Finite Group Databasebeta

← Dic13×#448 #15868511

Subgroups — Dic13×#448 #15868511

Order 3328.

1532 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×SD16×Dic13C212yesmaximal, complemented
3#121×Dic13C211yesmaximal, characteristic
4#13115193C212yesmaximal, complemented
5#13115154C211yesmaximal, characteristic
6#13115106C212yesmaximal, complemented
7#13115031C211yesmaximal, characteristic, complemented
8#13114771C211yesmaximal, characteristic, complemented
9#103×Dic13C212yesmaximal, complemented
10C22⋊C8×Dic13C211yesmaximal, characteristic, complemented
11C2×C13×#448C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C22×C13×SD16C2212yes—
14C2×C13×#121C2211yescharacteristic
15C2×Q8×Dic13—28no—
16C2×Q8×Dic13—21no—
17C2×Q8×Dic13—21no—
18C2×Q8×Dic13C2212yes—
19C2×Q8×Dic13C2212yes—
20C2×D4×Dic13—21no—
21C2×D4×Dic13C2211yescharacteristic
22C22×C4⋊Dic13—21no—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4×Dic13—21no—
25C22×C4×Dic13C2211yescharacteristic
26C13×#448C418yescomplemented
27C2×C13×#103C2212yes—
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×#88075C2212yes—
30C2×#88075C2212yes—
31#11718882C2211yescharacteristic
32#11718881—21no—
33C2×#88072C2212yes—
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36SD16×Dic13—28no—
37C2×#88057C2212yes—
38C2×C8×Dic13C2212yes—
39#11718646C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41#11718612—21no—
42C22⋊C4×Dic13—21no—
43#11718143C2212yes—
44#11718142C2212yes—
45#11718121C2212yes—
46C22×Q8×C13—24no—
47C22×Q8×C13—24no—
48C22×Q8×C13—21no—
49C22×Q8×C13—22no—
50C22×Q8×C13C2×C414yescomplemented
51C22×Q8×C13C2312yes—
52C22×D4×C13—21no—
53C22×D4×C13C2311yescharacteristic
54C23×C4×C13—21no—
55C23×C4×C13C2311yescharacteristic
56C23×Dic13—21no—
57C23×Dic13—21no—
58C23×Dic13D411yescharacteristic
59C23×Dic13D411yescharacteristic
60C2×C13×SD16—24no—
61C2×C13×SD16—24no—
62C2×C13×SD16C2×C418yescomplemented
63C22×C8×C13C2312yes—
64C13×#121—22no—
65C13×#121C2×C414yes—
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C22⋊C4—21no—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—21no—
71C2×C22⋊Dic13—21no—
72Q8×Dic13—28no—
73Q8×Dic13—28no—
74Q8×Dic13—24no—
75Q8×Dic13—24no—
76Q8×Dic13—24no—
77Q8×Dic13D418yescomplemented
78D4×Dic13—24no—
79D4×Dic13—44no—
80C2×C4⋊Dic13—28no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—24no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2312yes—
89C2×C4×Dic13—28no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C22×#1055C2312yes—
99C13×#103C2×C418yescomplemented
100C13×C22⋊C8C2×C414yescomplemented
101#88075—24no—
102#88075—24no—
103#88072—24no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107C22⋊#1055—22no—
108#88057—24no—
109C8×Dic13—24no—
110C4×#448—131nomaximal, Sylow
111C24×C13—21no—
112C24×C13C2×D411yescharacteristic
113C2×Q8×C13—24no—
114C2×Q8×C13—216no—
115C2×Q8×C13—24no—
116C2×Q8×C13—216no—
117C2×Q8×C13—24no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13C22×C414yes—
122C2×Q8×C13C2×D414yes—
123C2×Q8×C13#4114yes—
124C2×D4×C13—24no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13—42no—
129C2×D4×C13—42no—
130C2×D4×C13C22×C412yes—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—24no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13C22×C412yes—
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13#4112yes—
141C22×C4×C13C2411yescharacteristic
142C22×Dic13—22no—
143C22×Dic13—22no—
144C22×Dic13—24no—
145C22×Dic13—22no—
146C22×Dic13—22no—
147C22×Dic13—22no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—41no—
151C22×Dic13—42no—
152C22×Dic13—42no—
153C22×Dic13—42no—
154C22×Dic13—42no—
155C22×Dic13—42no—
156C22×Dic13SD1614yescomplemented
157C22×Dic13C2×D411yescharacteristic
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161C13×SD16—216no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13C22×C414yes—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C412yes—
167C13×C22⋊C4—24no—
168C22⋊Dic13—42no—
169C22⋊Dic13—42no—
170C22⋊Dic13—42no—
171C22⋊Dic13—42no—
172C4⋊Dic13—28no—
173C4⋊Dic13—24no—
174C4⋊Dic13—22no—
175C4⋊Dic13—28no—
176C4⋊Dic13—22no—
177C4⋊Dic13—22no—
178C4⋊Dic13—42no—
179C4⋊Dic13C2×D414yes—
180C4×Dic13—28no—
181C4×Dic13—22no—
182C4×Dic13—28no—
183C4×Dic13—22no—
184C4×Dic13—22no—
185C4×Dic13—42no—
186C4×Dic13C2×D414yes—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C22×C4×Q8—131no—
191C2×#448D1311yescharacteristic
192C2×C4×SD16—132no—
193C4×#121—131no—
194#1880—132no—
195#1874—131no—
196#1865—132no—
197#1853—131no—
198#1787—131no—
199C4×#103—132no—
200C4×C22⋊C8—131no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—21no—
205C23×C13—22no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13C4×D412yes—
213C23×C13C2×SD1612yes—
214C23×C13#13512yes—
215C23×C13C22×D411yescharacteristic
216Q8×C13—216no—
217Q8×C13—24no—
218Q8×C13—24no—
219Q8×C13—24no—
220Q8×C13C4×D418yescomplemented
221D4×C13—24no—
222D4×C13—48no—
223D4×C13—42no—
224C2×C4×C13—216no—
225C2×C4×C13—24no—
226C2×C4×C13—24no—
227C2×C4×C13—21no—
228C2×C4×C13—24no—
229C2×C4×C13—21no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—22no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13C4×D412yes—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C22×D412yes—
238C2×C4×C13C2×#4112yes—
239C2×C4×C13C2×#4111yescharacteristic
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—28no—
245C2×Dic13—21no—
246C2×Dic13—24no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—44no—
250C2×Dic13—48no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—84no—
260C2×Dic13#12012yes—
261C2×Dic13#12012yes—
262C2×Dic13C2×SD1612yes—
263C2×Dic13C2×SD1612yes—
264C2×Dic13#13712yes—
265C8×C13—24no—
266#1055—42no—
267C23×Q8C2×D1311yescharacteristic
268C22×SD16C2×D1312yes—
269C2×#121C2×D1311yescharacteristic
270C2×C4×Q8—132no—
271C2×C4×Q8—132no—
272C2×C4×Q8—261no—
273C2×C4×Q8—261no—
274C2×C4×Q8—268no—
275C2×C4×D4—131no—
276C2×C4×D4—261no—
277C22×C4⋊C4—131no—
278C22×C4⋊C4—261no—
279C22×C42—131no—
280C22×C42—261no—
281#448Dic1318yesdirect product factor
282C4×SD16—268no—
283C2×#106—132no—
284C2×#103—132no—
285C2×#103—132no—
286C2×#103C2×D1312yes—
287C2×#102—132no—
288C2×C22⋊C8—131no—
289C2×C22⋊C8C2×D1311yescharacteristic
290C2×C4×C8—132no—
291#390—131no—
292#389—131no—
293#388—261no—
294#386—261no—
295#380—131no—
296C4×C4⋊C4—131no—
297C4×C22⋊C4—261no—
298#340—132no—
299#340—132no—
300#336—132no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—22no—
304C22×C13—22no—
305C22×C13—22no—
306C22×C13—22no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13C4×SD1614yescomplemented
315C22×C13C2×C4×D411yescharacteristic
316C22×C13C2×#12011yescharacteristic
317C22×C13#52511yescharacteristic
318C22×C13C22×SD1611yescharacteristic
319C22×C13C2×#13511yescharacteristic
320C22×C13C2×#13711yescharacteristic
321C22×C13#57511yescharacteristic
322C4×C13—28no—
323C4×C13—22no—
324C4×C13—42no—
325C4×C13C2×C4×D412yes—
326C4×C13#52512yes—
327Dic13—22no—
328Dic13—22no—
329Dic13—41no—
330Dic13—44no—
331Dic13—81no—
332Dic13—81no—
333Dic13#44814yesdirect product factor
334C22×Q8—24no—
335C22×Q8—24no—
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8C2×Dic1314yescomplemented
339C22×Q8C22×D1312yes—
340C22×D4—21no—
341C22×D4C22×D1311yescharacteristic
342C23×C4—21no—
343C23×C4—131no—
344C23×C4—131no—
345C23×C4—261no—
346C23×C4—261no—
347C23×C4C22×D1311yescharacteristic
348C2×SD16—24no—
349C2×SD16—24no—
350C2×SD16C2×Dic1318yescomplemented
351C22×C8—132no—
352C22×C8C22×D1312yes—
353#121—22no—
354#121C2×Dic1314yes—
355C4×Q8—138no—
356C4×Q8—264no—
357C4×Q8—264no—
358C4×Q8—268no—
359C4×Q8—268no—
360C4×Q8—264no—
361C4×D4—264no—
362C4×D4—524no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—264no—
367C2×C4⋊C4—262no—
368C2×C4⋊C4—262no—
369C2×C4⋊C4—268no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4C22×D1311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42—264no—
383C2×C42—262no—
384C2×C42—262no—
385C2×C42—268no—
386C2×C42—261no—
387#106—264no—
388#103—264no—
389#103—264no—
390#103C2×Dic1318yescomplemented
391#102—264no—
392C22⋊C8—262no—
393C22⋊C8C2×Dic1314yescomplemented
394C4×C8—264no—
395#95—261no—
396#95—261no—
397#95—261no—
398C2×C13—24no—
399C2×C13—82no—
400C2×C13C4×#12011yescharacteristic
401C2×C13C2×C4×SD1611yescharacteristic
402C2×C13C4×#13711yescharacteristic
403C2×C13C2×#44811yescharacteristic
404C2×C13#300211yescharacteristic
405C2×C13#310311yescharacteristic
406C2×C13#310811yescharacteristic
407C24—21no—
408C24D4×D1311yescharacteristic
409C2×Q8—24no—
410C2×Q8—216no—
411C2×Q8—24no—
412C2×Q8—216no—
413C2×Q8—24no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8D4×D1314yes—
418C2×Q8#612914yes—
419C2×Q8C22×Dic1314yes—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4C22×Dic1312yes—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—131no—
435C22×C4—134no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—262no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—264no—
443C22×C4—262no—
444C22×C4—262no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—522no—
448C22×C4—522no—
449C22×C4—522no—
450C22×C4—521no—
451C22×C4—522no—
452C22×C4—522no—
453C22×C4D4×D1311yescharacteristic
454C22×C4#612912yes—
455C22×C4C22×Dic1312yes—
456C22×C4C23×D1311yescharacteristic
457SD16—216no—
458C2×C8—22no—
459C2×C8—22no—
460C2×C8—262no—
461C2×C8—262no—
462C2×C8—262no—
463C2×C8C22×Dic1314yes—
464C4⋊C4—21no—
465C4⋊C4—134no—
466C4⋊C4—268no—
467C4⋊C4—268no—
468C4⋊C4—264no—
469C4⋊C4—262no—
470C4⋊C4—262no—
471C4⋊C4—262no—
472C4⋊C4—522no—
473C4⋊C4C22×Dic1312yes—
474C22⋊C4—24no—
475C22⋊C4—522no—
476C22⋊C4—522no—
477C22⋊C4—522no—
478C22⋊C4—522no—
479C42—134no—
480C42—262no—
481C42—262no—
482C42—268no—
483C42—268no—
484C42—262no—
485C42—522no—
486C13C4×#44811yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23SD16×D1312yes—
499C23#8817012yes—
500C23D4×Dic1312yes—
501C23C2×D4×D1311yescharacteristic
502Q8—216no—
503Q8—24no—
504Q8—24no—
505Q8—24no—
506Q8D4×Dic1318yescomplemented
507D4—24no—
508D4—48no—
509D4—42no—
510C2×C4—216no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—132no—
525C2×C4—132no—
526C2×C4—268no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—264no—
534C2×C4—261no—
535C2×C4—524no—
536C2×C4—528no—
537C2×C4—522no—
538C2×C4—522no—
539C2×C4—521no—
540C2×C4—521no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—1044no—
546C2×C4D4×Dic1312yes—
547C2×C4C2×D4×D1312yes—
548C2×C4C2×#612912yes—
549C2×C4C2×#612911yescharacteristic
550C2×C4C23×Dic1311yescharacteristic
551C8—24no—
552C8—522no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22SD16×Dic1314yescomplemented
567C22#1171929111yescharacteristic
568C22D13×#12011yescharacteristic
569C22C2×SD16×D1311yescharacteristic
570C22C2×#8817011yescharacteristic
571C22D13×#13711yescharacteristic
572C22#1171948211yescharacteristic
573C22C2×D4×Dic1311yescharacteristic
574C4—28no—
575C4—22no—
576C4—42no—
577C4—134no—
578C4—262no—
579C4—262no—
580C4—521no—
581C4—524no—
582C4—1041no—
583C4—1041no—
584C4#1171929112yes—
585C4C2×D4×Dic1312yes—
586C2—24no—
587C2—82no—
588C2#120×Dic1311yescharacteristic
589C2C2×SD16×Dic1311yescharacteristic
590C2#137×Dic1311yescharacteristic
591C2D13×#44811yescharacteristic
592C2#1312405311yescharacteristic
593C2#1312486211yescharacteristic
594C2#1312491111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#448C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenterC2×#448D13
hypocenterC13C4×#448
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic13C2semidirect
2. C2×SD16×Dic13C2semidirect
4. #13115193C2semidirect
6. #13115106C2semidirect
7. #13115031C2semidirect
8. #13114771C2semidirect
9. #103×Dic13C2semidirect
10. C22⋊C8×Dic13C2semidirect
26. C13×#448C4semidirect
50. C22×Q8×C13C2×C4semidirect
62. C2×C13×SD16C2×C4semidirect
77. Q8×Dic13D4semidirect
99. C13×#103C2×C4semidirect
100. C13×C22⋊C8C2×C4semidirect
156. C22×Dic13SD16semidirect
220. Q8×C13C4×D4semidirect
281. #448Dic13direct (N × H)
314. C22×C13C4×SD16semidirect
333. Dic13#448direct (N × H)
338. C22×Q8C2×Dic13semidirect
350. C2×SD16C2×Dic13semidirect
390. #103C2×Dic13semidirect
393. C22⋊C8C2×Dic13semidirect
486. C13C4×#448semidirect
506. Q8D4×Dic13semidirect
566. C22SD16×Dic13semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic132
C2×SD16×Dic132
#121×Dic132
#131151932
#131151542
#131151062
#131150312
#131147712
#103×Dic132
C22⋊C8×Dic132
C2×C13×#4482
C4×#44813