Finite Group Databasebeta

← D13×#1763 #15860680

Subgroups — D13×#1763 #15860680

Order 3328.

1686 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D13C211yesmaximal, characteristic
2C2×D13×#103C212yesmaximal
3C2×D13×#97C211yesmaximal, characteristic
4C4×C4⋊C4×D13C211yesmaximal, characteristic
5#13114669C211yesmaximal, characteristic, complemented
6#13114668C212yesmaximal, complemented
7#13114667C211yesmaximal, characteristic, complemented
8#13114666C211yesmaximal, characteristic, complemented
9#13114665C212yesmaximal, complemented
10D13×#340C212yesmaximal
11C13×#1763C211yesmaximal, characteristic, complemented
12C22×Q8×D13C2211yescharacteristic
13C2×C4×Q8×C13C2211yescharacteristic
14C2×Q8×Dic13C2211yescharacteristic
15C22×C8×D13C2212yes—
16C4×Q8×D13—24no—
17C4×Q8×D13C418yescomplemented
18C2×C4⋊C4×D13—21no—
19C2×C4⋊C4×D13C2211yescharacteristic
20C2×C4⋊C4×D13C2212yes—
21C2×#88141—21no—
22C2×#88141C2211yescharacteristic
23C2×C42×D13—21no—
24C2×C42×D13—21no—
25C2×C42×D13C2211yescharacteristic
26C2×C4×Dic26—21no—
27C2×C4×Dic26C2211yescharacteristic
28C2×C13×#103C2212yes—
29C2×C13×#97C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C2×#88075C2212yes—
32C2×#88056C2212yes—
33C2×#88055C2212yes—
34C4⋊C4×Dic13C2212yes—
35C2×#88050C2212yes—
36C4×C4⋊Dic13C2211yescharacteristic
37C4×#6101—21no—
38C2×#88043C2211yescharacteristic
39D13×#103C4116yescomplemented
40D13×#97—24no—
41D13×#95—21no—
42#11718310—21no—
43C13×#340C2212yes—
44#11718143C2212yes—
45#11718121C2212yes—
46#11718121C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C2×Q8×D13—22no—
49C2×Q8×D13—24no—
50C2×Q8×D13C2×C418yes—
51C2×Q8×D13C2×C414yes—
52C22×C4×D13—21no—
53C22×C4×D13—21no—
54C22×C4×D13—22no—
55C22×C4×D13D411yescharacteristic
56C22×C4×D13D411yescharacteristic
57C22×C4×D13C2311yescharacteristic
58C22×Dic26—21no—
59C22×Dic26C2311yescharacteristic
60C22×C8×C13C2312yes—
61C4×Q8×C13—22no—
62C4×Q8×C13C2×C414yescomplemented
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4C2312yes—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C42×C13—21no—
67C2×C42×C13—21no—
68C2×C42×C13C2311yescharacteristic
69Q8×Dic13—22no—
70Q8×Dic13C2×C414yescomplemented
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13C2311yescharacteristic
73C2×C4⋊Dic13C2312yes—
74C2×#6101—21no—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×#6101—22no—
78C2×C4×Dic13—21no—
79C2×C4×Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—22no—
83C2×C4×Dic13D411yescharacteristic
84C2×C4×Dic13D411yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C22×#1055C2312yes—
87C2×C8×D13—24no—
88C2×C8×D13—24no—
89C2×C8×D13C2×C418yes—
90C4⋊C4×D13—28no—
91C4⋊C4×D13—22no—
92C4⋊C4×D13—24no—
93C4⋊C4×D13C2×C418yes—
94C4⋊C4×D13C2×C414yes—
95#88141—28no—
96#88141—22no—
97#88141C2×C414yescomplemented
98C42×D13—28no—
99C42×D13—44no—
100C42×D13C2×C414yes—
101C42×D13D414yes—
102C4×Dic26—22no—
103C4×Dic26—28no—
104C4×Dic26C2×C414yescomplemented
105C13×#103C2×C418yescomplemented
106C13×#97—22no—
107C13×#95—21no—
108#88075C2×C418yescomplemented
109#88071—21no—
110#88071—22no—
111#88056C2×C418yescomplemented
112#88055—24no—
113#88050C2×C418yescomplemented
114#88043—22no—
115C2×#1763—131nomaximal, Sylow
116C23×D13C2×D411yescharacteristic
117C2×Q8×C13—21no—
118C2×Q8×C13—22no—
119C2×Q8×C13C22×C414yes—
120C2×Q8×C13C22×C412yes—
121C22×C4×C13—21no—
122C22×C4×C13—22no—
123C22×C4×C13—21no—
124C22×C4×C13C2×D411yescharacteristic
125C22×C4×C13C2×D411yescharacteristic
126C22×C4×C13C2411yescharacteristic
127C22×Dic13—21no—
128C22×Dic13—22no—
129C22×Dic13—21no—
130C22×Dic13C2×D411yescharacteristic
131C22×Dic13C2×D411yescharacteristic
132C22×Dic13C2×D411yescharacteristic
133Q8×D13—28no—
134Q8×D13—216no—
135Q8×D13C42116yescomplemented
136C2×C4×D13—24no—
137C2×C4×D13—28no—
138C2×C4×D13—22no—
139C2×C4×D13—22no—
140C2×C4×D13—24no—
141C2×C4×D13—24no—
142C2×C4×D13—28no—
143C2×C4×D13—44no—
144C2×C4×D13—42no—
145C2×C4×D13—42no—
146C2×C4×D13—44no—
147C2×C4×D13C22⋊C414yes—
148C2×C4×D13C22⋊C414yes—
149C2×C4×D13C22×C412yes—
150C2×C4×D13C22×C414yes—
151C2×C4×D13C2×D412yes—
152C2×C4×D13#4114yes—
153C2×Dic26—21no—
154C2×Dic26—22no—
155C2×Dic26—24no—
156C2×Dic26—28no—
157C2×Dic26C22×C412yes—
158C2×Dic26C22×C414yes—
159C2×C8×C13—22no—
160C2×C8×C13—22no—
161C2×C8×C13C22×C414yes—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4C22×C414yes—
166C13×C4⋊C4C22×C412yes—
167C42×C13—24no—
168C42×C13—42no—
169C42×C13C22×C412yes—
170C42×C13C2×D412yes—
171C4⋊Dic13—21no—
172C4⋊Dic13—22no—
173C4⋊Dic13—24no—
174C4⋊Dic13C22×C414yes—
175C4⋊Dic13C22×C412yes—
176#6101—24no—
177#6101—24no—
178#6101—24no—
179#6101—28no—
180C4×Dic13—24no—
181C4×Dic13—24no—
182C4×Dic13—24no—
183C4×Dic13—44no—
184C4×Dic13—42no—
185C4×Dic13C22⋊C414yes—
186C4×Dic13C22⋊C414yes—
187C4×Dic13C22×C412yes—
188C4×Dic13C2×D412yes—
189C2×#1055—22no—
190C2×#1055—22no—
191C2×#1055C22×C414yes—
192C8×D13—216no—
193C22×C4×Q8—131no—
194C22×#103—132no—
195C22×#97—131no—
196C2×C4×C4⋊C4—131no—
197#1763—132no—
198#1763—131no—
199#1763—131no—
200#1763—132no—
201#1763—131no—
202#1763D1311yescharacteristic, direct product factor
203C2×#340—132no—
204C23×C13C22×D411yescharacteristic
205C22×D13C2×C22⋊C412yes—
206C22×D13C4×D414yes—
207C22×D13AGL(1,ℤ/8)12yes—
208C22×D13#13712yes—
209C22×D13#13714yes—
210Q8×C13—22no—
211Q8×C13—24no—
212Q8×C13C2×C4214yescomplemented
213C2×C4×C13—22no—
214C2×C4×C13—24no—
215C2×C4×C13—21no—
216C2×C4×C13—22no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—24no—
220C2×C4×C13—42no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—42no—
224C2×C4×C13C2×C22⋊C412yes—
225C2×C4×C13C2×C22⋊C412yes—
226C2×C4×C13C23×C411yescharacteristic
227C2×C4×C13C23×C412yes—
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C2×#4112yes—
230C2×Dic13—22no—
231C2×Dic13—24no—
232C2×Dic13—21no—
233C2×Dic13—22no—
234C2×Dic13—21no—
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—42no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—42no—
241C2×Dic13C2×C22⋊C412yes—
242C2×Dic13C2×C22⋊C412yes—
243C2×Dic13C2×C22⋊C412yes—
244C2×Dic13C4×D414yes—
245C4×D13—216no—
246C4×D13—28no—
247C4×D13—28no—
248C4×D13—48no—
249C4×D13—416no—
250C4×D13C2×C4214yes—
251C4×D13#11714yes—
252C4×D13C4×D418yes—
253Dic26—22no—
254Dic26—24no—
255Dic26—216no—
256Dic26C2×C4214yescomplemented
257C8×C13—24no—
258#1055—24no—
259C23×Q8—131no—
260C23×C8—132no—
261C2×C4×Q8—131no—
262C2×C4×Q8—138no—
263C2×C4×Q8—131no—
264C2×C4×Q8—131no—
265C2×C4×Q8—261no—
266C2×C4×Q8—261no—
267C2×C4×Q8—264no—
268C2×C4×Q8C2×D1311yescharacteristic
269C22×C4⋊C4—132no—
270C22×C4⋊C4—131no—
271C22×C4⋊C4—261no—
272C22×C42—131no—
273C22×C42—261no—
274C22×C42—261no—
275C2×#103—132no—
276C2×#103—132no—
277C2×#103—132no—
278C2×#103—1316no—
279C2×#103C2×D1312yes—
280C2×#97—132no—
281C2×#97—131no—
282C2×#97—264no—
283C2×#97C2×D1311yescharacteristic
284C4×C4⋊C4—132no—
285C4×C4⋊C4—131no—
286C4×C4⋊C4—261no—
287C4×C4⋊C4—261no—
288C4×C4⋊C4C2×D1311yescharacteristic
289C2×#95—261no—
290#340—132no—
291#340—132no—
292#340—132no—
293#340C2×D1312yes—
294C22×C13C22×C22⋊C411yescharacteristic
295C22×C13C2×C4×D412yes—
296C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C13C2×#13712yes—
298C22×C13C2×#13711yescharacteristic
299C2×D13C4×C22⋊C414yes—
300C2×D13#41714yes—
301C2×D13#41914yes—
302C2×D13#44018yes—
303C2×D13#44118yes—
304C4×C13—22no—
305C4×C13—22no—
306C4×C13—24no—
307C4×C13—42no—
308C4×C13—44no—
309C4×C13C22×C4211yescharacteristic
310C4×C13C2×#11711yescharacteristic
311C4×C13C2×C4×D412yes—
312Dic13—22no—
313Dic13—22no—
314Dic13—24no—
315Dic13—42no—
316Dic13—44no—
317Dic13C4×C22⋊C414yes—
318C22×Q8—134no—
319C22×Q8—138no—
320C22×Q8—131no—
321C22×Q8—261no—
322C22×Q8—262no—
323C22×Q8—264no—
324C22×Q8C22×D1311yescharacteristic
325C23×C4—131no—
326C23×C4—131no—
327C23×C4—131no—
328C23×C4—261no—
329C23×C4—261no—
330C23×C4—262no—
331C22×C8—132no—
332C22×C8—138no—
333C22×C8—264no—
334C22×C8—264no—
335C22×C8C22×D1312yes—
336C4×Q8—22no—
337C4×Q8—134no—
338C4×Q8—134no—
339C4×Q8—134no—
340C4×Q8—268no—
341C4×Q8—268no—
342C4×Q8—262no—
343C4×Q8—262no—
344C4×Q8—262no—
345C4×Q8C4×D1314yescomplemented
346C2×C4⋊C4—21no—
347C2×C4⋊C4—131no—
348C2×C4⋊C4—132no—
349C2×C4⋊C4—134no—
350C2×C4⋊C4—138no—
351C2×C4⋊C4—262no—
352C2×C4⋊C4—264no—
353C2×C4⋊C4—268no—
354C2×C4⋊C4—261no—
355C2×C4⋊C4—262no—
356C2×C4⋊C4—261no—
357C2×C4⋊C4—261no—
358C2×C4⋊C4—261no—
359C2×C4⋊C4C22×D1311yescharacteristic
360C2×C4⋊C4C22×D1312yes—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—131no—
364C2×C42—131no—
365C2×C42—131no—
366C2×C42—134no—
367C2×C42—134no—
368C2×C42—268no—
369C2×C42—261no—
370C2×C42—261no—
371C2×C42—261no—
372C2×C42—262no—
373C2×C42—261no—
374C2×C42—524no—
375C2×C42C22×D1311yescharacteristic
376#103—138no—
377#103—138no—
378#103—138no—
379#103C4×D1318yescomplemented
380#97—22no—
381#97—264no—
382#97—262no—
383#95—21no—
384#95—262no—
385#95—261no—
386C2×C13C2×C4×C22⋊C411yescharacteristic
387C2×C13C2×#41911yescharacteristic
388C2×C13C2×#41711yescharacteristic
389C2×C13C2×#44012yes—
390C2×C13C2×#44112yes—
391D13#176318yesdirect product factor
392C24—131no—
393C2×Q8—21no—
394C2×Q8—22no—
395C2×Q8—1316no—
396C2×Q8—134no—
397C2×Q8—132no—
398C2×Q8—264no—
399C2×Q8—268no—
400C2×Q8—268no—
401C2×Q8—2616no—
402C2×Q8—261no—
403C2×Q8—262no—
404C2×Q8C2×C4×D1314yes—
405C2×Q8C2×C4×D1312yes—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—131no—
410C22×C4—132no—
411C22×C4—134no—
412C22×C4—132no—
413C22×C4—134no—
414C22×C4—131no—
415C22×C4—131no—
416C22×C4—134no—
417C22×C4—134no—
418C22×C4—264no—
419C22×C4—262no—
420C22×C4—262no—
421C22×C4—264no—
422C22×C4—268no—
423C22×C4—264no—
424C22×C4—268no—
425C22×C4—261no—
426C22×C4—262no—
427C22×C4—261no—
428C22×C4—524no—
429C22×C4—522no—
430C22×C4—522no—
431C22×C4—524no—
432C22×C4D4×D1311yescharacteristic
433C22×C4D4×D1311yescharacteristic
434C22×C4C23×D1311yescharacteristic
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—134no—
438C2×C8—2616no—
439C2×C8—262no—
440C2×C8—262no—
441C2×C8C2×C4×D1314yes—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—134no—
446C4⋊C4—132no—
447C4⋊C4—264no—
448C4⋊C4—268no—
449C4⋊C4—264no—
450C4⋊C4—264no—
451C4⋊C4—264no—
452C4⋊C4—261no—
453C4⋊C4—262no—
454C4⋊C4C2×C4×D1314yes—
455C4⋊C4C2×C4×D1312yes—
456C42—24no—
457C42—42no—
458C42—134no—
459C42—134no—
460C42—132no—
461C42—132no—
462C42—264no—
463C42—264no—
464C42—264no—
465C42—522no—
466C42—524no—
467C42C2×C4×D1312yes—
468C42D4×D1312yes—
469C13C2×#176311yescharacteristic, complemented, Sylow
470C23—132no—
471C23—132no—
472C23—134no—
473C23—132no—
474C23—134no—
475C23C2×D4×D1311yescharacteristic
476Q8—22no—
477Q8—24no—
478Q8—134no—
479Q8—2616no—
480Q8—262no—
481Q8—264no—
482Q8C42×D1314yescomplemented
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—24no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—132no—
495C2×C4—134no—
496C2×C4—134no—
497C2×C4—134no—
498C2×C4—138no—
499C2×C4—132no—
500C2×C4—132no—
501C2×C4—268no—
502C2×C4—268no—
503C2×C4—2616no—
504C2×C4—262no—
505C2×C4—261no—
506C2×C4—262no—
507C2×C4—261no—
508C2×C4—264no—
509C2×C4—262no—
510C2×C4—264no—
511C2×C4—528no—
512C2×C4—5216no—
513C2×C4—522no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—522no—
517C2×C4C22⋊C4×D1312yes—
518C2×C4C22⋊C4×D1312yes—
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C22×C4×D1312yes—
521C2×C4C2×D4×D1311yescharacteristic
522C2×C4#41×D1312yes—
523C8—24no—
524C8—264no—
525C22—134no—
526C22—134no—
527C22—138no—
528C22—138no—
529C22—134no—
530C22C2×C22⋊C4×D1311yescharacteristic
531C22C4×D4×D1312yes—
532C22D13×AGL(1,ℤ/8)11yescharacteristic
533C22D13×#13712yes—
534C22D13×#13711yescharacteristic
535C4—22no—
536C4—22no—
537C4—24no—
538C4—42no—
539C4—44no—
540C4—134no—
541C4—262no—
542C4—262no—
543C4—264no—
544C4—522no—
545C4—524no—
546C4C2×C42×D1311yescharacteristic
547C4D13×#11711yescharacteristic
548C4C4×D4×D1312yes—
549C2—138no—
550C2C4×C22⋊C4×D1311yescharacteristic
551C2D13×#41911yescharacteristic
552C2D13×#41711yescharacteristic
553C2D13×#44012yes—
554C2D13×#44112yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1763C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1763D13
hypocenterC13C2×#1763
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
5. #13114669C2semidirect
6. #13114668C2semidirect
7. #13114667C2semidirect
8. #13114666C2semidirect
9. #13114665C2semidirect
11. C13×#1763C2semidirect
17. C4×Q8×D13C4semidirect
39. D13×#103C4semidirect
62. C4×Q8×C13C2×C4semidirect
70. Q8×Dic13C2×C4semidirect
97. #88141C2×C4semidirect
104. C4×Dic26C2×C4semidirect
105. C13×#103C2×C4semidirect
108. #88075C2×C4semidirect
111. #88056C2×C4semidirect
113. #88050C2×C4semidirect
135. Q8×D13C42semidirect
202. #1763D13direct (N × H)
212. Q8×C13C2×C42semidirect
256. Dic26C2×C42semidirect
345. C4×Q8C4×D13semidirect
379. #103C4×D13semidirect
391. D13#1763direct (N × H)
469. C13C2×#1763semidirect
482. Q8C42×D13semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D132
C2×D13×#1032
C2×D13×#972
C4×C4⋊C4×D132
#131146692
#131146682
#131146672
#131146662
#131146652
D13×#3402
C13×#17632
C2×#176313