Finite Group Databasebeta

← #15875221

Subgroups — #15875221

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124622C211yesmaximal, characteristic
2#13123769C211yesmaximal, characteristic, complemented
3#13123479C211yesmaximal, characteristic
4#13115778C211yesmaximal, characteristic, complemented
5#13115608C211yesmaximal, characteristic, complemented
6#13115581C211yesmaximal, characteristic, complemented
7#13115540C211yesmaximal, characteristic
8#13115539C211yesmaximal, characteristic
9#13115483C211yesmaximal, characteristic
10#13115482C211yesmaximal, characteristic
11#13115438C211yesmaximal, characteristic, complemented
12#13115437C211yesmaximal, characteristic, complemented
13#13114855C211yesmaximal, characteristic
14C8×#6101C211yesmaximal, characteristic, complemented
15C13×#1945C211yesmaximal, characteristic, complemented
16#11719227C2211yescharacteristic
17#11719222C2211yescharacteristic
18C2×C13×#108C2211yescharacteristic
19C13×#427C2211yescharacteristic
20C13×#424C2211yescharacteristic
21C13×#424C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C2×#88065C2211yescharacteristic
24#11718790C2211yescharacteristic
25C2×#88062C2211yescharacteristic
26#11718783C2211yescharacteristic
27#11718779C2211yescharacteristic
28M16×Dic13C2211yescharacteristic
29#11718774C2211yescharacteristic
30#11718771C2211yescharacteristic
31#11718763C2211yescharacteristic
32C2×#88054C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35#11718663C2211yescharacteristic
36#11718660C2211yescharacteristic
37#11718659C2211yescharacteristic
38#11718658C2211yescharacteristic
39C4×#6101C2211yescharacteristic
40C2×#88045C2211yescharacteristic
41#11718552C411yescharacteristic, complemented
42#11718551C411yescharacteristic, complemented
43#11718538C411yescharacteristic, complemented
44#11718536C411yescharacteristic, complemented
45#11718532C411yescharacteristic, complemented
46#11718531C411yescharacteristic, complemented
47#11718518C411yescharacteristic, complemented
48#11718515C411yescharacteristic, complemented
49#11718501—21no—
50#11718501—21no—
51#11718494—21no—
52#11718494—21no—
53#11718491—21no—
54#11718491—21no—
55#11718489—21no—
56#11718489—21no—
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59#11718150C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718144C2211yescharacteristic
62#11718142C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718124C2211yescharacteristic
65#11718116C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×#117C2311yescharacteristic
73C13×#117C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75#88180C2311yescharacteristic
76C2×#6101—21no—
77C2×C4×Dic13C2311yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C2×#6099C2311yescharacteristic
80C2×#6099C2311yescharacteristic
81C22×#1055C2311yescharacteristic
82C22×#1055C2311yescharacteristic
83#88147C2×C411yescharacteristic
84#88147C2×C411yescharacteristic
85#88144C2×C411yescharacteristic
86#88144C2×C411yescharacteristic
87#88142C2×C411yescharacteristic
88#88142C2×C411yescharacteristic
89#88141C2×C411yescharacteristic
90#88141C2×C411yescharacteristic
91#88135—21no—
92#88135—21no—
93#88132—21no—
94#88132—21no—
95#88126—21no—
96C42×D13—21no—
97C4×Dic26—21no—
98C4×Dic26—21no—
99C13×#108—41no—
100C13×#107C2×C411yescharacteristic
101C13×#107C2×C411yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×#106C2×C411yescharacteristic
104C13×C4⋊C8—21no—
105C13×C4⋊C8—21no—
106C13×C4⋊C8—21no—
107C13×C4⋊C8—21no—
108C4×C8×C13—41no—
109#88071—21no—
110#88065—41no—
111#88062—41no—
112#88061C2×C411yescharacteristic
113#88061C2×C411yescharacteristic
114#88060—21no—
115#88060—21no—
116#88060—21no—
117#88060—21no—
118#88056C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88055—21no—
121#88055—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054C2×C411yescharacteristic
127#88054C2×C411yescharacteristic
128#88054C2×C411yescharacteristic
129#88054C2×C411yescharacteristic
130C8×Dic13—21no—
131C8×Dic13—21no—
132C8×Dic13—41no—
133C8×Dic13D411yescharacteristic
134C8×Dic13D411yescharacteristic
135C8×Dic13D411yescharacteristic
136C8×Dic13D411yescharacteristic
137#88050C2×C411yescharacteristic
138#88050C2×C411yescharacteristic
139#88049C2×C411yescharacteristic
140#88049C2×C411yescharacteristic
141#88048C2×C411yescharacteristic
142#88048C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#88047C2×C411yescharacteristic
145#88045—41no—
146C4⋊#1055—21no—
147C4⋊#1055—21no—
148#88043—21no—
149C4×#1055—21no—
150#22130—131nomaximal, Sylow
151C22×C4×C13—21no—
152C22×C4×C13C2411yescharacteristic
153C2×C22⋊D13—21no—
154C22×Dic13—21no—
155C22×Dic13#4111yescharacteristic
156C22×Dic13#4111yescharacteristic
157#6127—21no—
158#6127—21no—
159#6127—21no—
160#6127—21no—
161C2×D52C22×C411yescharacteristic
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26C22×C411yescharacteristic
168C13×M16—21no—
169C13×M16—21no—
170C13×M16—21no—
171C13×M16—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C22×C411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2×D411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C4⋊C4C22×C411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C22⋊Dic13—21no—
193#6103—21no—
194#6103—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13C22×C411yescharacteristic
198C4⋊Dic13C22×C411yescharacteristic
199#6101—24no—
200#6101—21no—
201#6101—21no—
202#6101—21no—
203#6101—21no—
204#6101—21no—
205#6101—21no—
206C4×Dic13—21no—
207C4×Dic13—21no—
208C4×Dic13—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13C22×C411yescharacteristic
212C4×Dic13C22×C411yescharacteristic
213C4×Dic13C2×D411yescharacteristic
214C4×Dic13C2×D411yescharacteristic
215#6099—21no—
216#6099—21no—
217#6099—21no—
218#6099—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055C22×C411yescharacteristic
226C2×#1055C22×C411yescharacteristic
227C2×#1055C2×D411yescharacteristic
228C2×#1055C2×D411yescharacteristic
229#3076—131no—
230#2960—131no—
231#2922—131no—
232#1986—131no—
233#1950—131no—
234#1945—131no—
235#1945D1311yescharacteristic, complemented
236#1937—131no—
237#1937—131no—
238#1929—131no—
239#1929—131no—
240#1922—131no—
241#1922—131no—
242#1806—131no—
243C8×C4⋊C4—131no—
244C23×C13C2×#4111yescharacteristic
245C22×D13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13H(5,𝔽2)11yescharacteristic
256C2×C4×C132−1+411yescharacteristic
257C2×C4×C132−1+411yescharacteristic
258C2×C4×C132−1+411yescharacteristic
259C22⋊D13—41no—
260C22⋊D13—41no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13C4×D411yescharacteristic
270C2×Dic13C4×D411yescharacteristic
271C2×Dic13C4×D411yescharacteristic
272C2×Dic13C4×D411yescharacteristic
273D52—21no—
274D52—21no—
275C4×D13—42no—
276C4×D13—41no—
277C4×D13—41no—
278C4×D13—42no—
279Dic26—21no—
280Dic26—21no—
281Dic26—42no—
282Dic26—42no—
283C8×C13—21no—
284C8×C13—21no—
285C8×C13—21no—
286C8×C13—21no—
287C8×C13—41no—
288C8×C13—41no—
289#1055—21no—
290#1055—21no—
291#1055—21no—
292#1055—21no—
293#1055—41no—
294#1055—41no—
295#533—131no—
296C4×#41—131no—
297#479—131no—
298#479—131no—
299#478—131no—
300#478—131no—
301#477—131no—
302#476—131no—
303#475—131no—
304#474—131no—
305#446—261no—
306#446—261no—
307C8×Q8—261no—
308C8×Q8—261no—
309#433—261no—
310#433—261no—
311#431—261no—
312#431—261no—
313C2×#108—131no—
314C2×#108C2×D1311yescharacteristic
315#427—131no—
316#427C2×D1311yescharacteristic
317#424—131no—
318#424—131no—
319#424C2×D1311yescharacteristic
320#424C2×D1311yescharacteristic
321#423—131no—
322C2×C4⋊C8—131no—
323C2×#104—131no—
324C2×#104—131no—
325#416—131no—
326#416—131no—
327#408—131no—
328#408—131no—
329#405—131no—
330#405—131no—
331C4×M16—131no—
332C2×C4×C8—131no—
333C2×C4×C8—131no—
334C2×C4×C8C2×D1311yescharacteristic
335C4×C4⋊C4—131no—
336#341—131no—
337#341—131no—
338#339—131no—
339#339—131no—
340#339—131no—
341#339—131no—
342#339C2×D1311yescharacteristic
343#339C2×D1311yescharacteristic
344#336—131no—
345#336—131no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13C2×C4×D411yescharacteristic
349C22×C13#54111yescharacteristic
350C22×C13#54211yescharacteristic
351C2×D13—41no—
352C2×D13—41no—
353C2×D13—41no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13#51911yescharacteristic
360C4×C13#52011yescharacteristic
361C4×C13#53611yescharacteristic
362C4×C13#53711yescharacteristic
363Dic13—21no—
364Dic13—21no—
365Dic13—21no—
366Dic13—42no—
367Dic13—41no—
368Dic13—41no—
369Dic13—41no—
370Dic13#44312yes—
371C2×#41—131no—
372C2×M16—131no—
373C2×M16—131no—
374C2×M16C22×D1311yescharacteristic
375C2×M16C22×D1311yescharacteristic
376C22×C8—131no—
377C22×C8—131no—
378C22×C8C22×D1311yescharacteristic
379C22×C8C22×D1311yescharacteristic
380C4⋊Q8—131no—
381C4⋊Q8—131no—
382#125—131no—
383#125—131no—
384C22⋊Q8—261no—
385C22⋊Q8—261no—
386C4×Q8—131no—
387C4×Q8—131no—
388C4×Q8—261no—
389C4×Q8—261no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—261no—
393C4×D4—261no—
394#117—131no—
395#117—261no—
396#117C22×D1311yescharacteristic
397#117C22×D1311yescharacteristic
398C2×C4⋊C4—261no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—261no—
402C2×C42C22×D1311yescharacteristic
403#108—41no—
404#108—521no—
405#107—131no—
406#107—131no—
407#107C4×D1311yescharacteristic
408#107C4×D1311yescharacteristic
409#106—131no—
410#106—131no—
411#106C4×D1311yescharacteristic
412#106C4×D1311yescharacteristic
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—131no—
418C4⋊C8—131no—
419C4⋊C8—131no—
420C4⋊C8—131no—
421C4⋊C8—261no—
422C4⋊C8—261no—
423C4⋊C8—261no—
424C4⋊C8—261no—
425C4⋊C8—261no—
426C4⋊C8—261no—
427#104—521no—
428#104—521no—
429#103—131no—
430#103—131no—
431#103—131no—
432#103—131no—
433#102—131no—
434#102—131no—
435#102—131no—
436#102—131no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8—261no—
441#97—261no—
442#97—261no—
443#97—261no—
444C4×C8—41no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—131no—
448C4×C8—131no—
449C4×C8—261no—
450C4×C8—261no—
451C4×C8—261no—
452C4×C8—521no—
453#95—261no—
454C2×C13—21no—
455C2×C13—21no—
456C2×C13#232311yescharacteristic
457C2×C13C2×#44311yescharacteristic
458C2×C13#295511yescharacteristic
459D13—81no—
460#41—261no—
461#41—261no—
462#41—261no—
463#41—261no—
464C2×Q8—131no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×D4—131no—
468C2×D4—261no—
469C22×C4—21no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—261no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4C23×D1311yescharacteristic
477M16—21no—
478M16—21no—
479M16—21no—
480M16—21no—
481M16—261no—
482M16—261no—
483M16—261no—
484M16—261no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—131no—
492C2×C8—131no—
493C2×C8—131no—
494C2×C8—131no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8C2×C4×D1311yescharacteristic
502C2×C8C2×C4×D1311yescharacteristic
503C2×C8D4×D1311yescharacteristic
504C2×C8D4×D1311yescharacteristic
505C4⋊C4—131no—
506C4⋊C4—131no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—264no—
516C4⋊C4C2×C4×D1311yescharacteristic
517C4⋊C4C2×C4×D1311yescharacteristic
518C4⋊C4C2×C4×D1311yescharacteristic
519C4⋊C4C2×C4×D1311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—131no—
530C42—131no—
531C42—131no—
532C42—131no—
533C42—261no—
534C42—261no—
535C42—261no—
536C42—261no—
537C42—261no—
538C13#2213011yescharacteristic, complemented, Sylow
539C23—261no—
540C23#41×D1311yescharacteristic
541Q8—261no—
542Q8—261no—
543Q8—522no—
544Q8—522no—
545D4—261no—
546D4—261no—
547D4—521no—
548D4—521no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—131no—
557C2×C4—131no—
558C2×C4—131no—
559C2×C4—131no—
560C2×C4—262no—
561C2×C4—262no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—522no—
566C2×C4—522no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4C22×C4×D1311yescharacteristic
573C2×C4C2×D4×D1311yescharacteristic
574C2×C4#8825111yescharacteristic
575C2×C4#8825411yescharacteristic
576C2×C4#8825411yescharacteristic
577C2×C4#8825711yescharacteristic
578C8—21no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—261no—
588C8—521no—
589C8—521no—
590C22—21no—
591C22—21no—
592C22—521no—
593C22—521no—
594C22—521no—
595C22C4×D4×D1311yescharacteristic
596C22#1171934511yescharacteristic
597C22#1171940111yescharacteristic
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—132no—
604C4—261no—
605C4—261no—
606C4—261no—
607C4—522no—
608C4—521no—
609C4—521no—
610C4—521no—
611C4#1171920911yescharacteristic
612C4#1171927711yescharacteristic
613C4#1171930211yescharacteristic
614C4#1171942911yescharacteristic
615C2—21no—
616C2—21no—
617C2—1041no—
618C2#1311751311yescharacteristic
619C2D13×#44311yescharacteristic
620C2#1312373411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1945C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1945D13
hypocenterC13#22130
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
2. #13123769C2semidirect
4. #13115778C2semidirect
5. #13115608C2semidirect
6. #13115581C2semidirect
11. #13115438C2semidirect
12. #13115437C2semidirect
14. C8×#6101C2semidirect
15. C13×#1945C2semidirect
41. #11718552C4semidirect
42. #11718551C4semidirect
43. #11718538C4semidirect
44. #11718536C4semidirect
45. #11718532C4semidirect
46. #11718531C4semidirect
47. #11718518C4semidirect
48. #11718515C4semidirect
235. #1945D13semidirect
538. C13#22130semidirect

Maximal subgroups

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

subgroupindex
#131246222
#131237692
#131234792
#131157782
#131156082
#131155812
#131155402
#131155392
#131154832
#131154822
#131154382
#131154372
#131148552
C8×#61012
C13×#19452
#2213013