Finite Group Databasebeta

← D13⋊#1479 #16793295

Subgroups — D13⋊#1479 #16793295

Order 3328.

1282 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D13⋊#431C211yesmaximal, characteristic
2D13⋊#431C211yesmaximal, characteristic
3#13130140C212yesmaximal, complemented
4#13130139C214yesmaximal, complemented
5#13130138C212yesmaximal, complemented
6D13⋊(Q8⋊C8)C214yesmaximal, complemented
7C2×C4×Q8×D13C211yesmaximal, characteristic
8C22×Q8×D13C411yescharacteristic
9C2×C4×Q8×C13C411yescharacteristic
10C2×Q8×Dic13C2211yescharacteristic
11C4×Q8×D13—21no—
12C4×Q8×D13—21no—
13C4×Q8×D13—21no—
14C4×Q8×D13—21no—
15C4×Q8×D13C412yes—
16C4×Q8×D13C412yes—
17C4×Q8×D13C2212yes—
18C4×Q8×D13C2212yes—
19C2×C4⋊C4×D13—21no—
20C2×C4⋊C4×D13C411yescharacteristic
21C2×#88141—21no—
22C2×#88141C2211yescharacteristic
23C2×C42×D13—21no—
24C2×C42×D13C2211yescharacteristic
25C2×C4×Dic26—21no—
26C2×C4×Dic26C411yescharacteristic
27#11719125—21no—
28#11719125—21no—
29D13⋊(C22⋊C8)—21no—
30D13⋊(C22⋊C8)—21no—
31#11719119C2212yes—
32#11719119C2212yes—
33#11719051—21no—
34#11719051C2212yes—
35D13⋊(C4⋊C8)—21no—
36D13⋊(C4⋊C8)C2212yes—
37#11719049—21no—
38#11719049C2212yes—
39C4×D13⋊C8—21no—
40C4×D13⋊C8C2212yes—
41Q8⋊#1057C2218yescomplemented
42#11718244C2218yescomplemented
43C22×Q8×C13C2×C411yescharacteristic
44C2×Q8×D13—21no—
45C2×Q8×D13—21no—
46C2×Q8×D13—24no—
47C2×Q8×D13C818yescomplemented
48C2×Q8×D13C2×C412yes—
49C2×Q8×D13C2×C412yes—
50C22×C4×D13—21no—
51C22×C4×D13—21no—
52C22×C4×D13C2×C411yescharacteristic
53C22×C4×D13D411yescharacteristic
54C22×C4×D13D411yescharacteristic
55C22×Dic26—21no—
56C22×Dic26C2×C411yescharacteristic
57C2×D13⋊C8—22no—
58C2×D13⋊C8—22no—
59C4×Q8×C13—21no—
60C4×Q8×C13—21no—
61C4×Q8×C13C2×C412yes—
62C4×Q8×C13C2×C412yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2×C411yescharacteristic
65C2×C42×C13—21no—
66C2×C42×C13C2×C411yescharacteristic
67Q8×Dic13—21no—
68Q8×Dic13—21no—
69Q8×Dic13C2×C412yes—
70Q8×Dic13C2312yes—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13C2×C411yescharacteristic
73C2×#6101—21no—
74C2×#6101—21no—
75C2×#6101—21no—
76C2×C4×Dic13—21no—
77C2×C4×Dic13—21no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13D411yescharacteristic
80C2×C4×Dic13D411yescharacteristic
81C2×C4×Dic13C2311yescharacteristic
82C4⋊C4×D13—22no—
83C4⋊C4×D13—22no—
84C4⋊C4×D13—21no—
85C4⋊C4×D13—21no—
86C4⋊C4×D13—22no—
87C4⋊C4×D13—22no—
88C4⋊C4×D13C2×C412yes—
89C4⋊C4×D13C2×C412yes—
90#88141—22no—
91#88141—22no—
92#88141—22no—
93#88141—22no—
94#88141—21no—
95#88141—21no—
96#88141C2×C412yes—
97#88141C2312yes—
98C42×D13—22no—
99C42×D13—22no—
100C42×D13—22no—
101C42×D13—22no—
102C42×D13C2×C411yescharacteristic
103C42×D13C2×C411yescharacteristic
104C42×D13D411yescharacteristic
105C42×D13D411yescharacteristic
106C42×D13D411yescharacteristic
107C42×D13D411yescharacteristic
108C42×D13C2311yescharacteristic
109C42×D13C2311yescharacteristic
110C4×Dic26—21no—
111C4×Dic26—21no—
112C4×Dic26—22no—
113C4×Dic26—22no—
114C4×Dic26—22no—
115C4×Dic26—22no—
116C4×Dic26C2×C412yes—
117C4×Dic26C2×C412yes—
118C22⋊#1057—22no—
119C22⋊#1057—22no—
120#88112—22no—
121#88112—22no—
122#88111—22no—
123#88111—22no—
124C4⋊#1057—22no—
125C4⋊#1057C2314yes—
126C4×#1057—22no—
127C4×#1057—22no—
128C4×#1057—22no—
129C4×#1057C2314yes—
130C2×#1479—131nomaximal, Sylow
131C23×D13C22⋊C411yescharacteristic
132C2×Q8×C13—21no—
133C2×Q8×C13—22no—
134C2×Q8×C13C2×C814yescomplemented
135C2×Q8×C13C22×C412yes—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13C22⋊C411yescharacteristic
139C22×C4×C13C22⋊C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13C22⋊C411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C22×Dic13C2×D411yescharacteristic
146Q8×D13—28no—
147Q8×D13—28no—
148Q8×D13—24no—
149Q8×D13—24no—
150Q8×D13C2×C818yes—
151Q8×D13C2×C818yescomplemented
152C2×C4×D13—28no—
153C2×C4×D13—22no—
154C2×C4×D13—22no—
155C2×C4×D13—24no—
156C2×C4×D13—22no—
157C2×C4×D13—22no—
158C2×C4×D13—42no—
159C2×C4×D13—44no—
160C2×C4×D13C22⋊C411yescharacteristic
161C2×C4×D13C22⋊C411yescharacteristic
162C2×C4×D13C22⋊C411yescharacteristic
163C2×C4×D13C22⋊C411yescharacteristic
164C2×C4×D13C22⋊C411yescharacteristic
165C2×C4×D13C22⋊C411yescharacteristic
166C2×C4×D13C2×C814yes—
167C2×C4×D13M1614yes—
168C2×C4×D13C22×C411yescharacteristic
169C2×C4×D13C22×C411yescharacteristic
170C2×C4×D13C2×D411yescharacteristic
171C2×C4×D13C2×D411yescharacteristic
172C2×C4×D13C2×D411yescharacteristic
173C2×C4×D13C2×D411yescharacteristic
174C2×Dic26—21no—
175C2×Dic26—22no—
176C2×Dic26—28no—
177C2×Dic26—22no—
178C2×Dic26—22no—
179C2×Dic26C2×C814yescomplemented
180C2×Dic26C22×C412yes—
181C2×#1057—24no—
182C2×#1057—24no—
183D13⋊C8—44no—
184D13⋊C8—44no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4C22×C412yes—
189C42×C13—22no—
190C42×C13—22no—
191C42×C13C22⋊C411yescharacteristic
192C42×C13C22⋊C411yescharacteristic
193C42×C13C22×C411yescharacteristic
194C42×C13C22×C411yescharacteristic
195C4⋊Dic13—21no—
196C4⋊Dic13—22no—
197C4⋊Dic13—22no—
198C4⋊Dic13C22×C412yes—
199#6101—22no—
200#6101—22no—
201#6101—22no—
202#6101—22no—
203#6101—22no—
204#6101—22no—
205C4×Dic13—22no—
206C4×Dic13—22no—
207C4×Dic13—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×Dic13C2×D411yescharacteristic
217C4×Dic13C2×D411yescharacteristic
218C4×Dic13C2×D411yescharacteristic
219C4×Dic13C2×D411yescharacteristic
220C4×Dic13C2×D411yescharacteristic
221C4×Dic13C2×D411yescharacteristic
222C4×Dic13C2411yescharacteristic
223C22×C4×Q8—131no—
224C2×#431—131no—
225C2×#431—131no—
226#1479—132no—
227#1479—134no—
228#1479—132no—
229C2×Q8⋊C8—134no—
230C23×C13C2×C22⋊C411yescharacteristic
231C22×D13—22no—
232C22×D13—22no—
233C22×D13C22⋊C814yes—
234C22×D13C2×C22⋊C411yescharacteristic
235C22×D13C2×C22⋊C411yescharacteristic
236Q8×C13—22no—
237Q8×C13—24no—
238Q8×C13C22×C814yes—
239C2×C4×C13—22no—
240C2×C4×C13—24no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—41no—
244C2×C4×C13—42no—
245C2×C4×C13C2×C22⋊C411yescharacteristic
246C2×C4×C13C2×C22⋊C411yescharacteristic
247C2×C4×C13C2×C22⋊C411yescharacteristic
248C2×C4×C13C2×C22⋊C411yescharacteristic
249C2×C4×C13C2×C22⋊C411yescharacteristic
250C2×C4×C13C22×C812yes—
251C2×C4×C13C2×M1612yes—
252C2×C4×C13C23×C411yescharacteristic
253C2×Dic13—22no—
254C2×Dic13—24no—
255C2×Dic13—22no—
256C2×Dic13—22no—
257C2×Dic13—41no—
258C2×Dic13—42no—
259C2×Dic13C22⋊C814yes—
260C2×Dic13C2×C22⋊C411yescharacteristic
261C2×Dic13C2×C22⋊C411yescharacteristic
262C2×Dic13C2×C22⋊C411yescharacteristic
263C2×Dic13C2×C22⋊C411yescharacteristic
264C2×Dic13C22×D411yescharacteristic
265C2×Dic13C22×D411yescharacteristic
266C4×D13—28no—
267C4×D13—28no—
268C4×D13—22no—
269C4×D13—22no—
270C4×D13—22no—
271C4×D13—22no—
272C4×D13—22no—
273C4×D13—41no—
274C4×D13—41no—
275C4×D13—44no—
276C4×D13—44no—
277C4×D13C22⋊C814yes—
278C4×D13C22⋊C814yes—
279C4×D13C22×C812yes—
280C4×D13C22×C812yes—
281C4×D13C2×M1612yes—
282C4×D13C2×M1612yes—
283C4×D13#13714yes—
284Dic26—22no—
285Dic26—24no—
286Dic26—28no—
287Dic26—28no—
288Dic26C22×C814yes—
289#1057—44no—
290#1057—44no—
291C23×Q8—131no—
292C2×C4×Q8—131no—
293C2×C4×Q8—132no—
294C2×C4×Q8—132no—
295C2×C4×Q8—132no—
296C2×C4×Q8—132no—
297C2×C4×Q8—131no—
298C2×C4×Q8—131no—
299C2×C4×Q8—261no—
300C2×C4×Q8—261no—
301C2×C4×Q8—261no—
302C2×C4×Q8—261no—
303C2×C4×Q8—261no—
304C2×C4×Q8—261no—
305C2×C4×Q8#26111yescharacteristic
306C22×C4⋊C4—131no—
307C22×C4⋊C4—261no—
308C22×C42—131no—
309C22×C42—261no—
310#431—132no—
311#431—132no—
312#431—132no—
313#431—132no—
314#431—261no—
315#431—261no—
316#431—261no—
317#431—261no—
318C2×C4⋊C8—132no—
319C2×C4⋊C8—261no—
320C2×C22⋊C8—261no—
321C2×C22⋊C8—261no—
322C2×C4×C8—132no—
323C2×C4×C8—261no—
324Q8⋊C8—138no—
325Q8⋊C8—138no—
326C22×C13—21no—
327C22×C13—21no—
328C22×C13C2×C22⋊C812yes—
329C22×C13C22×C22⋊C411yescharacteristic
330C2×D13—21no—
331C2×D13—21no—
332C2×D13—28no—
333C2×D13C2×C22⋊C812yes—
334C2×D13C2×C22⋊C812yes—
335C2×D13#41912yes—
336C2×D13#42112yes—
337C4×C13—24no—
338C4×C13—21no—
339C4×C13—21no—
340C4×C13—21no—
341C4×C13—42no—
342C4×C13C2×C22⋊C812yes—
343C4×C13#41912yes—
344C4×C13C23×C811yescharacteristic
345C4×C13C22×M1611yescharacteristic
346Dic13—24no—
347Dic13—21no—
348Dic13—21no—
349Dic13—21no—
350Dic13—42no—
351Dic13C2×C22⋊C812yes—
352Dic13C2×C22⋊C812yes—
353Dic13C2×#13712yes—
354C22×Q8—138no—
355C22×Q8—132no—
356C22×Q8—132no—
357C22×Q8—131no—
358C22×Q8—261no—
359C22×Q8—261no—
360C22×Q8—261no—
361C22×Q8—264no—
362C22×Q8C2×#26111yescharacteristic
363C23×C4—131no—
364C23×C4—131no—
365C23×C4—131no—
366C23×C4—261no—
367C23×C4—261no—
368C22×C8—262no—
369C22×C8—262no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—132no—
373C4×Q8—132no—
374C4×Q8—132no—
375C4×Q8—132no—
376C4×Q8—132no—
377C4×Q8—132no—
378C4×Q8—262no—
379C4×Q8—262no—
380C4×Q8—262no—
381C4×Q8—262no—
382C4×Q8—262no—
383C4×Q8—261no—
384C4×Q8—262no—
385C4×Q8—261no—
386C4×Q8—262no—
387C4×Q8—262no—
388C4×Q8—261no—
389C4×Q8—261no—
390C4×Q8—261no—
391C4×Q8—261no—
392C4×Q8C2×#26112yes—
393C4×Q8C2×#26112yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—132no—
397C2×C4⋊C4—132no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—262no—
401C2×C4⋊C4—262no—
402C2×C4⋊C4—262no—
403C2×C4⋊C4—262no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4C2×#26111yescharacteristic
409C2×C42—21no—
410C2×C42—131no—
411C2×C42—131no—
412C2×C42—131no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—131no—
419C2×C42—131no—
420C2×C42—131no—
421C2×C42—262no—
422C2×C42—262no—
423C2×C42—262no—
424C2×C42—262no—
425C2×C42—261no—
426C2×C42—261no—
427C2×C42—261no—
428C2×C42C2×#26111yescharacteristic
429C4⋊C8—134no—
430C4⋊C8—262no—
431C4⋊C8—262no—
432C4⋊C8—262no—
433C22⋊C8—262no—
434C22⋊C8—262no—
435C22⋊C8—262no—
436C22⋊C8—262no—
437C4×C8—134no—
438C4×C8—262no—
439C4×C8—262no—
440C4×C8—262no—
441C2×C13—22no—
442C2×C13C22×C22⋊C811yescharacteristic
443C2×C13C2×#41911yescharacteristic
444C2×C13C2×#42111yescharacteristic
445D13—22no—
446D13#147914yescomplemented
447C24—131no—
448C2×Q8—22no—
449C2×Q8—21no—
450C2×Q8—138no—
451C2×Q8—138no—
452C2×Q8—134no—
453C2×Q8—132no—
454C2×Q8—262no—
455C2×Q8—262no—
456C2×Q8—268no—
457C2×Q8—264no—
458C2×Q8—264no—
459C2×Q8—268no—
460C2×Q8—268no—
461C2×Q8—262no—
462C2×Q8—261no—
463C2×Q8D13⋊C814yescomplemented
464C2×Q8C22×#26112yes—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—131no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—131no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—131no—
478C22×C4—131no—
479C22×C4—131no—
480C22×C4—131no—
481C22×C4—131no—
482C22×C4—131no—
483C22×C4—131no—
484C22×C4—264no—
485C22×C4—262no—
486C22×C4—262no—
487C22×C4—268no—
488C22×C4—262no—
489C22×C4—262no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—522no—
493C22×C4—524no—
494C22×C4C22⋊#26111yescharacteristic
495C22×C4C22⋊#26111yescharacteristic
496C22×C4C22×#26111yescharacteristic
497C2×C8—264no—
498C2×C8—264no—
499C2×C8—524no—
500C2×C8—524no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—132no—
505C4⋊C4—262no—
506C4⋊C4—262no—
507C4⋊C4—262no—
508C4⋊C4—262no—
509C4⋊C4—262no—
510C4⋊C4—262no—
511C4⋊C4—261no—
512C4⋊C4—262no—
513C4⋊C4—262no—
514C4⋊C4C22×#26112yes—
515C42—22no—
516C42—22no—
517C42—131no—
518C42—131no—
519C42—131no—
520C42—131no—
521C42—131no—
522C42—131no—
523C42—131no—
524C42—131no—
525C42—131no—
526C42—131no—
527C42—131no—
528C42—131no—
529C42—262no—
530C42—262no—
531C42—262no—
532C42—262no—
533C42—262no—
534C42—262no—
535C42C22⋊#26111yescharacteristic
536C42C22⋊#26111yescharacteristic
537C42C22×#26111yescharacteristic
538C42C22×#26111yescharacteristic
539C13C2×#147911yescharacteristic, complemented, Sylow
540C23—131no—
541C23—131no—
542C23—134no—
543C23—262no—
544C23—262no—
545C23C2×C22⋊#26111yescharacteristic
546Q8—22no—
547Q8—24no—
548Q8—134no—
549Q8—268no—
550Q8—268no—
551Q8—262no—
552Q8—264no—
553Q8C2×D13⋊C814yes—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—131no—
561C2×C4—131no—
562C2×C4—131no—
563C2×C4—134no—
564C2×C4—132no—
565C2×C4—132no—
566C2×C4—132no—
567C2×C4—132no—
568C2×C4—134no—
569C2×C4—134no—
570C2×C4—134no—
571C2×C4—131no—
572C2×C4—131no—
573C2×C4—131no—
574C2×C4—262no—
575C2×C4—262no—
576C2×C4—262no—
577C2×C4—262no—
578C2×C4—268no—
579C2×C4—268no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—264no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—524no—
588C2×C4—524no—
589C2×C4—521no—
590C2×C4—522no—
591C2×C4C2×D13⋊C812yes—
592C2×C4D13⋊M1612yes—
593C2×C4C2×C22⋊#26111yescharacteristic
594C2×C4C2×C22⋊#26111yescharacteristic
595C2×C4C2×C22⋊#26111yescharacteristic
596C2×C4C2×C22⋊#26111yescharacteristic
597C2×C4C2×C22⋊#26111yescharacteristic
598C2×C4C23×#26111yescharacteristic
599C8—524no—
600C8—524no—
601C22—21no—
602C22—21no—
603C22—132no—
604C22—132no—
605C22—132no—
606C22—132no—
607C22—268no—
608C22—261no—
609C22—261no—
610C22D13⋊(C22⋊C8)12yes—
611C22C22×C22⋊#26111yescharacteristic
612C4—24no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—132no—
618C4—132no—
619C4—132no—
620C4—264no—
621C4—261no—
622C4—261no—
623C4—261no—
624C4—522no—
625C4D13⋊(C22⋊C8)12yes—
626C4#1171915312yes—
627C4C22×D13⋊C811yescharacteristic
628C4C2×D13⋊M1611yescharacteristic
629C2—22no—
630C2—134no—
631C2—262no—
632C2C2×D13⋊(C22⋊C8)11yescharacteristic
633C2C2×#1171915311yescharacteristic
634C2D13⋊#42111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC4×C13C23×C8
FrattiniC2×C4C23×#261
FittingC2×C4×Q8×C13C4
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC4×Dic13C24
hypercenterC2×C4×Q8#261
hypocenterC13C2×#1479
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #13130140C2semidirect
4. #13130139C2semidirect
5. #13130138C2semidirect
6. D13⋊(Q8⋊C8)C2semidirect
41. Q8⋊#1057C22semidirect
42. #11718244C22semidirect
47. C2×Q8×D13C8semidirect
134. C2×Q8×C13C2×C8semidirect
151. Q8×D13C2×C8semidirect
179. C2×Dic26C2×C8semidirect
446. D13#1479semidirect
463. C2×Q8D13⋊C8semidirect
539. C13C2×#1479semidirect

Maximal subgroups

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

subgroupindex
D13⋊#4312
#131301402
#131301392
#131301382
D13⋊(Q8⋊C8)2
C2×C4×Q8×D132
C2×#147913