Finite Group Databasebeta

← #15833143

Subgroups — #15833143

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#13124854C211yesmaximal, characteristic
2#13123805C211yesmaximal, characteristic, complemented
3#13123803C211yesmaximal, characteristic, complemented
4#13113730C211yesmaximal, characteristic, complemented
5#13113729C211yesmaximal, characteristic, complemented
6#13113723C211yesmaximal, characteristic, complemented
7#13113718C211yesmaximal, characteristic, complemented
8#13113689C211yesmaximal, characteristic, complemented
9#13113682C211yesmaximal, characteristic, complemented
10#13113675C211yesmaximal, characteristic, complemented
11#13113668C211yesmaximal, characteristic, complemented
12#13113617C211yesmaximal, characteristic, complemented
13#13113245C211yesmaximal, characteristic, complemented
14#13113120C211yesmaximal, characteristic, complemented
15C13×#1488C211yesmaximal, characteristic, complemented
16C4×C13×#41C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718900C411yescharacteristic
21#11718899C411yescharacteristic
22C4×#6107C2211yescharacteristic
23#11718689C411yescharacteristic
24C4×#6106C2211yescharacteristic
25#11718685C2211yescharacteristic
26#11718685C2211yescharacteristic
27#11718683C411yescharacteristic
28C4×#6105C2211yescharacteristic
29#11718677C411yescharacteristic
30C4×#6104C2211yescharacteristic
31#11718673C2211yescharacteristic
32#11718673C2211yescharacteristic
33#11718672—21no—
34#11718672—21no—
35#11718670C411yescharacteristic
36#11718664C411yescharacteristic
37#11718657C411yescharacteristic
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718586C2211yescharacteristic
41C4×#6099—21no—
42C2×C4×#1055C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718495C2211yescharacteristic
45#11718492C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718391—21no—
48#11718386—21no—
49#11718370—21no—
50#11718369—21no—
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#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C4×Q8×C13C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×D4×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13C2×C411yescharacteristic
73C4×D4×C13C2311yescharacteristic
74C13×#117—21no—
75C13×#117C2×C411yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6106C2×C411yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6104C2×C411yescharacteristic
82#88184C2×C411yescharacteristic
83#88183—21no—
84C4×C22⋊D13—21no—
85#88178C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099—21no—
88C22×#1055D411yescharacteristic
89C22×#1055D411yescharacteristic
90C2×#6094—21no—
91C2×C8×D13—21no—
92#88130—21no—
93#88129C2×C411yescharacteristic
94C4×D52C2311yescharacteristic
95#88126—21no—
96#88124C2×C411yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C22⋊C8—21no—
102C13×C22⋊C8—21no—
103C13×#97—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110C22⋊#1055—21no—
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055C2×C411yescharacteristic
114C22⋊#1055C2×C411yescharacteristic
115#88060—21no—
116#88060—21no—
117#88055—21no—
118#88054—21no—
119#88054—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88049C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055C2×C411yescharacteristic
132C4⋊#1055C2×C411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137C4×#1055—21no—
138C4×#1055D411yescharacteristic
139C4×#1055D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17932—131nomaximal, Sylow
145C13×#41—41no—
146C13×#41—41no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13—21no—
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C2×C22⋊D13—21no—
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×Dic26C22×C411yescharacteristic
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C4⋊C4C22×C411yescharacteristic
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C13×C22⋊C4—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6107—41no—
180#6106—41no—
181#6105—41no—
182#6104—41no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194#6099—42no—
195#6099—42no—
196C2×#1055—22no—
197C2×#1055—22no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6094—42no—
209C8×D13—42no—
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#1581—131no—
221#1572—131no—
222#1488D1311yescharacteristic, complemented
223#1482—131no—
224#1450—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227C22×D13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—42no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C4×D411yescharacteristic
248C2×C4×C13C23×C411yescharacteristic
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C22⋊D13—42no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255D52—21no—
256D52—21no—
257C4×D13—41no—
258C4×D13—41no—
259Dic26—21no—
260Dic26—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
271#1055—41no—
272#1055—41no—
273#1055#13512yes—
274#1055#13512yes—
275#529—131no—
276C4×#41C2×D1311yescharacteristic
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×D8—131no—
293#436—131no—
294#436—131no—
295#436—131no—
296#435—261no—
297#435—261no—
298#435—261no—
299C8×D4—131no—
300C8×D4—261no—
301#433—261no—
302#432C2×D1311yescharacteristic
303#431—131no—
304#431—131no—
305#431—261no—
306#431C2×D1311yescharacteristic
307#405—261no—
308C4×M16—261no—
309C2×C4×C8—131no—
310#335—131no—
311#335—131no—
312#334—131no—
313#334—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8C2×D1311yescharacteristic
317Q8⋊C8C2×D1311yescharacteristic
318D4⋊C8—131no—
319D4⋊C8—131no—
320D4⋊C8C2×D1311yescharacteristic
321D4⋊C8C2×D1311yescharacteristic
322#322—131no—
323#322—131no—
324C82—131no—
325C82—131no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13—21no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13C2×C4×D411yescharacteristic
333C2×D13—41no—
334C2×D13—41no—
335C2×D13—41no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13—41no—
343C4×C13#56811yescharacteristic
344C4×C13#56811yescharacteristic
345C4×C13C2×#13511yescharacteristic
346C4×C13C2×#13511yescharacteristic
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350C2×#41C4×D1311yescharacteristic
351C2×Q16—131no—
352C2×SD16—131no—
353C2×SD16—131no—
354C2×D8—131no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—261no—
361#126—261no—
362#125—131no—
363#124—131no—
364#123—261no—
365C22⋊Q8—131no—
366#121—131no—
367C4×Q8—131no—
368C4×Q8C4×D1311yescharacteristic
369C4×Q8C22×D1311yescharacteristic
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—131no—
373C4×D4—261no—
374C4×D4C4×D1311yescharacteristic
375C4×D4C22×D1311yescharacteristic
376#117—21no—
377#117—261no—
378#117C4×D1311yescharacteristic
379C2×C42—21no—
380C2×C42C22×D1311yescharacteristic
381#107—131no—
382#107—131no—
383#106—131no—
384#106—131no—
385C4⋊C8—21no—
386C4⋊C8—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—131no—
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#102—131no—
403#102—131no—
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—21no—
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—131no—
423C4×C8—261no—
424C4×C8—261no—
425C4×C8C22×D1311yescharacteristic
426C4×C8C22×D1311yescharacteristic
427C2×C13—41no—
428C2×C13—81no—
429C2×C13#293011yescharacteristic
430C2×C13C4×#13511yescharacteristic
431C2×C13#295511yescharacteristic
432D13—81no—
433#41—41no—
434#41—41no—
435C2×Q8—131no—
436C2×Q8C2×C4×D1311yescharacteristic
437C2×D4—21no—
438C2×D4—131no—
439C2×D4—261no—
440C2×D4C2×C4×D1311yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—261no—
445C22×C4C2×C4×D1311yescharacteristic
446C22×C4D4×D1311yescharacteristic
447C22×C4#612911yescharacteristic
448Q16—521no—
449SD16—521no—
450SD16—521no—
451D8—521no—
452M16—522no—
453M16—522no—
454M16—522no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—131no—
462C2×C8—131no—
463C2×C8—131no—
464C2×C8—131no—
465C2×C8—131no—
466C2×C8—131no—
467C2×C8—262no—
468C2×C8—262no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—522no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—131no—
475C4⋊C4—131no—
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—21no—
485C22⋊C4—261no—
486C22⋊C4—261no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—261no—
494C42C2×C4×D1311yescharacteristic
495C42D4×D1311yescharacteristic
496C42#612911yescharacteristic
497C42C23×D1311yescharacteristic
498C13#1793211yescharacteristic, complemented, Sylow
499C23—21no—
500C23—261no—
501C23#8813511yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—261no—
505Q8—261no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—261no—
510D4—261no—
511D4—522no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4#8813511yescharacteristic
530C2×C4#8813511yescharacteristic
531C2×C4#8813511yescharacteristic
532C2×C4C22×C4×D1311yescharacteristic
533C2×C4C2×D4×D1311yescharacteristic
534C2×C4C2×#612911yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—132no—
540C8—132no—
541C8—261no—
542C8—261no—
543C8—261no—
544C8—261no—
545C8—261no—
546C8—261no—
547C8—521no—
548C8—521no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—521no—
556C22—521no—
557C22—521no—
558C22C2×#8813511yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—521no—
567C4—521no—
568C4—521no—
569C4#1171945011yescharacteristic
570C4#1171945011yescharacteristic
571C4D13×#13511yescharacteristic
572C4D13×#13511yescharacteristic
573C2—41no—
574C2—81no—
575C2—1041no—
576C2#1312353511yescharacteristic
577C2#1312360411yescharacteristic
578C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1488C2
socleC22×C13C2×C4×D4
prime radical#11718899C4
cosocleC42×C13C24
hypercenter#1488D13
hypocenterC13#17932
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #13123805C2semidirect
3. #13123803C2semidirect
4. #13113730C2semidirect
5. #13113729C2semidirect
6. #13113723C2semidirect
7. #13113718C2semidirect
8. #13113689C2semidirect
9. #13113682C2semidirect
10. #13113675C2semidirect
11. #13113668C2semidirect
12. #13113617C2semidirect
13. #13113245C2semidirect
14. #13113120C2semidirect
15. C13×#1488C2semidirect
222. #1488D13semidirect
498. C13#17932semidirect

Maximal subgroups

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

subgroupindex
#131248542
#131238052
#131238032
#131137302
#131137292
#131137232
#131137182
#131136892
#131136822
#131136752
#131136682
#131136172
#131132452
#131131202
C13×#14882
#1793213