Finite Group Databasebeta

← D13×#2646 #16029360

Subgroups — D13×#2646 #16029360

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13120809C212yesmaximal, complemented
2#13120808C214yesmaximal, complemented
3#13120807C214yesmaximal, complemented
4#13120806C211yesmaximal, characteristic, complemented
5#13120805C214yesmaximal, complemented
6D13×#400C214yesmaximal, complemented
7D13×#398C214yesmaximal, complemented
8D13×#385C214yesmaximal
9D13×#380C212yesmaximal
10C2×D13×#95C211yesmaximal, characteristic
11C13×#2646C211yesmaximal, characteristic, complemented
12C23×C4×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C2×C4⋊C4×D13C2212yes—
15C2×C4⋊C4×D13C2212yes—
16C2×C4⋊C4×D13C2214yes—
17C2×C4⋊C4×D13C2214yes—
18C2×C22⋊C4×D13C2214yes—
19C13×#400C2214yescomplemented
20C13×#398C2214yescomplemented
21C13×#385C2214yes—
22C13×#380C2212yes—
23C2×C13×#95C2211yescharacteristic
24#11718873C2212yes—
25#11718871C2214yes—
26C2×#88071C2212yes—
27C2×#88071C2211yescharacteristic
28#11718650C2214yes—
29#11718650C2214yes—
30#11718648C2212yes—
31#11718648C2212yes—
32#11718647C2214yescomplemented
33#11718645C2214yescomplemented
34#11718645C2214yescomplemented
35#11718644C2214yescomplemented
36#11718643C2214yescomplemented
37#11718641C2214yescomplemented
38#11718611C2214yes—
39#11718607C2214yes—
40#11718603C2214yes—
41#11718329C2214yes—
42#11718329C2214yes—
43#11718328C2214yes—
44D13×#95C2214yes—
45D13×#95C2214yes—
46D13×#95C2214yes—
47D13×#95C2214yes—
48D13×#95C2214yes—
49#11718322C2214yescomplemented
50#11718321C2214yescomplemented
51#11718321C2214yescomplemented
52#11718320C2214yescomplemented
53#11718319C2214yescomplemented
54#11718319C2214yescomplemented
55#11718318C2214yescomplemented
56#11718318C2214yescomplemented
57C24×D13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2312yes—
61C23×Dic13C2311yescharacteristic
62C22×C4×D13—28no—
63C22×C4×D13—44no—
64C22×C4×D13—44no—
65C22×C4×D13—44no—
66C22×C4×D13Q818yes—
67C22×C4×D13C2314yes—
68C22×C4×D13C2314yes—
69C22×C4×D13C2314yes—
70C22×C4×D13C2312yes—
71C22×C4×D13C2314yes—
72C22×C4×D13C2312yes—
73C2×C13×C4⋊C4C2312yes—
74C2×C13×C4⋊C4C2312yes—
75C2×C13×C4⋊C4C2314yes—
76C2×C13×C4⋊C4C2314yes—
77C2×C13×C22⋊C4C2314yes—
78C2×C22⋊Dic13C2314yes—
79C2×#6103C2314yes—
80C2×#6103C2314yes—
81C2×C4⋊Dic13C2312yes—
82C2×C4⋊Dic13C2314yes—
83C2×C4⋊Dic13C2312yes—
84C2×C4⋊Dic13C2314yes—
85C2×#6101C2314yes—
86C2×#6101C2314yes—
87C2×#6101C2314yes—
88C2×#6101C2314yes—
89C2×#6101C2314yes—
90C2×#6101C2314yes—
91C4⋊C4×D13—44no—
92C4⋊C4×D13—44no—
93C4⋊C4×D13—48no—
94C4⋊C4×D13—48no—
95C22⋊C4×D13—216no—
96C13×#95C2314yes—
97C13×#95C2314yes—
98C13×#95C2314yes—
99C13×#95C2314yes—
100#88071C2314yes—
101#88071C2314yes—
102#88071C2314yes—
103#88071C2314yes—
104#88071C2314yes—
105#88071C2314yes—
106#88071C2314yes—
107#88071C2314yes—
108#88071C2314yes—
109#88071C2314yes—
110#88071C2314yes—
111#88071C2314yes—
112C2×#2646—131nomaximal, Sylow
113C24×C13C2411yescharacteristic
114C23×D13—22no—
115C23×D13—24no—
116C23×D13—22no—
117C23×D13C2×Q814yes—
118C23×D13#4118yes—
119C23×D13C2411yescharacteristic
120C23×D13C2411yescharacteristic
121C22×C4×C13—24no—
122C22×C4×C13—42no—
123C22×C4×C13—42no—
124C22×C4×C13—42no—
125C22×C4×C13C2×Q814yes—
126C22×C4×C13C2414yes—
127C22×C4×C13C2414yes—
128C22×C4×C13C2414yes—
129C22×C4×C13C2412yes—
130C22×Dic13—24no—
131C22×Dic13—42no—
132C22×Dic13—42no—
133C22×Dic13—42no—
134C22×Dic13C2×Q814yes—
135C22×Dic13C2414yes—
136C22×Dic13C2414yes—
137C22×Dic13C2414yes—
138C22×Dic13C2412yes—
139C2×C4×D13—24no—
140C2×C4×D13—24no—
141C2×C4×D13—28no—
142C2×C4×D13—28no—
143C2×C4×D13—28no—
144C2×C4×D13—28no—
145C2×C4×D13—28no—
146C2×C4×D13—28no—
147C2×C4×D13—28no—
148C2×C4×D13—28no—
149C2×C4×D13—28no—
150C2×C4×D13—28no—
151C2×C4×D13—416no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C4×D13—44no—
155C2×C4×D13—44no—
156C2×C4×D13—432no—
157C2×C4×D13C2×Q818yes—
158C2×C4×D13C2×Q818yes—
159C13×C4⋊C4—42no—
160C13×C4⋊C4—42no—
161C13×C4⋊C4—44no—
162C13×C4⋊C4—44no—
163C13×C22⋊C4—28no—
164C22⋊Dic13—28no—
165#6103—28no—
166#6103—28no—
167C4⋊Dic13—42no—
168C4⋊Dic13—44no—
169C4⋊Dic13—42no—
170C4⋊Dic13—44no—
171#6101—44no—
172#6101—44no—
173#6101—44no—
174#6101—44no—
175#6101—44no—
176#6101—44no—
177#2646—134no—
178#2646—134no—
179#2646—134no—
180#2646—132no—
181#2646—131no—
182#2646D1311yescharacteristic, direct product factor
183C2×#400—134no—
184C2×#398—134no—
185C2×#385—134no—
186C2×#380—132no—
187C22×#95—131no—
188C23×C13—21no—
189C23×C13—22no—
190C23×C13—21no—
191C23×C13C22×Q812yes—
192C23×C13C2×#4114yes—
193C23×C13C2511yescharacteristic
194C22×D13—21no—
195C22×D13—22no—
196C22×D13—21no—
197C22×D13—216no—
198C22×D13—216no—
199C22×D13—28no—
200C22×D13—28no—
201C22×D13#125116yes—
202C22×D13C22×Q812yes—
203C22×D13C22×Q812yes—
204C22×D13C2×#4114yes—
205C22×D13C2×#4114yes—
206C22×D13H(5,𝔽2)12yes—
207C22×D13H(5,𝔽2)14yes—
208C22×D132−1+412yes—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—24no—
215C2×C4×C13—24no—
216C2×C4×C13—24no—
217C2×C4×C13—24no—
218C2×C4×C13—24no—
219C2×C4×C13—24no—
220C2×C4×C13—44no—
221C2×C4×C13—48no—
222C2×C4×C13C22×Q814yes—
223C2×Dic13—22no—
224C2×Dic13—22no—
225C2×Dic13—24no—
226C2×Dic13—24no—
227C2×Dic13—24no—
228C2×Dic13—24no—
229C2×Dic13—24no—
230C2×Dic13—24no—
231C2×Dic13—24no—
232C2×Dic13—24no—
233C2×Dic13—24no—
234C2×Dic13—44no—
235C2×Dic13—48no—
236C2×Dic13C22×Q814yes—
237C4×D13—216no—
238C4×D13—48no—
239C4×D13—416no—
240C4×D13—416no—
241C4×D13—416no—
242C4×D13—416no—
243C24×C4—131no—
244C24×C4—132no—
245C22×C4⋊C4—132no—
246C22×C4⋊C4—134no—
247C22×C4⋊C4—134no—
248C22×C4⋊C4—132no—
249C22×C22⋊C4—134no—
250#400—134no—
251#400—134no—
252#400—134no—
253#400—134no—
254#400—134no—
255#400—134no—
256#400—134no—
257#400C2×D1314yescomplemented
258#398—134no—
259#398—134no—
260#398—134no—
261#398—134no—
262#398—134no—
263#398—134no—
264#398—134no—
265#398C2×D1314yescomplemented
266#385—134no—
267#385—134no—
268#385—134no—
269#385—134no—
270#385—134no—
271#385—134no—
272#385—134no—
273#385C2×D1314yes—
274#380—132no—
275#380—132no—
276#380—132no—
277#380—134no—
278#380—134no—
279#380C2×D1312yes—
280C2×#95—132no—
281C2×#95—131no—
282C2×#95—134no—
283C2×#95—134no—
284C2×#95—134no—
285C2×#95—134no—
286C2×#95—134no—
287C2×#95C2×D1311yescharacteristic
288C22×C13—24no—
289C22×C13—24no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13C2×#12514yes—
293C22×C13C23×Q811yescharacteristic
294C22×C13C22×#4112yes—
295C22×C13C2×H(5,𝔽2)11yescharacteristic
296C22×C13C2×H(5,𝔽2)12yes—
297C22×C13C2×2−1+411yescharacteristic
298C2×D13—24no—
299C2×D13—24no—
300C2×D13—22no—
301C2×D13—22no—
302C2×D13—232no—
303C2×D13C2×#12514yes—
304C2×D13C2×#12514yes—
305C2×D13#53818yes—
306C2×D13#53918yes—
307C2×D13#54314yes—
308C2×D13#54414yes—
309C4×C13—24no—
310C4×C13—44no—
311C4×C13—44no—
312C4×C13—44no—
313Dic13—24no—
314Dic13—44no—
315Dic13—44no—
316Dic13—44no—
317C25—131no—
318C23×C4—131no—
319C23×C4—132no—
320C23×C4—138no—
321C23×C4—132no—
322C23×C4—132no—
323C23×C4—134no—
324C23×C4—134no—
325C23×C4—134no—
326C23×C4—134no—
327C23×C4—268no—
328C23×C4—524no—
329C23×C4—524no—
330C23×C4—524no—
331C23×C4C22×D1312yes—
332C23×C4C22×D1311yescharacteristic
333C2×C4⋊C4—134no—
334C2×C4⋊C4—134no—
335C2×C4⋊C4—134no—
336C2×C4⋊C4—134no—
337C2×C4⋊C4—134no—
338C2×C4⋊C4—134no—
339C2×C4⋊C4—132no—
340C2×C4⋊C4—132no—
341C2×C4⋊C4—134no—
342C2×C4⋊C4—134no—
343C2×C4⋊C4—524no—
344C2×C4⋊C4—524no—
345C2×C4⋊C4—528no—
346C2×C4⋊C4—528no—
347C2×C4⋊C4C22×D1312yes—
348C2×C4⋊C4C22×D1312yes—
349C2×C4⋊C4C22×D1314yes—
350C2×C4⋊C4C22×D1314yes—
351C2×C22⋊C4—134no—
352C2×C22⋊C4—134no—
353C2×C22⋊C4—134no—
354C2×C22⋊C4—2616no—
355C2×C22⋊C4C22×D1314yes—
356#95—134no—
357#95—134no—
358#95—134no—
359#95—134no—
360#95—134no—
361#95—134no—
362#95—134no—
363#95—134no—
364#95—134no—
365#95—134no—
366#95—134no—
367#95—134no—
368#95C22×D1314yes—
369#95C22×D1314yes—
370#95C22×D1314yes—
371#95C22×D1314yes—
372C2×C13—24no—
373C2×C13C22×#12511yescharacteristic
374C2×C13C2×#53812yes—
375C2×C13C2×#53912yes—
376C2×C13C2×#54311yescharacteristic
377C2×C13C2×#54411yescharacteristic
378D13—24no—
379D13#264618yesdirect product factor
380C24—131no—
381C24—134no—
382C24—138no—
383C24—131no—
384C24—264no—
385C24—262no—
386C24—262no—
387C24C23×D1311yescharacteristic
388C22×C4—24no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—42no—
392C22×C4—132no—
393C22×C4—134no—
394C22×C4—138no—
395C22×C4—138no—
396C22×C4—134no—
397C22×C4—134no—
398C22×C4—134no—
399C22×C4—264no—
400C22×C4—264no—
401C22×C4—268no—
402C22×C4—268no—
403C22×C4—268no—
404C22×C4—268no—
405C22×C4—268no—
406C22×C4—268no—
407C22×C4—268no—
408C22×C4—268no—
409C22×C4—268no—
410C22×C4—268no—
411C22×C4—264no—
412C22×C4—522no—
413C22×C4—522no—
414C22×C4—524no—
415C22×C4—524no—
416C22×C4—5216no—
417C22×C4—5232no—
418C22×C4—522no—
419C22×C4—522no—
420C22×C4—522no—
421C22×C4Q8×D1314yes—
422C22×C4C23×D1314yes—
423C22×C4C23×D1314yes—
424C22×C4C23×D1314yes—
425C22×C4C23×D1312yes—
426C4⋊C4—42no—
427C4⋊C4—42no—
428C4⋊C4—44no—
429C4⋊C4—44no—
430C4⋊C4—524no—
431C4⋊C4—524no—
432C4⋊C4—524no—
433C4⋊C4—524no—
434C4⋊C4—524no—
435C4⋊C4—524no—
436C4⋊C4—522no—
437C4⋊C4—522no—
438C4⋊C4—524no—
439C4⋊C4—524no—
440C22⋊C4—28no—
441C22⋊C4—268no—
442C22⋊C4—268no—
443C22⋊C4—268no—
444C13C2×#264611yescharacteristic, complemented, Sylow
445C23—22no—
446C23—21no—
447C23—21no—
448C23—132no—
449C23—134no—
450C23—134no—
451C23—132no—
452C23—132no—
453C23—132no—
454C23—134no—
455C23—1316no—
456C23—268no—
457C23—2616no—
458C23—268no—
459C23—2616no—
460C23—262no—
461C23—261no—
462C23—261no—
463C23C2×Q8×D1312yes—
464C23#41×D1314yes—
465C23C24×D1311yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—44no—
478C2×C4—48no—
479C2×C4—134no—
480C2×C4—2616no—
481C2×C4—262no—
482C2×C4—262no—
483C2×C4—264no—
484C2×C4—264no—
485C2×C4—264no—
486C2×C4—264no—
487C2×C4—264no—
488C2×C4—264no—
489C2×C4—264no—
490C2×C4—264no—
491C2×C4—264no—
492C2×C4—528no—
493C2×C4—5216no—
494C2×C4—5216no—
495C2×C4—5216no—
496C2×C4—5216no—
497C2×C4—524no—
498C2×C4—528no—
499C2×C4C2×Q8×D1314yes—
500C22—22no—
501C22—22no—
502C22—24no—
503C22—24no—
504C22—134no—
505C22—134no—
506C22—134no—
507C22—138no—
508C22—138no—
509C22—134no—
510C22—2632no—
511C22—262no—
512C22—262no—
513C22—264no—
514C22—264no—
515C22D13×#12514yes—
516C22C22×Q8×D1311yescharacteristic
517C22C2×#41×D1312yes—
518C22D13×H(5,𝔽2)12yes—
519C22D13×H(5,𝔽2)11yescharacteristic
520C22D13×2−1+411yescharacteristic
521C4—24no—
522C4—44no—
523C4—44no—
524C4—44no—
525C4—264no—
526C4—524no—
527C4—524no—
528C4—524no—
529C2—24no—
530C2—138no—
531C2—264no—
532C2C2×D13×#12511yescharacteristic
533C2D13×#53812yes—
534C2D13×#53912yes—
535C2D13×#54311yescharacteristic
536C2D13×#54411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2646C2
prime radicalC24×D13C23
hypercenter#2646D13
hypocenterC13C2×#2646
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2646

Complements

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

NH ≅ G/Ntype
1. #13120809C2semidirect
2. #13120808C2semidirect
3. #13120807C2semidirect
4. #13120806C2semidirect
5. #13120805C2semidirect
6. D13×#400C2semidirect
7. D13×#398C2semidirect
11. C13×#2646C2semidirect
19. C13×#400C22semidirect
20. C13×#398C22semidirect
32. #11718647C22semidirect
33. #11718645C22semidirect
34. #11718645C22semidirect
35. #11718644C22semidirect
36. #11718643C22semidirect
37. #11718641C22semidirect
49. #11718322C22semidirect
50. #11718321C22semidirect
51. #11718321C22semidirect
52. #11718320C22semidirect
53. #11718319C22semidirect
54. #11718319C22semidirect
55. #11718318C22semidirect
56. #11718318C22semidirect
182. #2646D13direct (N × H)
257. #400C2×D13semidirect
265. #398C2×D13semidirect
379. D13#2646direct (N × H)
444. C13C2×#2646semidirect

Maximal subgroups

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

subgroupindex
#131208092
#131208082
#131208072
#131208062
#131208052
D13×#4002
D13×#3982
D13×#3852
D13×#3802
C2×D13×#952
C13×#26462
C2×#264613