Finite Group Databasebeta

← D13×#2076 #15891751

Subgroups — D13×#2076 #15891751

Order 3328.

1270 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#107C211yesmaximal, characteristic, complemented
2C2×D13×C22⋊C8C211yesmaximal, characteristic
3D13×#380C212yesmaximal
4#13116268C212yesmaximal, complemented
5#13116267C212yesmaximal, complemented
6#13116266C211yesmaximal, characteristic, complemented
7#13116265C211yesmaximal, characteristic, complemented
8#13116264C211yesmaximal, characteristic, complemented
9D13×#340C212yesmaximal, complemented
10D13×#340C211yesmaximal, characteristic, complemented
11C13×#2076C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C8×D13C2211yescharacteristic
14C22×C8×D13C2211yescharacteristic
15C2×C4⋊C4×D13C2212yes—
16C2×C4⋊C4×D13C2212yes—
17C2×C22⋊C4×D13—22no—
18C2×C13×#107C2211yescharacteristic, complemented
19C2×C13×C22⋊C8C2211yescharacteristic
20C13×#380C2212yes—
21#11718873C2212yes—
22C2×C22⋊#1055C2211yescharacteristic
23C2×#88060C2211yescharacteristic
24C2×#88060C2211yescharacteristic
25C2×#88058C2211yescharacteristic, complemented
26#11718648C2212yes—
27#11718648C2212yes—
28C2×#88047C2212yescomplemented
29#11718603—22no—
30D13×#107—24no—
31D13×C22⋊C8—24no—
32#11718328—22no—
33D13×#95—22no—
34C13×#340C2211yescharacteristic, complemented
35C13×#340C2212yescomplemented
36#11718143C2211yescharacteristic, complemented
37#11718143C2212yescomplemented
38#11718121C2212yescomplemented
39#11718121C2212yescomplemented
40#11718121C2212yescomplemented
41C24×D13D411yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×Dic13D411yescharacteristic
44C22×C4×D13—22no—
45C22×C4×D13—22no—
46C22×C4×D13—24no—
47C22×C4×D13—24no—
48C22×C4×D13—22no—
49C22×C4×D13—22no—
50C22×C4×D13D411yescharacteristic
51C22×C4×D13D411yescharacteristic
52C22×C4×D13C2311yescharacteristic
53C22×C4×D13C2311yescharacteristic
54C22×C8×C13C2311yescharacteristic
55C22×C8×C13C2311yescharacteristic
56C2×C13×C4⋊C4C2312yes—
57C2×C13×C4⋊C4C2312yes—
58C2×C13×C22⋊C4—22no—
59C2×C22⋊Dic13—22no—
60C2×#6103—22no—
61C2×#6103—22no—
62C2×C4⋊Dic13C2312yes—
63C2×C4⋊Dic13C2312yes—
64C2×#6101—22no—
65C2×#6101—22no—
66C22×#1055C2311yescharacteristic
67C22×#1055C2311yescharacteristic
68C2×C8×D13—24no—
69C2×C8×D13—22no—
70C2×C8×D13—24no—
71C2×C8×D13D414yes—
72C4⋊C4×D13—24no—
73C4⋊C4×D13—24no—
74C4⋊C4×D13—24no—
75C4⋊C4×D13—24no—
76C22⋊C4×D13—48no—
77C13×#107—22no—
78C13×C22⋊C8—22no—
79C13×#95—22no—
80#88071—22no—
81#88071—22no—
82#88071—22no—
83C22⋊#1055—22no—
84#88060—22no—
85#88060—22no—
86#88058—22no—
87#88047—24no—
88C2×#2076—131nomaximal, Sylow
89C24×C13C2×D411yescharacteristic
90C23×D13—22no—
91C23×D13—24no—
92C23×D13—22no—
93C23×D13—24no—
94C23×D13Q1614yes—
95C23×D13C2×D411yescharacteristic
96C23×D13C2×D411yescharacteristic
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—22no—
100C22×C4×C13—22no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2411yescharacteristic
105C22×Dic13—22no—
106C22×Dic13—24no—
107C22×Dic13—22no—
108C22×Dic13—22no—
109C22×Dic13C2×D411yescharacteristic
110C22×Dic13C2×D411yescharacteristic
111C2×C4×D13—22no—
112C2×C4×D13—24no—
113C2×C4×D13—21no—
114C2×C4×D13—22no—
115C2×C4×D13—22no—
116C2×C4×D13—21no—
117C2×C4×D13—22no—
118C2×C4×D13—24no—
119C2×C4×D13—44no—
120C2×C4×D13—44no—
121C2×C4×D13—48no—
122C2×C4×D13—44no—
123C2×C4×D13—44no—
124C2×C4×D13—44no—
125C2×C4×D13—44no—
126C2×C4×D13—44no—
127C2×C4×D13—44no—
128C2×C4×D13C2×D412yes—
129C2×C4×D13#4114yes—
130C2×C4×D13#4114yes—
131C2×C4×D13#4112yes—
132C2×C8×C13—22no—
133C2×C8×C13—21no—
134C2×C8×C13—22no—
135C2×C8×C13C2×D412yes—
136C13×C4⋊C4—22no—
137C13×C4⋊C4—22no—
138C13×C4⋊C4—22no—
139C13×C4⋊C4—22no—
140C13×C22⋊C4—44no—
141C22⋊Dic13—44no—
142#6103—44no—
143#6103—44no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146C4⋊Dic13—22no—
147C4⋊Dic13—22no—
148#6101—44no—
149#6101—44no—
150C2×#1055—22no—
151C2×#1055—21no—
152C2×#1055—22no—
153C2×#1055C2×D412yes—
154C8×D13—28no—
155C8×D13—44no—
156C22×#107—131no—
157C22×C22⋊C8—131no—
158C2×#380—132no—
159#2076—131no—
160#2076—131no—
161#2076—132no—
162#2076—131no—
163#2076—132no—
164#2076D1311yescharacteristic, direct product factor
165C2×#340—132no—
166C2×#340—131no—
167C23×C13—21no—
168C23×C13—22no—
169C23×C13—21no—
170C23×C13—22no—
171C23×C13C2×Q1612yes—
172C23×C13C22×D411yescharacteristic
173C22×D13—21no—
174C22×D13—22no—
175C22×D13—21no—
176C22×D13—22no—
177C22×D13—28no—
178C22×D13—216no—
179C22×D13—44no—
180C22×D13—44no—
181C22×D13—48no—
182C22×D13#12112yes—
183C22×D13#12314yes—
184C22×D13C2×Q1612yes—
185C22×D13C2×Q1612yes—
186C22×D13#13512yes—
187C22×D13AGL(1,ℤ/8)14yes—
188C2×C4×C13—21no—
189C2×C4×C13—22no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—42no—
196C2×C4×C13—42no—
197C2×C4×C13—42no—
198C2×C4×C13—42no—
199C2×C4×C13C22×D411yescharacteristic
200C2×C4×C13C2×#4112yes—
201C2×C4×C13C2×#4112yes—
202C2×C4×C13C2×#4111yescharacteristic
203C2×Dic13—21no—
204C2×Dic13—22no—
205C2×Dic13—44no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13—42no—
209C2×Dic13—42no—
210C2×Dic13—42no—
211C2×Dic13—42no—
212C2×Dic13#12112yes—
213C2×Dic13#12314yes—
214C4×D13—44no—
215C4×D13—41no—
216C4×D13—41no—
217C4×D13—42no—
218C4×D13—44no—
219C4×D13—88no—
220C4×D13—88no—
221C4×D13#12314yes—
222C4×D13#12414yes—
223C4×D13#12618yes—
224C8×C13—22no—
225C8×C13—41no—
226#1055—22no—
227#1055—41no—
228C24×C4—131no—
229C23×C8—131no—
230C23×C8—131no—
231C22×C4⋊C4—132no—
232C22×C4⋊C4—132no—
233C22×C22⋊C4—262no—
234C2×#107—131no—
235C2×#107—132no—
236C2×#107—264no—
237C2×#107C2×D1311yescharacteristic, complemented
238C2×C22⋊C8—131no—
239C2×C22⋊C8—131no—
240C2×C22⋊C8—131no—
241C2×C22⋊C8—264no—
242C2×C22⋊C8C2×D1311yescharacteristic
243#380—132no—
244#380—132no—
245#380—132no—
246#380—262no—
247#380—262no—
248#380C2×D1312yes—
249C2×#95—262no—
250#340—131no—
251#340—132no—
252#340—132no—
253#340—132no—
254#340—132no—
255#340C2×D1311yescharacteristic, complemented
256#340C2×D1312yescomplemented
257C22×C13—24no—
258C22×C13—22no—
259C22×C13—42no—
260C22×C13—41no—
261C22×C13—41no—
262C22×C13C2×#12111yescharacteristic
263C22×C13C2×#12312yes—
264C22×C13C22×Q1611yescharacteristic
265C22×C13C2×#13511yescharacteristic
266C22×C13C2×AGL(1,ℤ/8)12yes—
267C2×D13—24no—
268C2×D13—22no—
269C2×D13—42no—
270C2×D13—41no—
271C2×D13—41no—
272C2×D13—416no—
273C2×D13#39714yes—
274C2×D13#46714yes—
275C2×D13#46914yes—
276C2×D13#48218yes—
277C2×D13#48418yes—
278C4×C13—41no—
279C4×C13—82no—
280C4×C13—82no—
281C4×C13C2×#12311yescharacteristic
282C4×C13C2×#12411yescharacteristic
283C4×C13C2×#12612yes—
284Dic13—41no—
285Dic13—82no—
286Dic13—82no—
287Dic13#39714yes—
288C25—131no—
289C23×C4—131no—
290C23×C4—131no—
291C23×C4—131no—
292C23×C4—131no—
293C23×C4—131no—
294C23×C4—262no—
295C23×C4—262no—
296C23×C4—264no—
297C23×C4—264no—
298C23×C4—262no—
299C23×C4—262no—
300C23×C4C22×D1311yescharacteristic
301C22×C8—131no—
302C22×C8—134no—
303C22×C8—131no—
304C22×C8—264no—
305C22×C8—264no—
306C22×C8—262no—
307C22×C8C22×D1311yescharacteristic
308C22×C8C22×D1311yescharacteristic
309C2×C4⋊C4—132no—
310C2×C4⋊C4—132no—
311C2×C4⋊C4—264no—
312C2×C4⋊C4—264no—
313C2×C4⋊C4—264no—
314C2×C4⋊C4—264no—
315C2×C4⋊C4—262no—
316C2×C4⋊C4—262no—
317C2×C4⋊C4C22×D1312yes—
318C2×C4⋊C4C22×D1312yes—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—262no—
321C2×C22⋊C4—262no—
322C2×C22⋊C4—262no—
323C2×C22⋊C4—528no—
324#107—22no—
325#107—264no—
326#107—262no—
327C22⋊C8—22no—
328C22⋊C8—262no—
329C22⋊C8—262no—
330C22⋊C8—262no—
331#95—22no—
332#95—262no—
333#95—262no—
334#95—262no—
335C2×C13—42no—
336C2×C13C2×#39711yescharacteristic
337C2×C13C2×#46711yescharacteristic
338C2×C13C2×#46911yescharacteristic
339C2×C13C2×#48212yes—
340C2×C13C2×#48412yes—
341D13—42no—
342D13#207618yesdirect product factor
343C24—131no—
344C24—134no—
345C24—131no—
346C24—264no—
347C24—262no—
348C24—264no—
349C24—262no—
350C24D4×D1311yescharacteristic
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—131no—
358C22×C4—132no—
359C22×C4—132no—
360C22×C4—134no—
361C22×C4—134no—
362C22×C4—131no—
363C22×C4—262no—
364C22×C4—264no—
365C22×C4—262no—
366C22×C4—264no—
367C22×C4—262no—
368C22×C4—264no—
369C22×C4—261no—
370C22×C4—261no—
371C22×C4—262no—
372C22×C4—262no—
373C22×C4—262no—
374C22×C4—262no—
375C22×C4—524no—
376C22×C4—524no—
377C22×C4—528no—
378C22×C4—524no—
379C22×C4—524no—
380C22×C4—524no—
381C22×C4—524no—
382C22×C4—524no—
383C22×C4—524no—
384C22×C4D4×D1311yescharacteristic
385C22×C4C23×D1311yescharacteristic
386C2×C8—22no—
387C2×C8—21no—
388C2×C8—22no—
389C2×C8—132no—
390C2×C8—268no—
391C2×C8—262no—
392C2×C8—261no—
393C2×C8—262no—
394C2×C8—524no—
395C2×C8D4×D1312yes—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—262no—
401C4⋊C4—262no—
402C4⋊C4—262no—
403C4⋊C4—262no—
404C4⋊C4—524no—
405C4⋊C4—524no—
406C22⋊C4—44no—
407C22⋊C4—524no—
408C22⋊C4—524no—
409C22⋊C4—524no—
410C13C2×#207611yescharacteristic, complemented, Sylow
411C23—21no—
412C23—22no—
413C23—21no—
414C23—22no—
415C23—132no—
416C23—132no—
417C23—134no—
418C23—132no—
419C23—134no—
420C23—132no—
421C23—268no—
422C23—2616no—
423C23—261no—
424C23—262no—
425C23—261no—
426C23—262no—
427C23—524no—
428C23—524no—
429C23—528no—
430C23Q16×D1312yes—
431C23C2×D4×D1311yescharacteristic
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—132no—
444C2×C4—134no—
445C2×C4—134no—
446C2×C4—134no—
447C2×C4—138no—
448C2×C4—261no—
449C2×C4—262no—
450C2×C4—524no—
451C2×C4—524no—
452C2×C4—524no—
453C2×C4—521no—
454C2×C4—521no—
455C2×C4—522no—
456C2×C4—522no—
457C2×C4—522no—
458C2×C4—522no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—522no—
462C2×C4—1048no—
463C2×C4—1048no—
464C2×C4C2×D4×D1311yescharacteristic
465C2×C4#41×D1312yes—
466C2×C4#41×D1312yes—
467C2×C4#41×D1311yescharacteristic
468C8—22no—
469C8—41no—
470C8—262no—
471C8—521no—
472C22—22no—
473C22—24no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22—134no—
478C22—134no—
479C22—134no—
480C22—138no—
481C22—138no—
482C22—262no—
483C22—264no—
484C22—5216no—
485C22—521no—
486C22—521no—
487C22—522no—
488C22D13×#12111yescharacteristic
489C22D13×#12312yes—
490C22C2×Q16×D1311yescharacteristic
491C22D13×#13511yescharacteristic
492C22D13×AGL(1,ℤ/8)12yes—
493C4—41no—
494C4—82no—
495C4—82no—
496C4—134no—
497C4—521no—
498C4—1042no—
499C4—1042no—
500C4D13×#12311yescharacteristic
501C4D13×#12411yescharacteristic
502C4D13×#12612yes—
503C2—42no—
504C2—138no—
505C2—522no—
506C2D13×#39711yescharacteristic
507C2D13×#46711yescharacteristic
508C2D13×#46911yescharacteristic
509C2D13×#48212yes—
510C2D13×#48412yes—
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2076C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenter#2076D13
hypocenterC13C2×#2076
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2076

Complements

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

NH ≅ G/Ntype
1. C2×D13×#107C2semidirect
4. #13116268C2semidirect
5. #13116267C2semidirect
6. #13116266C2semidirect
7. #13116265C2semidirect
8. #13116264C2semidirect
9. D13×#340C2semidirect
10. D13×#340C2semidirect
11. C13×#2076C2semidirect
18. C2×C13×#107C22semidirect
25. C2×#88058C22semidirect
28. C2×#88047C22semidirect
34. C13×#340C22semidirect
35. C13×#340C22semidirect
36. #11718143C22semidirect
37. #11718143C22semidirect
38. #11718121C22semidirect
39. #11718121C22semidirect
40. #11718121C22semidirect
164. #2076D13direct (N × H)
237. C2×#107C2×D13semidirect
255. #340C2×D13semidirect
256. #340C2×D13semidirect
342. D13#2076direct (N × H)
410. C13C2×#2076semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1072
C2×D13×C22⋊C82
D13×#3802
#131162682
#131162672
#131162662
#131162652
#131162642
D13×#3402
C13×#20762
C2×#207613