Finite Group Databasebeta

← D13⋊#1986 #16799357

Subgroups — D13⋊#1986 #16799357

Order 3328.

1290 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D13⋊M16C211yesmaximal, characteristic
2C2×C4×C4⋊#261C211yesmaximal, characteristic
3#13131013C214yesmaximal, complemented
4#13131012C212yesmaximal, complemented
5#13131011C212yesmaximal, complemented
6#13130512C214yesmaximal
7D13×#533C211yesmaximal, characteristic
8C22×C4⋊#261—21no—
9C22×C4×#261C2212yes—
10C2×D13⋊M16C2212yes—
11C13×#533C411yescharacteristic, complemented
12#11719433C2211yescharacteristic
13#11719433C2211yescharacteristic
14D13×C4⋊Q8C411yescharacteristic, complemented
15D13×C4⋊Q8C411yescharacteristic, complemented
16#11719393C2212yes—
17D13×#125C412yescomplemented
18D13×C22⋊Q8—21no—
19D13×C22⋊Q8—21no—
20#11719327—21no—
21#11719327—21no—
22#11719283—21no—
23#11719283—21no—
24C4×Q8×D13—21no—
25C4×Q8×D13—21no—
26D13×#117C2212yes—
27#11719222C412yescomplemented
28C2×C42×D13C2211yescharacteristic
29#11719175C411yescharacteristic, complemented
30C2×(C2×#261)⋊C4—21no—
31C4×#6122—21no—
32C4×#6122—21no—
33C4×C4⋊#261—21no—
34C4×C4⋊#261—21no—
35C4×C4⋊#261C2212yes—
36C4×C4⋊#261C2212yes—
37C4×#6118C2212yes—
38C4×#6118C2212yes—
39#11719047—21no—
40C4×D13⋊C8—21no—
41#11718247C2218yes—
42#11718247C2218yes—
43C23×#261—22no—
44C2×Q8×D13—21no—
45C2×Q8×D13—21no—
46C22×C4×D13D411yescharacteristic
47C22×C4×D13D411yescharacteristic
48C22×C4×D13C2311yescharacteristic
49C2×#6122—22no—
50C2×C4⋊#261—28no—
51C2×C4⋊#261—22no—
52C2×C4⋊#261—22no—
53C2×C4×#261—28no—
54C2×C4×#261—22no—
55C2×C4×#261C2314yes—
56D13⋊M16—24no—
57D13⋊M16Q818yescomplemented
58C2×#6118C2314yes—
59C2×D13⋊C8—22no—
60C13×C4⋊Q8C2×C411yescharacteristic, complemented
61C13×C4⋊Q8C2×C411yescharacteristic, complemented
62C13×#125C2×C412yescomplemented
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—21no—
65C4×Q8×C13—21no—
66C4×Q8×C13—21no—
67C13×#117C2×C412yes—
68C2×C42×C13C2×C411yescharacteristic
69#88200—21no—
70#88200—21no—
71Q8×Dic13—21no—
72Q8×Dic13—21no—
73#88198—21no—
74#88198—21no—
75#88180C2×C412yes—
76#88178—21no—
77#88178—21no—
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13D411yescharacteristic
81#88151—21no—
82#88151—21no—
83#88150—22no—
84#88150—22no—
85#88146C2312yes—
86#88146C2312yes—
87C4⋊C4×D13—21no—
88C4⋊C4×D13—21no—
89C4⋊C4×D13—22no—
90C4⋊C4×D13—22no—
91C4⋊C4×D13C2×C412yes—
92C4⋊C4×D13C2×C412yes—
93#88144C2×C412yescomplemented
94#88144C2×C412yescomplemented
95#88143—22no—
96#88143—22no—
97#88142—21no—
98#88142—21no—
99#88142C2×C412yescomplemented
100#88142C2×C412yescomplemented
101#88141—21no—
102#88141—21no—
103#88141—22no—
104#88141—22no—
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×D13D411yescharacteristic
114C42×D13D411yescharacteristic
115C42×D13D411yescharacteristic
116C42×D13D411yescharacteristic
117C42×D13C2311yescharacteristic
118C42×D13C2311yescharacteristic
119#88124C2×C412yescomplemented
120#88123C2×C411yescharacteristic, complemented
121#88123C2×C411yescharacteristic, complemented
122C4×Dic26—21no—
123C4×Dic26—21no—
124C4×Dic26—22no—
125C4×Dic26—22no—
126(C2×#261)⋊C4—22no—
127(C2×#261)⋊C4—22no—
128#88110—22no—
129#88110—22no—
130C4×#1057—22no—
131C4×#1057—22no—
132C2×#1986—131nomaximal, Sylow
133C23×D13C2×D411yescharacteristic
134C22×#261—28no—
135C22×#261—24no—
136C22×#261—44no—
137C22×#261—44no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C22×C4×C13C22⋊C411yescharacteristic
141C22×C4×C13C22⋊C411yescharacteristic
142C22×C4×C13C22×C411yescharacteristic
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C22⋊C411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146Q8×D13—44no—
147Q8×D13—44no—
148C2×C4×D13—24no—
149C2×C4×D13—22no—
150C2×C4×D13—22no—
151C2×C4×D13—42no—
152C2×C4×D13C22⋊C411yescharacteristic
153C2×C4×D13C22⋊C411yescharacteristic
154C2×C4×D13C22⋊C411yescharacteristic
155C2×C4×D13C22⋊C411yescharacteristic
156C2×C4×D13C22×C411yescharacteristic
157C2×C4×D13C2×D411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13C2×D411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13C2×Q814yes—
164C2×C4×D13#4114yes—
165C2×C4×D13C2411yescharacteristic
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—22no—
169C2×Dic26—22no—
170#6122—28no—
171C2×#1057—24no—
172C4⋊#261—28no—
173C4⋊#261—28no—
174C4×#261—28no—
175C4×#261—44no—
176#6118—24no—
177#6118C2×Q818yescomplemented
178D13⋊C8—28no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4C22×C412yes—
184C13×C4⋊C4C22×C412yes—
185C13×C22⋊C4—22no—
186C42×C13—22no—
187C42×C13C22⋊C411yescharacteristic
188C42×C13C22⋊C411yescharacteristic
189C42×C13C22×C411yescharacteristic
190C42×C13C22×C411yescharacteristic
191C22⋊Dic13—22no—
192#6103—22no—
193#6103—22no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—22no—
197C4⋊Dic13—22no—
198C4⋊Dic13C22×C412yes—
199C4⋊Dic13C22×C412yes—
200#6101—22no—
201#6101—22no—
202#6101—22no—
203#6101—22no—
204#6101—22no—
205#6101—22no—
206#6101—22no—
207#6101—22no—
208C4×Dic13—22no—
209C4×Dic13—22no—
210C4×Dic13—22no—
211C4×Dic13C22⋊C411yescharacteristic
212C4×Dic13C22⋊C411yescharacteristic
213C4×Dic13C22⋊C411yescharacteristic
214C4×Dic13C22⋊C411yescharacteristic
215C4×Dic13C22⋊C411yescharacteristic
216C4×Dic13C22⋊C411yescharacteristic
217C4×Dic13C22×C411yescharacteristic
218C4×Dic13C22×C411yescharacteristic
219C4×Dic13C2×D411yescharacteristic
220C4×Dic13C2×D411yescharacteristic
221C4×Dic13C2×D411yescharacteristic
222C4×Dic13C2×D411yescharacteristic
223C2×#533—131no—
224C2×C4×M16—131no—
225C2×C4×C4⋊C4—131no—
226#1986—132no—
227#1986—132no—
228#1986—134no—
229C2×#339—134no—
230C23×C13C2×C22⋊C411yescharacteristic
231C22×D13—22no—
232C22×D13—22no—
233C22×D13C2×C22⋊C411yescharacteristic
234C22×D13#12412yes—
235C22×D13C4⋊Q812yes—
236C22×D13C22×D411yescharacteristic
237C2×#261—28no—
238C2×#261—44no—
239C2×#261—416no—
240C2×#261—44no—
241Q8×C13—42no—
242Q8×C13—42no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—41no—
247C2×C4×C13C2×C22⋊C411yescharacteristic
248C2×C4×C13C2×C22⋊C411yescharacteristic
249C2×C4×C13C2×C22⋊C411yescharacteristic
250C2×C4×C13C2×C22⋊C411yescharacteristic
251C2×C4×C13C2×C22⋊C411yescharacteristic
252C2×C4×C13C4×Q814yes—
253C2×C4×C13C23×C411yescharacteristic
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—41no—
258C2×Dic13C2×C22⋊C411yescharacteristic
259C2×Dic13C2×C22⋊C411yescharacteristic
260C2×Dic13C2×C22⋊C411yescharacteristic
261C2×Dic13C2×C22⋊C411yescharacteristic
262C2×Dic13C2×C22⋊C411yescharacteristic
263C2×Dic13C22⋊Q814yes—
264C2×Dic13C22×D411yescharacteristic
265C4×D13—22no—
266C4×D13—22no—
267C4×D13—22no—
268C4×D13—22no—
269C4×D13—22no—
270C4×D13—41no—
271C4×D13—41no—
272C4×D13—44no—
273C4×D13—44no—
274C4×D13#10414yes—
275C4×D13C4×Q814yes—
276C4×D13C22⋊Q814yes—
277C4×D13#12412yes—
278C4×D13C4⋊Q812yes—
279C4×D13C22×Q812yes—
280C4×D13C2×#4112yes—
281Dic26—44no—
282Dic26—42no—
283Dic26—42no—
284Dic26—44no—
285#1057—28no—
286C22×M16—132no—
287#533—131no—
288#533—131no—
289#533—132no—
290#533—132no—
291#533—131no—
292#533—261no—
293#533—261no—
294#533—261no—
295#533—261no—
296#533#26111yescharacteristic, complemented
297C2×C4⋊Q8—131no—
298C2×C4⋊Q8—131no—
299C2×#125—132no—
300C2×C22⋊Q8—261no—
301C2×C22⋊Q8—261no—
302C2×C4×Q8—261no—
303C2×C4×Q8—261no—
304C2×#117—132no—
305C22×C4⋊C4—261no—
306C22×C42—131no—
307C22×C42—132no—
308C4×M16—132no—
309C4×M16—132no—
310C4×M16—261no—
311C4×M16—261no—
312C2×#97—261no—
313C2×C4×C8—261no—
314C4×C4⋊C4—132no—
315C4×C4⋊C4—132no—
316C4×C4⋊C4—261no—
317C4×C4⋊C4—261no—
318C2×#95—261no—
319#339—138no—
320#339—138no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13#39112yes—
324C22×C13C22×C22⋊C411yescharacteristic
325C2×D13—21no—
326C2×D13—21no—
327C2×D13—24no—
328C2×D13—24no—
329C2×D13#39112yes—
330C2×D13C2×#10412yes—
331C2×D13#42112yes—
332C2×D13C2×#12411yescharacteristic
333C2×D13C2×C4⋊Q811yescharacteristic
334#261—48no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—21no—
338C4×C13—42no—
339C4×C13—42no—
340C4×C13#39112yes—
341C4×C13C2×#10412yes—
342C4×C13C2×C4×Q812yes—
343Dic13—21no—
344Dic13—21no—
345Dic13—21no—
346Dic13—42no—
347Dic13—42no—
348Dic13#39112yes—
349Dic13C2×#10412yes—
350Dic13C2×C22⋊Q812yes—
351C22×Q8—261no—
352C22×Q8—261no—
353C23×C4—131no—
354C23×C4—131no—
355C23×C4—131no—
356C23×C4—262no—
357C2×M16—134no—
358C2×M16—138no—
359C2×M16—262no—
360C2×M16—264no—
361C22×C8—262no—
362C4⋊Q8—132no—
363C4⋊Q8—132no—
364C4⋊Q8—131no—
365C4⋊Q8—131no—
366C4⋊Q8—261no—
367C4⋊Q8—261no—
368C4⋊Q8—261no—
369C4⋊Q8—261no—
370C4⋊Q8C2×#26111yescharacteristic, complemented
371C4⋊Q8C2×#26111yescharacteristic, complemented
372#125—132no—
373#125—132no—
374#125—132no—
375#125—262no—
376#125—262no—
377#125C2×#26112yescomplemented
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—262no—
381C22⋊Q8—262no—
382C22⋊Q8—262no—
383C22⋊Q8—262no—
384C22⋊Q8—261no—
385C22⋊Q8—261no—
386C22⋊Q8—261no—
387C22⋊Q8—261no—
388C22⋊Q8—261no—
389C22⋊Q8—261no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—262no—
393C4×Q8—262no—
394C4×Q8—262no—
395C4×Q8—261no—
396C4×Q8—262no—
397C4×Q8—261no—
398C4×Q8—261no—
399C4×Q8—261no—
400C4×Q8—261no—
401C4×Q8—261no—
402#117—132no—
403#117—132no—
404#117—132no—
405#117—262no—
406#117—262no—
407#117C2×#26112yes—
408C2×C4⋊C4—132no—
409C2×C4⋊C4—132no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—262no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—262no—
415C2×C4⋊C4—262no—
416C2×C4⋊C4—268no—
417C2×C22⋊C4—262no—
418C2×C42—131no—
419C2×C42—131no—
420C2×C42—131no—
421C2×C42—131no—
422C2×C42—131no—
423C2×C42—131no—
424C2×C42—131no—
425C2×C42—131no—
426C2×C42—131no—
427C2×C42—131no—
428C2×C42—131no—
429C2×C42—134no—
430C2×C42—262no—
431C2×C42—268no—
432C2×C42—262no—
433C2×C42C2×#26111yescharacteristic
434#97—262no—
435#97—262no—
436C4×C8—262no—
437C4×C8—262no—
438#95—262no—
439#95—262no—
440C2×C13—22no—
441C2×C13C2×#39111yescharacteristic
442C2×C13C22×#10411yescharacteristic
443C2×C13C2×#42111yescharacteristic
444D13—21no—
445D13—21no—
446D13#198614yescomplemented
447C24—131no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—262no—
451C2×Q8—262no—
452C2×Q8—261no—
453C2×Q8—261no—
454C2×Q8—524no—
455C2×Q8—524no—
456C22×C4—131no—
457C22×C4—134no—
458C22×C4—134no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—131no—
463C22×C4—131no—
464C22×C4—131no—
465C22×C4—131no—
466C22×C4—131no—
467C22×C4—131no—
468C22×C4—131no—
469C22×C4—131no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—264no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—264no—
477C22×C4—268no—
478C22×C4—522no—
479C22×C4—524no—
480C22×C4—524no—
481C22×C4C22⋊#26111yescharacteristic
482C22×C4C22⋊#26111yescharacteristic
483C22×C4C22×#26111yescharacteristic
484M16—138no—
485M16—264no—
486M16—268no—
487C2×C8—264no—
488C2×C8—268no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—132no—
494C4⋊C4—132no—
495C4⋊C4—262no—
496C4⋊C4—262no—
497C4⋊C4—262no—
498C4⋊C4—262no—
499C4⋊C4—262no—
500C4⋊C4—262no—
501C4⋊C4—262no—
502C4⋊C4—262no—
503C4⋊C4—268no—
504C4⋊C4—268no—
505C4⋊C4—262no—
506C4⋊C4—262no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4C22×#26112yes—
510C4⋊C4C22×#26112yes—
511C22⋊C4—22no—
512C22⋊C4—262no—
513C22⋊C4—262no—
514C22⋊C4—262no—
515C42—22no—
516C42—131no—
517C42—131no—
518C42—131no—
519C42—131no—
520C42—131no—
521C42—131no—
522C42—131no—
523C42—131no—
524C42—131no—
525C42—131no—
526C42—131no—
527C42—131no—
528C42—262no—
529C42—262no—
530C42—268no—
531C42—262no—
532C42—524no—
533C42C22⋊#26111yescharacteristic
534C42C22⋊#26111yescharacteristic
535C42C22×#26111yescharacteristic
536C42C22×#26111yescharacteristic
537C13C2×#198611yescharacteristic, complemented, Sylow
538C23—131no—
539C23—131no—
540C23—132no—
541C23—132no—
542C23—262no—
543C23—262no—
544C23C2×C22⋊#26111yescharacteristic
545Q8—42no—
546Q8—42no—
547Q8—522no—
548Q8—524no—
549Q8—524no—
550Q8—522no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—131no—
556C2×C4—131no—
557C2×C4—131no—
558C2×C4—134no—
559C2×C4—132no—
560C2×C4—132no—
561C2×C4—134no—
562C2×C4—132no—
563C2×C4—134no—
564C2×C4—132no—
565C2×C4—134no—
566C2×C4—131no—
567C2×C4—131no—
568C2×C4—131no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—262no—
573C2×C4—262no—
574C2×C4—262no—
575C2×C4—268no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—524no—
581C2×C4—524no—
582C2×C4—521no—
583C2×C4—524no—
584C2×C4—5216no—
585C2×C4—524no—
586C2×C4Q8×#26114yes—
587C2×C4C2×C22⋊#26111yescharacteristic
588C2×C4C2×C22⋊#26111yescharacteristic
589C2×C4C2×C22⋊#26111yescharacteristic
590C2×C4C2×C22⋊#26111yescharacteristic
591C2×C4C2×C22⋊#26111yescharacteristic
592C2×C4C23×#26111yescharacteristic
593C8—268no—
594C22—21no—
595C22—21no—
596C22—132no—
597C22—132no—
598C22—132no—
599C22—131no—
600C22—131no—
601C22—264no—
602C22—264no—
603C22—261no—
604C22—261no—
605C22(C2×#261)⋊Q812yes—
606C22C22×C22⋊#26111yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—42no—
611C4—42no—
612C4—132no—
613C4—132no—
614C4—132no—
615C4—261no—
616C4—261no—
617C4—261no—
618C4—528no—
619C4—522no—
620C4—522no—
621C4(C2×#261)⋊Q812yes—
622C4D13⋊#10412yes—
623C4C2×Q8×#26112yes—
624C2—22no—
625C2—134no—
626C2—261no—
627C2—261no—
628C2C2×(C2×#261)⋊Q811yescharacteristic
629C2C2×D13⋊#10411yescharacteristic
630C2D13⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#533C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC2×C4×D13C24
hypercenter#533#261
hypocenterC13C2×#1986
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #13131013C2semidirect
4. #13131012C2semidirect
5. #13131011C2semidirect
11. C13×#533C4semidirect
14. D13×C4⋊Q8C4semidirect
15. D13×C4⋊Q8C4semidirect
17. D13×#125C4semidirect
27. #11719222C4semidirect
29. #11719175C4semidirect
57. D13⋊M16Q8semidirect
60. C13×C4⋊Q8C2×C4semidirect
61. C13×C4⋊Q8C2×C4semidirect
62. C13×#125C2×C4semidirect
93. #88144C2×C4semidirect
94. #88144C2×C4semidirect
99. #88142C2×C4semidirect
100. #88142C2×C4semidirect
119. #88124C2×C4semidirect
120. #88123C2×C4semidirect
121. #88123C2×C4semidirect
177. #6118C2×Q8semidirect
296. #533#261semidirect
370. C4⋊Q8C2×#261semidirect
371. C4⋊Q8C2×#261semidirect
377. #125C2×#261semidirect
446. D13#1986semidirect
537. C13C2×#1986semidirect

Maximal subgroups

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

subgroupindex
C4×D13⋊M162
C2×C4×C4⋊#2612
#131310132
#131310122
#131310112
#131305122
D13×#5332
C2×#198613