Finite Group Databasebeta

← D13×#1853 #15863627

Subgroups — D13×#1853 #15863627

Order 3328.

1966 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C2×D13×#106C212yesmaximal, complemented
3C2×D13×C22⋊C8C211yesmaximal, characteristic
4D13×#380C211yesmaximal, characteristic
5#13115031C211yesmaximal, characteristic, complemented
6#13115030C212yesmaximal, complemented
7#13115029C211yesmaximal, characteristic, complemented
8#13115028C211yesmaximal, characteristic, complemented
9#13115027C212yesmaximal, complemented
10D13×#340C212yesmaximal, complemented
11C13×#1853C211yesmaximal, characteristic, complemented
12C23×C4×D13—21no—
13C23×C4×D13C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101—21no—
17C22×C8×D13C2212yes—
18C2×C4⋊C4×D13—21no—
19C2×C4⋊C4×D13—21no—
20C2×C4⋊C4×D13—28no—
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23C2×C4⋊C4×D13C2212yes—
24C2×C4⋊C4×D13C2212yes—
25C2×C22⋊C4×D13—21no—
26C2×C13×#106C2212yescomplemented
27C2×C13×C22⋊C8C2211yescharacteristic
28C13×#380C2211yescharacteristic
29#11718873C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31C2×#88060C2212yes—
32C2×#88057C2212yescomplemented
33#11718648C2211yescharacteristic
34#11718648C2211yescharacteristic
35C2×#88048C2212yescomplemented
36C2×#88048C2212yescomplemented
37#11718603—21no—
38D13×#106—28no—
39D13×C22⋊C8C418yescomplemented
40#11718328—21no—
41D13×#95—21no—
42C13×#340C2212yescomplemented
43#11718143C2212yescomplemented
44#11718121C2212yescomplemented
45#11718121C2212yescomplemented
46C24×D13D411yescharacteristic
47C23×C4×C13—21no—
48C23×C4×C13C2311yescharacteristic
49C23×Dic13—21no—
50C23×Dic13D411yescharacteristic
51C22×C4×D13—24no—
52C22×C4×D13—24no—
53C22×C4×D13—28no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—21no—
57C22×C4×D13—21no—
58C22×C4×D13—44no—
59C22×C4×D13—44no—
60C22×C4×D13C2×C414yes—
61C22×C4×D13D411yescharacteristic
62C22×C4×D13D411yescharacteristic
63C22×C4×D13Q814yes—
64C22×C4×D13C2311yescharacteristic
65C22×C4×D13C2311yescharacteristic
66C22×C8×C13C2312yes—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2312yes—
72C2×C13×C22⋊C4—21no—
73C2×C22⋊Dic13—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—24no—
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2312yes—
81C2×#6101—28no—
82C2×#6101—22no—
83C2×#6101—22no—
84C2×#6101—21no—
85C2×#6101—21no—
86C22×#1055C2312yes—
87C2×C8×D13—24no—
88C2×C8×D13—24no—
89C2×C8×D13C2×C418yescomplemented
90C4⋊C4×D13—28no—
91C4⋊C4×D13—28no—
92C4⋊C4×D13—24no—
93C4⋊C4×D13—24no—
94C4⋊C4×D13—24no—
95C4⋊C4×D13—24no—
96C4⋊C4×D13—24no—
97C4⋊C4×D13D418yes—
98C22⋊C4×D13—44no—
99C13×#106—24no—
100C13×C22⋊C8C2×C414yescomplemented
101C13×#95—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105C22⋊#1055C2×C414yescomplemented
106#88060C2×C418yescomplemented
107#88057—24no—
108#88048—24no—
109#88048—24no—
110C2×#1853—131nomaximal, Sylow
111C24×C13C2×D411yescharacteristic
112C23×D13—22no—
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13C4⋊C414yes—
117C23×D13SD1614yes—
118C23×D13SD1614yes—
119C23×D13C2×D411yescharacteristic
120C23×D13C2×D411yescharacteristic
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—24no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13C22×C412yes—
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×Q812yes—
132C22×C4×C13C2411yescharacteristic
133C22×Dic13—22no—
134C22×Dic13—22no—
135C22×Dic13—24no—
136C22×Dic13—22no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—42no—
140C22×Dic13—42no—
141C22×Dic13C4⋊C414yes—
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—22no—
149C2×C4×D13—22no—
150C2×C4×D13—216no—
151C2×C4×D13—216no—
152C2×C4×D13—28no—
153C2×C4×D13—28no—
154C2×C4×D13—44no—
155C2×C4×D13—432no—
156C2×C4×D13—44no—
157C2×C4×D13—44no—
158C2×C4×D13—44no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C2×C4×D13—42no—
162C2×C4×D13—42no—
163C2×C4×D13—42no—
164C2×C4×D13—42no—
165C2×C4×D13C4⋊C414yes—
166C2×C4×D13C4⋊C414yes—
167C2×C4×D13C22×C412yes—
168C2×C4×D13C22×C412yes—
169C2×C4×D13C2×D414yes—
170C2×C4×D13C2×Q812yes—
171C2×C4×D13C2×Q812yes—
172C2×C4×D13#4114yes—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13C22×C414yescomplemented
176C13×C4⋊C4—24no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4C2×D414yes—
181C13×C22⋊C4—42no—
182C22⋊Dic13—42no—
183#6103—42no—
184#6103—42no—
185C4⋊Dic13—24no—
186C4⋊Dic13—22no—
187C4⋊Dic13—22no—
188C4⋊Dic13—22no—
189C4⋊Dic13C2×D414yes—
190#6101—28no—
191#6101—28no—
192#6101—42no—
193#6101—42no—
194C2×#1055—22no—
195C2×#1055—22no—
196C2×#1055C22×C414yescomplemented
197C8×D13—216no—
198C23×C4⋊C4—131no—
199C22×#106—132no—
200C22×C22⋊C8—131no—
201C2×#380—131no—
202#1853—132no—
203#1853—131no—
204#1853—131no—
205#1853—132no—
206#1853—131no—
207#1853D1311yescharacteristic, direct product factor
208C2×#340—132no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13C2×C4⋊C412yes—
214C23×C13C2×SD1612yes—
215C23×C13C2×SD1612yes—
216C23×C13C22×D411yescharacteristic
217C22×D13—21no—
218C22×D13—21no—
219C22×D13—21no—
220C22×D13—21no—
221C22×D13—28no—
222C22×D13—28no—
223C22×D13—28no—
224C22×D13—28no—
225C22×D13—28no—
226C22×D13—28no—
227C22×D13#106116yescomplemented
228C22×D13C2×C4⋊C412yes—
229C22×D13C2×C4⋊C412yes—
230C22×D13#12012yes—
231C22×D13#12312yes—
232C22×D13C2×SD1612yes—
233C22×D13C2×SD1612yes—
234C22×D13C2×SD1612yes—
235C22×D13C2×SD1612yes—
236C22×D13AGL(1,ℤ/8)12yes—
237C22×D13#13712yes—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—24no—
241C2×C4×C13—24no—
242C2×C4×C13—24no—
243C2×C4×C13—48no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13C2×C4⋊C412yes—
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C22×D412yes—
255C2×C4×C13C22×Q811yescharacteristic
256C2×C4×C13C2×#4112yes—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—28no—
260C2×Dic13—24no—
261C2×Dic13—48no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13C2×C4⋊C412yes—
271C2×Dic13C2×C4⋊C412yes—
272C2×Dic13#12012yes—
273C2×Dic13#12312yes—
274C4×D13—28no—
275C4×D13—24no—
276C4×D13—24no—
277C4×D13—28no—
278C4×D13—416no—
279C4×D13—416no—
280C4×D13—84no—
281C4×D13—84no—
282C4×D13C4×D418yes—
283C4×D13C22⋊Q818yes—
284C8×C13—24no—
285#1055—24no—
286C24×C4—131no—
287C24×C4—261no—
288C23×C8—132no—
289C22×C4⋊C4—132no—
290C22×C4⋊C4—131no—
291C22×C4⋊C4—132no—
292C22×C4⋊C4—131no—
293C22×C4⋊C4—131no—
294C22×C4⋊C4—268no—
295C22×C4⋊C4—261no—
296C22×C4⋊C4—261no—
297C22×C4⋊C4—261no—
298C22×C4⋊C4C2×D1311yescharacteristic
299C22×C22⋊C4—261no—
300C2×#106—132no—
301C2×#106—132no—
302C2×#106—132no—
303C2×#106—268no—
304C2×#106C2×D1312yescomplemented
305C2×C22⋊C8—131no—
306C2×C22⋊C8—132no—
307C2×C22⋊C8—138no—
308C2×C22⋊C8C2×D1311yescharacteristic
309#380—131no—
310#380—131no—
311#380—131no—
312#380—261no—
313#380—261no—
314#380C2×D1311yescharacteristic
315C2×#95—261no—
316#340—132no—
317#340—132no—
318#340—132no—
319#340C2×D1312yescomplemented
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—22no—
326C22×C13C2×#10614yescomplemented
327C22×C13C22×C4⋊C411yescharacteristic
328C22×C13C2×#12011yescharacteristic
329C22×C13C2×#12311yescharacteristic
330C22×C13C22×SD1611yescharacteristic
331C22×C13C22×SD1611yescharacteristic
332C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C13C2×#13711yescharacteristic
334C2×D13—22no—
335C2×D13—22no—
336C2×D13—22no—
337C2×D13—22no—
338C2×D13—22no—
339C2×D13—22no—
340C2×D13—232no—
341C2×D13#38514yes—
342C2×D13C2×#10614yes—
343C2×D13C2×#10614yescomplemented
344C2×D13#42814yes—
345C2×D13#44814yes—
346C2×D13#45014yes—
347C2×D13#48114yes—
348C2×D13#48314yes—
349C4×C13—22no—
350C4×C13—44no—
351C4×C13—81no—
352C4×C13—81no—
353C4×C13C2×C4×D412yes—
354C4×C13C2×C22⋊Q812yes—
355Dic13—22no—
356Dic13—44no—
357Dic13—81no—
358Dic13—81no—
359Dic13#38514yes—
360C25—131no—
361C23×C4—21no—
362C23×C4—131no—
363C23×C4—131no—
364C23×C4—134no—
365C23×C4—131no—
366C23×C4—131no—
367C23×C4—134no—
368C23×C4—131no—
369C23×C4—264no—
370C23×C4—264no—
371C23×C4—262no—
372C23×C4—262no—
373C23×C4—268no—
374C23×C4—261no—
375C23×C4—261no—
376C23×C4—261no—
377C23×C4—524no—
378C23×C4—524no—
379C23×C4C22×D1311yescharacteristic
380C22×C8—132no—
381C22×C8—138no—
382C22×C8—264no—
383C22×C8—264no—
384C22×C8C22×D1312yes—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—138no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—264no—
392C2×C4⋊C4—264no—
393C2×C4⋊C4—268no—
394C2×C4⋊C4—268no—
395C2×C4⋊C4—264no—
396C2×C4⋊C4—264no—
397C2×C4⋊C4—264no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—268no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—264no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1312yes—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—524no—
413#106—24no—
414#106—264no—
415#106—264no—
416#106—264no—
417C22⋊C8—134no—
418C22⋊C8—138no—
419C22⋊C8C4×D1314yescomplemented
420#95—21no—
421#95—261no—
422#95—261no—
423#95—261no—
424C2×C13—24no—
425C2×C13C2×#38511yescharacteristic
426C2×C13C22×#10611yescharacteristic
427C2×C13C2×#42811yescharacteristic
428C2×C13C2×#45011yescharacteristic
429C2×C13C2×#44811yescharacteristic
430C2×C13C2×#48311yescharacteristic
431C2×C13C2×#48111yescharacteristic
432D13—24no—
433D13#185318yesdirect product factor
434C24—131no—
435C24—134no—
436C24—134no—
437C24—134no—
438C24—131no—
439C24—262no—
440C24—262no—
441C24—262no—
442C24—262no—
443C24D4×D1311yescharacteristic
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—131no—
453C22×C4—132no—
454C22×C4—134no—
455C22×C4—132no—
456C22×C4—134no—
457C22×C4—134no—
458C22×C4—131no—
459C22×C4—134no—
460C22×C4—134no—
461C22×C4—132no—
462C22×C4—132no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—2616no—
466C22×C4—2616no—
467C22×C4—262no—
468C22×C4—262no—
469C22×C4—268no—
470C22×C4—268no—
471C22×C4—262no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—264no—
476C22×C4—262no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—524no—
480C22×C4—524no—
481C22×C4—524no—
482C22×C4—5232no—
483C22×C4—524no—
484C22×C4—522no—
485C22×C4—522no—
486C22×C4—522no—
487C22×C4—522no—
488C22×C4—522no—
489C22×C4—522no—
490C22×C4—522no—
491C22×C4—522no—
492C22×C4C2×C4×D1312yes—
493C22×C4D4×D1311yescharacteristic
494C22×C4Q8×D1312yes—
495C22×C4C23×D1311yescharacteristic
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—134no—
499C2×C8—2616no—
500C2×C8—262no—
501C2×C8—262no—
502C2×C8C2×C4×D1314yescomplemented
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—134no—
508C4⋊C4—268no—
509C4⋊C4—268no—
510C4⋊C4—264no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—262no—
514C4⋊C4—522no—
515C4⋊C4—522no—
516C4⋊C4D4×D1314yes—
517C22⋊C4—42no—
518C22⋊C4—522no—
519C22⋊C4—522no—
520C22⋊C4—522no—
521C13C2×#185311yescharacteristic, complemented, Sylow
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—132no—
527C23—132no—
528C23—132no—
529C23—132no—
530C23—132no—
531C23—132no—
532C23—132no—
533C23—132no—
534C23—132no—
535C23—132no—
536C23—1316no—
537C23—268no—
538C23—268no—
539C23—268no—
540C23—268no—
541C23—268no—
542C23—268no—
543C23—261no—
544C23—261no—
545C23—261no—
546C23—261no—
547C23C4⋊C4×D1312yes—
548C23SD16×D1312yes—
549C23SD16×D1312yes—
550C23C2×D4×D1311yescharacteristic
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—132no—
566C2×C4—132no—
567C2×C4—132no—
568C2×C4—138no—
569C2×C4—138no—
570C2×C4—132no—
571C2×C4—268no—
572C2×C4—268no—
573C2×C4—268no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—264no—
577C2×C4—264no—
578C2×C4—264no—
579C2×C4—5216no—
580C2×C4—5216no—
581C2×C4—528no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—1044no—
591C2×C4—1044no—
592C2×C4C4⋊C4×D1312yes—
593C2×C4C22×C4×D1311yescharacteristic
594C2×C4C2×D4×D1312yes—
595C2×C4C2×Q8×D1311yescharacteristic
596C2×C4#41×D1312yes—
597C8—24no—
598C8—264no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—134no—
606C22—134no—
607C22—134no—
608C22—134no—
609C22—134no—
610C22—134no—
611C22—134no—
612C22—134no—
613C22—2632no—
614C22—262no—
615C22—262no—
616C22—262no—
617C22—262no—
618C22—262no—
619C22—262no—
620C22D13×#10614yescomplemented
621C22C2×C4⋊C4×D1311yescharacteristic
622C22D13×#12011yescharacteristic
623C22D13×#12311yescharacteristic
624C22C2×SD16×D1311yescharacteristic
625C22C2×SD16×D1311yescharacteristic
626C22D13×AGL(1,ℤ/8)11yescharacteristic
627C22D13×#13711yescharacteristic
628C4—22no—
629C4—44no—
630C4—81no—
631C4—81no—
632C4—134no—
633C4—262no—
634C4—524no—
635C4—1041no—
636C4—1041no—
637C4C4×D4×D1312yes—
638C4D13×C22⋊Q812yes—
639C2—24no—
640C2—138no—
641C2—264no—
642C2D13×#38511yescharacteristic
643C2C2×D13×#10611yescharacteristic
644C2D13×#42811yescharacteristic
645C2D13×#45011yescharacteristic
646C2D13×#44811yescharacteristic
647C2D13×#48311yescharacteristic
648C2D13×#48111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1853C2
socleC23×C13C22×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenter#1853D13
hypocenterC13C2×#1853
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
2. C2×D13×#106C2semidirect
5. #13115031C2semidirect
6. #13115030C2semidirect
7. #13115029C2semidirect
8. #13115028C2semidirect
9. #13115027C2semidirect
10. D13×#340C2semidirect
11. C13×#1853C2semidirect
26. C2×C13×#106C22semidirect
32. C2×#88057C22semidirect
35. C2×#88048C22semidirect
36. C2×#88048C22semidirect
39. D13×C22⋊C8C4semidirect
42. C13×#340C22semidirect
43. #11718143C22semidirect
44. #11718121C22semidirect
45. #11718121C22semidirect
89. C2×C8×D13C2×C4semidirect
100. C13×C22⋊C8C2×C4semidirect
105. C22⋊#1055C2×C4semidirect
106. #88060C2×C4semidirect
175. C2×C8×C13C22×C4semidirect
196. C2×#1055C22×C4semidirect
207. #1853D13direct (N × H)
227. C22×D13#106semidirect
304. C2×#106C2×D13semidirect
319. #340C2×D13semidirect
326. C22×C13C2×#106semidirect
343. C2×D13C2×#106semidirect
419. C22⋊C8C4×D13semidirect
433. D13#1853direct (N × H)
502. C2×C8C2×C4×D13semidirect
521. C13C2×#1853semidirect
620. C22D13×#106semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C2×D13×#1062
C2×D13×C22⋊C82
D13×#3802
#131150312
#131150302
#131150292
#131150282
#131150272
D13×#3402
C13×#18532
C2×#185313