Finite Group Databasebeta

← #15868423

Subgroups — #15868423

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718788C212yesmaximal, complemented
2C2×C8×C22⋊D13C211yesmaximal, characteristic, complemented
3C4×#88207C211yesmaximal, characteristic
4#13115133C212yesmaximal, complemented
5#13115128C211yesmaximal, characteristic, complemented
6#13115019C212yesmaximal, complemented
7#13115014C211yesmaximal, characteristic, complemented
8#13114746C211yesmaximal, characteristic, complemented
9#13114617C212yesmaximal, complemented
10#13114612C211yesmaximal, characteristic, complemented
11C23×C13×M16C211yesmaximal, characteristic, complemented
12C24×C4×C13C2211yescharacteristic
13C22×C13×M16—28no—
14C22×C13×M16—24no—
15C22×C13×M16C2212yes—
16C22×C13×M16C2212yes—
17C23×C8×C13C2211yescharacteristic
18C23×C8×C13C2211yescharacteristic
19C2×#88207C411yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C2×C4×C22⋊D13C2212yes—
22C22×C8×D13C2211yescharacteristic, complemented
23#11718908C411yescharacteristic
24#11718874C411yescharacteristic
25#11718874C412yes—
26#11718871C412yes—
27#11718871C411yescharacteristic
28C4×C22⋊Dic13C2211yescharacteristic
29C4×C22⋊Dic13C2212yes—
30C2×C22⋊#1055C2211yescharacteristic
31C2×C22⋊#1055C2212yes—
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yes—
34#11718788—28no—
35C8×C22⋊D13—24no—
36C2×#88060C2211yescharacteristic, complemented
37C2×#88060C2212yescomplemented
38C2×#88055C2212yescomplemented
39C2×#88054C2212yescomplemented
40C2×#88054C2211yescharacteristic, complemented
41C2×C8×Dic13C2211yescharacteristic, complemented
42#11718142C2212yescomplemented
43#11718142C2212yescomplemented
44#11718142C2212yescomplemented
45C25×C13C2×C411yescharacteristic
46C23×C4×C13—24no—
47C23×C4×C13—22no—
48C23×C4×C13—24no—
49C23×C4×C13—22no—
50C23×C4×C13C2×C412yes—
51C23×C4×C13C2×C411yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2312yes—
54C22×C22⋊D13C2×C412yes—
55C22×C22⋊D13C2×C411yescharacteristic
56C22×C4×D13C2311yescharacteristic
57C2×C13×M16—232no—
58C2×C13×M16—24no—
59C2×C13×M16—24no—
60C2×C13×M16—24no—
61C2×C13×M16—24no—
62C2×C13×M16—24no—
63C2×C13×M16D418yescomplemented
64C22×C8×C13—22no—
65C22×C8×C13—24no—
66C22×C8×C13—24no—
67C22×C8×C13D414yescomplemented
68C22×C8×C13C2312yes—
69C22×C8×C13C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71#88207—24no—
72C2×C22⋊Dic13C2×C412yes—
73C2×C22⋊Dic13C2×C411yescharacteristic
74C2×C22⋊Dic13C2×C411yescharacteristic
75C2×C22⋊Dic13C2×C412yes—
76C2×C22⋊Dic13C2×C411yescharacteristic
77C2×C22⋊Dic13C2×C412yes—
78C4×C22⋊D13—22no—
79C4×C22⋊D13—24no—
80C4×C22⋊D13—22no—
81C4×C22⋊D13—24no—
82C2×#6103C2×C411yescharacteristic
83C2×#6103C2×C412yes—
84C2×#6101C2×C412yes—
85C2×#6101C2×C411yescharacteristic
86C2×C4×Dic13C2311yescharacteristic
87C2×C4×Dic13C2312yes—
88C22×#1055C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2312yes—
91C2×C8×D13—22no—
92C2×C8×D13—24no—
93#88071C2×C412yes—
94#88071C2×C412yes—
95#88071C2×C412yes—
96C22⋊#1055—22no—
97C22⋊#1055—24no—
98C22⋊#1055—22no—
99C22⋊#1055—24no—
100#88060—22no—
101#88060—24no—
102#88055—24no—
103#88054—22no—
104#88054—24no—
105C8×Dic13—22no—
106#21439—131nomaximal, Sylow
107C24×C13—24no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—42no—
112C24×C13C22×C412yes—
113C24×C13C22×C411yescharacteristic
114C23×D13C22×C411yescharacteristic
115C22×C4×C13—28no—
116C22×C4×C13—28no—
117C22×C4×C13—216no—
118C22×C4×C13—24no—
119C22×C4×C13—22no—
120C22×C4×C13—24no—
121C22×C4×C13—24no—
122C22×C4×C13—24no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C412yes—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D414yes—
133C22×C4×C13#4114yes—
134C22×C4×C13#4112yes—
135C22×C4×C13C2411yescharacteristic
136C2×C22⋊D13—22no—
137C2×C22⋊D13—22no—
138C2×C22⋊D13—24no—
139C2×C22⋊D13—24no—
140C2×C22⋊D13—42no—
141C2×C22⋊D13M1614yescomplemented
142C22×Dic13C22×C412yes—
143C22×Dic13C22×C412yes—
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C2×C4×D13—21no—
148C2×C4×D13—22no—
149C2×C4×D13—21no—
150C2×C4×D13—22no—
151C13×M16—216no—
152C13×M16—216no—
153C2×C8×C13—28no—
154C2×C8×C13—22no—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C2×C8×C13—28no—
158C2×C8×C13C2×D414yes—
159C2×C8×C13C2×D412yes—
160C2×C8×C13C2×D414yes—
161C2×C8×C13C2×D412yes—
162C22⋊Dic13—24no—
163C22⋊Dic13—22no—
164C22⋊Dic13—22no—
165C22⋊Dic13—22no—
166C22⋊Dic13—24no—
167C22⋊Dic13—42no—
168#6103—22no—
169#6103—24no—
170#6101—22no—
171#6101—24no—
172C4×Dic13—21no—
173C4×Dic13—22no—
174C4×Dic13—21no—
175C4×Dic13—22no—
176C2×#1055—21no—
177C2×#1055—22no—
178C2×#1055—21no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C8×D13—44no—
184C23×M16D1311yescharacteristic, complemented
185C2×#435—132no—
186C2×C8×D4—131no—
187C4×#120—131no—
188#1870—132no—
189#1869—131no—
190#1851—132no—
191#1850—131no—
192#1779—131no—
193#1753—132no—
194#1752—131no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—28no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—22no—
202C23×C13—22no—
203C23×C13—22no—
204C23×C13—48no—
205C23×C13—48no—
206C23×C13—44no—
207C23×C13—44no—
208C23×C13C4×D414yes—
209C23×C13C4×D412yes—
210C23×C13C2×M1612yes—
211C23×C13#13112yes—
212C23×C13C23×C411yescharacteristic
213C22×D13—21no—
214C22×D13—22no—
215C22×D13—21no—
216C22×D13—22no—
217C22×D13C2×M1612yescomplemented
218C2×C4×C13—28no—
219C2×C4×C13—216no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—22no—
226C2×C4×C13—24no—
227C2×C4×C13—24no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13C4×D412yes—
231C2×C4×C13C4×D414yes—
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C22×D412yes—
234C2×C4×C13C2×#4111yescharacteristic
235C2×C4×C13C2×#4112yes—
236C22⋊D13—28no—
237C22⋊D13—48no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—22no—
241C2×Dic13—21no—
242C2×Dic13—22no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—22no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13C2×M1612yescomplemented
251C4×D13—41no—
252C4×D13—41no—
253C4×D13—42no—
254C8×C13—24no—
255C8×C13—22no—
256C8×C13#12014yescomplemented
257#1055—41no—
258#1055—41no—
259#1055—42no—
260C24×C4C2×D1311yescharacteristic
261C22×M16—28no—
262C22×M16—24no—
263C22×M16C2×D1312yes—
264C22×M16C2×D1312yes—
265C23×C8—131no—
266C23×C8C2×D1311yescharacteristic
267C23×C8C2×D1311yescharacteristic
268C2×#120—131no—
269C2×C4×D4—131no—
270C2×C4×D4—132no—
271#435—268no—
272C8×D4—264no—
273C2×C4⋊C8—132no—
274C2×C4⋊C8—131no—
275C2×C22⋊C8—131no—
276C2×C22⋊C8—132no—
277C2×C22⋊C8—131no—
278C2×C22⋊C8—132no—
279C2×C22⋊C8—132no—
280C2×C22⋊C8—131no—
281C2×#97—132no—
282C2×C4×C8—131no—
283#386—131no—
284#386—132no—
285#385—132no—
286#385—131no—
287#379—131no—
288C4×C22⋊C4—131no—
289C4×C22⋊C4—132no—
290#336—132no—
291#336—132no—
292#336—132no—
293C22×C13—22no—
294C22×C13—24no—
295C22×C13—24no—
296C22×C13—22no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—24no—
300C22×C13—416no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13#43514yescomplemented
306C22×C13C2×C4×D411yescharacteristic
307C22×C13C2×C4×D412yes—
308C22×C13C22×M1611yescharacteristic
309C22×C13C2×#13111yescharacteristic
310C22×C13#56812yes—
311C2×D13—22no—
312C2×D13—24no—
313C2×D13—41no—
314C2×D13—42no—
315C2×D13—41no—
316C4×C13—22no—
317C4×C13—24no—
318C4×C13C2×#12011yescharacteristic
319C4×C13#52511yescharacteristic
320C4×C13#52512yes—
321Dic13—22no—
322Dic13—41no—
323Dic13—42no—
324Dic13—42no—
325Dic13—41no—
326C25C4×D1311yescharacteristic
327C22×D4—131no—
328C22×D4—132no—
329C23×C4—24no—
330C23×C4—22no—
331C23×C4—24no—
332C23×C4—22no—
333C23×C4—131no—
334C23×C4C4×D1312yes—
335C23×C4C4×D1311yescharacteristic
336C23×C4C22×D1311yescharacteristic
337C23×C4C22×D1312yes—
338C2×M16—232no—
339C2×M16—24no—
340C2×M16—24no—
341C2×M16—24no—
342C2×M16—24no—
343C2×M16—24no—
344C2×M16C22⋊D1318yescomplemented
345C22×C8—22no—
346C22×C8—24no—
347C22×C8—24no—
348C22×C8—131no—
349C22×C8—131no—
350C22×C8—132no—
351C22×C8—262no—
352C22×C8—264no—
353C22×C8C22⋊D1314yescomplemented
354C22×C8C22×D1312yes—
355C22×C8C22×D1311yescharacteristic
356C22×C8C22×D1311yescharacteristic
357#120—264no—
358C4×D4—262no—
359C4×D4—264no—
360C4×D4—262no—
361C4×D4—264no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—132no—
364C2×C22⋊C4—132no—
365C2×C22⋊C4—131no—
366C2×C22⋊C4—132no—
367C2×C22⋊C4—131no—
368C2×C22⋊C4—131no—
369C2×C22⋊C4—131no—
370C2×C22⋊C4—132no—
371C2×C22⋊C4—132no—
372C2×C42—131no—
373C2×C42—132no—
374C4⋊C8—262no—
375C4⋊C8—264no—
376C22⋊C8—262no—
377C22⋊C8—264no—
378C22⋊C8—262no—
379C22⋊C8—264no—
380C22⋊C8—262no—
381C22⋊C8—264no—
382#97—264no—
383C4×C8—262no—
384#95—132no—
385#95—132no—
386#95—132no—
387C2×C13—24no—
388C2×C13—44no—
389C2×C13C4×#12011yescharacteristic
390C2×C13C2×#43511yescharacteristic
391C2×C13#293011yescharacteristic
392C2×C13#293312yes—
393C2×C13D4×M1612yes—
394D13—42no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—42no—
400C24—131no—
401C24C2×C4×D1312yes—
402C24C2×C4×D1311yescharacteristic
403C2×D4—134no—
404C2×D4—262no—
405C2×D4—262no—
406C2×D4—264no—
407C2×D4—264no—
408C2×D4—522no—
409C22×C4—28no—
410C22×C4—216no—
411C22×C4—28no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—131no—
424C22×C4—132no—
425C22×C4—131no—
426C22×C4—132no—
427C22×C4—131no—
428C22×C4—261no—
429C22×C4—262no—
430C22×C4—261no—
431C22×C4—262no—
432C22×C4C2×C4×D1311yescharacteristic
433C22×C4C2×C4×D1312yes—
434C22×C4#612714yes—
435C22×C4#612712yes—
436C22×C4C2×C22⋊D1312yes—
437C22×C4C2×C22⋊D1314yes—
438C22×C4C23×D1311yescharacteristic
439M16—216no—
440M16—216no—
441C2×C8—28no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—28no—
446C2×C8—262no—
447C2×C8—262no—
448C2×C8—262no—
449C2×C8—261no—
450C2×C8—262no—
451C2×C8—261no—
452C2×C8—262no—
453C2×C8—524no—
454C2×C8C2×C22⋊D1314yes—
455C2×C8C2×C22⋊D1312yes—
456C2×C8C2×C22⋊D1312yes—
457C2×C8C2×C22⋊D1314yes—
458C4⋊C4—262no—
459C4⋊C4—264no—
460C22⋊C4—264no—
461C22⋊C4—262no—
462C22⋊C4—262no—
463C22⋊C4—264no—
464C22⋊C4—262no—
465C22⋊C4—262no—
466C22⋊C4—264no—
467C22⋊C4—522no—
468C42—261no—
469C42—262no—
470C42—261no—
471C42—262no—
472C13#2143911yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—28no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—48no—
483C23—48no—
484C23—44no—
485C23—44no—
486C23—132no—
487C23—261no—
488C23—262no—
489C23—261no—
490C23—262no—
491C23M16×D1312yes—
492C23#8816112yes—
493C23C4×C22⋊D1314yes—
494C23C4×C22⋊D1312yes—
495C23C22×C4×D1311yescharacteristic
496D4—268no—
497D4—528no—
498C2×C4—28no—
499C2×C4—216no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—132no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—261no—
519C2×C4—262no—
520C2×C4—262no—
521C2×C4—261no—
522C2×C4—262no—
523C2×C4—521no—
524C2×C4—522no—
525C2×C4—521no—
526C2×C4C4×C22⋊D1312yes—
527C2×C4C4×C22⋊D1314yes—
528C2×C4C2×#612711yescharacteristic
529C2×C4C2×#612712yes—
530C2×C4C22×C22⋊D1311yescharacteristic
531C2×C4C22×C22⋊D1312yes—
532C8—24no—
533C8—22no—
534C8—521no—
535C8—522no—
536C8—521no—
537C8#8820714yescomplemented
538C22—22no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—24no—
543C22—24no—
544C22—24no—
545C22—416no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—262no—
551C22—264no—
552C22—521no—
553C22—521no—
554C22—522no—
555C22#1171878814yescomplemented
556C22C2×M16×D1311yescharacteristic
557C22C2×#8816111yescharacteristic
558C22#1171945012yes—
559C22C2×C4×C22⋊D1311yescharacteristic
560C22C2×C4×C22⋊D1312yes—
561C4—22no—
562C4—24no—
563C4—262no—
564C4—521no—
565C4—521no—
566C4—522no—
567C4—522no—
568C4#1171949611yescharacteristic
569C4#1171949612yes—
570C4C2×#8820711yescharacteristic
571C2—24no—
572C2—44no—
573C2—522no—
574C2C4×#8820711yescharacteristic
575C2C2×#1171878811yescharacteristic
576C2#1312353911yescharacteristic
577C2#1312356112yes—
578C2M16×C22⋊D1312yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC23×C13×M16C2
prime radicalC2×#88207C4
cosocleC22×C4×C13C24
hypercenterC23×M16D13
hypocenterC13#21439
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11718788C2semidirect
2. C2×C8×C22⋊D13C2semidirect
4. #13115133C2semidirect
5. #13115128C2semidirect
6. #13115019C2semidirect
7. #13115014C2semidirect
8. #13114746C2semidirect
9. #13114617C2semidirect
10. #13114612C2semidirect
11. C23×C13×M16C2semidirect
22. C22×C8×D13C22semidirect
36. C2×#88060C22semidirect
37. C2×#88060C22semidirect
38. C2×#88055C22semidirect
39. C2×#88054C22semidirect
40. C2×#88054C22semidirect
41. C2×C8×Dic13C22semidirect
42. #11718142C22semidirect
43. #11718142C22semidirect
44. #11718142C22semidirect
63. C2×C13×M16D4semidirect
67. C22×C8×C13D4semidirect
141. C2×C22⋊D13M16semidirect
184. C23×M16D13semidirect
217. C22×D13C2×M16semidirect
250. C2×Dic13C2×M16semidirect
256. C8×C13#120semidirect
305. C22×C13#435semidirect
344. C2×M16C22⋊D13semidirect
353. C22×C8C22⋊D13semidirect
472. C13#21439semidirect
537. C8#88207semidirect
555. C22#11718788semidirect

Maximal subgroups

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

subgroupindex
C2×#117187882
C2×C8×C22⋊D132
C4×#882072
#131151332
#131151282
#131150192
#131150142
#131147462
#131146172
#131146122
C23×C13×M162
#2143913