Finite Group Databasebeta

← #15832884

Subgroups — #15832884

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124881C211yesmaximal, characteristic
2#13123808C211yesmaximal, characteristic, complemented
3C8×D4×D13C211yesmaximal, characteristic, complemented
4#13113703C211yesmaximal, characteristic, complemented
5#13113701C211yesmaximal, characteristic, complemented
6#13113692C211yesmaximal, characteristic, complemented
7#13113690C211yesmaximal, characteristic, complemented
8C8×#6095C211yesmaximal, characteristic, complemented
9C8×#6105C211yesmaximal, characteristic, complemented
10C8×#6104C211yesmaximal, characteristic, complemented
11#13113620C211yesmaximal, characteristic, complemented
12#13113277C211yesmaximal, characteristic, complemented
13#13113246C211yesmaximal, characteristic, complemented
14C8×#6094C211yesmaximal, characteristic, complemented
15C8×C13×D8C211yesmaximal, characteristic, complemented
16C22×C8×D13—21no—
17#11719262C2211yescharacteristic
18C4×D4×D13C2211yescharacteristic
19C4×C13×D8C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic, complemented
22#11718817C411yescharacteristic
23#11718814C411yescharacteristic
24C8×C22⋊D13—21no—
25C8×C22⋊D13—21no—
26#11718762—21no—
27C4×#6105C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic, complemented
30D4×#1055C2211yescharacteristic
31#11718552C411yescharacteristic
32#11718545C411yescharacteristic
33#11718496C2211yescharacteristic
34#11718495C2211yescharacteristic
35D13×C4⋊C8C2211yescharacteristic
36#11718492C2211yescharacteristic, complemented
37#11718448C411yescharacteristic
38#11718438C411yescharacteristic
39#11718437C411yescharacteristic
40#11718424C411yescharacteristic
41#11718389—21no—
42#11718386—21no—
43D13×C22⋊C8—21no—
44#11718381—21no—
45C4×#6095C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47C8×D52C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50C8×Dic26C2211yescharacteristic, complemented
51C13×#335C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic, complemented
54C82×C13C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic, complemented
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×D8C2×C411yescharacteristic
70C22×C8×C13—21no—
71C22×C8×C13—21no—
72C4×D4×C13C2311yescharacteristic
73C4×D4×C13C2311yescharacteristic
74#88192C2×C411yescharacteristic
75#88190C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C4×C22⋊D13—21no—
80C4×C22⋊D13—21no—
81#88180—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84C2×#6095C2×C411yescharacteristic
85C2×#6094—21no—
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89C2×C8×D13—44no—
90C2×C8×D13D411yescharacteristic
91C2×C8×D13D411yescharacteristic
92#88151C2×C411yescharacteristic
93#88147C2×C411yescharacteristic
94C4⋊C4×D13C2×C411yescharacteristic
95#88144C2×C411yescharacteristic
96#88137—21no—
97#88135—21no—
98C22⋊C4×D13—21no—
99#88133—21no—
100C4×D52C2311yescharacteristic
101C42×D13C2311yescharacteristic
102C4×Dic26C2311yescharacteristic
103C13×#107C2×C411yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×#102C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×C22⋊C8—21no—
109C13×C22⋊C8—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117#88061C2×C411yescharacteristic
118#88060—21no—
119#88060—21no—
120#88060—21no—
121#88060C2×C411yescharacteristic
122#88060C2×C411yescharacteristic
123#88057C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88055—21no—
126#88055—21no—
127#88055—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133C8×Dic13—21no—
134C8×Dic13D411yescharacteristic
135C8×Dic13D411yescharacteristic
136#88050C2×C411yescharacteristic
137#88049C2×C411yescharacteristic
138#88048C2×C411yescharacteristic
139#88047C2×C411yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17910—131nomaximal, Sylow
146C23×D13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C2×C22⋊D13—21no—
152C2×C22⋊D13—21no—
153C22×Dic13—21no—
154D4×D13—22no—
155D4×D13—22no—
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—42no—
161C2×C4×D13—42no—
162C2×C4×D13C22×C411yescharacteristic
163C2×C4×D13C2×D411yescharacteristic
164C2×C4×D13#4111yescharacteristic
165C2×Dic26C22×C411yescharacteristic
166C13×D8—22no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—42no—
171C2×C8×C13—42no—
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182C22⋊Dic13—21no—
183C22⋊Dic13—21no—
184C22⋊Dic13—21no—
185#6105—22no—
186#6104—22no—
187#6103—21no—
188#6103—21no—
189#6103—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197C4×Dic13—21no—
198C4×Dic13C22×C411yescharacteristic
199C4×Dic13C2×D411yescharacteristic
200C4×Dic13#4111yescharacteristic
201#6099—42no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—42no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210#6095—22no—
211#6094—24no—
212C8×D13—22no—
213C8×D13—41no—
214C8×D13—42no—
215C8×D13—42no—
216C8×D13—42no—
217#3105—131no—
218#2966—131no—
219C2×C8×D4—131no—
220#1586—131no—
221#1586—131no—
222#1585—131no—
223#1585—131no—
224C8×SD16—131no—
225C8×SD16—131no—
226C8×D8—131no—
227C8×D8D1311yescharacteristic, complemented
228#1573—131no—
229#1490—131no—
230#1483—131no—
231C8×M16—131no—
232C23×C13—21no—
233C23×C13—21no—
234C22×D13—24no—
235C22×D13—21no—
236C22×D13—42no—
237C22×D13—42no—
238C22×D13C4×D411yescharacteristic
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13#13112yes—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13C23×C411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C22⋊D13—24no—
253C22⋊D13—42no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—42no—
258C2×Dic13C4×D411yescharacteristic
259C2×Dic13C4×D411yescharacteristic
260C2×Dic13C4×D411yescharacteristic
261D52—21no—
262D52#13112yes—
263C4×D13—22no—
264C4×D13—21no—
265C4×D13—21no—
266C4×D13—21no—
267C4×D13—21no—
268C4×D13—42no—
269C4×D13—42no—
270C4×D13—41no—
271C4×D13—41no—
272Dic26—21no—
273Dic26—21no—
274C8×C13—22no—
275C8×C13—21no—
276C8×C13—21no—
277C8×C13—21no—
278C8×C13—41no—
279C8×C13—41no—
280C8×C13AGL(1,ℤ/8)12yes—
281#1055—22no—
282#1055—21no—
283#1055—21no—
284#1055—21no—
285#1055—21no—
286#1055—41no—
287#1055—41no—
288C23×C8—261no—
289#529—131no—
290C2×C4×D4—131no—
291#484—131no—
292#481—131no—
293#478—131no—
294#478—131no—
295#463—131no—
296#463—131no—
297#450—131no—
298#447—131no—
299#446—131no—
300C8×Q8—131no—
301C4×SD16—131no—
302C4×SD16—131no—
303C4×D8—131no—
304C4×D8C2×D1311yescharacteristic
305#436—131no—
306#435—261no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—261no—
311C8×D4—261no—
312C8×D4—261no—
313C8×D4C2×D1311yescharacteristic
314C8×D4C2×D1311yescharacteristic, complemented
315#433—261no—
316#432—131no—
317#431—131no—
318C2×C4⋊C8—131no—
319C2×C22⋊C8—261no—
320#405—261no—
321C4×M16—131no—
322C2×C4×C8—131no—
323#335—131no—
324#335C2×D1311yescharacteristic, complemented
325#334—131no—
326#334—131no—
327Q8⋊C8—131no—
328Q8⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332D4⋊C8—131no—
333D4⋊C8C2×D1311yescharacteristic
334D4⋊C8C2×D1311yescharacteristic, complemented
335#322—131no—
336#322—131no—
337C82—131no—
338C82C2×D1311yescharacteristic, complemented
339C22×C13—22no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13C2×C4×D411yescharacteristic
346C2×D13—21no—
347C2×D13—21no—
348C2×D13—22no—
349C2×D13—48no—
350C2×D13—41no—
351C2×D13—41no—
352C2×D13#44312yes—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13C2×#13111yescharacteristic
357C4×C13C2×#13111yescharacteristic
358C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
359C4×C13#57511yescharacteristic
360Dic13—21no—
361Dic13—21no—
362Dic13—21no—
363Dic13—41no—
364Dic13—41no—
365Dic13—41no—
366C22×D4—131no—
367C23×C4—261no—
368C2×SD16—131no—
369C2×SD16—131no—
370C2×D8—131no—
371C2×D8C4×D1311yescharacteristic
372C2×M16—261no—
373C2×M16—261no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—261no—
379C22×C8—261no—
380C22×C8—261no—
381C22×C8—261no—
382C22×C8—524no—
383#126—261no—
384#125—131no—
385#124—131no—
386#123—261no—
387C22⋊Q8—131no—
388#121—131no—
389C4×Q8—131no—
390C4×D4—131no—
391C4×D4—131no—
392C4×D4—131no—
393C4×D4—261no—
394C4×D4—261no—
395C4×D4—261no—
396C4×D4C22×D1311yescharacteristic
397C4×D4C22×D1311yescharacteristic
398#117—261no—
399C2×C4⋊C4—131no—
400C2×C22⋊C4—261no—
401C2×C42—131no—
402#107—131no—
403#107C4×D1311yescharacteristic
404#106—131no—
405#106—131no—
406C4⋊C8—131no—
407C4⋊C8—131no—
408C4⋊C8—131no—
409C4⋊C8—131no—
410C4⋊C8—261no—
411C4⋊C8—261no—
412C4⋊C8—261no—
413C4⋊C8C22×D1311yescharacteristic
414C4⋊C8C22×D1311yescharacteristic
415#103—131no—
416#103—131no—
417#102—131no—
418#102—131no—
419#102—131no—
420#102—131no—
421#102C4×D1311yescharacteristic
422#102C4×D1311yescharacteristic
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—131no—
426C22⋊C8—131no—
427C22⋊C8—261no—
428C22⋊C8—261no—
429C22⋊C8—261no—
430C22⋊C8—261no—
431C22⋊C8—261no—
432#97—261no—
433#97—261no—
434#97—261no—
435C4×C8—131no—
436C4×C8—131no—
437C4×C8—131no—
438C4×C8—131no—
439C4×C8—131no—
440C4×C8—261no—
441C4×C8C22×D1311yescharacteristic
442C4×C8C22×D1311yescharacteristic
443C4×C8C22×D1311yescharacteristic
444C2×C13—42no—
445C2×C13—81no—
446C2×C13#292911yescharacteristic
447C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
448C2×C13C2×#44311yescharacteristic
449D13—22no—
450D13—42no—
451C24—261no—
452C2×Q8—131no—
453C2×D4—131no—
454C2×D4—261no—
455C2×D4—262no—
456C2×D4—262no—
457C2×D4—261no—
458C2×D4C2×C4×D1311yescharacteristic
459C2×D4C2×C4×D1311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—131no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—261no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—522no—
470C22×C4—522no—
471SD16—262no—
472SD16—262no—
473D8—22no—
474D8—262no—
475M16—264no—
476M16—522no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—42no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—131no—
486C2×C8—261no—
487C2×C8—262no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—521no—
491C2×C8—522no—
492C2×C8—522no—
493C2×C8—522no—
494C2×C8—522no—
495C2×C8C2×C4×D1311yescharacteristic
496C2×C8C2×C4×D1311yescharacteristic
497C2×C8D4×D1311yescharacteristic
498C2×C8D4×D1311yescharacteristic
499C4⋊C4—131no—
500C4⋊C4—131no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4C2×C4×D1311yescharacteristic
507C4⋊C4C2×C4×D1311yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—261no—
511C22⋊C4—261no—
512C22⋊C4—261no—
513C22⋊C4—261no—
514C22⋊C4—261no—
515C22⋊C4—261no—
516C22⋊C4—261no—
517C42—131no—
518C42—131no—
519C42—131no—
520C42—261no—
521C42C23×D1311yescharacteristic
522C13#1791011yescharacteristic, complemented, Sylow
523C23—21no—
524C23—21no—
525C23—131no—
526C23—264no—
527C23—261no—
528C23—522no—
529C23—522no—
530Q8—261no—
531Q8—261no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—132no—
536D4—264no—
537D4—261no—
538D4—522no—
539D4#8815512yes—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—131no—
547C2×C4—131no—
548C2×C4—131no—
549C2×C4—262no—
550C2×C4—261no—
551C2×C4—261no—
552C2×C4—261no—
553C2×C4—261no—
554C2×C4—261no—
555C2×C4—261no—
556C2×C4—261no—
557C2×C4—522no—
558C2×C4—522no—
559C2×C4—522no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×D4×D1311yescharacteristic
564C2×C4#41×D1311yescharacteristic
565C8—22no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—262no—
572C8—261no—
573C8—261no—
574C8—261no—
575C8—261no—
576C8—521no—
577C8—521no—
578C8#8816512yes—
579C22—22no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—132no—
586C22—261no—
587C22—261no—
588C22—262no—
589C22—528no—
590C22—521no—
591C22—521no—
592C22C4×D4×D1311yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—261no—
597C4—261no—
598C4—261no—
599C4—521no—
600C4—521no—
601C4—521no—
602C4C2×#8815511yescharacteristic
603C4D13×#13111yescharacteristic
604C4C2×#8816511yescharacteristic
605C4#1171947311yescharacteristic
606C2—42no—
607C2—81no—
608C2—262no—
609C2—522no—
610C2#1312352511yescharacteristic
611C2C4×#8816511yescharacteristic
612C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C8D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×D8C2
socleC22×C13C2×C4×D4
prime radical#11718817C4
cosocleC42×C13C24
hypercenterC8×D8D13
hypocenterC13#17910
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #13123808C2semidirect
3. C8×D4×D13C2semidirect
4. #13113703C2semidirect
5. #13113701C2semidirect
6. #13113692C2semidirect
7. #13113690C2semidirect
8. C8×#6095C2semidirect
9. C8×#6105C2semidirect
10. C8×#6104C2semidirect
11. #13113620C2semidirect
12. #13113277C2semidirect
13. #13113246C2semidirect
14. C8×#6094C2semidirect
15. C8×C13×D8C2semidirect
21. C8×D4×C13C22semidirect
29. #11718673C22semidirect
36. #11718492C22semidirect
50. C8×Dic26C22semidirect
51. C13×#335C22semidirect
53. C13×D4⋊C8C22semidirect
54. C82×C13C22semidirect
56. D4⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718049C22semidirect
63. #11718048C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
227. C8×D8D13semidirect
314. C8×D4C2×D13semidirect
324. #335C2×D13semidirect
334. D4⋊C8C2×D13semidirect
338. C82C2×D13semidirect
522. C13#17910semidirect

Maximal subgroups

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

subgroupindex
#131248812
#131238082
C8×D4×D132
#131137032
#131137012
#131136922
#131136902
C8×#60952
C8×#61052
C8×#61042
#131136202
#131132772
#131132462
C8×#60942
C8×C13×D82
#1791013