristic
519C42C23×D1311yescharacteristic
520C13#1800611yescharacteristic, complemented, Sylow
521C23—261no—
522C23—261no—
523C23—261no—
524C23—522no—
525C23—522no—
526C23—1041no—
527C23#8814711yescharacteristic
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×C4#8814711yescharacteristic
558C2×C4#8814711yescharacteristic
559C2×C4#8814711yescharacteristic
560C2×C4C22×C4×D1311yescharacteristic
561C2×C4C2×D4×D1311yescharacteristic
562C2×C4C2×#613111yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—132no—
572C8—261no—
573C8—261no—
574C8—261no—
575C8—521no—
576C8—521no—
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×#8814711yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—521no—
596C4—521no—
597C4—521no—
598C4—521no—
599C4—521no—
600C4D13×#13111yescharacteristic
601C4#1171945511yescharacteristic
602C4D13×AGL(1,ℤ/8)11yescharacteristic
603C4#1171948211yescharacteristic
604C2—41no—
605C2—522no—
606C2—1041no—
607C2—1041no—
608C2#1312356011yescharacteristic
609C2#1312364311yescharacteristic
610C2#1312375211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1574C2
socleC22×C13C2×C4×D4
prime radical#11718393C4
cosocleC42×C13C24
hypercenter#1574D13
hypocenterC13#18006
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
2. #13123834C2semidirect
3. #13123571C2semidirect
4. #13113749C2semidirect
5. #13113725C2semidirect
6. #13113713C2semidirect
7. #13113699C2semidirect
8. #13113671C2semidirect
9. #13113664C2semidirect
10. #13113647C2semidirect
11. #13113630C2semidirect
12. #13113299C2semidirect
13. #13113226C2semidirect
14. #13113131C2semidirect
15. C13×#1574C2semidirect
31. #11718499C22semidirect
36. #11718495C22semidirect
37. #11718492C22semidirect
38. #11718491C22semidirect
51. C13×#335C22semidirect
52. C13×#335C22semidirect
53. C13×#334C22semidirect
54. C13×#334C22semidirect
55. #11718076C22semidirect
56. #11718076C22semidirect
61. #11718075C22semidirect
62. #11718075C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
227. #1574D13semidirect
322. #335C2×D13semidirect
323. #335C2×D13semidirect
324. #334C2×D13semidirect
325. #334C2×D13semidirect
520. C13#18006semidirect

Maximal subgroups

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

subgroupindex
#131248852
#131238342
#131235712
#131137492
#131137252
#131137132
#131136992
#131136712
#131136642
#131136472
#131136302
#131132992
#131132262
#131131312
C13×#15742
#1800613