Finite Group Databasebeta

← D13×#1824 #15862702

Subgroups — D13×#1824 #15862702

Order 3328.

1878 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C2×D13×C22⋊C8C211yesmaximal, characteristic
3D13×#380C211yesmaximal, characteristic
4#13114927C211yesmaximal, characteristic, complemented
5#13114926C211yesmaximal, characteristic, complemented
6#13114925C214yesmaximal, complemented
7#13114924C211yesmaximal, characteristic, complemented
8D13×#340C214yesmaximal, complemented
9C13×#1824C211yesmaximal, characteristic, complemented
10C23×C4×D13—21no—
11C23×C4×D13C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic13C2211yescharacteristic
14C22×#6101—21no—
15C22×C8×D13C2212yes—
16C2×C4⋊C4×D13—21no—
17C2×C4⋊C4×D13—21no—
18C2×C4⋊C4×D13—24no—
19C2×C4⋊C4×D13C418yescomplemented
20C2×C4⋊C4×D13C2212yes—
21C2×C4⋊C4×D13C2212yes—
22C2×C4⋊C4×D13C2212yes—
23C2×C22⋊C4×D13—21no—
24C2×C13×C22⋊C8C2211yescharacteristic
25C13×#380C2211yescharacteristic
26#11718873C2211yescharacteristic
27C2×C22⋊#1055C2211yescharacteristic
28C2×#88060C2212yes—
29#11718648C2212yes—
30#11718603—21no—
31D13×C22⋊C8—24no—
32#11718328—21no—
33D13×#95—21no—
34C13×#340C2214yescomplemented
35#11718143C2214yescomplemented
36#11718121C2214yescomplemented
37#11718121C2214yescomplemented
38C24×D13D411yescharacteristic
39C23×C4×C13—21no—
40C23×C4×C13C2311yescharacteristic
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C22×C4×D13—28no—
44C22×C4×D13—28no—
45C22×C4×D13—22no—
46C22×C4×D13—22no—
47C22×C4×D13—22no—
48C22×C4×D13—48no—
49C22×C4×D13C2×C414yes—
50C22×C4×D13D411yescharacteristic
51C22×C4×D13D411yescharacteristic
52C22×C4×D13D414yes—
53C22×C4×D13C2311yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×C8×C13C2312yes—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—22no—
58C2×C13×C4⋊C4C2×C414yescomplemented
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C22⋊C4—21no—
62C2×C22⋊Dic13—21no—
63C2×#6103—22no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13—22no—
66C2×C4⋊Dic13C2×C414yescomplemented
67C2×C4⋊Dic13C2312yes—
68C2×C4⋊Dic13C2312yes—
69C2×#6101—28no—
70C2×#6101—22no—
71C2×#6101—22no—
72C2×#6101—22no—
73C22×#1055C2312yes—
74C2×C8×D13—24no—
75C2×C8×D13—28no—
76C4⋊C4×D13—28no—
77C4⋊C4×D13—28no—
78C4⋊C4×D13—24no—
79C4⋊C4×D13—24no—
80C4⋊C4×D13—28no—
81C4⋊C4×D13C2×C418yes—
82C4⋊C4×D13C2×C418yescomplemented
83C22⋊C4×D13—44no—
84C13×C22⋊C8—22no—
85C13×#95—21no—
86#88071—21no—
87#88071—22no—
88C22⋊#1055—22no—
89#88060—24no—
90C2×#1824—131nomaximal, Sylow
91C24×C13C2×D411yescharacteristic
92C23×D13—24no—
93C23×D13—24no—
94C23×D13C22⋊C414yes—
95C23×D13SD1614yes—
96C23×D13Q1614yes—
97C23×D13C2×D411yescharacteristic
98C23×D13C2×D411yescharacteristic
99C22×C4×C13—24no—
100C22×C4×C13—24no—
101C22×C4×C13—22no—
102C22×C4×C13—22no—
103C22×C4×C13—44no—
104C22×C4×C13C22×C412yes—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D412yes—
107C22×C4×C13C2411yescharacteristic
108C22×Dic13—24no—
109C22×Dic13—24no—
110C22×Dic13—22no—
111C22×Dic13—22no—
112C22×Dic13—44no—
113C22×Dic13C22⋊C414yes—
114C22×Dic13C2×D411yescharacteristic
115C22×Dic13C2×D411yescharacteristic
116C2×C4×D13—24no—
117C2×C4×D13—24no—
118C2×C4×D13—24no—
119C2×C4×D13—216no—
120C2×C4×D13—216no—
121C2×C4×D13—28no—
122C2×C4×D13—28no—
123C2×C4×D13—48no—
124C2×C4×D13—432no—
125C2×C4×D13—48no—
126C2×C4×D13—44no—
127C2×C4×D13—44no—
128C2×C4×D13—44no—
129C2×C4×D13C22⋊C414yes—
130C2×C4×D13C22⋊C414yes—
131C2×C4×D13C22×C412yes—
132C2×C4×D13C22×C412yes—
133C2×C4×D13C2×D412yes—
134C2×C4×D13C2×D412yes—
135C2×C4×D13#4118yes—
136C2×C8×C13—22no—
137C2×C8×C13—24no—
138C13×C4⋊C4—24no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—24no—
141C13×C4⋊C4C22×C414yes—
142C13×C22⋊C4—42no—
143C22⋊Dic13—42no—
144#6103—44no—
145C4⋊Dic13—24no—
146C4⋊Dic13—22no—
147C4⋊Dic13—24no—
148C4⋊Dic13C22×C414yes—
149#6101—28no—
150#6101—28no—
151#6101—44no—
152C2×#1055—22no—
153C2×#1055—24no—
154C8×D13—48no—
155C23×C4⋊C4—131no—
156C22×C22⋊C8—131no—
157C2×#380—131no—
158#1824—131no—
159#1824—131no—
160#1824—134no—
161#1824—131no—
162#1824D1311yescharacteristic, direct product factor
163C2×#340—134no—
164C23×C13—22no—
165C23×C13—22no—
166C23×C13C2×C22⋊C412yes—
167C23×C13C2×SD1612yes—
168C23×C13C2×Q1612yes—
169C23×C13C22×D411yescharacteristic
170C22×D13—22no—
171C22×D13—22no—
172C22×D13—28no—
173C22×D13—28no—
174C22×D13—216no—
175C22×D13—216no—
176C22×D13#103116yes—
177C22×D13C2×C22⋊C412yes—
178C22×D13C2×C22⋊C412yes—
179C22×D13#12314yes—
180C22×D13C2×SD1612yes—
181C22×D13C2×SD1612yes—
182C22×D13C2×Q1612yes—
183C22×D13C2×Q1612yes—
184C22×D13AGL(1,ℤ/8)14yes—
185C2×C4×C13—22no—
186C2×C4×C13—24no—
187C2×C4×C13—24no—
188C2×C4×C13—24no—
189C2×C4×C13—48no—
190C2×C4×C13—44no—
191C2×C4×C13—42no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13C2×C22⋊C412yes—
195C2×C4×C13C23×C411yescharacteristic
196C2×C4×C13C22×D411yescharacteristic
197C2×C4×C13C2×#4114yes—
198C2×Dic13—22no—
199C2×Dic13—28no—
200C2×Dic13—24no—
201C2×Dic13—48no—
202C2×Dic13—44no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205C2×Dic13—42no—
206C2×Dic13C2×C22⋊C412yes—
207C2×Dic13C2×C22⋊C412yes—
208C2×Dic13#12314yes—
209C4×D13—28no—
210C4×D13—24no—
211C4×D13—24no—
212C4×D13—28no—
213C4×D13—416no—
214C4×D13—416no—
215C4×D13—88no—
216C4×D13#11718yes—
217C4×D13#12318yes—
218C8×C13—42no—
219#1055—42no—
220C24×C4—131no—
221C24×C4—261no—
222C23×C8—132no—
223C22×C4⋊C4—131no—
224C22×C4⋊C4—138no—
225C22×C4⋊C4—132no—
226C22×C4⋊C4—132no—
227C22×C4⋊C4—132no—
228C22×C4⋊C4—261no—
229C22×C4⋊C4—261no—
230C22×C4⋊C4—264no—
231C22×C4⋊C4—261no—
232C22×C4⋊C4C2×D1311yescharacteristic
233C22×C22⋊C4—261no—
234C2×C22⋊C8—131no—
235C2×C22⋊C8—132no—
236C2×C22⋊C8—264no—
237C2×C22⋊C8C2×D1311yescharacteristic
238#380—131no—
239#380—132no—
240#380—261no—
241#380—261no—
242#380C2×D1311yescharacteristic
243C2×#95—261no—
244#340—134no—
245#340—134no—
246#340—134no—
247#340C2×D1314yescomplemented
248C22×C13—24no—
249C22×C13—24no—
250C22×C13—22no—
251C22×C13—22no—
252C22×C13C2×#10314yes—
253C22×C13C22×C22⋊C411yescharacteristic
254C22×C13C2×#12312yes—
255C22×C13C22×SD1611yescharacteristic
256C22×C13C22×Q1611yescharacteristic
257C22×C13C2×AGL(1,ℤ/8)12yes—
258C2×D13—24no—
259C2×D13—24no—
260C2×D13—22no—
261C2×D13—22no—
262C2×D13—232no—
263C2×D13#38114yes—
264C2×D13C2×#10314yes—
265C2×D13C2×#10314yes—
266C2×D13#41814yes—
267C2×D13#48118yes—
268C2×D13#48418yes—
269C4×C13—22no—
270C4×C13—44no—
271C4×C13—82no—
272C4×C13C2×#11712yes—
273C4×C13C2×#12312yes—
274Dic13—22no—
275Dic13—44no—
276Dic13—82no—
277Dic13#38114yes—
278C25—131no—
279C23×C4—21no—
280C23×C4—131no—
281C23×C4—131no—
282C23×C4—134no—
283C23×C4—131no—
284C23×C4—131no—
285C23×C4—134no—
286C23×C4—131no—
287C23×C4—268no—
288C23×C4—268no—
289C23×C4—262no—
290C23×C4—262no—
291C23×C4—262no—
292C23×C4—261no—
293C23×C4—528no—
294C23×C4C22×D1311yescharacteristic
295C22×C8—132no—
296C22×C8—268no—
297C22×C8—264no—
298C22×C8C22×D1312yes—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—134no—
302C2×C4⋊C4—132no—
303C2×C4⋊C4—138no—
304C2×C4⋊C4—138no—
305C2×C4⋊C4—132no—
306C2×C4⋊C4—268no—
307C2×C4⋊C4—268no—
308C2×C4⋊C4—264no—
309C2×C4⋊C4—264no—
310C2×C4⋊C4—268no—
311C2×C4⋊C4—268no—
312C2×C4⋊C4—262no—
313C2×C4⋊C4—262no—
314C2×C4⋊C4—261no—
315C2×C4⋊C4—262no—
316C2×C4⋊C4—262no—
317C2×C4⋊C4C4×D1314yescomplemented
318C2×C4⋊C4C22×D1312yes—
319C2×C4⋊C4C22×D1312yes—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—262no—
322C2×C22⋊C4—261no—
323C2×C22⋊C4—524no—
324C22⋊C8—22no—
325C22⋊C8—264no—
326C22⋊C8—262no—
327#95—21no—
328#95—262no—
329#95—261no—
330C2×C13—24no—
331C2×C13C2×#38111yescharacteristic
332C2×C13C22×#10311yescharacteristic
333C2×C13C2×#41811yescharacteristic
334C2×C13C2×#48112yes—
335C2×C13C2×#48412yes—
336D13—24no—
337D13#182418yesdirect product factor
338C24—131no—
339C24—134no—
340C24—134no—
341C24—134no—
342C24—131no—
343C24—264no—
344C24—264no—
345C24D4×D1311yescharacteristic
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—44no—
351C22×C4—131no—
352C22×C4—132no—
353C22×C4—132no—
354C22×C4—138no—
355C22×C4—134no—
356C22×C4—131no—
357C22×C4—134no—
358C22×C4—134no—
359C22×C4—132no—
360C22×C4—132no—
361C22×C4—264no—
362C22×C4—2616no—
363C22×C4—2616no—
364C22×C4—264no—
365C22×C4—268no—
366C22×C4—268no—
367C22×C4—264no—
368C22×C4—264no—
369C22×C4—264no—
370C22×C4—262no—
371C22×C4—262no—
372C22×C4—528no—
373C22×C4—5232no—
374C22×C4—528no—
375C22×C4—524no—
376C22×C4—524no—
377C22×C4—524no—
378C22×C4—524no—
379C22×C4C2×C4×D1312yes—
380C22×C4D4×D1311yescharacteristic
381C22×C4D4×D1312yes—
382C22×C4C23×D1311yescharacteristic
383C2×C8—22no—
384C2×C8—24no—
385C2×C8—262no—
386C2×C8—264no—
387C2×C8—528no—
388C4⋊C4—24no—
389C4⋊C4—22no—
390C4⋊C4—24no—
391C4⋊C4—134no—
392C4⋊C4—268no—
393C4⋊C4—268no—
394C4⋊C4—264no—
395C4⋊C4—262no—
396C4⋊C4—264no—
397C4⋊C4—524no—
398C4⋊C4C2×C4×D1314yes—
399C22⋊C4—42no—
400C22⋊C4—524no—
401C22⋊C4—522no—
402C13C2×#182411yescharacteristic, complemented, Sylow
403C23—22no—
404C23—22no—
405C23—132no—
406C23—132no—
407C23—132no—
408C23—134no—
409C23—134no—
410C23—132no—
411C23—132no—
412C23—132no—
413C23—1316no—
414C23—268no—
415C23—268no—
416C23—2616no—
417C23—2616no—
418C23—262no—
419C23—262no—
420C23C22⋊C4×D1312yes—
421C23SD16×D1312yes—
422C23Q16×D1312yes—
423C23C2×D4×D1311yescharacteristic
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—48no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—132no—
434C2×C4—134no—
435C2×C4—138no—
436C2×C4—138no—
437C2×C4—132no—
438C2×C4—268no—
439C2×C4—268no—
440C2×C4—268no—
441C2×C4—262no—
442C2×C4—264no—
443C2×C4—264no—
444C2×C4—264no—
445C2×C4—5216no—
446C2×C4—5216no—
447C2×C4—528no—
448C2×C4—524no—
449C2×C4—522no—
450C2×C4—522no—
451C2×C4—522no—
452C2×C4—1048no—
453C2×C4C22⋊C4×D1312yes—
454C2×C4C22×C4×D1311yescharacteristic
455C2×C4C2×D4×D1311yescharacteristic
456C2×C4#41×D1314yes—
457C8—42no—
458C8—522no—
459C22—22no—
460C22—22no—
461C22—24no—
462C22—24no—
463C22—134no—
464C22—134no—
465C22—138no—
466C22—138no—
467C22—134no—
468C22—134no—
469C22—2632no—
470C22—262no—
471C22—262no—
472C22—264no—
473C22—264no—
474C22D13×#10314yes—
475C22C2×C22⋊C4×D1311yescharacteristic
476C22D13×#12312yes—
477C22C2×SD16×D1311yescharacteristic
478C22C2×Q16×D1311yescharacteristic
479C22D13×AGL(1,ℤ/8)12yes—
480C4—22no—
481C4—44no—
482C4—82no—
483C4—134no—
484C4—262no—
485C4—524no—
486C4—1042no—
487C4D13×#11712yes—
488C4D13×#12312yes—
489C2—24no—
490C2—138no—
491C2—264no—
492C2D13×#38111yescharacteristic
493C2C2×D13×#10311yescharacteristic
494C2D13×#41811yescharacteristic
495C2D13×#48112yes—
496C2D13×#48412yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1824C2
socleC23×C13C22×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenter#1824D13
hypocenterC13C2×#1824
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13114927C2semidirect
5. #13114926C2semidirect
6. #13114925C2semidirect
7. #13114924C2semidirect
8. D13×#340C2semidirect
9. C13×#1824C2semidirect
19. C2×C4⋊C4×D13C4semidirect
34. C13×#340C22semidirect
35. #11718143C22semidirect
36. #11718121C22semidirect
37. #11718121C22semidirect
58. C2×C13×C4⋊C4C2×C4semidirect
66. C2×C4⋊Dic13C2×C4semidirect
82. C4⋊C4×D13C2×C4semidirect
162. #1824D13direct (N × H)
247. #340C2×D13semidirect
317. C2×C4⋊C4C4×D13semidirect
337. D13#1824direct (N × H)
402. C13C2×#1824semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C2×D13×C22⋊C82
D13×#3802
#131149272
#131149262
#131149252
#131149242
D13×#3402
C13×#18242
C2×#182413