Finite Group Databasebeta

← #15834702

Subgroups — #15834702

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125400C211yesmaximal, characteristic
2#13123840C211yesmaximal, characteristic, complemented
3#13113731C211yesmaximal, characteristic, complemented
4#13113719C211yesmaximal, characteristic, complemented
5#13113679C211yesmaximal, characteristic, complemented
6#13113677C211yesmaximal, characteristic, complemented
7#13113672C211yesmaximal, characteristic, complemented
8#13113670C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10C8×#6104C211yesmaximal, characteristic, complemented
11#13113582C211yesmaximal, characteristic, complemented
12#13113244C211yesmaximal, characteristic, complemented
13#13113242C211yesmaximal, characteristic, complemented
14M16×#1055C211yesmaximal, characteristic, complemented
15C13×#2969C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436—21no—
21C13×#436C2211yescharacteristic
22C13×#435—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#405—21no—
27C4×C13×M16C2211yescharacteristic
28#11718789—21no—
29#11718788—21no—
30#11718729C411yescharacteristic
31#11718725C411yescharacteristic
32#11718720C411yescharacteristic
33#11718717C411yescharacteristic
34#11718712C411yescharacteristic
35#11718709C411yescharacteristic
36#11718702C411yescharacteristic
37#11718699C411yescharacteristic
38C4×#6107C2211yescharacteristic
39C4×#6106C2211yescharacteristic
40C4×#6105C2211yescharacteristic
41C4×#6104C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718370—21no—
46#11718369—21no—
47#11718349C2211yescharacteristic
48C8×D52C2211yescharacteristic
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16—21no—
68C2×C13×M16D411yescharacteristic
69C2×C13×M16D411yescharacteristic
70C22×C8×C13—21no—
71C13×#126—21no—
72C13×#125C2×C411yescharacteristic
73C13×#124C2×C411yescharacteristic
74C13×#123—21no—
75C13×C22⋊Q8C2×C411yescharacteristic
76C13×#121C2×C411yescharacteristic
77C4×Q8×C13C2311yescharacteristic
78C4×D4×C13—21no—
79C4×D4×C13C2311yescharacteristic
80C13×#117—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86#88184C2×C411yescharacteristic
87#88183—21no—
88C4×C22⋊D13—21no—
89#88178C2×C411yescharacteristic
90C22×#1055C2×C411yescharacteristic
91C22×#1055C2×C411yescharacteristic
92C2×#6094—21no—
93C2×C8×D13—21no—
94#88130—21no—
95#88129C2×C411yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98#88124C2×C411yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×#97—21no—
108C13×#97D411yescharacteristic
109C13×#97D411yescharacteristic
110C4×C8×C13—21no—
111C4×C8×C13—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88075C2×C411yescharacteristic
115#88075C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—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⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4×#1055—21no—
138C4×#1055C2×C411yescharacteristic
139C4×#1055C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18069—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×C22⋊D13—21no—
153C2×D52C22×C411yescharacteristic
154C2×C4×D13—21no—
155C2×Dic26C22×C411yescharacteristic
156C13×M16—22no—
157C13×M16—22no—
158C13×M16—42no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—42no—
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C42×C13—21no—
178C42×C13C22×C411yescharacteristic
179C42×C13C2×D411yescharacteristic
180C42×C13#4111yescharacteristic
181C42×C13C2411yescharacteristic
182C22⋊Dic13—21no—
183#6107—22no—
184#6106—41no—
185#6105—41no—
186#6104—22no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190#6103—21no—
191C4⋊Dic13C22×C411yescharacteristic
192C4⋊Dic13C22×C411yescharacteristic
193#6101—21no—
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13—21no—
198C2×#1055—22no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—41no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208#6094—42no—
209C8×D13—42no—
210#3168—131no—
211#2969—131no—
212#2969D1311yescharacteristic, complemented
213#1591—131no—
214#1589—131no—
215#1583—131no—
216#1583—131no—
217#1582—131no—
218#1582—131no—
219C8×Q16—131no—
220C8×D8—131no—
221#1564—131no—
222#1482—131no—
223#1482—131no—
224C8×M16—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227C22×D13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230D4×C13—21no—
231D4×C13—21no—
232D4×C13—81no—
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—41no—
242C2×C4×C13—41no—
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C22⋊D13—81no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253D52—21no—
254D52—21no—
255C4×D13—41no—
256C4×D13—41no—
257Dic26—21no—
258Dic26—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13#13512yes—
264C8×C13#13512yes—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272#1055#13112yes—
273#529—131no—
274#529C2×D1311yescharacteristic
275#499—131no—
276#495—131no—
277#488—131no—
278#488—131no—
279#467—131no—
280#466—131no—
281#465—131no—
282#465—131no—
283#446—131no—
284#446C2×D1311yescharacteristic
285C8×Q8—131no—
286C8×Q8C2×D1311yescharacteristic
287C4×Q16—131no—
288C4×SD16—131no—
289C4×SD16—131no—
290C4×D8—131no—
291#436—21no—
292#436—131no—
293#436—261no—
294#436C2×D1311yescharacteristic
295#435—21no—
296#435—261no—
297C8×D4—131no—
298C8×D4C2×D1311yescharacteristic
299#433—21no—
300#433—261no—
301#431—131no—
302#431—131no—
303#431C2×D1311yescharacteristic
304#405—21no—
305#405—261no—
306C4×M16C2×D1311yescharacteristic
307C2×C4×C8—131no—
308#335—131no—
309#335—131no—
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8—131no—
319D4⋊C8—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C82—131no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13C2×C4×D411yescharacteristic
331C2×D13—41no—
332C2×D13—41no—
333C2×D13—41no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13C2×#13111yescharacteristic
342C4×C13#56811yescharacteristic
343C4×C13C2×#13511yescharacteristic
344C4×C13C2×#13511yescharacteristic
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348C2×Q16—131no—
349C2×SD16—131no—
350C2×SD16—131no—
351C2×D8—131no—
352C2×M16—21no—
353C2×M16—261no—
354C2×M16C22⋊D1311yescharacteristic
355C2×M16C22⋊D1311yescharacteristic
356C22×C8—21no—
357C22×C8—131no—
358C22×C8—131no—
359C22×C8—261no—
360#126—21no—
361#126—261no—
362#125—131no—
363#125C4×D1311yescharacteristic
364#124—131no—
365#124C4×D1311yescharacteristic
366#123—21no—
367#123—261no—
368C22⋊Q8—131no—
369C22⋊Q8C4×D1311yescharacteristic
370#121—131no—
371#121C4×D1311yescharacteristic
372C4×Q8—131no—
373C4×Q8C22×D1311yescharacteristic
374C4×D4—21no—
375C4×D4—131no—
376C4×D4—261no—
377C4×D4C22×D1311yescharacteristic
378#117—21no—
379#117—261no—
380C2×C42C22×D1311yescharacteristic
381#107—131no—
382#107—131no—
383#106—131no—
384#106—131no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—131no—
388C4⋊C8—131no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8C22×D1311yescharacteristic
393C4⋊C8C22×D1311yescharacteristic
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400#102—131no—
401#102—131no—
402C22⋊C8—21no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409#97—21no—
410#97—261no—
411#97C22⋊D1311yescharacteristic
412#97C22⋊D1311yescharacteristic
413C4×C8—21no—
414C4×C8—21no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—131no—
420C4×C8—131no—
421C4×C8—261no—
422C4×C8—261no—
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C2×C13—41no—
426C2×C13—81no—
427C2×C13#293511yescharacteristic
428C2×C13C4×#13511yescharacteristic
429C2×C13#295711yescharacteristic
430D13—81no—
431C2×Q8—131no—
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—21no—
434C2×D4—131no—
435C2×D4—261no—
436C2×D4C2×C4×D1311yescharacteristic
437C22×C4—21no—
438C22×C4—261no—
439C22×C4C2×C4×D1311yescharacteristic
440C22×C4#612711yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442Q16—262no—
443SD16—521no—
444SD16—521no—
445D8—262no—
446M16—22no—
447M16—22no—
448M16—42no—
449M16—522no—
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—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—521no—
463C2×C8—522no—
464C2×C8C2×C22⋊D1311yescharacteristic
465C2×C8C2×C22⋊D1311yescharacteristic
466C2×C8C2×C22⋊D1311yescharacteristic
467C2×C8C2×C22⋊D1311yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—131no—
473C4⋊C4—131no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4C2×C4×D1311yescharacteristic
479C4⋊C4C2×C4×D1311yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
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—261no—
492C42C2×C4×D1311yescharacteristic
493C42#612711yescharacteristic
494C42C2×C22⋊D1311yescharacteristic
495C42C23×D1311yescharacteristic
496C13#1806911yescharacteristic, complemented, Sylow
497C23—21no—
498C23—261no—
499C23C4×C22⋊D1311yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—261no—
503Q8—261no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—261no—
508D4—261no—
509D4—1041no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4C4×C22⋊D1311yescharacteristic
526C2×C4C4×C22⋊D1311yescharacteristic
527C2×C4C4×C22⋊D1311yescharacteristic
528C2×C4C22×C4×D1311yescharacteristic
529C2×C4C2×#612711yescharacteristic
530C2×C4C22×C22⋊D1311yescharacteristic
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—132no—
536C8—261no—
537C8—261no—
538C8—261no—
539C8—521no—
540C8—521no—
541C8—521no—
542C8—521no—
543C8#8820412yes—
544C8#8820412yes—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—521no—
552C22—521no—
553C22—521no—
554C22C2×C4×C22⋊D1311yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—521no—
563C4—521no—
564C4—521no—
565C4D13×#13111yescharacteristic
566C4#1171945511yescharacteristic
567C4C2×#8820411yescharacteristic
568C4C2×#8820411yescharacteristic
569C2—41no—
570C2—81no—
571C2—1041no—
572C2#1312357811yescharacteristic
573C2C4×#8820411yescharacteristic
574C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2969C2
socleC22×C13C2×C4×D4
prime radical#11718699C4
cosocleC42×C13C24
hypercenter#2969D13
hypocenterC13#18069
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #13123840C2semidirect
3. #13113731C2semidirect
4. #13113719C2semidirect
5. #13113679C2semidirect
6. #13113677C2semidirect
7. #13113672C2semidirect
8. #13113670C2semidirect
9. C8×#6107C2semidirect
10. C8×#6104C2semidirect
11. #13113582C2semidirect
12. #13113244C2semidirect
13. #13113242C2semidirect
14. M16×#1055C2semidirect
15. C13×#2969C2semidirect
212. #2969D13semidirect
496. C13#18069semidirect

Maximal subgroups

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

subgroupindex
#131254002
#131238402
#131137312
#131137192
#131136792
#131136772
#131136722
#131136702
C8×#61072
C8×#61042
#131135822
#131132442
#131132422
M16×#10552
C13×#29692
#1806913