Finite Group Databasebeta

← #15834779

Subgroups — #15834779

Order 3328.

656 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#13125432C211yesmaximal, characteristic
2#13123841C211yesmaximal, characteristic, complemented
3#13123579C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113723C211yesmaximal, characteristic, complemented
6#13113711C211yesmaximal, characteristic, complemented
7#13113703C211yesmaximal, characteristic, complemented
8#13113675C211yesmaximal, characteristic, complemented
9#13113662C211yesmaximal, characteristic, complemented
10#13113651C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113586C211yesmaximal, characteristic, complemented
13#13113254C211yesmaximal, characteristic, complemented
14#13113139C211yesmaximal, characteristic, complemented
15C13×#1483C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17C2×#88155—21no—
18#11719182C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718771—21no—
22#11718728C411yescharacteristic
23#11718726C411yescharacteristic
24#11718719C411yescharacteristic
25#11718716C411yescharacteristic
26#11718710C411yescharacteristic
27#11718710C411yescharacteristic
28#11718700C411yescharacteristic
29#11718700C411yescharacteristic
30C4×#6106C2211yescharacteristic
31C4×#6106C2211yescharacteristic
32#11718685C2211yescharacteristic
33Q8×#1055C2211yescharacteristic
34C4×#6104C2211yescharacteristic
35C4×#6104C2211yescharacteristic
36#11718673—21no—
37#11718673C2211yescharacteristic
38#11718672—21no—
39D4×#1055C2211yescharacteristic
40#11718661—21no—
41#11718658—21no—
42#11718586C2211yescharacteristic
43C4×#6099C2211yescharacteristic
44C4×#6099C2211yescharacteristic
45#11718499C2211yescharacteristic
46#11718499C2211yescharacteristic
47#11718497—21no—
48#11718497—21no—
49#11718495C2211yescharacteristic
50#11718495C2211yescharacteristic
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6127—21no—
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C13×#126—21no—
71C13×#125C2×C411yescharacteristic
72C13×#124C2×C411yescharacteristic
73C13×#123—21no—
74C13×C22⋊Q8C2×C411yescharacteristic
75C13×#121C2×C411yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C4×D4×C13—21no—
78C4×D4×C13C2311yescharacteristic
79C13×#117—21no—
80C2×C42×C13C2311yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84C2×#6104C2×C411yescharacteristic
85#88184—21no—
86#88184C2×C411yescharacteristic
87#88184C2×C411yescharacteristic
88C2×#6099—21no—
89C2×#6099C2×C411yescharacteristic
90C2×#6099C2×C411yescharacteristic
91C2×#6099D411yescharacteristic
92C2×#6099D411yescharacteristic
93C22×#1055—21no—
94#88155—44no—
95C2×#6094—21no—
96C2×#6094—21no—
97C2×C8×D13—21no—
98C2×C8×D13—21no—
99#88129—21no—
100#88128C2×C411yescharacteristic
101C4×D52—21no—
102C4×D52C2311yescharacteristic
103C4×D52C2311yescharacteristic
104#88123C2×C411yescharacteristic
105C13×C4⋊C8—21no—
106C13×C4⋊C8C2311yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×#97—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060—21no—
122#88049C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88049C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88048C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129#88047C2×C411yescharacteristic
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134#88043—21no—
135#88043C2×C411yescharacteristic
136#88043C2×C411yescharacteristic
137#88043D411yescharacteristic
138#88043D411yescharacteristic
139C4×#1055—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#18076—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13—21no—
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13#4111yescharacteristic
153C2×C22⋊D13—21no—
154C2×C22⋊D13—21no—
155#6127—42no—
156#6127—42no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52C22×C411yescharacteristic
160C2×D52C22×C411yescharacteristic
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×Dic26—21no—
164C13×M16—42no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—42no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4C22×C411yescharacteristic
175C13×C4⋊C4C22×C411yescharacteristic
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C42×C13—21no—
182C42×C13C22×C411yescharacteristic
183C42×C13C2×D411yescharacteristic
184C42×C13#4111yescharacteristic
185C42×C13C2411yescharacteristic
186#6106—22no—
187#6106—41no—
188#6104—22no—
189#6104—41no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6099—22no—
198#6099—22no—
199#6099—41no—
200#6099—41no—
201#6099—42no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—42no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213#6094—42no—
214#6094—42no—
215C8×D13—42no—
216C8×D13—42no—
217#3171—131no—
218#2969—131no—
219#2935—131no—
220#1594—131no—
221#1590—131no—
222#1588—131no—
223#1586—131no—
224#1582—131no—
225#1581—131no—
226SD16⋊C8—131no—
227C8×D8—131no—
228#1565—131no—
229#1484—131no—
230#1483D1311yescharacteristic, complemented
231#1455—131no—
232C23×C13—21no—
233C23×C13C4×D411yescharacteristic
234C22×D13—21no—
235C22×D13—21no—
236Q8×C13—21no—
237Q8×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—81no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C22⋊D13—42no—
258C22⋊D13—42no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261D52—21no—
262D52—21no—
263D52—21no—
264D52—21no—
265D52—42no—
266D52—81no—
267C4×D13—41no—
268C4×D13—41no—
269C4×D13—41no—
270C4×D13—41no—
271Dic26—42no—
272C8×C13—22no—
273C8×C13—41no—
274C8×C13—41no—
275C8×C13—41no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—41no—
283#1055—41no—
284#1055#13112yescomplemented
285#1055AGL(1,ℤ/8)12yes—
286C2×#131—261no—
287#532—131no—
288#529C2×D1311yescharacteristic
289#501—131no—
290#496—131no—
291#490—131no—
292#489—131no—
293#469—131no—
294#469—131no—
295#468—131no—
296#468—131no—
297#446—131no—
298C8×Q8—131no—
299C4×SD16—131no—
300C4×SD16—131no—
301C4×D8—131no—
302C4×D8—131no—
303#436—131no—
304#436—131no—
305#436—131no—
306#436—261no—
307#435—261no—
308#435—261no—
309#435—261no—
310C8×D4—131no—
311C8×D4—131no—
312C8×D4—131no—
313#433—261no—
314#431—131no—
315C2×C4⋊C8C2×D1311yescharacteristic
316#408—261no—
317#405—261no—
318C4×M16—131no—
319C4×M16—131no—
320C4×M16C2×D1311yescharacteristic
321#335—131no—
322#335—131no—
323#334—131no—
324#334—131no—
325Q8⋊C8C2×D1311yescharacteristic
326Q8⋊C8C2×D1311yescharacteristic
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8C2×D1311yescharacteristic
332D4⋊C8C2×D1311yescharacteristic
333#322—131no—
334#322—131no—
335#322—131no—
336C82—131no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13C2×C4×D411yescharacteristic
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13C2×#13111yescharacteristic
358C4×C13#56811yescharacteristic
359C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
360C4×C13#57511yescharacteristic
361Dic13—41no—
362Dic13—41no—
363C2×#41—261no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×D8—131no—
367C2×D8—131no—
368#131—524no—
369C2×M16—21no—
370C2×M16—131no—
371C2×M16—131no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16—261no—
375C2×M16—261no—
376C2×M16—261no—
377C22×C8—21no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381C4⋊Q8—131no—
382#127—131no—
383#126—21no—
384#125C4×D1311yescharacteristic
385#124—261no—
386#124C4×D1311yescharacteristic
387#123—21no—
388C22⋊Q8C4×D1311yescharacteristic
389#121—131no—
390#121—131no—
391#121—261no—
392#121C4×D1311yescharacteristic
393C4×Q8C22×D1311yescharacteristic
394C4×D4—21no—
395C4×D4—131no—
396C4×D4—131no—
397C4×D4—261no—
398C4×D4C22×D1311yescharacteristic
399#117—21no—
400C2×C42C22×D1311yescharacteristic
401#107—131no—
402#107—131no—
403#106—131no—
404#106—131no—
405C4⋊C8—21no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—261no—
409C4⋊C8—261no—
410C4⋊C8C22×D1311yescharacteristic
411C4⋊C8C22×D1311yescharacteristic
412#103—131no—
413#103—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427#97—21no—
428#97—131no—
429#97—131no—
430#97—131no—
431#97—131no—
432#97—261no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—131no—
437C4×C8—261no—
438C4×C8—261no—
439C4×C8C22×D1311yescharacteristic
440C4×C8C22×D1311yescharacteristic
441C2×C13—41no—
442C2×C13—81no—
443C2×C13#293511yescharacteristic
444C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
445C2×C13#295611yescharacteristic
446D13—81no—
447D13—81no—
448#41—522no—
449#41—522no—
450C2×Q8—261no—
451C2×Q8C2×C4×D1311yescharacteristic
452C2×D4—21no—
453C2×D4—131no—
454C2×D4—131no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4C2×C4×D1311yescharacteristic
460C22×C4—21no—
461C22×C4—261no—
462C22×C4—261no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4D4×D1311yescharacteristic
465C22×C4#612911yescharacteristic
466SD16—262no—
467SD16—521no—
468D8—262no—
469D8—521no—
470M16—42no—
471M16—262no—
472M16—262no—
473M16—522no—
474M16—522no—
475M16—521no—
476M16—521no—
477M16—522no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—42no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—131no—
487C2×C8—131no—
488C2×C8—131no—
489C2×C8—131no—
490C2×C8—131no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—522no—
494C2×C8—522no—
495C2×C8—522no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—131no—
501C4⋊C4—131no—
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—21no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C42—21no—
515C42C2×C4×D1311yescharacteristic
516C42D4×D1311yescharacteristic
517C42#612911yescharacteristic
518C42C23×D1311yescharacteristic
519C13#1807611yescharacteristic, complemented, Sylow
520C23—21no—
521C23—261no—
522C23—261no—
523C23#8813511yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—522no—
527D4—21no—
528D4—21no—
529D4—81no—
530D4—261no—
531D4—261no—
532D4—261no—
533D4—261no—
534D4—522no—
535D4—522no—
536D4—522no—
537D4—1041no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4#8813511yescharacteristic
555C2×C4#8813511yescharacteristic
556C2×C4#8813511yescharacteristic
557C2×C4C22×C4×D1311yescharacteristic
558C2×C4C2×D4×D1311yescharacteristic
559C2×C4C2×#612911yescharacteristic
560C8—22no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—132no—
565C8—132no—
566C8—261no—
567C8—261no—
568C8—261no—
569C8—261no—
570C8—261no—
571C8—261no—
572C8—521no—
573C8—521no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22—521no—
586C22C2×#8813511yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—521no—
595C4—521no—
596C4D13×#13111yescharacteristic
597C4#1171945511yescharacteristic
598C4D13×AGL(1,ℤ/8)11yescharacteristic
599C4#1171948211yescharacteristic
600C2—41no—
601C2—81no—
602C2—1041no—
603C2—1041no—
604C2#1312357611yescharacteristic
605C2#1312364911yescharacteristic
606C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1483C2
socleC22×C13C2×C4×D4
prime radical#13125432C2
cosocleC42×C13C24
hypercenter#1483D13
hypocenterC13#18076
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #13123841C2semidirect
3. #13123579C2semidirect
4. #13113747C2semidirect
5. #13113723C2semidirect
6. #13113711C2semidirect
7. #13113703C2semidirect
8. #13113675C2semidirect
9. #13113662C2semidirect
10. #13113651C2semidirect
11. #13113628C2semidirect
12. #13113586C2semidirect
13. #13113254C2semidirect
14. #13113139C2semidirect
15. C13×#1483C2semidirect
230. #1483D13semidirect
284. #1055#131semidirect
519. C13#18076semidirect

Maximal subgroups

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

subgroupindex
#131254322
#131238412
#131235792
#131137472
#131137232
#131137112
#131137032
#131136752
#131136622
#131136512
#131136282
#131135862
#131132542
#131131392
C13×#14832
#1807613