Finite Group Databasebeta

← #15834786

Subgroups — #15834786

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125442C211yesmaximal, characteristic
2#13123834C211yesmaximal, characteristic
3#13123779C211yesmaximal, characteristic, complemented
4#13113737C211yesmaximal, characteristic, complemented
5#13113732C211yesmaximal, characteristic, complemented
6#13113713C211yesmaximal, characteristic, complemented
7#13113706C211yesmaximal, characteristic, complemented
8#13113685C211yesmaximal, characteristic, complemented
9#13113671C211yesmaximal, characteristic, complemented
10#13113654C211yesmaximal, characteristic, complemented
11#13113635C211yesmaximal, characteristic, complemented
12#13113256C211yesmaximal, characteristic, complemented
13#13113247C211yesmaximal, characteristic
14#13113139C211yesmaximal, characteristic, complemented
15C13×#1565C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C2×C13×C4⋊C8C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21#11718798C411yescharacteristic
22#11718798C411yescharacteristic
23#11718795C411yescharacteristic
24#11718795C411yescharacteristic
25#11718763—21no—
26#11718762—21no—
27C4×#6099C2211yescharacteristic
28C4×#6099C2211yescharacteristic
29#11718499C2211yescharacteristic
30#11718495C2211yescharacteristic
31#11718492C2211yescharacteristic
32#11718492C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718491C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718489—21no—
38#11718489—21no—
39#11718390—21no—
40#11718389—21no—
41#11718376C411yescharacteristic
42#11718375C411yescharacteristic
43#11718364C411yescharacteristic
44#11718363C411yescharacteristic
45C4×Dic52C2211yescharacteristic
46C4×Dic52C2211yescharacteristic
47C4×#6095C2211yescharacteristic
48C4×#6095C2211yescharacteristic
49#11718351—21no—
50#11718350—21no—
51C13×#335C2211yescharacteristic
52C13×#335C2211yescharacteristic
53C13×#334C2211yescharacteristic
54C13×#334C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718076C2211yescharacteristic
60#11718076C2211yescharacteristic
61#11718075C2211yescharacteristic
62#11718075C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16C2×C411yescharacteristic
68C2×C13×M16C2×C411yescharacteristic
69C22×C8×C13—21no—
70C2×C42×C13C2311yescharacteristic
71#88184C2×C411yescharacteristic
72#88183—21no—
73C4×C22⋊D13—21no—
74#88180—21no—
75#88178—21no—
76#88178C2×C411yescharacteristic
77#88178C2×C411yescharacteristic
78#88178C2×C411yescharacteristic
79C2×#6099—21no—
80C2×#6099D411yescharacteristic
81C2×#6099D411yescharacteristic
82C2×Dic52C2×C411yescharacteristic
83C2×Dic52C2×C411yescharacteristic
84C2×#6095C2×C411yescharacteristic
85C2×#6095C2×C411yescharacteristic
86C2×#6094—21no—
87C2×C8×D13—21no—
88#88130—21no—
89#88129C2×C411yescharacteristic
90C4×D52C2311yescharacteristic
91#88126—21no—
92#88124—21no—
93#88124C2×C411yescharacteristic
94#88123C2×C411yescharacteristic
95#88123C2×C411yescharacteristic
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×#97C2×C411yescharacteristic
107C13×#97C2×C411yescharacteristic
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88061C2×C411yescharacteristic
112#88061C2×C411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88058C2×C411yescharacteristic
116#88058C2×C411yescharacteristic
117#88057C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88055—21no—
126#88055—21no—
127#88055—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137#88043—21no—
138#88043D411yescharacteristic
139#88043D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18077—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C2×D52C22×C411yescharacteristic
150C2×C4×D13—21no—
151C2×Dic26—21no—
152C2×Dic26C22×C411yescharacteristic
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C13×M16—22no—
156C13×M16—41no—
157C2×C8×C13—21no—
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×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C42×C13C22×C411yescharacteristic
167C42×C13C2×D411yescharacteristic
168C42×C13#4111yescharacteristic
169C42×C13C2411yescharacteristic
170C22⋊Dic13—21no—
171C22⋊Dic13—21no—
172C22⋊Dic13—21no—
173#6103—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195#6099—22no—
196#6099—41no—
197#6099—42no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204Dic52—22no—
205Dic52—41no—
206#6095—22no—
207#6095—41no—
208#6094—42no—
209C8×D13—42no—
210#3172—131no—
211#2969—131no—
212#2962—131no—
213#1592—131no—
214#1591—131no—
215#1588—131no—
216#1587—131no—
217#1584—131no—
218#1582—131no—
219#1579—131no—
220C8×SD16—131no—
221#1565D1311yescharacteristic, complemented
222#1485—131no—
223#1483—131no—
224#1455—131no—
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—41no—
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C4×D411yescharacteristic
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C22⋊D13—81no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—21no—
246D52—21no—
247D52—21no—
248C4×D13—41no—
249C4×D13—41no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—81no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13#13112yes—
265#1055—22no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055#13712yes—
271#533—131no—
272#529—131no—
273#501—131no—
274#497—131no—
275#491—131no—
276#489—131no—
277#470—131no—
278#470—131no—
279#468—131no—
280#468—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436—131no—
294#436—261no—
295#435—261no—
296C8×D4—131no—
297#433—261no—
298#431C2×D1311yescharacteristic
299#424—261no—
300C2×C4⋊C8C2×D1311yescharacteristic
301#405—261no—
302#405—261no—
303C4×M16—131no—
304C4×M16—131no—
305C4×M16C2×D1311yescharacteristic
306#335C2×D1311yescharacteristic
307#335C2×D1311yescharacteristic
308#334C2×D1311yescharacteristic
309#334C2×D1311yescharacteristic
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322—131no—
319#322—131no—
320#322—131no—
321C82—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13C2×C4×D411yescharacteristic
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13C2×#13111yescharacteristic
334C4×C13#56811yescharacteristic
335C4×C13C2×#13711yescharacteristic
336C4×C13#57511yescharacteristic
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—131no—
349C2×M16—131no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16C4×D1311yescharacteristic
353C2×M16C4×D1311yescharacteristic
354C22×C8—21no—
355C22×C8—261no—
356C4⋊Q8—131no—
357C4⋊Q8—131no—
358#126—261no—
359#125—131no—
360#125—261no—
361#124—131no—
362#123—261no—
363C22⋊Q8—131no—
364C22⋊Q8—131no—
365C22⋊Q8—131no—
366C22⋊Q8—261no—
367#121—131no—
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—131no—
371C4×Q8—261no—
372C4×D4—131no—
373C4×D4—261no—
374#117—261no—
375#117—261no—
376C2×C42C22×D1311yescharacteristic
377#107—131no—
378#107—131no—
379#106—131no—
380#106—131no—
381C4⋊C8—21no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—21no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—131no—
404#97—131no—
405#97—261no—
406#97—261no—
407#97—261no—
408#97—261no—
409#97C4×D1311yescharacteristic
410#97C4×D1311yescharacteristic
411C4×C8—21no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—41no—
422C2×C13#293511yescharacteristic
423C2×C13C4×#13711yescharacteristic
424C2×C13#295611yescharacteristic
425D13—81no—
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×D4—131no—
431C2×D4—261no—
432C22×C4—261no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4D4×D1311yescharacteristic
435C22×C4#613111yescharacteristic
436Q16—262no—
437Q16—521no—
438SD16—262no—
439SD16—521no—
440M16—22no—
441M16—41no—
442M16—262no—
443M16—522no—
444M16—521no—
445M16—522no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—522no—
458C2×C8C2×C4×D1311yescharacteristic
459C2×C8C2×C4×D1311yescharacteristic
460C2×C8C2×C4×D1311yescharacteristic
461C2×C8C2×C4×D1311yescharacteristic
462C4⋊C4—131no—
463C4⋊C4—131no—
464C4⋊C4—131no—
465C4⋊C4—131no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42D4×D1311yescharacteristic
489C42#613111yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1807711yescharacteristic, complemented, Sylow
492C23—261no—
493C23#8814711yescharacteristic
494Q8—261no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—261no—
502D4—261no—
503D4—1041no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4#8814711yescharacteristic
519C2×C4#8814711yescharacteristic
520C2×C4#8814711yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4C2×#613111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—132no—
532C8—262no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8#8815512yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—521no—
542C22—521no—
543C22—521no—
544C22C2×#8814711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4C2×#8815511yescharacteristic
557C4#1171945011yescharacteristic
558C4#1171947811yescharacteristic
559C4D13×#13711yescharacteristic
560C2—41no—
561C2—1041no—
562C2#1312357911yescharacteristic
563C2#1312365411yescharacteristic
564C2#1312374511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1565C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1565D13
hypocenterC13#18077
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
3. #13123779C2semidirect
4. #13113737C2semidirect
5. #13113732C2semidirect
6. #13113713C2semidirect
7. #13113706C2semidirect
8. #13113685C2semidirect
9. #13113671C2semidirect
10. #13113654C2semidirect
11. #13113635C2semidirect
12. #13113256C2semidirect
14. #13113139C2semidirect
15. C13×#1565C2semidirect
221. #1565D13semidirect
491. C13#18077semidirect

Maximal subgroups

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

subgroupindex
#131254422
#131238342
#131237792
#131137372
#131137322
#131137132
#131137062
#131136852
#131136712
#131136542
#131136352
#131132562
#131132472
#131131392
C13×#15652
#1807713