Finite Group Databasebeta

← #15875219

Subgroups — #15875219

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#13124620C211yesmaximal, characteristic
2#13123769C211yesmaximal, characteristic, complemented
3#13123476C211yesmaximal, characteristic
4#13115778C211yesmaximal, characteristic, complemented
5#13115610C211yesmaximal, characteristic, complemented
6#13115584C211yesmaximal, characteristic, complemented
7#13115581C211yesmaximal, characteristic, complemented
8#13115543C211yesmaximal, characteristic
9#13115487C211yesmaximal, characteristic
10#13115486C211yesmaximal, characteristic
11#13115434C211yesmaximal, characteristic, complemented
12#13115433C211yesmaximal, characteristic, complemented
13#13114854C211yesmaximal, characteristic
14C8×#6101C211yesmaximal, characteristic, complemented
15C13×#1937C211yesmaximal, characteristic
16#41×Dic13C2211yescharacteristic
17#11719222C2211yescharacteristic
18C13×#424C2211yescharacteristic
19C2×C13×#104C2211yescharacteristic
20C13×#416C2211yescharacteristic
21C13×#408C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C2×#88077C2211yescharacteristic
24#11718895C2211yescharacteristic
25#11718894C2211yescharacteristic
26C2×#88062C2211yescharacteristic
27#11718783C2211yescharacteristic
28#11718780C2211yescharacteristic
29#11718779C2211yescharacteristic
30M16×Dic13C2211yescharacteristic
31C2×#88059C2211yescharacteristic
32#11718767C2211yescharacteristic
33#11718763C2211yescharacteristic
34#11718763C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36C2×C8×Dic13C2211yescharacteristic
37C2×C8×Dic13C2211yescharacteristic
38#11718659C2211yescharacteristic
39#11718658C2211yescharacteristic
40C4×#6101C2211yescharacteristic
41#11718491—21no—
42#11718491—21no—
43#11718489—21no—
44#11718489—21no—
45#11718460C411yescharacteristic, complemented
46#11718457C411yescharacteristic, complemented
47#11718455C411yescharacteristic, complemented
48#11718452C411yescharacteristic, complemented
49#11718427C411yescharacteristic, complemented
50#11718424C411yescharacteristic, complemented
51#11718422C411yescharacteristic, complemented
52#11718420C411yescharacteristic, complemented
53#11718381—21no—
54#11718381—21no—
55#11718379—21no—
56#11718379—21no—
57C13×#341C2211yescharacteristic
58C13×#339C2211yescharacteristic
59#11718150C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718147C2211yescharacteristic
62#11718142C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718116C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×C13×#41C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×#117C2311yescharacteristic
73C2×C42×C13C2311yescharacteristic
74Q8×Dic13C2×C411yescharacteristic
75Q8×Dic13C2×C411yescharacteristic
76D4×Dic13—21no—
77D4×Dic13—21no—
78D4×Dic13C2×C411yescharacteristic
79D4×Dic13C2×C411yescharacteristic
80#88180—21no—
81#88180C2311yescharacteristic
82#88180C2311yescharacteristic
83C2×#6101—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13C2311yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×#6099C2311yescharacteristic
88C2×#6099C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91#88144C2×C411yescharacteristic
92#88144C2×C411yescharacteristic
93#88142C2×C411yescharacteristic
94#88142C2×C411yescharacteristic
95#88132—21no—
96#88132—21no—
97C4×Dic26—21no—
98C4×Dic26—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×#104—41no—
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#102C2×C411yescharacteristic
105C13×#102C2×C411yescharacteristic
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C4×C8×C13—41no—
109#88077—41no—
110#88075C2×C411yescharacteristic
111#88075C2×C411yescharacteristic
112#88072C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114#88071—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117#88062—41no—
118#88059—41no—
119#88058C2×C411yescharacteristic
120#88058C2×C411yescharacteristic
121#88057C2×C411yescharacteristic
122#88057C2×C411yescharacteristic
123#88055—21no—
124#88055—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054C2×C411yescharacteristic
134#88054C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136#88054C2×C411yescharacteristic
137C8×Dic13—21no—
138C8×Dic13—21no—
139C8×Dic13—41no—
140C8×Dic13D411yescharacteristic
141C8×Dic13D411yescharacteristic
142C8×Dic13D411yescharacteristic
143C8×Dic13D411yescharacteristic
144#88048C2×C411yescharacteristic
145#88048C2×C411yescharacteristic
146#88047C2×C411yescharacteristic
147#88047C2×C411yescharacteristic
148#88043—21no—
149C4×#1055—21no—
150#22130—131nomaximal, Sylow
151C13×#41—21no—
152C13×#41—21no—
153C13×#41—21no—
154C13×#41—21no—
155C2×Q8×C13C22×C411yescharacteristic
156C2×D4×C13—21no—
157C2×D4×C13C22×C411yescharacteristic
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C2411yescharacteristic
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13#4111yescharacteristic
165C22×Dic13#4111yescharacteristic
166C2×Dic26—21no—
167C2×Dic26—21no—
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×C22⋊C4—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C22⋊Dic13—21no—
189C22⋊Dic13—21no—
190C22⋊Dic13—21no—
191C22⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13C22×C411yescharacteristic
197C4⋊Dic13C22×C411yescharacteristic
198C4⋊Dic13C22×C411yescharacteristic
199C4⋊Dic13C22×C411yescharacteristic
200#6101—24no—
201#6101—21no—
202#6101—21no—
203#6101—21no—
204#6101—21no—
205C4×Dic13—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#1945—131no—
236#1937—131no—
237#1937D1311yescharacteristic
238#1929—131no—
239#1929—131no—
240#1922—131no—
241#1922—131no—
242#1806—131no—
243C8×C4⋊C4—131no—
244C23×C13—21no—
245C23×C13C2×#4111yescharacteristic
246Q8×C13—21no—
247Q8×C13—21no—
248D4×C13—21no—
249D4×C13—21no—
250D4×C13—41no—
251D4×C13—41no—
252C2×C4×C13—22no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13C23×C411yescharacteristic
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13H(5,𝔽2)11yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C2×C4×C132−1+411yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—41no—
273C2×Dic13—42no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—42no—
277C2×Dic13C4×D411yescharacteristic
278C2×Dic13C4×D411yescharacteristic
279C2×Dic13C4×D411yescharacteristic
280C2×Dic13C4×D411yescharacteristic
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×#108—131no—
315#427—131no—
316#427—131no—
317#424—131no—
318#424—131no—
319#424—131no—
320#424C2×D1311yescharacteristic
321#423—131no—
322C2×C4⋊C8—131no—
323C2×#104—131no—
324C2×#104C2×D1311yescharacteristic
325#416—131no—
326#416C2×D1311yescharacteristic
327#408—131no—
328#408C2×D1311yescharacteristic
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#341C2×D1311yescharacteristic
338#339—131no—
339#339—131no—
340#339—131no—
341#339—131no—
342#339—131no—
343#339C2×D1311yescharacteristic
344#336—131no—
345#336—131no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13C2×C4×D411yescharacteristic
352C22×C13#54111yescharacteristic
353C22×C13#54211yescharacteristic
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13#51911yescharacteristic
359C4×C13#52011yescharacteristic
360C4×C13#53611yescharacteristic
361C4×C13#53711yescharacteristic
362Dic13—21no—
363Dic13—21no—
364Dic13—21no—
365Dic13—42no—
366Dic13—41no—
367Dic13—41no—
368Dic13—41no—
369Dic13—41no—
370Dic13#44312yes—
371C2×#41C22×D1311yescharacteristic
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—131no—
396#117—261no—
397#117C22×D1311yescharacteristic
398C2×C4⋊C4—261no—
399C2×C42—131no—
400C2×C42—131no—
401C2×C42—261no—
402C2×C42C22×D1311yescharacteristic
403#108—521no—
404#108—521no—
405#107—131no—
406#107—131no—
407#107—131no—
408#107—131no—
409#106—131no—
410#106—131no—
411#106—131no—
412#106—131no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8—131no—
416C4⋊C8—131no—
417C4⋊C8—131no—
418C4⋊C8—131no—
419C4⋊C8—261no—
420C4⋊C8—261no—
421C4⋊C8—261no—
422C4⋊C8—261no—
423C4⋊C8—261no—
424C4⋊C8—261no—
425C4⋊C8—261no—
426C4⋊C8—261no—
427#104—41no—
428#104—521no—
429#103—131no—
430#103—131no—
431#103C4×D1311yescharacteristic
432#103C4×D1311yescharacteristic
433#102—131no—
434#102—131no—
435#102C4×D1311yescharacteristic
436#102C4×D1311yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
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—81no—
457C2×C13#232311yescharacteristic
458C2×C13C2×#44311yescharacteristic
459C2×C13#295511yescharacteristic
460#41—21no—
461#41—21no—
462#41—21no—
463#41—21no—
464C2×Q8—261no—
465C2×Q8—261no—
466C2×Q8C2×C4×D1311yescharacteristic
467C2×D4—21no—
468C2×D4C2×C4×D1311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—131no—
472C22×C4—131no—
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—131no—
508C4⋊C4—131no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—264no—
518C4⋊C4C2×C4×D1311yescharacteristic
519C4⋊C4C2×C4×D1311yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—131no—
529C42—131no—
530C42—131no—
531C42—131no—
532C42—261no—
533C42—261no—
534C42—261no—
535C42—261no—
536C42—261no—
537C42—261no—
538C13#2213011yescharacteristic, complemented, Sylow
539C23—21no—
540C23#41×D1311yescharacteristic
541Q8—21no—
542Q8—21no—
543Q8—522no—
544Q8—522no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—131no—
558C2×C4—131no—
559C2×C4—131no—
560C2×C4—131no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—522no—
568C2×C4—521no—
569C2×C4—522no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4C22×C4×D1311yescharacteristic
573C2×C4C2×D4×D1311yescharacteristic
574C2×C4#8825111yescharacteristic
575C2×C4#8825711yescharacteristic
576C2×C4#8825711yescharacteristic
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—41no—
593C22—41no—
594C22—41no—
595C22C4×D4×D1311yescharacteristic
596C22#1171936711yescharacteristic
597C22#1171940611yescharacteristic
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—132no—
603C4—261no—
604C4—261no—
605C4—261no—
606C4—522no—
607C4—521no—
608C4—521no—
609C4—521no—
610C4—521no—
611C4#1171922111yescharacteristic
612C4#1171925111yescharacteristic
613C4#1171930211yescharacteristic
614C4#1171938011yescharacteristic
615C2—21no—
616C2—21no—
617C2—81no—
618C2#1311751111yescharacteristic
619C2D13×#44311yescharacteristic
620C2#1312373411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1937C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C23
cosocleC22×C4×C13C24
hypercenter#1937D13
hypocenterC13#22130
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. #13123769C2semidirect
4. #13115778C2semidirect
5. #13115610C2semidirect
6. #13115584C2semidirect
7. #13115581C2semidirect
11. #13115434C2semidirect
12. #13115433C2semidirect
14. C8×#6101C2semidirect
45. #11718460C4semidirect
46. #11718457C4semidirect
47. #11718455C4semidirect
48. #11718452C4semidirect
49. #11718427C4semidirect
50. #11718424C4semidirect
51. #11718422C4semidirect
52. #11718420C4semidirect
538. C13#22130semidirect

Maximal subgroups

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

subgroupindex
#131246202
#131237692
#131234762
#131157782
#131156102
#131155842
#131155812
#131155432
#131154872
#131154862
#131154342
#131154332
#131148542
C8×#61012
C13×#19372
#2213013