Finite Group Databasebeta

← #15833647

Subgroups — #15833647

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#13125400C211yesmaximal, characteristic
2#13123811C211yesmaximal, characteristic, complemented
3#13113686C211yesmaximal, characteristic, complemented
4#13113684C211yesmaximal, characteristic, complemented
5#13113679C211yesmaximal, characteristic, complemented
6#13113677C211yesmaximal, characteristic, complemented
7#13113672C211yesmaximal, characteristic, complemented
8#13113670C211yesmaximal, characteristic, complemented
9#13113665C211yesmaximal, characteristic, complemented
10#13113663C211yesmaximal, characteristic, complemented
11#13113597C211yesmaximal, characteristic, complemented
12#13113296C211yesmaximal, characteristic, complemented
13#13113294C211yesmaximal, characteristic, complemented
14C2×#11718047C211yesmaximal, characteristic, complemented
15C13×#2966C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436C2211yescharacteristic
21C13×#435—21no—
22C8×D4×C13—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#432C2211yescharacteristic
26C13×#405—21no—
27C2×C4×C8×C13C2211yescharacteristic
28#11718772—21no—
29C8×C22⋊D13—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#11718587C2211yescharacteristic
43C2×C4×#1055C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718351—21no—
46#11718350—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
65#11718047C2211yescharacteristic
66#11718047C2211yescharacteristic
67C2×C13×M16—21no—
68C22×C8×C13—21no—
69C22×C8×C13D411yescharacteristic
70C22×C8×C13D411yescharacteristic
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×#1055—21no—
91C22×#1055C2×C411yescharacteristic
92C22×#1055C2×C411yescharacteristic
93C2×#6094—21no—
94C2×C8×D13—21no—
95#88130—21no—
96#88129C2×C411yescharacteristic
97C4×D52C2311yescharacteristic
98#88126—21no—
99#88124C2×C411yescharacteristic
100C4×Dic26C2311yescharacteristic
101C13×C4⋊C8—21no—
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×#97—21no—
109C13×#97—21no—
110C4×C8×C13—21no—
111C4×C8×C13D411yescharacteristic
112C4×C8×C13D411yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115#88075C2×C411yescharacteristic
116#88075C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
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⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137C4×#1055—21no—
138C4×#1055C2×C411yescharacteristic
139C4×#1055C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17978—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—42no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
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—41no—
184#6106—41no—
185#6105—41no—
186#6104—41no—
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—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—41no—
203C2×#1055—41no—
204C2×#1055—42no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209#6094—42no—
210C8×D13—42no—
211#3168—131no—
212#2966—131no—
213#2966D1311yescharacteristic, complemented
214#1584—131no—
215#1584—131no—
216#1583—131no—
217#1583—131no—
218#1582—131no—
219#1582—131no—
220#1581—131no—
221#1581—131no—
222#1568—131no—
223#1494—131no—
224#1494—131no—
225C2×#322—131no—
226C23×C13—21no—
227C23×C13C4×D411yescharacteristic
228C22×D13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231D4×C13—21no—
232D4×C13—21no—
233D4×C13—42no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C23×C411yescharacteristic
248C2×C4×C13C22×D411yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C22⋊D13—42no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254D52—21no—
255D52—21no—
256C4×D13—41no—
257C4×D13—41no—
258Dic26—21no—
259Dic26—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13#13512yes—
265C8×C13#13512yes—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—41no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274#529—131no—
275#529C2×D1311yescharacteristic
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#446C2×D1311yescharacteristic
286C8×Q8—131no—
287C8×Q8C2×D1311yescharacteristic
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16—131no—
291C4×D8—131no—
292#436—131no—
293#436C2×D1311yescharacteristic
294#435—21no—
295#435—261no—
296C8×D4—21no—
297C8×D4—131no—
298C8×D4—261no—
299C8×D4C2×D1311yescharacteristic
300#433—21no—
301#433—261no—
302#432—131no—
303#432C2×D1311yescharacteristic
304#405—21no—
305#405—261no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308C2×C4×C8C2×D1311yescharacteristic
309#335—131no—
310#335—131no—
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⋊C8—131no—
320D4⋊C8—131no—
321#322—131no—
322#322—131no—
323#322—131no—
324#322—131no—
325C22×C13—21no—
326C22×C13—21no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13—41no—
330C22×C13#44412yes—
331C22×C13C2×C4×D411yescharacteristic
332C2×D13—41no—
333C2×D13—41no—
334C2×D13—41no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—21no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13—41no—
342C4×C13#56811yescharacteristic
343C4×C13#56811yescharacteristic
344C4×C13C2×#13511yescharacteristic
345C4×C13C2×#13511yescharacteristic
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349C2×Q16—131no—
350C2×SD16—131no—
351C2×SD16—131no—
352C2×D8—131no—
353C2×M16—21no—
354C2×M16—261no—
355C22×C8—21no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8—261no—
359C22×C8—261no—
360C22×C8C22⋊D1311yescharacteristic
361C22×C8C22⋊D1311yescharacteristic
362#126—21no—
363#126—261no—
364#125—131no—
365#125C4×D1311yescharacteristic
366#124—131no—
367#124C4×D1311yescharacteristic
368#123—21no—
369#123—261no—
370C22⋊Q8—131no—
371C22⋊Q8C4×D1311yescharacteristic
372#121—131no—
373#121C4×D1311yescharacteristic
374C4×Q8—131no—
375C4×Q8C22×D1311yescharacteristic
376C4×D4—21no—
377C4×D4—131no—
378C4×D4—261no—
379C4×D4C22×D1311yescharacteristic
380#117—21no—
381#117—261no—
382C2×C42C22×D1311yescharacteristic
383#107—131no—
384#107—131no—
385#106—131no—
386#106—131no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—131no—
390C4⋊C8—131no—
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#102—131no—
402#102—131no—
403C22⋊C8—21no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—261no—
407C22⋊C8—261no—
408C22⋊C8—261no—
409#97—21no—
410#97—21no—
411#97—261no—
412#97—261no—
413C4×C8—21no—
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×C8C22⋊D1311yescharacteristic
423C4×C8C22⋊D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C4×C8C22×D1311yescharacteristic
426C2×C13—22no—
427C2×C13—81no—
428C2×C13#293211yescharacteristic
429C2×C13C4×#13511yescharacteristic
430C2×C13C2×#44411yescharacteristic
431D13—81no—
432C2×Q8—131no—
433C2×Q8C2×C4×D1311yescharacteristic
434C2×D4—21no—
435C2×D4—131no—
436C2×D4—261no—
437C2×D4C2×C4×D1311yescharacteristic
438C22×C4—21no—
439C22×C4—261no—
440C22×C4C2×C4×D1311yescharacteristic
441C22×C4#612711yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443Q16—521no—
444SD16—521no—
445SD16—521no—
446D8—521no—
447M16—42no—
448M16—522no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—521no—
463C2×C8—521no—
464C2×C8—522no—
465C2×C8—522no—
466C2×C8C2×C22⋊D1311yescharacteristic
467C2×C8C2×C22⋊D1311yescharacteristic
468C2×C8C2×C22⋊D1311yescharacteristic
469C2×C8C2×C22⋊D1311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
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—21no—
486C22⋊C4—21no—
487C22⋊C4—261no—
488C22⋊C4—261no—
489C22⋊C4—261no—
490C22⋊C4—261no—
491C22⋊C4—261no—
492C42—21no—
493C42—261no—
494C42C2×C4×D1311yescharacteristic
495C42#612711yescharacteristic
496C42C2×C22⋊D1311yescharacteristic
497C42C23×D1311yescharacteristic
498C13#1797811yescharacteristic, complemented, Sylow
499C23—21no—
500C23—261no—
501C23C4×C22⋊D1311yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—261no—
505Q8—261no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—261no—
510D4—261no—
511D4—522no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4C4×C22⋊D1311yescharacteristic
528C2×C4C4×C22⋊D1311yescharacteristic
529C2×C4C4×C22⋊D1311yescharacteristic
530C2×C4C22×C4×D1311yescharacteristic
531C2×C4C2×#612711yescharacteristic
532C2×C4C22×C22⋊D1311yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—261no—
538C8—261no—
539C8—261no—
540C8—261no—
541C8—521no—
542C8—521no—
543C8—521no—
544C8—521no—
545C8#8820412yes—
546C8#8820412yes—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—521no—
553C22—521no—
554C22—521no—
555C22#1171880612yes—
556C22C2×C4×C22⋊D1311yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—521no—
565C4—521no—
566C4—521no—
567C4#1171945511yescharacteristic
568C4#1171945511yescharacteristic
569C4C2×#8820411yescharacteristic
570C4C2×#8820411yescharacteristic
571C2—22no—
572C2—81no—
573C2—1041no—
574C2#1312355211yescharacteristic
575C2C4×#8820411yescharacteristic
576C2C2×#1171880611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2966C2
socleC22×C13C2×C4×D4
prime radical#11718699C4
cosocleC42×C13C24
hypercenter#2966D13
hypocenterC13#17978
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13123811C2semidirect
3. #13113686C2semidirect
4. #13113684C2semidirect
5. #13113679C2semidirect
6. #13113677C2semidirect
7. #13113672C2semidirect
8. #13113670C2semidirect
9. #13113665C2semidirect
10. #13113663C2semidirect
11. #13113597C2semidirect
12. #13113296C2semidirect
13. #13113294C2semidirect
14. C2×#11718047C2semidirect
15. C13×#2966C2semidirect
213. #2966D13semidirect
498. C13#17978semidirect

Maximal subgroups

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

subgroupindex
#131254002
#131238112
#131136862
#131136842
#131136792
#131136772
#131136722
#131136702
#131136652
#131136632
#131135972
#131132962
#131132942
C2×#117180472
C13×#29662
#1797813