Finite Group Databasebeta

← #15833644

Subgroups — #15833644

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125404C211yesmaximal, characteristic
2#13123814C211yesmaximal, characteristic, complemented
3#13123808C211yesmaximal, characteristic, complemented
4#13113688C211yesmaximal, characteristic, complemented
5#13113685C211yesmaximal, characteristic, complemented
6#13113682C211yesmaximal, characteristic, complemented
7#13113677C211yesmaximal, characteristic, complemented
8#13113672C211yesmaximal, characteristic, complemented
9#13113669C211yesmaximal, characteristic, complemented
10#13113666C211yesmaximal, characteristic, complemented
11#13113598C211yesmaximal, characteristic, complemented
12#13113293C211yesmaximal, characteristic, complemented
13#13113293C211yesmaximal, characteristic, complemented
14D13×#322C211yesmaximal, characteristic, complemented
15C13×#1581C211yesmaximal, characteristic, complemented
16#11719262C2211yescharacteristic
17#11719262C2211yescharacteristic
18C4×C13×D8C2211yescharacteristic
19C13×#436C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718818C411yescharacteristic
22#11718816C411yescharacteristic
23#11718788—21no—
24#11718783—21no—
25C8×C22⋊D13—21no—
26#11718762—21no—
27C4×#6105C2211yescharacteristic
28C4×#6105C2211yescharacteristic
29#11718673C2211yescharacteristic
30D4×#1055C2211yescharacteristic
31#11718548C411yescharacteristic
32#11718539C411yescharacteristic
33#11718496C2211yescharacteristic
34#11718496C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718439C411yescharacteristic
38#11718439C411yescharacteristic
39#11718429C411yescharacteristic
40#11718429C411yescharacteristic
41#11718389—21no—
42#11718386—21no—
43#11718381—21no—
44#11718381—21no—
45C4×Dic52C2211yescharacteristic
46C4×C8×D13C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
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
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×C13×D8C2×C411yescharacteristic
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C4×D4×C13C2311yescharacteristic
71C4×D4×C13C2311yescharacteristic
72#88192C2×C411yescharacteristic
73#88192C2×C411yescharacteristic
74#88190C2×C411yescharacteristic
75#88190C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C4×C22⋊D13—21no—
80#88180—21no—
81#88180—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84C2×Dic52C2×C411yescharacteristic
85C2×C8×D13—21no—
86C2×C8×D13C2×C411yescharacteristic
87C2×C8×D13C2×C411yescharacteristic
88C2×C8×D13D411yescharacteristic
89C2×C8×D13D411yescharacteristic
90#88151C2×C411yescharacteristic
91#88151C2×C411yescharacteristic
92#88144C2×C411yescharacteristic
93#88144C2×C411yescharacteristic
94#88137—21no—
95#88137—21no—
96#88133—21no—
97#88133—21no—
98C42×D13C2311yescharacteristic
99C4×Dic26C2311yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×#107C2×C411yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#102C2×C411yescharacteristic
105C13×#102C2×C411yescharacteristic
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88072C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115#88060—21no—
116#88060—21no—
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—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131C8×Dic13C2×C411yescharacteristic
132C8×Dic13C2×C411yescharacteristic
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#17978—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—
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C2×D411yescharacteristic
153C2×C4×D13#4111yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C2×Dic26C22×C411yescharacteristic
156C13×D8—41no—
157C13×M16—42no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—42no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C4⋊C4C22×C411yescharacteristic
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C42×C13C2411yescharacteristic
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173C22⋊Dic13—21no—
174C22⋊Dic13—21no—
175C22⋊Dic13—21no—
176C22⋊Dic13—21no—
177#6105—41no—
178#6105—41no—
179#6103—21no—
180#6103—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—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×Dic13C22×C411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13#4111yescharacteristic
196#6099—42no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—42no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205Dic52—41no—
206C8×D13—22no—
207C8×D13—22no—
208C8×D13—41no—
209C8×D13—41no—
210C8×D13—42no—
211#3168—131no—
212#2966—131no—
213#2966—131no—
214#1584—131no—
215#1584—131no—
216#1583—131no—
217#1583—131no—
218#1582—131no—
219#1582—131no—
220#1581—131no—
221#1581D1311yescharacteristic, complemented
222#1568—131no—
223#1494—131no—
224#1494—131no—
225C2×#322—131no—
226C23×C13—21no—
227C23×C13—21no—
228C22×D13C4×D411yescharacteristic
229D4×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13C23×C411yescharacteristic
240C2×C4×C13C22×D411yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C22⋊D13—42no—
243C22⋊D13—42no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13C4×D411yescharacteristic
249C2×Dic13C4×D411yescharacteristic
250C2×Dic13C4×D411yescharacteristic
251C4×D13—22no—
252C4×D13—21no—
253C4×D13—21no—
254C4×D13—21no—
255C4×D13—21no—
256Dic26—21no—
257Dic26—21no—
258Dic26—21no—
259Dic26—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13#13512yes—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273#1055#13512yes—
274#529—131no—
275#529—131no—
276#499—131no—
277#495—131no—
278#488—131no—
279#488—131no—
280#467—131no—
281#466—131no—
282#465—131no—
283#465—131no—
284#446—131no—
285#446—131no—
286C8×Q8—131no—
287C8×Q8—131no—
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16—131no—
291C4×D8C2×D1311yescharacteristic
292#436—131no—
293#436C2×D1311yescharacteristic
294#435—261no—
295#435—261no—
296C8×D4—131no—
297C8×D4—261no—
298C8×D4—261no—
299C8×D4C2×D1311yescharacteristic
300#433—261no—
301#433—261no—
302#432—131no—
303#432—131no—
304#405—261no—
305#405—261no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308C2×C4×C8—131no—
309#335—131no—
310#335C2×D1311yescharacteristic
311#334—131no—
312#334—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8C2×D1311yescharacteristic
320D4⋊C8C2×D1311yescharacteristic
321#322—131no—
322#322—131no—
323#322—131no—
324#322C2×D1311yescharacteristic
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13C2×C4×D411yescharacteristic
332C2×D13—21no—
333C2×D13—21no—
334C2×D13#44412yes—
335C4×C13—21no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13#56811yescharacteristic
339C4×C13#56811yescharacteristic
340C4×C13C2×#13511yescharacteristic
341C4×C13C2×#13511yescharacteristic
342Dic13—21no—
343Dic13—21no—
344Dic13—21no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349C2×Q16—131no—
350C2×SD16—131no—
351C2×SD16—131no—
352C2×D8C4×D1311yescharacteristic
353C2×M16—21no—
354C2×M16—261no—
355C22×C8—21no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—131no—
360C22×C8—261no—
361C22×C8—261no—
362#126—261no—
363#126—261no—
364#125—131no—
365#125—131no—
366#124—131no—
367#124—131no—
368#123—261no—
369#123—261no—
370C22⋊Q8—131no—
371C22⋊Q8—131no—
372#121—131no—
373#121—131no—
374C4×Q8—131no—
375C4×Q8—131no—
376C4×D4—261no—
377C4×D4—261no—
378C4×D4C22×D1311yescharacteristic
379C4×D4C22×D1311yescharacteristic
380#117—261no—
381#117—261no—
382C2×C42—131no—
383#107—131no—
384#107C4×D1311yescharacteristic
385#106—131no—
386#106—131no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8C22×D1311yescharacteristic
394C4⋊C8C22×D1311yescharacteristic
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#102—131no—
400#102—131no—
401#102C4×D1311yescharacteristic
402#102C4×D1311yescharacteristic
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409#97—261no—
410#97—261no—
411#97—261no—
412#97—261no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—261no—
421C4×C8—261no—
422C4×C8—261no—
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C2×C13—81no—
427C2×C13—81no—
428C2×C13#293211yescharacteristic
429C2×C13C4×#13511yescharacteristic
430C2×C13C2×#44411yescharacteristic
431D13—22no—
432C2×Q8—131no—
433C2×Q8—131no—
434C2×D4—261no—
435C2×D4—261no—
436C2×D4C2×C4×D1311yescharacteristic
437C2×D4C2×C4×D1311yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443Q16—521no—
444SD16—521no—
445SD16—521no—
446D8—41no—
447M16—42no—
448M16—522no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—42no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—262no—
458C2×C8—262no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—521no—
463C2×C8—521no—
464C2×C8—522no—
465C2×C8—522no—
466C2×C8C2×C4×D1311yescharacteristic
467C2×C8C2×C4×D1311yescharacteristic
468C2×C8D4×D1311yescharacteristic
469C2×C8D4×D1311yescharacteristic
470C4⋊C4—131no—
471C4⋊C4—131no—
472C4⋊C4—261no—
473C4⋊C4—261no—
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—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—131no—
493C42—131no—
494C42—131no—
495C42—261no—
496C42—261no—
497C42C23×D1311yescharacteristic
498C13#1797811yescharacteristic, 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—262no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4C22×C4×D1311yescharacteristic
531C2×C4C2×D4×D1311yescharacteristic
532C2×C4#41×D1311yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—132no—
540C8—261no—
541C8—261no—
542C8—261no—
543C8—521no—
544C8—521no—
545C8—521no—
546C8#8816612yes—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—132no—
554C22—261no—
555C22—261no—
556C22C4×D4×D1311yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—261no—
561C4—261no—
562C4—261no—
563C4—521no—
564C4—521no—
565C4—521no—
566C4—521no—
567C4#1171945011yescharacteristic
568C4#1171945511yescharacteristic
569C4C2×#8816611yescharacteristic
570C4D13×#13511yescharacteristic
571C2—81no—
572C2—81no—
573C2—262no—
574C2#1312355011yescharacteristic
575C2C4×#8816611yescharacteristic
576C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1581C2
socleC22×C13C2×C4×D4
prime radical#11718818C4
cosocleC42×C13C24
hypercenter#1581D13
hypocenterC13#17978
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. #13123814C2semidirect
3. #13123808C2semidirect
4. #13113688C2semidirect
5. #13113685C2semidirect
6. #13113682C2semidirect
7. #13113677C2semidirect
8. #13113672C2semidirect
9. #13113669C2semidirect
10. #13113666C2semidirect
11. #13113598C2semidirect
12. #13113293C2semidirect
13. #13113293C2semidirect
14. D13×#322C2semidirect
15. C13×#1581C2semidirect
221. #1581D13semidirect
498. C13#17978semidirect

Maximal subgroups

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

subgroupindex
#131254042
#131238142
#131238082
#131136882
#131136852
#131136822
#131136772
#131136722
#131136692
#131136662
#131135982
#131132932
D13×#3222
C13×#15812
#1797813