Finite Group Databasebeta

← D13×#1542 #15831213

Subgroups — D13×#1542 #15831213

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13×#533C211yesmaximal, characteristic
2D13×#431C211yesmaximal, characteristic
3C2×D13×C4⋊C8C211yesmaximal, characteristic
4#13113494C211yesmaximal, characteristic, complemented
5#13113493C211yesmaximal, characteristic, complemented
6#13113492C212yesmaximal, complemented
7#13113491C211yesmaximal, characteristic, complemented
8#13113490C212yesmaximal, complemented
9D13×#333C212yesmaximal, complemented
10D13×#332C212yesmaximal, complemented
11C13×#1542C211yesmaximal, characteristic, complemented
12C13×#533C2211yescharacteristic
13C22×C8×D13—21no—
14#11719433C2211yescharacteristic
15#11719433C2211yescharacteristic
16D13×C4⋊Q8C2211yescharacteristic
17D13×C4⋊Q8C2211yescharacteristic
18#11719393—21no—
19D13×#125—21no—
20D13×C22⋊Q8—21no—
21D13×C22⋊Q8C412yes—
22#11719327—21no—
23#11719327C412yes—
24#11719283—21no—
25#11719283C412yes—
26C4×Q8×D13—21no—
27C4×Q8×D13C412yes—
28D13×#117—21no—
29#11719222—21no—
30C2×C42×D13C2211yescharacteristic
31#11719175C2211yescharacteristic
32C13×#431C2211yescharacteristic
33C2×C13×C4⋊C8C2211yescharacteristic
34C2×#88054—21no—
35#11718586C2211yescharacteristic
36C2×C4⋊#1055C2211yescharacteristic
37#11718494C2212yes—
38D13×C4⋊C8—21no—
39D13×C4⋊C8—21no—
40D13×C4⋊C8C2212yes—
41D13×C4⋊C8C2212yes—
42D13×C4⋊C8C2212yes—
43D13×C22⋊C8—21no—
44#11718379—21no—
45#11718346—21no—
46C4×C8×D13—21no—
47C13×#333C2212yescomplemented
48C13×#332C2212yescomplemented
49#11718139C2212yescomplemented
50#11718138C2212yescomplemented
51#11718078C2212yescomplemented
52#11718074C2212yescomplemented
53#11718073C2212yescomplemented
54#11718073C2212yescomplemented
55C2×Q8×D13—21no—
56C2×Q8×D13C2×C412yes—
57C22×C4×D13C2×C411yescharacteristic
58C22×C4×D13D411yescharacteristic
59C22×C4×D13D411yescharacteristic
60C22×C8×C13—21no—
61C13×C4⋊Q8C2311yescharacteristic
62C13×C4⋊Q8C2311yescharacteristic
63C13×#125—21no—
64C13×C22⋊Q8—21no—
65C13×C22⋊Q8C2×C412yes—
66C4×Q8×C13—21no—
67C4×Q8×C13C2×C412yes—
68C13×#117—21no—
69C2×C42×C13C2311yescharacteristic
70#88200—21no—
71#88200C2×C412yes—
72Q8×Dic13—21no—
73Q8×Dic13C2×C412yes—
74#88198—21no—
75#88198C2×C412yes—
76#88180—21no—
77#88178—21no—
78#88178C2×C412yes—
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13D411yescharacteristic
81C2×C4×Dic13D411yescharacteristic
82C22×#1055—21no—
83C2×C8×D13—22no—
84C2×C8×D13—22no—
85C2×C8×D13—22no—
86C2×C8×D13—44no—
87#88151—21no—
88#88151C2×C412yes—
89#88150—22no—
90#88150—22no—
91#88146—21no—
92#88146—21no—
93C4⋊C4×D13—22no—
94C4⋊C4×D13—22no—
95C4⋊C4×D13—21no—
96C4⋊C4×D13—21no—
97C4⋊C4×D13—21no—
98C4⋊C4×D13C2×C412yes—
99#88144—21no—
100#88144—21no—
101#88143—22no—
102#88143—22no—
103#88142—21no—
104#88142—21no—
105#88142—21no—
106#88142C2×C412yes—
107#88141—22no—
108#88141—22no—
109#88141—21no—
110#88141C2×C412yes—
111C22⋊C4×D13—22no—
112#88132—22no—
113#88132—22no—
114#88131—22no—
115#88126—22no—
116C42×D13—22no—
117C42×D13C2×C411yescharacteristic
118C42×D13C2×C411yescharacteristic
119C42×D13D411yescharacteristic
120C42×D13D411yescharacteristic
121C42×D13D411yescharacteristic
122C42×D13D411yescharacteristic
123C42×D13C2311yescharacteristic
124C42×D13C2311yescharacteristic
125#88124—21no—
126#88123C2311yescharacteristic
127#88123C2311yescharacteristic
128C4×Dic26—21no—
129C4×Dic26—22no—
130C4×Dic26—22no—
131C4×Dic26C2×C412yes—
132C13×C4⋊C8—21no—
133C13×C4⋊C8C2312yes—
134C13×C4⋊C8C2312yes—
135C13×C22⋊C8—21no—
136C4×C8×C13—21no—
137C22⋊#1055—21no—
138#88060—22no—
139#88054—22no—
140#88054—22no—
141#88054—22no—
142C8×Dic13—22no—
143C4⋊#1055—21no—
144C4⋊#1055C2312yes—
145C4⋊#1055C2312yes—
146C4×#1055—21no—
147C2×#1542—131nomaximal, Sylow
148C23×D13C22⋊C411yescharacteristic
149C2×Q8×C13—21no—
150C2×Q8×C13C22×C412yes—
151C22×C4×C13C22×C411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×Dic13C22⋊C411yescharacteristic
155C22×Dic13C22⋊C411yescharacteristic
156C22×Dic13C22⋊C411yescharacteristic
157Q8×D13—44no—
158Q8×D13—44no—
159C2×C4×D13—24no—
160C2×C4×D13—22no—
161C2×C4×D13—22no—
162C2×C4×D13—42no—
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×D13SD1614yes—
170C2×C4×D13Q1614yes—
171C2×C4×D13C22×C411yescharacteristic
172C2×C4×D13C22×C411yescharacteristic
173C2×C4×D13C2×D411yescharacteristic
174C2×C4×D13C2×D411yescharacteristic
175C2×C4×D13C2×D411yescharacteristic
176C2×C4×D13C2×D411yescharacteristic
177C2×Dic26—21no—
178C2×Dic26—22no—
179C2×Dic26—22no—
180C2×Dic26C22×C412yes—
181C2×C8×C13—22no—
182C2×C8×C13—22no—
183C2×C8×C13—42no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4C22×C412yes—
190C13×C22⋊C4—22no—
191C42×C13—22no—
192C42×C13C22×C411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C42×C13C2×D411yescharacteristic
195C42×C13C2411yescharacteristic
196C22⋊Dic13—22no—
197#6103—22no—
198#6103—22no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—22no—
203C4⋊Dic13—22no—
204C4⋊Dic13C22×C412yes—
205#6101—22no—
206#6101—22no—
207#6101—22no—
208#6101—22no—
209#6101—22no—
210#6101—22no—
211#6101—22no—
212#6101—22no—
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×Dic13C2×D411yescharacteristic
225C4×Dic13C2×D411yescharacteristic
226C4×Dic13C2×D411yescharacteristic
227C4×Dic13C2×D411yescharacteristic
228C2×#1055—22no—
229C2×#1055—22no—
230C2×#1055—42no—
231C8×D13—44no—
232C8×D13—44no—
233C8×D13—44no—
234C2×#533—131no—
235C2×#431—131no—
236C22×C4⋊C8—131no—
237#1542—131no—
238#1542—131no—
239#1542—132no—
240#1542—132no—
241#1542—131no—
242#1542D1311yescharacteristic, direct product factor
243C2×#333—132no—
244C2×#332—132no—
245C23×C13C2×C22⋊C411yescharacteristic
246C22×D13—22no—
247C22×D13—22no—
248C22×D13#10314yes—
249C22×D13C2×C22⋊C411yescharacteristic
250C22×D13C2×C22⋊C411yescharacteristic
251Q8×C13—42no—
252Q8×C13—42no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—41no—
257C2×C4×C13C2×C22⋊C411yescharacteristic
258C2×C4×C13C2×C22⋊C411yescharacteristic
259C2×C4×C13C2×C22⋊C411yescharacteristic
260C2×C4×C13C2×SD1612yes—
261C2×C4×C13C2×Q1612yes—
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C22×D411yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C2×Dic13—22no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—41no—
269C2×Dic13#10314yes—
270C2×Dic13C2×C22⋊C411yescharacteristic
271C2×Dic13C2×C22⋊C411yescharacteristic
272C2×Dic13C2×C22⋊C411yescharacteristic
273C2×Dic13C2×C22⋊C411yescharacteristic
274C2×Dic13C2×C22⋊C411yescharacteristic
275C2×Dic13C2×C22⋊C411yescharacteristic
276C4×D13—22no—
277C4×D13—22no—
278C4×D13—22no—
279C4×D13—22no—
280C4×D13—22no—
281C4×D13—41no—
282C4×D13—41no—
283C4×D13—44no—
284C4×D13—44no—
285C4×D13#10314yes—
286C4×D13#10314yes—
287C4×D13C2×SD1612yes—
288C4×D13C2×SD1612yes—
289C4×D13C2×Q1612yes—
290C4×D13C2×Q1612yes—
291C4×D13#13514yes—
292Dic26—44no—
293Dic26—42no—
294Dic26—44no—
295Dic26—42no—
296C8×C13—42no—
297C8×C13—42no—
298#1055—42no—
299#1055—42no—
300C23×C8—261no—
301#533—131no—
302#533—131no—
303#533—132no—
304#533—132no—
305#533—131no—
306#533—261no—
307#533—261no—
308#533—261no—
309#533—261no—
310#533C2×D1311yescharacteristic
311C2×C4⋊Q8—131no—
312C2×C4⋊Q8—131no—
313C2×#125—261no—
314C2×C22⋊Q8—132no—
315C2×C22⋊Q8—261no—
316C2×C4×Q8—132no—
317C2×C4×Q8—261no—
318C2×#117—261no—
319C22×C42—131no—
320#431—131no—
321#431—132no—
322#431—261no—
323#431—261no—
324#431C2×D1311yescharacteristic
325C2×C4⋊C8—131no—
326C2×C4⋊C8—132no—
327C2×C4⋊C8—132no—
328C2×C4⋊C8—132no—
329C2×C4⋊C8—261no—
330C2×C4⋊C8—261no—
331C2×C4⋊C8—261no—
332C2×C4⋊C8C2×D1311yescharacteristic
333C2×C22⋊C8—261no—
334C2×C4×C8—261no—
335#333—132no—
336#333—132no—
337#333—132no—
338#333C2×D1312yescomplemented
339#332—132no—
340#332—132no—
341#332—132no—
342#332C2×D1312yescomplemented
343C22×C13—21no—
344C22×C13—21no—
345C22×C13C2×#10312yes—
346C22×C13C22×C22⋊C411yescharacteristic
347C2×D13—21no—
348C2×D13—21no—
349C2×D13—28no—
350C2×D13#41312yes—
351C2×D13C2×#10312yes—
352C2×D13C2×#10312yes—
353C2×D13#41612yes—
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—42no—
358C4×C13—42no—
359C4×C13C2×#10312yes—
360C4×C13C22×SD1611yescharacteristic
361C4×C13C22×Q1611yescharacteristic
362C4×C13C2×#13512yes—
363Dic13—21no—
364Dic13—21no—
365Dic13—21no—
366Dic13—42no—
367Dic13—42no—
368Dic13C2×#10312yes—
369Dic13C2×#10312yes—
370Dic13#41612yes—
371C22×Q8—132no—
372C22×Q8—261no—
373C23×C4—131no—
374C23×C4—131no—
375C23×C4—131no—
376C22×C8—21no—
377C22×C8—262no—
378C22×C8—262no—
379C22×C8—262no—
380C22×C8—261no—
381C22×C8—524no—
382C4⋊Q8—132no—
383C4⋊Q8—132no—
384C4⋊Q8—131no—
385C4⋊Q8—131no—
386C4⋊Q8—261no—
387C4⋊Q8—261no—
388C4⋊Q8—261no—
389C4⋊Q8—261no—
390C4⋊Q8C22×D1311yescharacteristic
391C4⋊Q8C22×D1311yescharacteristic
392#125—21no—
393#125—262no—
394#125—262no—
395#125—261no—
396#125—261no—
397#125—261no—
398C22⋊Q8—21no—
399C22⋊Q8—132no—
400C22⋊Q8—132no—
401C22⋊Q8—132no—
402C22⋊Q8—262no—
403C22⋊Q8—262no—
404C22⋊Q8—262no—
405C22⋊Q8—262no—
406C22⋊Q8—261no—
407C22⋊Q8—261no—
408C22⋊Q8—261no—
409C22⋊Q8C4×D1312yes—
410C4×Q8—21no—
411C4×Q8—132no—
412C4×Q8—132no—
413C4×Q8—132no—
414C4×Q8—262no—
415C4×Q8—262no—
416C4×Q8—262no—
417C4×Q8—262no—
418C4×Q8—261no—
419C4×Q8—261no—
420C4×Q8—261no—
421C4×Q8C4×D1312yes—
422#117—21no—
423#117—262no—
424#117—262no—
425#117—261no—
426#117—261no—
427#117—261no—
428C2×C4⋊C4—132no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—262no—
432C2×C4⋊C4—262no—
433C2×C4⋊C4—261no—
434C2×C22⋊C4—262no—
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—131no—
445C2×C42—131no—
446C2×C42—262no—
447C2×C42C22×D1311yescharacteristic
448C4⋊C8—21no—
449C4⋊C8—132no—
450C4⋊C8—132no—
451C4⋊C8—262no—
452C4⋊C8—262no—
453C4⋊C8—262no—
454C4⋊C8—261no—
455C4⋊C8C22×D1312yes—
456C4⋊C8C22×D1312yes—
457C22⋊C8—21no—
458C22⋊C8—262no—
459C22⋊C8—261no—
460C4×C8—21no—
461C4×C8—262no—
462C4×C8—261no—
463C2×C13—22no—
464C2×C13C2×#41311yescharacteristic
465C2×C13C22×#10311yescharacteristic
466C2×C13C2×#41611yescharacteristic
467D13—22no—
468D13#154214yesdirect product factor
469C24—131no—
470C2×Q8—21no—
471C2×Q8—132no—
472C2×Q8—262no—
473C2×Q8—262no—
474C2×Q8—261no—
475C2×Q8—524no—
476C2×Q8—524no—
477C2×Q8C2×C4×D1312yes—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—134no—
482C22×C4—134no—
483C22×C4—131no—
484C22×C4—131no—
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—264no—
496C22×C4—262no—
497C22×C4—262no—
498C22×C4—522no—
499C22×C4C2×C4×D1311yescharacteristic
500C22×C4D4×D1311yescharacteristic
501C22×C4D4×D1311yescharacteristic
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—42no—
505C2×C8—262no—
506C2×C8—262no—
507C2×C8—524no—
508C2×C8—524no—
509C2×C8—524no—
510C2×C8—522no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—132no—
517C4⋊C4—262no—
518C4⋊C4—262no—
519C4⋊C4—262no—
520C4⋊C4—262no—
521C4⋊C4—262no—
522C4⋊C4—262no—
523C4⋊C4—262no—
524C4⋊C4—262no—
525C4⋊C4—262no—
526C4⋊C4—262no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4C2×C4×D1312yes—
531C22⋊C4—22no—
532C22⋊C4—262no—
533C22⋊C4—262no—
534C22⋊C4—262no—
535C42—22no—
536C42—131no—
537C42—131no—
538C42—131no—
539C42—131no—
540C42—131no—
541C42—131no—
542C42—131no—
543C42—131no—
544C42—131no—
545C42—131no—
546C42—131no—
547C42—131no—
548C42—262no—
549C42—262no—
550C42—262no—
551C42C2×C4×D1311yescharacteristic
552C42D4×D1311yescharacteristic
553C42D4×D1311yescharacteristic
554C42C23×D1311yescharacteristic
555C13C2×#154211yescharacteristic, complemented, Sylow
556C23—131no—
557C23—131no—
558C23—134no—
559C23—262no—
560C23—262no—
561C23C22⋊C4×D1311yescharacteristic
562Q8—42no—
563Q8—42no—
564Q8—522no—
565Q8—524no—
566Q8—524no—
567Q8—522no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—131no—
573C2×C4—131no—
574C2×C4—131no—
575C2×C4—134no—
576C2×C4—132no—
577C2×C4—132no—
578C2×C4—132no—
579C2×C4—132no—
580C2×C4—134no—
581C2×C4—134no—
582C2×C4—134no—
583C2×C4—131no—
584C2×C4—131no—
585C2×C4—131no—
586C2×C4—262no—
587C2×C4—262no—
588C2×C4—262no—
589C2×C4—262no—
590C2×C4—262no—
591C2×C4—262no—
592C2×C4—262no—
593C2×C4—262no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—524no—
597C2×C4—524no—
598C2×C4—521no—
599C2×C4C22⋊C4×D1311yescharacteristic
600C2×C4C22⋊C4×D1311yescharacteristic
601C2×C4C22⋊C4×D1311yescharacteristic
602C2×C4SD16×D1312yes—
603C2×C4Q16×D1312yes—
604C2×C4C22×C4×D1311yescharacteristic
605C2×C4C2×D4×D1311yescharacteristic
606C2×C4C2×D4×D1311yescharacteristic
607C8—42no—
608C8—42no—
609C8—522no—
610C8—522no—
611C22—21no—
612C22—21no—
613C22—132no—
614C22—132no—
615C22—132no—
616C22—132no—
617C22—268no—
618C22—261no—
619C22—261no—
620C22D13×#10312yes—
621C22C2×C22⋊C4×D1311yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—42no—
626C4—42no—
627C4—132no—
628C4—132no—
629C4—132no—
630C4—261no—
631C4—261no—
632C4—261no—
633C4—522no—
634C4—522no—
635C4D13×#10312yes—
636C4C2×SD16×D1311yescharacteristic
637C4C2×Q16×D1311yescharacteristic
638C4D13×#13512yes—
639C2—22no—
640C2—134no—
641C2—262no—
642C2D13×#41311yescharacteristic
643C2C2×D13×#10311yescharacteristic
644C2D13×#41611yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1542C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC42×C13C24
hypercenter#1542D13
hypocenterC13C2×#1542
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
4. #13113494C2semidirect
5. #13113493C2semidirect
6. #13113492C2semidirect
7. #13113491C2semidirect
8. #13113490C2semidirect
9. D13×#333C2semidirect
10. D13×#332C2semidirect
11. C13×#1542C2semidirect
47. C13×#333C22semidirect
48. C13×#332C22semidirect
49. #11718139C22semidirect
50. #11718138C22semidirect
51. #11718078C22semidirect
52. #11718074C22semidirect
53. #11718073C22semidirect
54. #11718073C22semidirect
242. #1542D13direct (N × H)
338. #333C2×D13semidirect
342. #332C2×D13semidirect
468. D13#1542direct (N × H)
555. C13C2×#1542semidirect

Maximal subgroups

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

subgroupindex
D13×#5332
D13×#4312
C2×D13×C4⋊C82
#131134942
#131134932
#131134922
#131134912
#131134902
D13×#3332
D13×#3322
C13×#15422
C2×#154213