Finite Group Databasebeta

← Dic13×#478 #15870526

Subgroups — Dic13×#478 #15870526

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×Dic13C211yesmaximal, characteristic, complemented
2C4×D4×Dic13C211yesmaximal, characteristic
3#13115794C211yesmaximal, characteristic, complemented
4#13115606C211yesmaximal, characteristic, complemented
5#13115430C211yesmaximal, characteristic, complemented
6#13115416C211yesmaximal, characteristic, complemented
7#13115099C211yesmaximal, characteristic
8#13115085C211yesmaximal, characteristic
9#13114846C211yesmaximal, characteristic
10#107×Dic13C211yesmaximal, characteristic, complemented
11#106×Dic13C211yesmaximal, characteristic, complemented
12C4⋊C8×Dic13C211yesmaximal, characteristic, complemented
13#102×Dic13C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C2×C13×#478C211yesmaximal, characteristic
16C2×C13×#125C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×D4×Dic13C2211yescharacteristic
20C22×C4×Dic13—21no—
21C13×#478C418yescomplemented
22C2×C13×#107C2211yescharacteristic
23C2×C13×#106C2211yescharacteristic
24C2×C13×C4⋊C8C2211yescharacteristic
25C2×C13×#102C2211yescharacteristic
26C2×C13×#102C2211yescharacteristic
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29C4×C22⋊Dic13—21no—
30C2×#88058C2211yescharacteristic
31C2×#88057C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718646C2211yescharacteristic
35#11718646C2211yescharacteristic
36#11718642—21no—
37#11718642—21no—
38C4⋊C4×Dic13—21no—
39C4⋊C4×Dic13—21no—
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C22⋊C4×Dic13—21no—
45C22⋊C4×Dic13—21no—
46#11718597C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C42×Dic13C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×Dic13—21no—
63C23×Dic13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C13×#125—22no—
67C13×#125C2×C414yescomplemented
68C4×D4×C13—22no—
69C4×D4×C13C2×C414yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C42×C13C2311yescharacteristic
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79D4×Dic13—22no—
80D4×Dic13—22no—
81D4×Dic13—22no—
82D4×Dic13Q814yes—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—44no—
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13D411yescharacteristic
98C2×C4×Dic13D411yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100C2×C4×Dic13C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C13×#107C2×C414yescomplemented
104C13×#106C2×C414yescomplemented
105C13×C4⋊C8C2×C414yescomplemented
106C13×#102C2×C414yes—
107C13×#102C2×C414yes—
108#88072—22no—
109#88072—22no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88058—22no—
120#88057—22no—
121C8×Dic13—22no—
122C8×Dic13—22no—
123C4⋊#1055—22no—
124C4×#478—131nomaximal, Sylow
125C24×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13C22×C412yes—
130C2×D4×C13C2×Q812yes—
131C2×D4×C13#4112yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—24no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—24no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—24no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13C22×C412yes—
160C2×C8×C13C22×C412yes—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C412yes—
167C13×C4⋊C4C22×C412yes—
168C13×C4⋊C4C22×C412yes—
169C13×C22⋊C4—24no—
170C42×C13C22×C412yes—
171C42×C13#4112yes—
172C22⋊Dic13—24no—
173C22⋊Dic13—24no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—42no—
181C4⋊Dic13—42no—
182C4⋊Dic13C2×Q812yes—
183C4⋊Dic13#4112yes—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—22no—
189C4×Dic13—41no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13—42no—
193C4×Dic13—42no—
194C4×Dic13—42no—
195C4×Dic13C2×Q812yes—
196C4×Dic13#4112yes—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#478D1311yescharacteristic
204C4×#125—131no—
205C42×D4—131no—
206#1989—131no—
207#1949—131no—
208#1921—131no—
209#1919—131no—
210#1864—131no—
211#1862—131no—
212#1804—131no—
213C4×#107—131no—
214C4×#106—131no—
215C4×C4⋊C8—131no—
216C4×#102—131no—
217C4×#102—131no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226D4×C13—22no—
227D4×C13—22no—
228D4×C13—22no—
229D4×C13C4×Q814yes—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—48no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13C4×D412yes—
245C2×C4×C13C4×D412yes—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×Q811yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—22no—
257C2×Dic13—21no—
258C2×Dic13—22no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—48no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—48no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13C22⋊Q812yes—
274C2×Dic13C22⋊Q812yes—
275C2×Dic13#13512yes—
276C2×Dic13#13512yes—
277C2×Dic13AGL(1,ℤ/8)12yes—
278C8×C13—22no—
279C8×C13—22no—
280#1055—41no—
281#1055—41no—
282C2×#125C2×D1311yescharacteristic
283C2×C4×D4—131no—
284C2×C4×D4—131no—
285C2×C4×D4C2×D1311yescharacteristic
286C22×C42—261no—
287#478Dic1318yesdirect product factor
288C2×#107—131no—
289C2×#107C2×D1311yescharacteristic
290C2×#106—131no—
291C2×#106C2×D1311yescharacteristic
292C2×C4⋊C8—131no—
293C2×C4⋊C8C2×D1311yescharacteristic
294C2×#102—131no—
295C2×#102—131no—
296C2×#102C2×D1311yescharacteristic
297C2×#102C2×D1311yescharacteristic
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#389—131no—
301#389—131no—
302#387—261no—
303#387—261no—
304#382—131no—
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—261no—
311C4×C4⋊C4—261no—
312C4×C22⋊C4—261no—
313C4×C22⋊C4—261no—
314C4×C22⋊C4—261no—
315C43—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#336—131no—
325#336—131no—
326C22×C13—24no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13C2×C4×D411yescharacteristic
334C22×C13C2×C22⋊Q811yescharacteristic
335C22×C13#52511yescharacteristic
336C22×C13C2×#13511yescharacteristic
337C22×C13C2×#13511yescharacteristic
338C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C13#57511yescharacteristic
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—42no—
344C4×C13—42no—
345C4×C13C2×C4×Q811yescharacteristic
346C4×C13C4×#4111yescharacteristic
347C4×C13#52911yescharacteristic
348C4×C13#53311yescharacteristic
349Dic13—22no—
350Dic13—22no—
351Dic13—42no—
352Dic13—41no—
353Dic13—42no—
354Dic13—81no—
355Dic13—81no—
356Dic13#47814yesdirect product factor
357C22×D4C22×D1311yescharacteristic
358C23×C4—21no—
359C23×C4—261no—
360C23×C4—261no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8C22×D1311yescharacteristic
364C22×C8C22×D1311yescharacteristic
365#125—22no—
366#125C2×Dic1314yescomplemented
367C4×D4—22no—
368C4×D4—134no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—262no—
372C4×D4C2×Dic1314yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—524no—
399C2×C42C22×D1311yescharacteristic
400#107—262no—
401#107C2×Dic1314yescomplemented
402#106—262no—
403#106C2×Dic1314yescomplemented
404C4⋊C8—262no—
405C4⋊C8C2×Dic1314yescomplemented
406#102—262no—
407#102—262no—
408#102C2×Dic1314yes—
409#102C2×Dic1314yes—
410C4×C8—262no—
411C4×C8—262no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13—44no—
422C2×C13C4×C22⋊Q811yescharacteristic
423C2×C13C4×#13511yescharacteristic
424C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
425C2×C13C2×#47811yescharacteristic
426C2×C13#307611yescharacteristic
427C2×C13#310211yescharacteristic
428C2×C13#310511yescharacteristic
429C24—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4Q8×D1312yes—
434C2×D4#613112yes—
435C2×D4C22×Dic1312yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—522no—
453C22×C4—522no—
454C22×C4—522no—
455C22×C4—522no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8C22×Dic1312yes—
470C2×C8C22×Dic1312yes—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—132no—
477C4⋊C4—132no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C4⋊C4C22×Dic1312yes—
487C4⋊C4C22×Dic1312yes—
488C4⋊C4C22×Dic1312yes—
489C22⋊C4—24no—
490C22⋊C4—264no—
491C22⋊C4—264no—
492C42—132no—
493C42—132no—
494C42—262no—
495C42—262no—
496C42—262no—
497C42—261no—
498C42—261no—
499C42—521no—
500C42—522no—
501C42—522no—
502C42—522no—
503C42—522no—
504C42—522no—
505C42#612912yes—
506C42C22×Dic1312yes—
507C13C4×#47811yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C2×D4×D1311yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4Q8×Dic1314yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—48no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—262no—
546C2×C4—261no—
547C2×C4—262no—
548C2×C4—528no—
549C2×C4—528no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4D4×Dic1312yes—
561C2×C4D4×Dic1312yes—
562C2×C4C2×#612911yescharacteristic
563C2×C4C2×Q8×D1311yescharacteristic
564C2×C4C2×#613111yescharacteristic
565C2×C4#41×D1311yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4C23×Dic1311yescharacteristic
568C8—22no—
569C8—22no—
570C8—521no—
571C8—521no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22D13×C22⋊Q811yescharacteristic
580C22#1171933211yescharacteristic
581C22D13×#13511yescharacteristic
582C22D13×#13511yescharacteristic
583C22D13×AGL(1,ℤ/8)11yescharacteristic
584C22#1171947811yescharacteristic
585C22C2×D4×Dic1311yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—134no—
592C4—262no—
593C4—262no—
594C4—522no—
595C4—522no—
596C4—521no—
597C4—1041no—
598C4—1041no—
599C4#1171932711yescharacteristic
600C4#1171932911yescharacteristic
601C4C2×Q8×Dic1311yescharacteristic
602C4#41×Dic1311yescharacteristic
603C2—44no—
604C2C22⋊Q8×Dic1311yescharacteristic
605C2#135×Dic1311yescharacteristic
606C2AGL(1,ℤ/8)×Dic1311yescharacteristic
607C2D13×#47811yescharacteristic
608C2#1312462111yescharacteristic
609C2#1312485911yescharacteristic
610C2#1312488811yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenterC2×#478D13
hypocenterC13C4×#478
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. #125×Dic13C2semidirect
3. #13115794C2semidirect
4. #13115606C2semidirect
5. #13115430C2semidirect
6. #13115416C2semidirect
10. #107×Dic13C2semidirect
11. #106×Dic13C2semidirect
12. C4⋊C8×Dic13C2semidirect
21. C13×#478C4semidirect
67. C13×#125C2×C4semidirect
103. C13×#107C2×C4semidirect
104. C13×#106C2×C4semidirect
105. C13×C4⋊C8C2×C4semidirect
287. #478Dic13direct (N × H)
356. Dic13#478direct (N × H)
366. #125C2×Dic13semidirect
401. #107C2×Dic13semidirect
403. #106C2×Dic13semidirect
405. C4⋊C8C2×Dic13semidirect
507. C13C4×#478semidirect

Maximal subgroups

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

subgroupindex
#125×Dic132
C4×D4×Dic132
#131157942
#131156062
#131154302
#131154162
#131150992
#131150852
#131148462
#107×Dic132
#106×Dic132
C4⋊C8×Dic132
#102×Dic132
C2×C13×#4782
C4×#47813