Finite Group Databasebeta

← D13×#1518 #15830260

Subgroups — D13×#1518 #15830260

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#533C211yesmaximal, characteristic
2D13×#431C211yesmaximal, characteristic
3D13×#382C211yesmaximal, characteristic
4#13113401C211yesmaximal, characteristic, complemented
5#13113400C211yesmaximal, characteristic, complemented
6#13113399C211yesmaximal, characteristic, complemented
7#13113398C214yesmaximal, complemented
8D13×#328C214yesmaximal
9C13×#1518C211yesmaximal, characteristic, complemented
10C13×#533C2211yescharacteristic
11#11719433C411yescharacteristic, complemented
12#11719433C411yescharacteristic, complemented
13D13×C4⋊Q8C411yescharacteristic, complemented
14D13×C4⋊Q8C411yescharacteristic, complemented
15#11719393—21no—
16D13×#125—21no—
17D13×C22⋊Q8—21no—
18D13×C22⋊Q8C2212yes—
19#11719327—21no—
20#11719327C2212yes—
21#11719283—21no—
22#11719283C412yescomplemented
23C4×Q8×D13—21no—
24C4×Q8×D13C412yescomplemented
25D13×#117—21no—
26#11719222—21no—
27C2×C4⋊C4×D13—21no—
28C2×C42×D13C2211yescharacteristic
29#11719175C2211yescharacteristic
30C13×#431C2211yescharacteristic
31C13×#382C2211yescharacteristic
32#11718638—21no—
33#11718597C2211yescharacteristic
34#11718586C2211yescharacteristic
35#11718494—21no—
36D13×C4⋊C8—21no—
37D13×C22⋊C8C2212yes—
38#11718379C2212yes—
39#11718346—21no—
40C4×C8×D13—21no—
41D13×#95—21no—
42D13×#95C2212yes—
43#11718311—21no—
44#11718311C2212yes—
45C13×#328C2214yes—
46#11718130C2214yes—
47#11718059C2214yes—
48#11718044C2214yes—
49C2×Q8×D13—21no—
50C2×Q8×D13C2×C412yes—
51C22×C4×D13—22no—
52C22×C4×D13D411yescharacteristic
53C22×C4×D13D411yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C13×C4⋊Q8C2×C411yescharacteristic, complemented
56C13×C4⋊Q8C2×C411yescharacteristic, complemented
57C13×#125—21no—
58C13×C22⋊Q8—21no—
59C13×C22⋊Q8C2312yes—
60C4×Q8×C13—21no—
61C4×Q8×C13C2×C412yescomplemented
62C13×#117—21no—
63C2×C13×C4⋊C4—21no—
64C2×C42×C13C2311yescharacteristic
65#88200—21no—
66#88200C2×C412yes—
67Q8×Dic13—21no—
68Q8×Dic13C2×C412yescomplemented
69#88198—21no—
70#88198C2×C412yescomplemented
71#88180—21no—
72C2×C4⋊Dic13—21no—
73#88178—21no—
74#88178C2312yes—
75C2×#6101—22no—
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13C2311yescharacteristic
79C2×C8×D13—22no—
80#88151—21no—
81#88151C2×C412yes—
82#88150—22no—
83#88150—22no—
84#88146—21no—
85#88146—21no—
86C4⋊C4×D13—21no—
87C4⋊C4×D13—21no—
88C4⋊C4×D13—21no—
89C4⋊C4×D13—22no—
90C4⋊C4×D13—22no—
91C4⋊C4×D13—44no—
92C4⋊C4×D13C2×C412yes—
93#88144—21no—
94#88144—21no—
95#88143—22no—
96#88143—22no—
97#88142—21no—
98#88142—21no—
99#88142—21no—
100#88142C2×C412yescomplemented
101#88141—21no—
102#88141—22no—
103#88141—22no—
104#88141C2×C412yescomplemented
105C22⋊C4×D13—22no—
106#88132—22no—
107#88132—22no—
108#88131—22no—
109#88126—22no—
110C42×D13—22no—
111C42×D13C2×C411yescharacteristic
112C42×D13C2×C411yescharacteristic
113C42×D13C2×C411yescharacteristic
114C42×D13C2×C411yescharacteristic
115C42×D13D411yescharacteristic
116C42×D13D411yescharacteristic
117C42×D13D411yescharacteristic
118C42×D13D411yescharacteristic
119#88124—21no—
120#88123C2×C411yescharacteristic, complemented
121#88123C2×C411yescharacteristic, complemented
122C4×Dic26—21no—
123C4×Dic26—22no—
124C4×Dic26—22no—
125C4×Dic26C2×C412yescomplemented
126C13×C4⋊C8—21no—
127C13×C22⋊C8C2312yes—
128C4×C8×C13—21no—
129C13×#95—21no—
130C13×#95C2312yes—
131#88071—21no—
132#88071—22no—
133#88071—22no—
134#88071C2312yes—
135C22⋊#1055C2312yes—
136#88060—22no—
137#88054—22no—
138C8×Dic13—22no—
139C4⋊#1055—21no—
140C4×#1055—21no—
141C2×#1518—131nomaximal, Sylow
142C23×D13C2×D411yescharacteristic
143C2×Q8×C13—21no—
144C2×Q8×C13C22×C412yes—
145C22×C4×C13—22no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2411yescharacteristic
149C22×Dic13—22no—
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153Q8×D13—44no—
154Q8×D13—44no—
155C2×C4×D13—22no—
156C2×C4×D13—22no—
157C2×C4×D13—42no—
158C2×C4×D13—42no—
159C2×C4×D13—44no—
160C2×C4×D13—44no—
161C2×C4×D13—44no—
162C2×C4×D13C22⋊C411yescharacteristic
163C2×C4×D13C22⋊C411yescharacteristic
164C2×C4×D13C22⋊C411yescharacteristic
165C2×C4×D13C22⋊C411yescharacteristic
166C2×C4×D13C22⋊C411yescharacteristic
167C2×C4×D13C22⋊C411yescharacteristic
168C2×C4×D13C22⋊C411yescharacteristic
169C2×C4×D13C22⋊C411yescharacteristic
170C2×C4×D13SD1614yes—
171C2×C4×D13Q1614yes—
172C2×C4×D13C22×C411yescharacteristic
173C2×C4×D13C22×C411yescharacteristic
174C2×C4×D13C2×D411yescharacteristic
175C2×C4×D13C2×D411yescharacteristic
176C2×Dic26—21no—
177C2×Dic26—22no—
178C2×Dic26—22no—
179C2×Dic26C22×C412yes—
180C2×C8×C13—22no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—42no—
187C13×C4⋊C4C22×C412yes—
188C13×C22⋊C4—22no—
189C42×C13—22no—
190C42×C13C22×C411yescharacteristic
191C42×C13C22×C411yescharacteristic
192C42×C13C2×D411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C22⋊Dic13—22no—
195#6103—22no—
196#6103—22no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—22no—
201C4⋊Dic13—22no—
202C4⋊Dic13—42no—
203C4⋊Dic13C22×C412yes—
204#6101—22no—
205#6101—22no—
206#6101—22no—
207#6101—22no—
208#6101—22no—
209#6101—22no—
210#6101—22no—
211#6101—22no—
212#6101—44no—
213C4×Dic13—22no—
214C4×Dic13—22no—
215C4×Dic13—22no—
216C4×Dic13C22⋊C411yescharacteristic
217C4×Dic13C22⋊C411yescharacteristic
218C4×Dic13C22⋊C411yescharacteristic
219C4×Dic13C22⋊C411yescharacteristic
220C4×Dic13C22⋊C411yescharacteristic
221C4×Dic13C22⋊C411yescharacteristic
222C4×Dic13C22⋊C411yescharacteristic
223C4×Dic13C22⋊C411yescharacteristic
224C4×Dic13C22×C411yescharacteristic
225C4×Dic13C22×C411yescharacteristic
226C4×Dic13C2×D411yescharacteristic
227C4×Dic13C2×D411yescharacteristic
228C2×#1055—22no—
229C8×D13—44no—
230C2×#533—131no—
231C2×#431—131no—
232C2×#382—131no—
233#1518—131no—
234#1518—131no—
235#1518—134no—
236#1518—131no—
237#1518D1311yescharacteristic, direct product factor
238C2×#328—134no—
239C23×C13C22×D411yescharacteristic
240C22×D13—22no—
241C22×D13—22no—
242C22×D13C2×C22⋊C411yescharacteristic
243C22×D13C2×C22⋊C411yescharacteristic
244C22×D13C2×SD1612yes—
245C22×D13C2×Q1612yes—
246Q8×C13—42no—
247Q8×C13—42no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13C2×C22⋊C411yescharacteristic
256C2×C4×C13C2×C22⋊C411yescharacteristic
257C2×C4×C13C2×C22⋊C411yescharacteristic
258C2×C4×C13C2×C22⋊C411yescharacteristic
259C2×C4×C13C2×SD1612yes—
260C2×C4×C13C2×Q1612yes—
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—42no—
268C2×Dic13—42no—
269C2×Dic13—42no—
270C2×Dic13C2×C22⋊C411yescharacteristic
271C2×Dic13C2×C22⋊C411yescharacteristic
272C2×Dic13C2×C22⋊C411yescharacteristic
273C2×Dic13C2×C22⋊C411yescharacteristic
274C2×Dic13C2×C22⋊C411yescharacteristic
275C2×Dic13C2×C22⋊C411yescharacteristic
276C2×Dic13C2×SD1612yes—
277C2×Dic13C2×Q1612yes—
278C4×D13—22no—
279C4×D13—22no—
280C4×D13—22no—
281C4×D13—22no—
282C4×D13—41no—
283C4×D13—41no—
284C4×D13—41no—
285C4×D13—41no—
286C4×D13—44no—
287C4×D13—44no—
288C4×D13—88no—
289C4×D13#10314yes—
290C4×D13#10314yes—
291C4×D13#10314yes—
292C4×D13#10314yes—
293Dic26—44no—
294Dic26—44no—
295Dic26—42no—
296Dic26—42no—
297C8×C13—42no—
298#1055—42no—
299#533—131no—
300#533—131no—
301#533—132no—
302#533—132no—
303#533—131no—
304#533—261no—
305#533—261no—
306#533—261no—
307#533—261no—
308#533C2×D1311yescharacteristic
309C2×C4⋊Q8—131no—
310C2×C4⋊Q8—131no—
311C2×#125—261no—
312C2×C22⋊Q8—132no—
313C2×C22⋊Q8—261no—
314C2×C4×Q8—132no—
315C2×C4×Q8—261no—
316C2×#117—261no—
317C22×C4⋊C4—261no—
318C22×C42—131no—
319#431—131no—
320#431—132no—
321#431—261no—
322#431—261no—
323#431C2×D1311yescharacteristic
324C2×C4⋊C8—261no—
325C2×C22⋊C8—132no—
326C2×C4×C8—261no—
327#382—131no—
328#382—132no—
329#382—261no—
330#382—261no—
331#382C2×D1311yescharacteristic
332C2×#95—132no—
333C2×#95—261no—
334#328—134no—
335#328—134no—
336#328—134no—
337#328C2×D1314yes—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13C22×C22⋊C411yescharacteristic
341C22×C13C22×SD1611yescharacteristic
342C22×C13C22×Q1611yescharacteristic
343C2×D13—21no—
344C2×D13—21no—
345C2×D13—24no—
346C2×D13—24no—
347C2×D13#41012yes—
348C2×D13C2×#10312yes—
349C2×D13C2×#10312yes—
350C2×D13#42112yes—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—21no—
355C4×C13—42no—
356C4×C13—42no—
357C4×C13—82no—
358C4×C13C2×#10312yes—
359C4×C13C2×#10312yes—
360Dic13—21no—
361Dic13—21no—
362Dic13—21no—
363Dic13—21no—
364Dic13—42no—
365Dic13—42no—
366Dic13—82no—
367Dic13C2×#10312yes—
368Dic13C2×#10312yes—
369C22×Q8—132no—
370C22×Q8—261no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—131no—
374C23×C4—262no—
375C22×C8—262no—
376C4⋊Q8—132no—
377C4⋊Q8—132no—
378C4⋊Q8—131no—
379C4⋊Q8—131no—
380C4⋊Q8—261no—
381C4⋊Q8—261no—
382C4⋊Q8—261no—
383C4⋊Q8—261no—
384C4⋊Q8C4×D1311yescharacteristic, complemented
385C4⋊Q8C4×D1311yescharacteristic, complemented
386#125—21no—
387#125—262no—
388#125—262no—
389#125—261no—
390#125—261no—
391#125—261no—
392C22⋊Q8—21no—
393C22⋊Q8—132no—
394C22⋊Q8—132no—
395C22⋊Q8—132no—
396C22⋊Q8—262no—
397C22⋊Q8—262no—
398C22⋊Q8—262no—
399C22⋊Q8—262no—
400C22⋊Q8—261no—
401C22⋊Q8—261no—
402C22⋊Q8—261no—
403C22⋊Q8C22×D1312yes—
404C4×Q8—21no—
405C4×Q8—132no—
406C4×Q8—132no—
407C4×Q8—132no—
408C4×Q8—262no—
409C4×Q8—262no—
410C4×Q8—262no—
411C4×Q8—261no—
412C4×Q8—262no—
413C4×Q8—261no—
414C4×Q8—261no—
415C4×Q8C4×D1312yescomplemented
416#117—21no—
417#117—262no—
418#117—262no—
419#117—261no—
420#117—261no—
421#117—261no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—132no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—262no—
427C2×C4⋊C4—262no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—262no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—524no—
432C2×C22⋊C4—262no—
433C2×C42—131no—
434C2×C42—131no—
435C2×C42—131no—
436C2×C42—131no—
437C2×C42—131no—
438C2×C42—131no—
439C2×C42—131no—
440C2×C42—131no—
441C2×C42—131no—
442C2×C42—131no—
443C2×C42—131no—
444C2×C42—262no—
445C2×C42C22×D1311yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—262no—
448C4⋊C8—261no—
449C22⋊C8—132no—
450C22⋊C8—262no—
451C22⋊C8C22×D1312yes—
452C4×C8—21no—
453C4×C8—262no—
454C4×C8—261no—
455#95—21no—
456#95—132no—
457#95—262no—
458#95—262no—
459#95—261no—
460#95C22×D1312yes—
461C2×C13—21no—
462C2×C13—21no—
463C2×C13C2×#41011yescharacteristic
464C2×C13C22×#10311yescharacteristic
465C2×C13C2×#42111yescharacteristic
466D13—22no—
467D13#151814yesdirect product factor
468C24—131no—
469C2×Q8—21no—
470C2×Q8—132no—
471C2×Q8—262no—
472C2×Q8—262no—
473C2×Q8—261no—
474C2×Q8—524no—
475C2×Q8—524no—
476C2×Q8C2×C4×D1312yes—
477C22×C4—22no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—134no—
484C22×C4—134no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—131no—
488C22×C4—131no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—131no—
492C22×C4—131no—
493C22×C4—131no—
494C22×C4—131no—
495C22×C4—262no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—522no—
499C22×C4—522no—
500C22×C4—524no—
501C22×C4—524no—
502C22×C4—524no—
503C22×C4D4×D1311yescharacteristic
504C22×C4D4×D1311yescharacteristic
505C22×C4C23×D1311yescharacteristic
506C2×C8—22no—
507C2×C8—262no—
508C2×C8—524no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—42no—
515C4⋊C4—132no—
516C4⋊C4—262no—
517C4⋊C4—262no—
518C4⋊C4—262no—
519C4⋊C4—262no—
520C4⋊C4—262no—
521C4⋊C4—262no—
522C4⋊C4—262no—
523C4⋊C4—262no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—262no—
527C4⋊C4—261no—
528C4⋊C4—262no—
529C4⋊C4—524no—
530C4⋊C4—522no—
531C4⋊C4C2×C4×D1312yes—
532C22⋊C4—22no—
533C22⋊C4—262no—
534C22⋊C4—262no—
535C22⋊C4—262no—
536C42—22no—
537C42—131no—
538C42—131no—
539C42—131no—
540C42—131no—
541C42—131no—
542C42—131no—
543C42—131no—
544C42—131no—
545C42—131no—
546C42—131no—
547C42—131no—
548C42—131no—
549C42—262no—
550C42—262no—
551C42—262no—
552C42C2×C4×D1311yescharacteristic
553C42C2×C4×D1311yescharacteristic
554C42D4×D1311yescharacteristic
555C42D4×D1311yescharacteristic
556C13C2×#151811yescharacteristic, complemented, Sylow
557C23—131no—
558C23—131no—
559C23—132no—
560C23—132no—
561C23—262no—
562C23—262no—
563C23C2×D4×D1311yescharacteristic
564Q8—42no—
565Q8—42no—
566Q8—522no—
567Q8—522no—
568Q8—524no—
569Q8—524no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—131no—
578C2×C4—131no—
579C2×C4—132no—
580C2×C4—132no—
581C2×C4—134no—
582C2×C4—134no—
583C2×C4—134no—
584C2×C4—134no—
585C2×C4—131no—
586C2×C4—131no—
587C2×C4—131no—
588C2×C4—131no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—262no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—524no—
600C2×C4—524no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—522no—
604C2×C4—522no—
605C2×C4—522no—
606C2×C4—1048no—
607C2×C4C22⋊C4×D1311yescharacteristic
608C2×C4C22⋊C4×D1311yescharacteristic
609C2×C4C22⋊C4×D1311yescharacteristic
610C2×C4C22⋊C4×D1311yescharacteristic
611C2×C4SD16×D1312yes—
612C2×C4Q16×D1312yes—
613C2×C4C22×C4×D1311yescharacteristic
614C2×C4C2×D4×D1311yescharacteristic
615C8—42no—
616C8—522no—
617C22—21no—
618C22—21no—
619C22—132no—
620C22—132no—
621C22—132no—
622C22—132no—
623C22—264no—
624C22—264no—
625C22—261no—
626C22—261no—
627C22C2×C22⋊C4×D1311yescharacteristic
628C22C2×SD16×D1311yescharacteristic
629C22C2×Q16×D1311yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—42no—
635C4—42no—
636C4—82no—
637C4—132no—
638C4—132no—
639C4—261no—
640C4—261no—
641C4—261no—
642C4—261no—
643C4—522no—
644C4—522no—
645C4—1042no—
646C4D13×#10312yes—
647C4D13×#10312yes—
648C2—21no—
649C2—21no—
650C2—134no—
651C2—262no—
652C2D13×#41011yescharacteristic
653C2C2×D13×#10311yescharacteristic
654C2D13×#42111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1518C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1518D13
hypocenterC13C2×#1518
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
4. #13113401C2semidirect
5. #13113400C2semidirect
6. #13113399C2semidirect
7. #13113398C2semidirect
9. C13×#1518C2semidirect
11. #11719433C4semidirect
12. #11719433C4semidirect
13. D13×C4⋊Q8C4semidirect
14. D13×C4⋊Q8C4semidirect
22. #11719283C4semidirect
24. C4×Q8×D13C4semidirect
55. C13×C4⋊Q8C2×C4semidirect
56. C13×C4⋊Q8C2×C4semidirect
61. C4×Q8×C13C2×C4semidirect
68. Q8×Dic13C2×C4semidirect
70. #88198C2×C4semidirect
100. #88142C2×C4semidirect
104. #88141C2×C4semidirect
120. #88123C2×C4semidirect
121. #88123C2×C4semidirect
125. C4×Dic26C2×C4semidirect
237. #1518D13direct (N × H)
384. C4⋊Q8C4×D13semidirect
385. C4⋊Q8C4×D13semidirect
415. C4×Q8C4×D13semidirect
467. D13#1518direct (N × H)
556. C13C2×#1518semidirect

Maximal subgroups

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

subgroupindex
D13×#5332
D13×#4312
D13×#3822
#131134012
#131134002
#131133992
#131133982
D13×#3282
C13×#15182
C2×#151813