Finite Group Databasebeta

← #15833142

Subgroups — #15833142

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124850C211yesmaximal, characteristic
2#13123808C211yesmaximal, characteristic, complemented
3#13123799C211yesmaximal, characteristic, complemented
4#13113732C211yesmaximal, characteristic, complemented
5#13113729C211yesmaximal, characteristic, complemented
6#13113729C211yesmaximal, characteristic, complemented
7#13113721C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113677C211yesmaximal, characteristic, complemented
10#13113672C211yesmaximal, characteristic, complemented
11#13113615C211yesmaximal, characteristic, complemented
12#13113267C211yesmaximal, characteristic, complemented
13#13113241C211yesmaximal, characteristic, complemented
14#13113121C211yesmaximal, characteristic, complemented
15C13×#1581C211yesmaximal, characteristic, complemented
16#11719262C2211yescharacteristic
17C4×#6129C2211yescharacteristic
18C4×C13×D8C2211yescharacteristic
19C13×#436C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718819C411yescharacteristic
22#11718814C411yescharacteristic
23#11718788—21no—
24M16×Dic13—21no—
25C8×C22⋊D13—21no—
26#11718762—21no—
27C4×#6105C2211yescharacteristic
28C4×#6105C2211yescharacteristic
29#11718673C2211yescharacteristic
30#11718673C2211yescharacteristic
31#11718549C411yescharacteristic
32#11718538C411yescharacteristic
33#11718496C2211yescharacteristic
34#11718494C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718492C2211yescharacteristic
37#11718445C411yescharacteristic
38#11718444C411yescharacteristic
39#11718428C411yescharacteristic
40#11718427C411yescharacteristic
41#11718389—21no—
42#11718389—21no—
43#11718381—21no—
44#11718379—21no—
45C4×Dic52C2211yescharacteristic
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6129C2×C411yescharacteristic
68C2×C13×D8C2×C411yescharacteristic
69C2×C13×M16—21no—
70C22×C8×C13—21no—
71C4×D4×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73#88192C2×C411yescharacteristic
74#88190C2×C411yescharacteristic
75D4×Dic13C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C4×C22⋊D13—21no—
80#88180—21no—
81C2×C4×Dic13—21no—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×Dic52C2×C411yescharacteristic
85C2×C8×D13D411yescharacteristic
86C2×C8×D13D411yescharacteristic
87#88151C2×C411yescharacteristic
88#88146C2×C411yescharacteristic
89#88144C2×C411yescharacteristic
90#88141C2×C411yescharacteristic
91#88137—21no—
92#88135—21no—
93#88133—21no—
94#88131—21no—
95C42×D13C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×#107C2×C411yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×#102C2×C411yescharacteristic
102C13×#102C2×C411yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110C22⋊#1055—21no—
111C22⋊#1055—21no—
112#88060—21no—
113#88060—21no—
114#88060—21no—
115#88060C2×C411yescharacteristic
116#88060C2×C411yescharacteristic
117#88058C2×C411yescharacteristic
118#88056C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88055—21no—
121#88055—21no—
122#88055—21no—
123#88055—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054C2×C411yescharacteristic
130#88054C2×C411yescharacteristic
131C8×Dic13—21no—
132C8×Dic13—21no—
133C8×Dic13D411yescharacteristic
134C8×Dic13D411yescharacteristic
135#88050C2×C411yescharacteristic
136#88050C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138#88048C2×C411yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17932—131nomaximal, Sylow
145C2×D4×C13C22×C411yescharacteristic
146C2×D4×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153#6129—41no—
154#6129—41no—
155C2×C4×D13C22×C411yescharacteristic
156C2×C4×D13C2×D411yescharacteristic
157C2×C4×D13#4111yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C2×Dic26C22×C411yescharacteristic
160C13×D8—41no—
161C13×M16—42no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—42no—
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C22×C411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C42×C13C2411yescharacteristic
175C22⋊Dic13—21no—
176C22⋊Dic13—21no—
177C22⋊Dic13—21no—
178C22⋊Dic13—21no—
179#6105—41no—
180#6105—41no—
181#6103—21no—
182#6103—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13C22×C411yescharacteristic
196C4×Dic13C2×D411yescharacteristic
197C4×Dic13#4111yescharacteristic
198#6099—42no—
199#6099—42no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055C22×C411yescharacteristic
204C2×#1055C22×C411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207Dic52—41no—
208C8×D13—22no—
209C8×D13—22no—
210#3102—131no—
211#2966—131no—
212#2965—131no—
213#1591—131no—
214#1590—131no—
215#1590—131no—
216#1589—131no—
217#1584—131no—
218#1583—131no—
219#1582—131no—
220#1581D1311yescharacteristic, complemented
221#1572—131no—
222#1488—131no—
223#1482—131no—
224#1450—131no—
225C23×C13—21no—
226C23×C13—21no—
227C22×D13C4×D411yescharacteristic
228D4×C13—21no—
229D4×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13C23×C411yescharacteristic
239C2×C4×C13C22×D411yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C22⋊D13—42no—
242C22⋊D13—42no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—42no—
248C2×Dic13—42no—
249C2×Dic13C4×D411yescharacteristic
250C2×Dic13C4×D411yescharacteristic
251C2×Dic13C4×D411yescharacteristic
252C4×D13—21no—
253C4×D13—21no—
254C4×D13—21no—
255C4×D13—21no—
256C4×D13—41no—
257Dic26—21no—
258Dic26—21no—
259Dic26—21no—
260Dic26—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13#13512yes—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274#1055#13512yes—
275#529—131no—
276C4×#41—131no—
277#485—131no—
278#482—131no—
279#479—131no—
280#478—131no—
281#464—131no—
282#463—131no—
283#452—131no—
284#449—131no—
285#446—131no—
286#446—131no—
287#446—131no—
288C8×Q8—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16—131no—
292C4×D8C2×D1311yescharacteristic
293#436—131no—
294#436—131no—
295#436C2×D1311yescharacteristic
296#435—261no—
297#435—261no—
298#435—261no—
299C8×D4—261no—
300C8×D4C2×D1311yescharacteristic
301#433—261no—
302#432—131no—
303#431—131no—
304#431—131no—
305#431—131no—
306#431—261no—
307#405—261no—
308C4×M16—261no—
309C2×C4×C8—131no—
310#335—131no—
311#335C2×D1311yescharacteristic
312#334—131no—
313#334—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8—131no—
320D4⋊C8C2×D1311yescharacteristic
321D4⋊C8C2×D1311yescharacteristic
322#322—131no—
323#322C2×D1311yescharacteristic
324C82—131no—
325C82—131no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13C2×C4×D411yescharacteristic
333C2×D13—21no—
334C2×D13—21no—
335C2×D13—21no—
336C4×C13—21no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13#56811yescharacteristic
340C4×C13#56811yescharacteristic
341C4×C13C2×#13511yescharacteristic
342C4×C13C2×#13511yescharacteristic
343Dic13—21no—
344Dic13—21no—
345Dic13—21no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350C2×#41—131no—
351C2×Q16—131no—
352C2×SD16—131no—
353C2×SD16—131no—
354C2×D8C4×D1311yescharacteristic
355C2×M16—21no—
356C2×M16—261no—
357C2×M16—261no—
358C22×C8—21no—
359C22×C8—131no—
360C22×C8—131no—
361#126—261no—
362#125—131no—
363#124—131no—
364#123—261no—
365C22⋊Q8—131no—
366#121—131no—
367C4×Q8—131no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×D4—131no—
371C4×D4—261no—
372C4×D4—261no—
373C4×D4—261no—
374C4×D4C22×D1311yescharacteristic
375C4×D4C22×D1311yescharacteristic
376#117—131no—
377#117—261no—
378#117—261no—
379C2×C42—131no—
380C2×C42—261no—
381#107—131no—
382#107C4×D1311yescharacteristic
383#106—131no—
384#106—131no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8C22×D1311yescharacteristic
395C4⋊C8C22×D1311yescharacteristic
396#103—131no—
397#103—131no—
398#103—131no—
399#103—131no—
400#102—131no—
401#102—131no—
402#102C4×D1311yescharacteristic
403#102C4×D1311yescharacteristic
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—131no—
407C22⋊C8—131no—
408C22⋊C8—261no—
409C22⋊C8—261no—
410C22⋊C8—261no—
411C22⋊C8—261no—
412C22⋊C8—261no—
413#97—261no—
414#97—261no—
415#97—261no—
416#97—261no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—131no—
422C4×C8—261no—
423C4×C8—261no—
424C4×C8C22×D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C4×C8C22×D1311yescharacteristic
427C2×C13—81no—
428C2×C13—81no—
429C2×C13#293011yescharacteristic
430C2×C13C4×#13511yescharacteristic
431C2×C13#295511yescharacteristic
432D13—41no—
433#41—521no—
434#41—521no—
435C2×Q8—131no—
436C2×Q8—131no—
437C2×D4—261no—
438C2×D4—261no—
439C2×D4C2×C4×D1311yescharacteristic
440C2×D4C2×C4×D1311yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—261no—
447C22×C4—261no—
448Q16—521no—
449SD16—521no—
450SD16—521no—
451D8—41no—
452M16—42no—
453M16—522no—
454M16—522no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—42no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—131no—
463C2×C8—262no—
464C2×C8—262no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8C2×C4×D1311yescharacteristic
469C2×C8C2×C4×D1311yescharacteristic
470C2×C8D4×D1311yescharacteristic
471C2×C8D4×D1311yescharacteristic
472C4⋊C4—131no—
473C4⋊C4—131no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4C2×C4×D1311yescharacteristic
481C4⋊C4C2×C4×D1311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—261no—
485C22⋊C4—261no—
486C22⋊C4—261no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C42—131no—
491C42—131no—
492C42—131no—
493C42—261no—
494C42—261no—
495C42—261no—
496C42—261no—
497C42C23×D1311yescharacteristic
498C13#1793211yescharacteristic, complemented, Sylow
499C23—21no—
500C23—21no—
501C23—131no—
502Q8—261no—
503Q8—261no—
504Q8—261no—
505Q8—261no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—522no—
511D4—522no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—131no—
519C2×C4—131no—
520C2×C4—131no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—521no—
530C2×C4—522no—
531C2×C4—522no—
532C2×C4C22×C4×D1311yescharacteristic
533C2×C4C2×D4×D1311yescharacteristic
534C2×C4#41×D1311yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—132no—
542C8—261no—
543C8—261no—
544C8—261no—
545C8—521no—
546C8—521no—
547C8—521no—
548C8#8816612yes—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—261no—
556C22—261no—
557C22—261no—
558C22C4×D4×D1311yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—261no—
563C4—261no—
564C4—261no—
565C4—521no—
566C4—521no—
567C4—521no—
568C4—521no—
569C4#1171945011yescharacteristic
570C4#1171945511yescharacteristic
571C4C2×#8816611yescharacteristic
572C4D13×#13511yescharacteristic
573C2—81no—
574C2—81no—
575C2—521no—
576C2#1312353411yescharacteristic
577C2C4×#8816611yescharacteristic
578C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1581C2
socleC22×C13C2×C4×D4
prime radical#11718819C4
cosocleC42×C13C24
hypercenter#1581D13
hypocenterC13#17932
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #13123808C2semidirect
3. #13123799C2semidirect
4. #13113732C2semidirect
5. #13113729C2semidirect
6. #13113729C2semidirect
7. #13113721C2semidirect
8. #13113688C2semidirect
9. #13113677C2semidirect
10. #13113672C2semidirect
11. #13113615C2semidirect
12. #13113267C2semidirect
13. #13113241C2semidirect
14. #13113121C2semidirect
15. C13×#1581C2semidirect
220. #1581D13semidirect
498. C13#17932semidirect

Maximal subgroups

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

subgroupindex
#131248502
#131238082
#131237992
#131137322
#131137292
#131137212
#131136882
#131136772
#131136722
#131136152
#131132672
#131132412
#131131212
C13×#15812
#1793213