Finite Group Databasebeta

← Dic13×#327 #15753795

Subgroups — Dic13×#327 #15753795

Order 3328.

816 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×Dic13C211yesmaximal, characteristic
2C22⋊C8×Dic13C211yesmaximal, characteristic, complemented
3C2×#11718129C211yesmaximal, characteristic
4#95×Dic13C211yesmaximal, characteristic, complemented
5#13112716C211yesmaximal, characteristic, complemented
6#13112715C211yesmaximal, characteristic, complemented
7C2×C13×#327C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C2×D4×Dic13—21no—
10C2×D4×Dic13C411yescharacteristic, complemented
11C22×C4×Dic13—21no—
12C22×C4×Dic13C2211yescharacteristic
13C2×C13×C22⋊C8C2211yescharacteristic
14C2×C13×#95C2211yescharacteristic
15#11718882C411yescharacteristic, complemented
16#11718881—21no—
17#11718873C2211yescharacteristic
18C2×#88071—21no—
19C2×#88071C2211yescharacteristic
20C2×C22⋊#1055C2211yescharacteristic
21C2×C8×Dic13—21no—
22#11718646C411yescharacteristic, complemented
23C4⋊C4×Dic13C411yescharacteristic, complemented
24#11718612—21no—
25C22⋊C4×Dic13—21no—
26C13×#327C414yescomplemented
27#11718142—21no—
28#11718129C414yescomplemented
29C22×D4×C13—21no—
30C22×D4×C13C2×C411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13C2311yescharacteristic
33C23×Dic13—21no—
34C23×Dic13—21no—
35C23×Dic13D411yescharacteristic
36C23×Dic13D411yescharacteristic
37C22×C8×C13—21no—
38C13×#121—21no—
39C13×#121—21no—
40C13×#121C2×C412yes—
41C13×#121C2×C412yes—
42C2×C13×C4⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4—21no—
44C2×C22⋊Dic13—21no—
45C2×C22⋊Dic13—21no—
46C2×C22⋊Dic13—21no—
47C2×C22⋊Dic13—21no—
48D4×Dic13—42no—
49D4×Dic13—42no—
50D4×Dic13—42no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13C2×C411yescharacteristic
53C2×C4⋊Dic13C2×C411yescharacteristic
54C2×C4×Dic13—24no—
55C2×C4×Dic13—21no—
56C2×C4×Dic13—42no—
57C2×C4×Dic13—42no—
58C2×C4×Dic13—42no—
59C2×C4×Dic13C2×C411yescharacteristic
60C2×C4×Dic13C2×C411yescharacteristic
61C2×C4×Dic13D411yescharacteristic
62C2×C4×Dic13D411yescharacteristic
63C22×#1055—21no—
64C13×C22⋊C8—21no—
65C13×C22⋊C8C2×C412yescomplemented
66C13×#95—21no—
67C13×#95C2×C412yescomplemented
68#88071—24no—
69#88071—21no—
70#88071—21no—
71#88071—21no—
72#88071—21no—
73#88071C2×C412yescomplemented
74C22⋊#1055—21no—
75C22⋊#1055C2×C412yescomplemented
76C8×Dic13—42no—
77C4×#327—131nomaximal, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×D4×C13—22no—
81C2×D4×C13—22no—
82C2×D4×C13—21no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13C4212yescomplemented
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—21no—
93C22×C4×C13—22no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C22×C411yescharacteristic
102C22×C4×C13C22×C411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C22×Dic13—22no—
107C22×Dic13—22no—
108C22×Dic13—22no—
109C22×Dic13—22no—
110C22×Dic13—22no—
111C22×Dic13—21no—
112C22×Dic13—21no—
113C22×Dic13—22no—
114C22×Dic13—21no—
115C22×Dic13—21no—
116C22×Dic13—41no—
117C22×Dic13—41no—
118C22×Dic13—41no—
119C22×Dic13—41no—
120C22×Dic13—41no—
121C22×Dic13—42no—
122C22×Dic13—42no—
123C22×Dic13—42no—
124C22×Dic13C22⋊C411yescharacteristic
125C22×Dic13C22⋊C411yescharacteristic
126C22×Dic13C22⋊C411yescharacteristic
127C22×Dic13C22⋊C411yescharacteristic
128C22×Dic13D812yes—
129C22×Dic13SD1612yes—
130C2×C8×C13—22no—
131C2×C8×C13—41no—
132C2×C8×C13—41no—
133C13×C4⋊C4—21no—
134C13×C4⋊C4C4212yescomplemented
135C13×C22⋊C4—22no—
136C13×C22⋊C4—22no—
137C22⋊Dic13—42no—
138C22⋊Dic13—41no—
139C22⋊Dic13—41no—
140C22⋊Dic13—42no—
141C22⋊Dic13—42no—
142C4⋊Dic13—42no—
143C4⋊Dic13—41no—
144C4⋊Dic13—41no—
145C4×Dic13—22no—
146C4×Dic13—22no—
147C4×Dic13—41no—
148C4×Dic13—41no—
149C4×Dic13—48no—
150C4×Dic13—42no—
151C2×#1055—22no—
152C2×#1055—41no—
153C2×#1055—41no—
154C4×#121—131no—
155C4×C22⋊C8—131no—
156C2×#327—131no—
157C2×#327D1311yescharacteristic
158C4×#95—131no—
159#1294—131no—
160#1294—131no—
161C23×C13—21no—
162C23×C13—21no—
163C23×C13—21no—
164C23×C13—21no—
165C23×C13—22no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13C2×C22⋊C411yescharacteristic
173C23×C13C4×D411yescharacteristic
174C23×C13C4×D411yescharacteristic
175C23×C13C2×D811yescharacteristic
176C23×C13C2×SD1611yescharacteristic
177C23×C13#13511yescharacteristic
178C23×C13#13511yescharacteristic
179D4×C13—42no—
180D4×C13—42no—
181D4×C13—42no—
182D4×C13—42no—
183D4×C13—42no—
184D4×C13—42no—
185C2×C4×C13—21no—
186C2×C4×C13—21no—
187C2×C4×C13—21no—
188C2×C4×C13—21no—
189C2×C4×C13—24no—
190C2×C4×C13—22no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—41no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13—42no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—42no—
203C2×C4×C13C2×C4211yescharacteristic
204C2×C4×C13#11711yescharacteristic
205C2×C4×C13C4×D411yescharacteristic
206C2×C4×C13C4×D411yescharacteristic
207C2×Dic13—21no—
208C2×Dic13—21no—
209C2×Dic13—21no—
210C2×Dic13—21no—
211C2×Dic13—24no—
212C2×Dic13—24no—
213C2×Dic13—24no—
214C2×Dic13—21no—
215C2×Dic13—21no—
216C2×Dic13—21no—
217C2×Dic13—42no—
218C2×Dic13—42no—
219C2×Dic13—42no—
220C2×Dic13—42no—
221C2×Dic13—42no—
222C2×Dic13—42no—
223C2×Dic13—42no—
224C2×Dic13—42no—
225C2×Dic13—41no—
226C2×Dic13—41no—
227C2×Dic13—41no—
228C2×Dic13—41no—
229C2×Dic13—41no—
230C2×Dic13—41no—
231C2×Dic13—84no—
232C2×Dic13#9912yes—
233C2×Dic13#10212yes—
234C2×Dic13#10212yes—
235C2×Dic13#10412yes—
236C2×Dic13#10412yes—
237C8×C13—42no—
238#1055—42no—
239C2×#121C2×D1311yescharacteristic
240C2×C4×D4—131no—
241C2×C4×D4—261no—
242C22×C42—131no—
243C22×C42—261no—
244C2×C22⋊C8—131no—
245C2×C22⋊C8C2×D1311yescharacteristic
246C2×C4×C8—261no—
247#390—131no—
248#389—131no—
249#388—261no—
250#386—261no—
251#380—131no—
252C4×C4⋊C4—131no—
253C4×C22⋊C4—261no—
254C2×#95—131no—
255C2×#95—261no—
256C2×#95C2×D1311yescharacteristic
257#336—261no—
258#327—134no—
259#327Dic1314yesdirect product factor
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—21no—
271C22×C13—21no—
272C22×C13—42no—
273C22×C13—42no—
274C22×C13—42no—
275C22×C13—81no—
276C22×C13—81no—
277C22×C13—81no—
278C22×C13—81no—
279C22×C13C4×C22⋊C411yescharacteristic
280C22×C13C2×#9911yescharacteristic
281C22×C13#41011yescharacteristic
282C22×C13C2×#10211yescharacteristic
283C22×C13#41611yescharacteristic
284C22×C13C2×#10411yescharacteristic
285C22×C13C2×#10411yescharacteristic
286C22×C13C4×D811yescharacteristic
287C22×C13C4×D811yescharacteristic
288C22×C13C4×SD1611yescharacteristic
289C22×C13C4×SD1611yescharacteristic
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—44no—
295C4×C13—42no—
296Dic13—22no—
297Dic13—22no—
298Dic13—44no—
299Dic13—41no—
300Dic13—81no—
301Dic13—81no—
302Dic13#32714yesdirect product factor
303C22×D4—21no—
304C22×D4C4×D1311yescharacteristic
305C23×C4—21no—
306C23×C4—131no—
307C23×C4—131no—
308C23×C4—261no—
309C23×C4—261no—
310C23×C4C22×D1311yescharacteristic
311C22×C8—21no—
312C22×C8—261no—
313#121—21no—
314#121—21no—
315#121C4×D1312yes—
316#121C2×Dic1312yes—
317C4×D4—522no—
318C4×D4—522no—
319C4×D4—522no—
320C2×C4⋊C4—131no—
321C2×C4⋊C4—131no—
322C2×C4⋊C4—261no—
323C2×C4⋊C4C4×D1311yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—261no—
326C2×C22⋊C4—261no—
327C2×C22⋊C4—261no—
328C2×C22⋊C4—261no—
329C2×C42—131no—
330C2×C42—131no—
331C2×C42—131no—
332C2×C42—131no—
333C2×C42—261no—
334C2×C42—264no—
335C2×C42—522no—
336C2×C42—522no—
337C2×C42—522no—
338C22⋊C8—21no—
339C22⋊C8—132no—
340C22⋊C8—261no—
341C22⋊C8C2×Dic1312yescomplemented
342C4×C8—522no—
343#95—21no—
344#95—132no—
345#95—261no—
346#95—261no—
347#95—264no—
348#95—261no—
349#95—261no—
350#95C2×Dic1312yescomplemented
351C2×C13—21no—
352C2×C13—21no—
353C2×C13—21no—
354C2×C13—21no—
355C2×C13—82no—
356C2×C13C2×#32711yescharacteristic
357C2×C13#150011yescharacteristic
358C2×C13#150111yescharacteristic
359C2×C13#150211yescharacteristic
360C2×C13C4×#9911yescharacteristic
361C2×C13C4×#10411yescharacteristic
362C2×C13C4×#10211yescharacteristic
363C24—21no—
364C24D4×D1311yescharacteristic
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4C4×Dic1312yescomplemented
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—131no—
386C22×C4—131no—
387C22×C4—131no—
388C22×C4—132no—
389C22×C4—132no—
390C22×C4—131no—
391C22×C4—262no—
392C22×C4—262no—
393C22×C4—262no—
394C22×C4—262no—
395C22×C4—262no—
396C22×C4—262no—
397C22×C4—261no—
398C22×C4—261no—
399C22×C4—261no—
400C22×C4—261no—
401C22×C4—522no—
402C22×C4—522no—
403C22×C4—522no—
404C22×C4—521no—
405C22×C4—521no—
406C22×C4—521no—
407C22×C4—521no—
408C22×C4—521no—
409C22×C4C2×C4×D1311yescharacteristic
410C22×C4C2×C4×D1311yescharacteristic
411C22×C4D4×D1311yescharacteristic
412C22×C4#612911yescharacteristic
413C22×C4#612911yescharacteristic
414C22×C4C22×Dic1311yescharacteristic
415C2×C8—22no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—262no—
419C2×C8—521no—
420C2×C8—521no—
421C4⋊C4—21no—
422C4⋊C4—521no—
423C4⋊C4—521no—
424C4⋊C4—522no—
425C4⋊C4C4×Dic1312yescomplemented
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—522no—
429C22⋊C4—522no—
430C22⋊C4—522no—
431C22⋊C4—521no—
432C22⋊C4—521no—
433C42—262no—
434C42—262no—
435C42—521no—
436C42—521no—
437C42—522no—
438C42—528no—
439C13C4×#32711yescharacteristic, complemented, Sylow
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23C22⋊C4×D1311yescharacteristic
452C23#8813511yescharacteristic
453C23D8×D1311yescharacteristic
454C23#8816611yescharacteristic
455C23SD16×D1311yescharacteristic
456C23#8817011yescharacteristic
457C23D4×Dic1311yescharacteristic
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—42no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—132no—
483C2×C4—132no—
484C2×C4—132no—
485C2×C4—132no—
486C2×C4—132no—
487C2×C4—264no—
488C2×C4—264no—
489C2×C4—261no—
490C2×C4—261no—
491C2×C4—261no—
492C2×C4—261no—
493C2×C4—264no—
494C2×C4—261no—
495C2×C4—261no—
496C2×C4—261no—
497C2×C4—522no—
498C2×C4—522no—
499C2×C4—522no—
500C2×C4—522no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4—522no—
504C2×C4—522no—
505C2×C4—521no—
506C2×C4—521no—
507C2×C4—521no—
508C2×C4—521no—
509C2×C4—521no—
510C2×C4—521no—
511C2×C4—1044no—
512C2×C4#8813111yescharacteristic
513C2×C4#8813511yescharacteristic
514C2×C4C2×C4×Dic1311yescharacteristic
515C2×C4D4×Dic1311yescharacteristic
516C8—42no—
517C8—522no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#1171840111yescharacteristic
538C22D13×#9911yescharacteristic
539C22#1171841711yescharacteristic
540C22#1171841911yescharacteristic
541C22D13×#10211yescharacteristic
542C22#1171843311yescharacteristic
543C22D13×#10411yescharacteristic
544C22D13×#10411yescharacteristic
545C22C22⋊C4×Dic1311yescharacteristic
546C22D8×Dic1311yescharacteristic
547C22SD16×Dic1311yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—42no—
554C4—134no—
555C4—262no—
556C4—262no—
557C4—524no—
558C4—521no—
559C4—1041no—
560C4—1041no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—21no—
565C2—82no—
566C2D13×#32711yescharacteristic
567C2#1311331911yescharacteristic
568C2#1311332411yescharacteristic
569C2#1311332911yescharacteristic
570C2#99×Dic1311yescharacteristic
571C2#104×Dic1311yescharacteristic
572C2#102×Dic1311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#327C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenterC2×#327D13
hypocenterC13C4×#327
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×Dic13C2semidirect
4. #95×Dic13C2semidirect
5. #13112716C2semidirect
6. #13112715C2semidirect
10. C2×D4×Dic13C4semidirect
15. #11718882C4semidirect
22. #11718646C4semidirect
23. C4⋊C4×Dic13C4semidirect
26. C13×#327C4semidirect
28. #11718129C4semidirect
65. C13×C22⋊C8C2×C4semidirect
67. C13×#95C2×C4semidirect
73. #88071C2×C4semidirect
75. C22⋊#1055C2×C4semidirect
89. C2×D4×C13C42semidirect
134. C13×C4⋊C4C42semidirect
259. #327Dic13direct (N × H)
302. Dic13#327direct (N × H)
341. C22⋊C8C2×Dic13semidirect
350. #95C2×Dic13semidirect
374. C2×D4C4×Dic13semidirect
425. C4⋊C4C4×Dic13semidirect
439. C13C4×#327semidirect

Maximal subgroups

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

subgroupindex
#121×Dic132
C22⋊C8×Dic132
C2×#117181292
#95×Dic132
#131127162
#131127152
C2×C13×#3272
C4×#32713