Finite Group Databasebeta

← C2×#13126061 #16735045

Subgroups — C2×#13126061 #16735045

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#11719285C211yesmaximal, characteristic
3#13126061C2116yesmaximal, direct product factor
4C2×#11718537C212yesmaximal, complemented
5C2×#11718456C212yesmaximal, complemented
6C2×#11718466C212yesmaximal, complemented
7C2×#11718543C212yesmaximal
8C2×#11718682C211yesmaximal, characteristic, complemented
9C2×#11718503C211yesmaximal, characteristic, complemented
10C2×#11718745C211yesmaximal, characteristic, complemented
11C2×#11718496C211yesmaximal, characteristic, complemented
12C2×C13×#477C211yesmaximal, characteristic, complemented
13C22×Q8×D13—21no—
14C2×C13×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C13C2211yescharacteristic
16C2×#88201C2211yescharacteristic
17C2×#88200C2211yescharacteristic
18C2×#88198—21no—
19D13×C4⋊Q8—24no—
20D13×C4⋊Q8C2218yescomplemented
21#11719285—24no—
22#11719285C2218yes—
23C2×#88152—21no—
24C2×#88149C2211yescharacteristic
25C2×#88148—21no—
26C2×C4⋊C4×D13—21no—
27C2×C4⋊C4×D13C2212yes—
28C2×#88144C2211yescharacteristic
29C2×#88142—21no—
30C2×#88142C2212yes—
31C2×C4×D52—21no—
32C2×C4×D52C2211yescharacteristic
33C2×#88126—21no—
34C2×C42×D13C2211yescharacteristic
35C2×#88123C2211yescharacteristic
36C13×#477C2218yescomplemented
37C2×C13×#107C2212yes—
38C2×C13×C4⋊C8C2211yescharacteristic
39C2×C13×#103C2212yes—
40C2×#88075C2212yes—
41C2×#88061C2212yes—
42C2×#88060C2212yes—
43C2×#88057C2212yes—
44C2×#88055C2212yes—
45#11718745C2218yescomplemented
46#11718682C2218yescomplemented
47C2×#88049C2212yes—
48C2×#88048C2212yes—
49C2×#88047C2212yes—
50C2×C4⋊#1055C2211yescharacteristic
51#11718543C22116yes—
52#11718537C22116yescomplemented
53#11718503C2218yescomplemented
54#11718496C2218yescomplemented
55#11718466C22116yescomplemented
56#11718456C22116yescomplemented
57C22×Q8×C13—21no—
58C22×Q8×C13C2311yescharacteristic
59C2×Q8×D13—28no—
60C2×Q8×D13—48no—
61C22×D52—21no—
62C22×D52C2311yescharacteristic
63C22×C4×D13—22no—
64C22×C4×D13—21no—
65C22×C4×D13D411yescharacteristic
66C22×C4×D13D411yescharacteristic
67C22×C4×D13C2311yescharacteristic
68C22×Dic26—21no—
69C22×Dic26—22no—
70C22×C8×C13C2312yes—
71C13×C4⋊Q8—22no—
72C13×C4⋊Q8C2314yes—
73C4×Q8×C13—22no—
74C4×Q8×C13C2314yes—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2312yes—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81#88201—22no—
82#88201C2314yes—
83#88200—22no—
84#88200C2314yes—
85#88198—28no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2312yes—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×C4×Dic13D411yescharacteristic
100C2×C4×Dic13D411yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2312yes—
103#88152—28no—
104#88149—22no—
105#88149C2314yes—
106#88148—28no—
107C4⋊C4×D13—24no—
108C4⋊C4×D13—28no—
109C4⋊C4×D13C2318yes—
110#88144—22no—
111#88144C2314yes—
112#88142—24no—
113#88142—28no—
114#88142C2318yes—
115C4×D52—28no—
116C4×D52—22no—
117C4×D52C2314yes—
118#88126—28no—
119C42×D13D414yes—
120C42×D13C2314yes—
121#88123—22no—
122#88123C2314yes—
123C13×#107C2318yes—
124C13×C4⋊C8C2314yes—
125C13×#103C2318yes—
126#88075C2318yes—
127#88061C2318yes—
128#88060C2318yes—
129#88057C2318yes—
130#88055C2318yes—
131#88049C2318yes—
132#88048C2318yes—
133#88047C2318yes—
134C4⋊#1055C2314yes—
135C2×#3238—131nomaximal, Sylow
136C23×D13—21no—
137C23×D13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—21no—
140C2×Q8×C13—22no—
141C2×Q8×C13—22no—
142C2×Q8×C13—44no—
143C2×Q8×C13C2412yes—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—22no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155Q8×D13—432no—
156C2×D52—22no—
157C2×D52—22no—
158C2×D52—24no—
159C2×D52—21no—
160C2×D52—44no—
161C2×D52C2412yes—
162C2×C4×D13—24no—
163C2×C4×D13—24no—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—28no—
167C2×C4×D13—24no—
168C2×C4×D13—48no—
169C2×C4×D13—44no—
170C2×C4×D13C2×D412yes—
171C2×C4×D13C2×D414yes—
172C2×C4×D13C2×D414yes—
173C2×C4×D13C2412yes—
174C2×Dic26—24no—
175C2×Dic26—28no—
176C2×Dic26—48no—
177C2×Dic26—44no—
178C2×C8×C13—24no—
179C2×C8×C13C2414yes—
180C13×C4⋊C4—24no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—24no—
184C13×C4⋊C4C2414yes—
185C13×C4⋊C4C2412yes—
186C42×C13—24no—
187C42×C13C2×D412yes—
188C42×C13C2412yes—
189#6103—24no—
190#6103—24no—
191#6103—24no—
192#6103—24no—
193#6103—24no—
194C4⋊Dic13—22no—
195C4⋊Dic13—24no—
196C4⋊Dic13—21no—
197C4⋊Dic13—24no—
198C4⋊Dic13C2414yes—
199C4⋊Dic13C2412yes—
200#6101—24no—
201#6101—24no—
202#6101—28no—
203#6101—28no—
204C4×Dic13C2×D412yes—
205C4×Dic13C2×D414yes—
206C4×Dic13C2×D414yes—
207C4×Dic13C2412yes—
208C2×#1055—24no—
209C2×#1055C2414yes—
210C22×C4⋊Q8—131no—
211C2×#529—131no—
212#3238—1316no—
213C2×#501—132no—
214C2×#489—132no—
215C2×#483—132no—
216C2×#480—132no—
217C2×#477—131no—
218C2×#477D1311yescharacteristic, complemented
219C2×#476—131no—
220C2×#476—131no—
221C2×#432—131no—
222C23×C13C22×D411yescharacteristic
223C22×D13—22no—
224C22×D13—22no—
225C22×D13—22no—
226C22×D13—42no—
227C22×D13—42no—
228C22×D13—42no—
229C22×D13AGL(1,ℤ/8)14yes—
230C22×D13C22×D412yes—
231Q8×C13—22no—
232Q8×C13—22no—
233Q8×C13—48no—
234Q8×C13—42no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—42no—
240C2×C4×C13—44no—
241C2×C4×C13—42no—
242C2×C4×C13#13714yes—
243C2×C4×C13C22×D412yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D412yes—
246C2×C4×C132−1+412yes—
247C2×C4×C132−1+412yes—
248C2×C4×C13C2511yescharacteristic
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—24no—
254C2×Dic13—44no—
255C2×Dic13—42no—
256C2×Dic13C22×D412yes—
257C2×Dic13C22×D412yes—
258C2×Dic13C22×D412yes—
259D52—22no—
260D52—22no—
261D52—48no—
262D52—42no—
263C4×D13—28no—
264C4×D13—24no—
265C4×D13—28no—
266C4×D13—22no—
267C4×D13—22no—
268C4×D13—416no—
269C4×D13—48no—
270Dic26—416no—
271Dic26—48no—
272C8×C13—24no—
273#1055—24no—
274C23×Q8—261no—
275C2×C4⋊Q8—138no—
276C2×C4⋊Q8—132no—
277C2×C4⋊Q8—131no—
278C2×C4⋊Q8—261no—
279C2×C4⋊Q8—264no—
280C2×C4⋊Q8—261no—
281C2×C4⋊Q8C2×D1311yescharacteristic
282#529—138no—
283#529—264no—
284C2×#126—261no—
285C2×#125—131no—
286C2×#124—131no—
287C2×#123—261no—
288C2×C22⋊Q8—131no—
289C2×#121—131no—
290C2×C4×Q8C2×D1311yescharacteristic
291C2×C4×D4—131no—
292C2×C4×D4—261no—
293C2×#117—261no—
294C22×C4⋊C4—132no—
295C22×C4⋊C4—261no—
296C22×C42—131no—
297#501—1316no—
298#489—1316no—
299#483—1316no—
300#480—1316no—
301#477—138no—
302#477C2×D1318yescomplemented
303#476—138no—
304#476—138no—
305#432—138no—
306C2×#107—132no—
307C2×#107C2×D1312yes—
308C2×#106—132no—
309C2×#106—132no—
310C2×C4⋊C8—131no—
311C2×C4⋊C8C2×D1311yescharacteristic
312C2×#103—132no—
313C2×#103C2×D1312yes—
314C2×#102—132no—
315C2×#102—132no—
316C2×C22⋊C8—132no—
317C2×#97—132no—
318C22×C13#53612yes—
319C22×C13C2×AGL(1,ℤ/8)12yes—
320C22×C13C2×#13712yes—
321C22×C13C23×D411yescharacteristic
322C2×D13—22no—
323C2×D13—28no—
324C2×D13—22no—
325C2×D13—42no—
326C2×D13—42no—
327C2×D13—42no—
328C2×D13—84no—
329C2×D13C2×AGL(1,ℤ/8)14yes—
330C4×C13—22no—
331C4×C13—42no—
332C4×C13—44no—
333C4×C13—42no—
334C4×C13#53612yes—
335C4×C13C2×#13714yes—
336C4×C13C2×2−1+411yescharacteristic
337C4×C13C2×2−1+411yescharacteristic
338Dic13—22no—
339Dic13—22no—
340Dic13—22no—
341Dic13—44no—
342Dic13—42no—
343C22×Q8—21no—
344C22×Q8—262no—
345C22×Q8—268no—
346C22×Q8—261no—
347C22×Q8—528no—
348C22×Q8C22×D1311yescharacteristic
349C22×D4—131no—
350C22×D4—261no—
351C23×C4—131no—
352C23×C4—131no—
353C23×C4—131no—
354C23×C4—262no—
355C23×C4—261no—
356C22×C8—132no—
357C22×C8C22×D1312yes—
358C4⋊Q8—22no—
359C4⋊Q8—138no—
360C4⋊Q8—134no—
361C4⋊Q8—268no—
362C4⋊Q8—264no—
363C4⋊Q8—268no—
364C4⋊Q8—262no—
365C4⋊Q8C22×D1314yes—
366#126—268no—
367#125—134no—
368#125—262no—
369#124—134no—
370#124—262no—
371#123—268no—
372C22⋊Q8—134no—
373C22⋊Q8—262no—
374#121—134no—
375#121—262no—
376C4×Q8—22no—
377C4×Q8C22×D1314yes—
378C4×D4—134no—
379C4×D4—268no—
380C4×D4—262no—
381#117—268no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—132no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—138no—
387C2×C4⋊C4—264no—
388C2×C4⋊C4—268no—
389C2×C4⋊C4—262no—
390C2×C4⋊C4—262no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4C22×D1312yes—
396C2×C4⋊C4C22×D1311yescharacteristic
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C22⋊C4—261no—
400C2×C22⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C42—21no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—134no—
407C2×C42—134no—
408C2×C42C22×D1311yescharacteristic
409#107—138no—
410#107C22×D1318yes—
411#106—138no—
412#106—138no—
413C4⋊C8—134no—
414C4⋊C8C22×D1314yes—
415#103—138no—
416#103C22×D1318yes—
417#102—138no—
418#102—138no—
419C22⋊C8—138no—
420#97—138no—
421C2×C13#323814yescomplemented
422C2×C13C2×#53611yescharacteristic
423C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C13C22×#13711yescharacteristic
425D13—24no—
426D13—82no—
427C24—131no—
428C24—261no—
429C2×Q8—21no—
430C2×Q8—24no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—44no—
434C2×Q8—268no—
435C2×Q8—264no—
436C2×Q8—524no—
437C2×Q8—528no—
438C2×Q8—5232no—
439C2×Q8C23×D1312yes—
440C2×D4—132no—
441C2×D4—264no—
442C2×D4—261no—
443C2×D4—262no—
444C2×D4—262no—
445C2×D4—524no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—131no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—134no—
453C22×C4—132no—
454C22×C4—134no—
455C22×C4—132no—
456C22×C4—264no—
457C22×C4—268no—
458C22×C4—264no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—261no—
462C22×C4—262no—
463C22×C4—264no—
464C22×C4—528no—
465C22×C4—524no—
466C22×C4D4×D1311yescharacteristic
467C22×C4D4×D1311yescharacteristic
468C22×C4C23×D1311yescharacteristic
469C2×C8—24no—
470C2×C8—134no—
471C2×C8—264no—
472C2×C8C23×D1314yes—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—134no—
478C4⋊C4—132no—
479C4⋊C4—268no—
480C4⋊C4—268no—
481C4⋊C4—264no—
482C4⋊C4—264no—
483C4⋊C4—264no—
484C4⋊C4—262no—
485C4⋊C4—261no—
486C4⋊C4—264no—
487C4⋊C4C23×D1314yes—
488C4⋊C4C23×D1312yes—
489C22⋊C4—264no—
490C22⋊C4—264no—
491C22⋊C4—264no—
492C22⋊C4—264no—
493C22⋊C4—264no—
494C42—24no—
495C42—134no—
496C42—132no—
497C42—134no—
498C42—132no—
499C42D4×D1312yes—
500C42C23×D1312yes—
501C13C2×#323811yescharacteristic, complemented, Sylow
502C23—134no—
503C23—132no—
504C23—262no—
505C23—262no—
506C23—262no—
507C23—522no—
508C23—522no—
509C23—522no—
510C23C2×D4×D1311yescharacteristic
511Q8—22no—
512Q8—22no—
513Q8—48no—
514Q8—42no—
515Q8—528no—
516Q8—5216no—
517D4—262no—
518D4—262no—
519D4—528no—
520D4—522no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—132no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—268no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—268no—
536C2×C4—264no—
537C2×C4—262no—
538C2×C4—262no—
539C2×C4—262no—
540C2×C4—264no—
541C2×C4—5216no—
542C2×C4—522no—
543C2×C4—524no—
544C2×C4—528no—
545C2×C4#8817214yes—
546C2×C4C2×D4×D1312yes—
547C2×C4C2×D4×D1312yes—
548C2×C4C2×D4×D1311yescharacteristic
549C2×C4#8825412yes—
550C2×C4#8825712yes—
551C2×C4C24×D1311yescharacteristic
552C8—24no—
553C8—264no—
554C22—134no—
555C22—262no—
556C22—268no—
557C22—262no—
558C22—522no—
559C22—522no—
560C22—522no—
561C22—1044no—
562C22#1171933312yes—
563C22C2×#8817212yes—
564C22D13×AGL(1,ℤ/8)12yes—
565C22C22×D4×D1311yescharacteristic
566C4—22no—
567C4—44no—
568C4—42no—
569C4—42no—
570C4—262no—
571C4—262no—
572C4—262no—
573C4—524no—
574C4—522no—
575C4#1171933312yes—
576C4C2×#8817214yes—
577C4C2×#8825411yescharacteristic
578C4C2×#8825711yescharacteristic
579C2—264no—
580C2—1042no—
581C2#1312606114yesdirect product factor
582C2C2×#1171933311yescharacteristic
583C2C2×D13×AGL(1,ℤ/8)11yescharacteristic
584C2C22×#8817211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#477C2
socleC23×C13C22×D4
prime radicalC2×#88149C22
hypercenterC2×#477D13
hypocenterC13C2×#3238
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×D13×C4⋊Q8C2semidirect
3. #13126061C2direct (N × H)
4. C2×#11718537C2semidirect
5. C2×#11718456C2semidirect
6. C2×#11718466C2semidirect
8. C2×#11718682C2semidirect
9. C2×#11718503C2semidirect
10. C2×#11718745C2semidirect
11. C2×#11718496C2semidirect
12. C2×C13×#477C2semidirect
20. D13×C4⋊Q8C22semidirect
36. C13×#477C22semidirect
45. #11718745C22semidirect
46. #11718682C22semidirect
52. #11718537C22semidirect
53. #11718503C22semidirect
54. #11718496C22semidirect
55. #11718466C22semidirect
56. #11718456C22semidirect
218. C2×#477D13semidirect
302. #477C2×D13semidirect
421. C2×C13#3238semidirect
501. C13C2×#3238semidirect
581. C2#13126061direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×#117192852
#131260612
C2×#117185372
C2×#117184562
C2×#117184662
C2×#117185432
C2×#117186822
C2×#117185032
C2×#117187452
C2×#117184962
C2×C13×#4772
C2×#323813