Finite Group Databasebeta

← #15834036

Subgroups — #15834036

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124890C211yesmaximal, characteristic
2#13123853C211yesmaximal, characteristic, complemented
3#13123580C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113718C211yesmaximal, characteristic, complemented
6#13113717C211yesmaximal, characteristic, complemented
7#13113697C211yesmaximal, characteristic, complemented
8#13113682C211yesmaximal, characteristic, complemented
9#13113662C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113639C211yesmaximal, characteristic, complemented
12#13113622C211yesmaximal, characteristic, complemented
13#13113224C211yesmaximal, characteristic, complemented
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1496C211yesmaximal, characteristic, complemented
16C13×#532C2211yescharacteristic
17C2×#88202—21no—
18C4×#6127C2211yescharacteristic
19C13×#432C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718895—21no—
22#11718752C411yescharacteristic
23#11718745C411yescharacteristic
24#11718736C411yescharacteristic
25#11718733C411yescharacteristic
26#11718698C411yescharacteristic
27#11718698C411yescharacteristic
28#11718696C411yescharacteristic
29#11718696C411yescharacteristic
30C4×#6105C2211yescharacteristic
31C4×#6105C2211yescharacteristic
32C4×#6104C2211yescharacteristic
33C4×#6104C2211yescharacteristic
34#11718673C2211yescharacteristic
35#11718673C2211yescharacteristic
36#11718672—21no—
37#11718672—21no—
38D4×#1055C2211yescharacteristic
39D4×#1055C2211yescharacteristic
40#11718586C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718499C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718390—21no—
48#11718390—21no—
49#11718368—21no—
50#11718366—21no—
51C13×D4⋊C8C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C2×#6127C2×C411yescharacteristic
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×#127C2×C411yescharacteristic
71C13×#124—21no—
72C13×#121—21no—
73C13×#121C2×C411yescharacteristic
74C13×#121C2×C411yescharacteristic
75C4×D4×C13—21no—
76C4×D4×C13C2311yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C2×C42×C13C2311yescharacteristic
79#88202—44no—
80C2×#6105C2×C411yescharacteristic
81C2×#6105C2×C411yescharacteristic
82C2×#6104C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84C4×C22⋊D13—21no—
85C4×C22⋊D13—21no—
86#88180C2×C411yescharacteristic
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099D411yescharacteristic
90C2×#6099D411yescharacteristic
91C22×#1055—21no—
92C22×#1055—21no—
93C22×#1055—21no—
94C2×#6094—21no—
95C2×#6094—21no—
96C4×D52C2×C411yescharacteristic
97C4×D52C2311yescharacteristic
98#88126—21no—
99C42×D13—21no—
100C4×Dic26C2×C411yescharacteristic
101C4×Dic26C2311yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×#97—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043D411yescharacteristic
140#88043D411yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18011—131nomaximal, Sylow
146C13×#41—42no—
147C13×#41—42no—
148C2×Q8×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13C22×C411yescharacteristic
154C2×D4×C13C22×C411yescharacteristic
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13C22×C411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13#4111yescharacteristic
160C2×C22⋊D13—21no—
161#6127—22no—
162#6127—41no—
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×Dic26C22×C411yescharacteristic
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C42×C13C22×C411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13#4111yescharacteristic
182C42×C13C2411yescharacteristic
183C22⋊Dic13—21no—
184#6105—22no—
185#6105—22no—
186#6104—41no—
187#6104—41no—
188#6103—21no—
189#6103—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197#6099—22no—
198#6099—41no—
199#6099—42no—
200#6099—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—42no—
204C2×#1055—42no—
205C2×#1055—42no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213C2×#1055C2×D411yescharacteristic
214#6094—42no—
215#6094—42no—
216#3106—131no—
217#2971—131no—
218#2935—131no—
219#1594—131no—
220#1589—131no—
221#1588—131no—
222#1586—131no—
223#1583—131no—
224#1581—131no—
225SD16⋊C8—131no—
226C8×SD16—131no—
227#1573—131no—
228#1496D1311yescharacteristic, complemented
229#1477—131no—
230#1453—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13C4×D411yescharacteristic
234C22×D13—21no—
235Q8×C13—42no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—42no—
241D4×C13—42no—
242D4×C13—42no—
243D4×C13—81no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13C4×D411yescharacteristic
256C2×C4×C13C4×D411yescharacteristic
257C2×C4×C13C4×D411yescharacteristic
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C22⋊D13—42no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265D52—21no—
266D52—21no—
267C4×D13—42no—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—81no—
271Dic26—21no—
272Dic26#13112yescomplemented
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—21no—
283#1055—21no—
284#1055—41no—
285#1055—41no—
286#1055AGL(1,ℤ/8)12yes—
287C2×#131—261no—
288#532C2×D1311yescharacteristic
289C4×#41—131no—
290#482—131no—
291#482—131no—
292#477—131no—
293#476—131no—
294#460—131no—
295#459—131no—
296#449—131no—
297#449—131no—
298C8×Q8—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—131no—
308#436—261no—
309#436—261no—
310#435—261no—
311#435—261no—
312C8×D4—131no—
313C8×D4—131no—
314#432—261no—
315#432C2×D1311yescharacteristic
316#431—131no—
317#431C2×D1311yescharacteristic
318C2×C4⋊C8—131no—
319#408—261no—
320C4×M16—131no—
321C4×M16—261no—
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⋊C8C2×D1311yescharacteristic
331D4⋊C8C2×D1311yescharacteristic
332D4⋊C8C2×D1311yescharacteristic
333D4⋊C8C2×D1311yescharacteristic
334#322—131no—
335#322—131no—
336#322—131no—
337C82—131no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13C2×C4×D411yescharacteristic
348C2×D13—41no—
349C2×D13—41no—
350C2×D13—41no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13C2×#13111yescharacteristic
358C4×C13#56811yescharacteristic
359C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
360C4×C13#57511yescharacteristic
361Dic13—22no—
362Dic13—41no—
363Dic13—41no—
364C2×#41—21no—
365C2×#41—131no—
366C2×SD16—131no—
367C2×SD16—131no—
368C2×D8—131no—
369C2×D8—131no—
370#131—524no—
371C2×M16—131no—
372C2×M16—131no—
373C2×M16—261no—
374C2×M16—261no—
375C2×M16—261no—
376C2×M16—261no—
377C22×C8—261no—
378C22×C8—261no—
379C22×C8—261no—
380C4⋊Q8C4×D1311yescharacteristic
381#127C4×D1311yescharacteristic
382#124—21no—
383#121—21no—
384#121C4×D1311yescharacteristic
385#121C4×D1311yescharacteristic
386C4×Q8—131no—
387C4×Q8—131no—
388C4×D4—21no—
389C4×D4—131no—
390C4×D4—131no—
391C4×D4—261no—
392C4×D4—261no—
393C4×D4C22×D1311yescharacteristic
394C4×D4C22×D1311yescharacteristic
395#117—131no—
396#117—261no—
397C2×C42—261no—
398C2×C42C22×D1311yescharacteristic
399#107—131no—
400#107—131no—
401#106—131no—
402#106—131no—
403C4⋊C8—21no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—261no—
409C4⋊C8—261no—
410C4⋊C8—261no—
411C4⋊C8C22×D1311yescharacteristic
412C4⋊C8C22×D1311yescharacteristic
413#103—131no—
414#103—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—131no—
424C22⋊C8—131no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431#97—21no—
432#97—131no—
433#97—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—261no—
439C4×C8—261no—
440C4×C8C22×D1311yescharacteristic
441C4×C8C22×D1311yescharacteristic
442C2×C13—41no—
443C2×C13—81no—
444C2×C13—81no—
445C2×C13#293311yescharacteristic
446C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C13#295711yescharacteristic
448D13—81no—
449#41—42no—
450#41—42no—
451#41—262no—
452#41—521no—
453C2×Q8—21no—
454C2×Q8—131no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—131no—
460C2×D4—261no—
461C2×D4C2×C4×D1311yescharacteristic
462C2×D4C2×C4×D1311yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4C2×C4×D1311yescharacteristic
469C22×C4D4×D1311yescharacteristic
470C22×C4#612911yescharacteristic
471SD16—262no—
472SD16—262no—
473D8—521no—
474D8—521no—
475M16—262no—
476M16—522no—
477M16—522no—
478M16—522no—
479M16—521no—
480M16—522no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—131no—
488C2×C8—131no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—522no—
496C2×C8—522no—
497C2×C8—522no—
498C4⋊C4—21no—
499C4⋊C4—131no—
500C4⋊C4—131no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4C2×C4×D1311yescharacteristic
504C4⋊C4C2×C4×D1311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C42—261no—
513C42—261no—
514C42—261no—
515C42C2×C4×D1311yescharacteristic
516C42D4×D1311yescharacteristic
517C42#612911yescharacteristic
518C42C23×D1311yescharacteristic
519C13#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—261no—
523C23#8813511yescharacteristic
524Q8—42no—
525Q8—132no—
526Q8—261no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—81no—
535D4—261no—
536D4—261no—
537D4—522no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—522no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—1041no—
556C2×C4#8813511yescharacteristic
557C2×C4#8813511yescharacteristic
558C2×C4#8813511yescharacteristic
559C2×C4C22×C4×D1311yescharacteristic
560C2×C4C2×D4×D1311yescharacteristic
561C2×C4C2×#612911yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—132no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—261no—
571C8—261no—
572C8—261no—
573C8—261no—
574C8—521no—
575C8—521no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—521no—
586C22—521no—
587C22—521no—
588C22C2×#8813511yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—41no—
594C4—41no—
595C4—262no—
596C4—521no—
597C4—521no—
598C4D13×#13111yescharacteristic
599C4#1171945511yescharacteristic
600C4D13×AGL(1,ℤ/8)11yescharacteristic
601C4#1171947811yescharacteristic
602C2—41no—
603C2—81no—
604C2—81no—
605C2—1041no—
606C2#1312356611yescharacteristic
607C2#1312364011yescharacteristic
608C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1496C2
socleC22×C13C2×C4×D4
prime radical#13124890C2
cosocleC42×C13C24
hypercenter#1496D13
hypocenterC13#18011
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1496

Complements

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

NH ≅ G/Ntype
2. #13123853C2semidirect
3. #13123580C2semidirect
4. #13113747C2semidirect
5. #13113718C2semidirect
6. #13113717C2semidirect
7. #13113697C2semidirect
8. #13113682C2semidirect
9. #13113662C2semidirect
10. #13113645C2semidirect
11. #13113639C2semidirect
12. #13113622C2semidirect
13. #13113224C2semidirect
14. #13113131C2semidirect
15. C13×#1496C2semidirect
228. #1496D13semidirect
272. Dic26#131semidirect
519. C13#18011semidirect

Maximal subgroups

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

subgroupindex
#131248902
#131238532
#131235802
#131137472
#131137182
#131137172
#131136972
#131136822
#131136622
#131136452
#131136392
#131136222
#131132242
#131131312
C13×#14962
#1801113