Finite Group Databasebeta

← C2×#13128980 #16769817

Subgroups — C2×#13128980 #16769817

Order 3328.

6554 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128980C2132yesmaximal, direct product factor
2C2×C13⋊#564C211yesmaximal, characteristic, complemented
3C2×#11719356C214yesmaximal, complemented
4C2×#11719351C214yesmaximal, complemented
5C2×#11719377C212yesmaximal, complemented
6C2×#11719326C214yesmaximal, complemented
7C2×#11719393C211yesmaximal, characteristic, complemented
8C2×#11719327C214yesmaximal, complemented
9C2×#11719305C214yesmaximal, complemented
10C2×#11719385C212yesmaximal, complemented
11C2×#11719354C214yesmaximal, complemented
12C2×C13×#562C211yesmaximal, characteristic, complemented
13C13×#562C22116yescomplemented
14C2×C13×#125C2211yescharacteristic
15C2×C13×#124C2212yes—
16C2×C13×#123C2214yes—
17C2×C13×C22⋊Q8C2214yes—
18C2×C13×#121C2214yes—
19C2×#88200C2212yes—
20C2×Q8×Dic13C2212yes—
21C2×#88198C2214yes—
22C2×#88193C2214yes—
23C2×#88192C2212yes—
24C2×#88190C2214yes—
25C2×#88189C2214yes—
26C2×#88189C2214yes—
27C2×D4×Dic13C2214yes—
28C2×D4×Dic13C2212yes—
29C2×#88183C2214yes—
30C2×#88178C2214yes—
31C2×#88178C2214yes—
32C22×C4×Dic13C2214yes—
33#11719393C22116yescomplemented
34C13⋊#564C22116yescomplemented
35#11719385C22132yescomplemented
36#11719377C22132yescomplemented
37#11719356C22164yescomplemented
38#11719354C22164yescomplemented
39#11719351C22164yescomplemented
40#11719327C22164yescomplemented
41#11719326C22164yescomplemented
42#11719305C22164yescomplemented
43C2×#88152C2214yes—
44C2×#88150C2214yes—
45C2×#88146C2212yes—
46C2×#88144C2214yes—
47C2×#88143C2214yes—
48C2×#88143C2214yes—
49C2×#88143C2214yes—
50C2×#88142C2214yes—
51C2×#88142C2212yes—
52C2×#88141C2214yes—
53C2×#88141C2214yes—
54C2×#88139C2214yes—
55C2×#88137C2214yes—
56C2×#88135C2214yes—
57C2×#88133C2214yes—
58C2×#88133C2214yes—
59C2×#88133C2214yes—
60C2×#88133C2214yes—
61C2×#88132C2214yes—
62C2×#88132C2214yes—
63C2×#88132C2214yes—
64C2×#88131C2214yes—
65C2×#88131C2214yes—
66C2×C42×D13C2211yescharacteristic
67C2×#88124C2211yescharacteristic
68C2×#88124C2212yes—
69C22×Q8×C13C2312yes—
70C22×D4×C13C2312yes—
71C22×D4×C13C2314yes—
72C23×C4×C13C2314yes—
73C22×C22⋊D13C2314yes—
74C23×Dic13C2314yes—
75C23×Dic13C2314yes—
76C22×C4×D13C2311yescharacteristic
77C22×C4×D13C2312yes—
78C22×Dic26C2314yes—
79C22×Dic26C2314yes—
80C13×#125C2318yes—
81C13×#124C23116yes—
82C13×#123C23132yes—
83C13×C22⋊Q8C23132yes—
84C13×#121C23132yes—
85C2×C13×C4⋊C4C2314yes—
86C2×C13×C4⋊C4C2314yes—
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C22⋊C4C2314yes—
89C2×C13×C22⋊C4C2314yes—
90C2×C13×C22⋊C4C2314yes—
91C2×C42×C13C2311yescharacteristic
92C2×C22⋊Dic13C2314yes—
93C2×C22⋊Dic13C2314yes—
94C2×C22⋊Dic13C2314yes—
95C2×C22⋊Dic13C2314yes—
96C2×C22⋊Dic13C2314yes—
97#88200C23116yes—
98Q8×Dic13C23116yes—
99#88198C23132yes—
100#88193C23132yes—
101#88192C23116yes—
102#88190C23132yes—
103#88189C23132yes—
104#88189C23132yes—
105D4×Dic13C23132yes—
106D4×Dic13C23116yes—
107#88183C23132yes—
108C2×#6103C2314yes—
109C2×#6103C2314yes—
110C2×C4⋊Dic13C2312yes—
111C2×C4⋊Dic13C2312yes—
112C2×C4⋊Dic13C2312yes—
113C2×C4⋊Dic13C2314yes—
114C2×C4⋊Dic13C2314yes—
115#88178C23132yes—
116#88178C23132yes—
117C2×#6101C2314yes—
118C2×#6101C2314yes—
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×C4×Dic13C2312yes—
127C2×C4×Dic13C2311yescharacteristic
128C2×C4×Dic13C2314yes—
129C2×C4×Dic13C2314yes—
130C2×C4×Dic13C2314yes—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C23132yes—
133#88152C23132yes—
134#88150C23132yes—
135#88146C23116yes—
136#88144C23132yes—
137#88143C23132yes—
138#88143C23132yes—
139#88143C23132yes—
140#88142C23132yes—
141#88142C23116yes—
142#88141C23132yes—
143#88141C23132yes—
144#88139C23132yes—
145#88137C23132yes—
146#88135C23132yes—
147#88133C23132yes—
148#88133C23132yes—
149#88133C23132yes—
150#88133C23132yes—
151#88132C23132yes—
152#88132C23132yes—
153#88132C23132yes—
154#88131C23132yes—
155#88131C23132yes—
156C42×D13C2318yes—
157#88124C2318yes—
158#88124C23116yes—
159C2×#3531—131nomaximal, Sylow
160C24×C13C2414yes—
161C23×D13C2411yescharacteristic
162C2×Q8×C13—44no—
163C2×Q8×C13C2418yes—
164C2×D4×C13—48no—
165C2×D4×C13—44no—
166C2×D4×C13C2418yes—
167C2×D4×C13C24116yes—
168C22×C4×C13—48no—
169C22×C4×C13C2414yes—
170C22×C4×C13C2414yes—
171C22×C4×C13C2411yescharacteristic
172C22×C4×C13C2412yes—
173C22×C4×C13C24116yes—
174C2×C22⋊D13—48no—
175C2×C22⋊D13C24116yes—
176C22×Dic13—216no—
177C22×Dic13—48no—
178C22×Dic13C24116yes—
179C22×Dic13C2414yes—
180C22×Dic13C2414yes—
181C22×Dic13C2414yes—
182C22×Dic13C2412yes—
183C22×Dic13C24116yes—
184C22×Dic13C2411yescharacteristic
185C2×C4×D13—24no—
186C2×C4×D13—44no—
187C2×C4×D13C2414yes—
188C2×C4×D13C2418yes—
189C2×Dic26—48no—
190C2×Dic26—48no—
191C2×Dic26C24116yes—
192C2×Dic26C24116yes—
193C13×C4⋊C4C24116yes—
194C13×C4⋊C4C24116yes—
195C13×C4⋊C4C2418yes—
196C13×C22⋊C4C24116yes—
197C13×C22⋊C4C24116yes—
198C13×C22⋊C4C24116yes—
199C42×C13C2414yes—
200C22⋊Dic13C24116yes—
201C22⋊Dic13C24116yes—
202C22⋊Dic13C24116yes—
203C22⋊Dic13C24116yes—
204C22⋊Dic13C24116yes—
205#6103C24116yes—
206#6103C24116yes—
207C4⋊Dic13C2418yes—
208C4⋊Dic13C2418yes—
209C4⋊Dic13C2418yes—
210C4⋊Dic13C24116yes—
211C4⋊Dic13C24116yes—
212#6101C24116yes—
213#6101C24116yes—
214#6101C24116yes—
215#6101C24116yes—
216#6101C24116yes—
217#6101C24116yes—
218#6101C24116yes—
219#6101C24116yes—
220#6101C24116yes—
221C4×Dic13C2418yes—
222C4×Dic13C2414yes—
223C4×Dic13C24116yes—
224C4×Dic13C24116yes—
225C4×Dic13C24116yes—
226C4×Dic13C24116yes—
227#3531—1332no—
228C2×#564—131no—
229C2×#563—132no—
230C2×#563—134no—
231C2×#563—134no—
232C2×#562—134no—
233C2×#562D1311yescharacteristic, complemented
234C2×#533—131no—
235C2×#533—134no—
236C2×#529—132no—
237C2×#529—134no—
238C2×#529—134no—
239C23×C13—28no—
240C23×C13—28no—
241C23×C13—28no—
242C23×C13C2518yes—
243C23×C13C2511yescharacteristic
244C22×D13—22no—
245C22×D13—24no—
246C22×D13C2512yes—
247Q8×C13—48no—
248D4×C13—416no—
249D4×C13—48no—
250C2×C4×C13—22no—
251C2×C4×C13—28no—
252C2×C4×C13—28no—
253C2×C4×C13—24no—
254C2×C4×C13—416no—
255C2×C4×C13C2518yes—
256C2×C4×C13C2518yes—
257C2×C4×C13C2512yes—
258C2×C4×C13C2514yes—
259C22⋊D13—416no—
260C2×Dic13—28no—
261C2×Dic13—24no—
262C2×Dic13—28no—
263C2×Dic13—28no—
264C2×Dic13—232no—
265C2×Dic13—416no—
266C2×Dic132−1+414yes—
267C2×Dic13C2518yes—
268C2×Dic13C2518yes—
269C2×Dic13C2518yes—
270C2×Dic13C2514yes—
271C2×Dic13C2512yes—
272C4×D13—28no—
273C4×D13—48no—
274Dic26—416no—
275Dic26—416no—
276#564—1316no—
277#563—1332no—
278#563—1364no—
279#563—1364no—
280#562—1364no—
281#562C2×D13116yescomplemented
282#533—1316no—
283#533—1364no—
284C2×C4⋊Q8—134no—
285C2×C4⋊Q8—134no—
286C2×C4⋊Q8—132no—
287#529—1332no—
288#529—1364no—
289#529—1364no—
290C2×#126—134no—
291C2×#126—134no—
292C2×#126—134no—
293C2×#126—134no—
294C2×#126—134no—
295C2×#125—134no—
296C2×#125—134no—
297C2×#125—134no—
298C2×#125—134no—
299C2×#125—132no—
300C2×#125—131no—
301C2×#125C2×D1311yescharacteristic
302C2×#124—134no—
303C2×#124—134no—
304C2×#124C2×D1312yes—
305C2×#123—134no—
306C2×#123—134no—
307C2×#123—134no—
308C2×#123—134no—
309C2×#123C2×D1314yes—
310C2×C22⋊Q8—132no—
311C2×C22⋊Q8—134no—
312C2×C22⋊Q8—134no—
313C2×C22⋊Q8—134no—
314C2×C22⋊Q8—134no—
315C2×C22⋊Q8—134no—
316C2×C22⋊Q8—134no—
317C2×C22⋊Q8C2×D1314yes—
318C2×#121—132no—
319C2×#121—134no—
320C2×#121C2×D1314yes—
321C2×C4×Q8—132no—
322C2×C4×Q8—134no—
323C2×C4×Q8—134no—
324C2×C4×D4—132no—
325C2×C4×D4—134no—
326C2×C4×D4—134no—
327C2×#117—132no—
328C2×#117—134no—
329C2×#117—134no—
330C22×C42—134no—
331C22×C42—131no—
332C22×C13—28no—
333C22×C13—28no—
334C22×C13—28no—
335C22×C13—416no—
336C22×C13C2×2−1+412yes—
337C22×C13#58514yes—
338C22×C13C2611yescharacteristic
339C2×D13—22no—
340C2×D13—24no—
341C2×D13—44no—
342C4×C13—22no—
343C4×C13—28no—
344C4×C13—28no—
345C4×C13—24no—
346Dic13—28no—
347Dic13—24no—
348Dic13—28no—
349Dic13—28no—
350Dic13C2×2−1+414yes—
351C22×Q8—134no—
352C22×Q8—134no—
353C22×Q8C22×D1312yes—
354C22×D4—134no—
355C22×D4C22×D1312yes—
356C22×D4C22×D1314yes—
357C23×C4—134no—
358C23×C4—134no—
359C23×C4—131no—
360C23×C4—132no—
361C23×C4C22×D1314yes—
362C4⋊Q8—1332no—
363C4⋊Q8—1332no—
364C4⋊Q8—1316no—
365#126—1332no—
366#126—1332no—
367#126—1332no—
368#126—1332no—
369#126—1332no—
370#125—1332no—
371#125—1332no—
372#125—1332no—
373#125—1332no—
374#125—1316no—
375#125—138no—
376#125C22×D1318yes—
377#124—1332no—
378#124—1332no—
379#124C22×D13116yes—
380#123—1332no—
381#123—1332no—
382#123—1332no—
383#123—1332no—
384#123C22×D13132yes—
385C22⋊Q8—1316no—
386C22⋊Q8—1332no—
387C22⋊Q8—1332no—
388C22⋊Q8—1332no—
389C22⋊Q8—1332no—
390C22⋊Q8—1332no—
391C22⋊Q8—1332no—
392C22⋊Q8C22×D13132yes—
393#121—1316no—
394#121—1332no—
395#121C22×D13132yes—
396C4×Q8—1316no—
397C4×Q8—1332no—
398C4×Q8—1332no—
399C4×D4—1316no—
400C4×D4—1332no—
401C4×D4—1332no—
402#117—1316no—
403#117—1332no—
404#117—1332no—
405C2×C4⋊C4—134no—
406C2×C4⋊C4—134no—
407C2×C4⋊C4—132no—
408C2×C4⋊C4—134no—
409C2×C4⋊C4—134no—
410C2×C4⋊C4—134no—
411C2×C4⋊C4—134no—
412C2×C4⋊C4—132no—
413C2×C4⋊C4—134no—
414C2×C4⋊C4—132no—
415C2×C4⋊C4—134no—
416C2×C4⋊C4—134no—
417C2×C4⋊C4—134no—
418C2×C4⋊C4—134no—
419C2×C4⋊C4C22×D1312yes—
420C2×C4⋊C4C22×D1314yes—
421C2×C4⋊C4C22×D1314yes—
422C2×C22⋊C4—134no—
423C2×C22⋊C4—134no—
424C2×C22⋊C4—134no—
425C2×C22⋊C4—134no—
426C2×C22⋊C4—134no—
427C2×C22⋊C4—134no—
428C2×C22⋊C4—134no—
429C2×C22⋊C4C22×D1314yes—
430C2×C22⋊C4C22×D1314yes—
431C2×C22⋊C4C22×D1314yes—
432C2×C42—134no—
433C2×C42—132no—
434C2×C42—134no—
435C2×C42—134no—
436C2×C42—134no—
437C2×C42—131no—
438C2×C42—1332no—
439C2×C42—138no—
440C2×C42C22×D1311yescharacteristic
441C2×C13—48no—
442C2×C13#353114yescomplemented
443C2×C13C22×2−1+411yescharacteristic
444C2×C13C2×#58512yes—
445D13—42no—
446C24—131no—
447C24C23×D1314yes—
448C2×Q8—44no—
449C2×Q8—1316no—
450C2×Q8—1316no—
451C2×Q8—528no—
452C2×Q8—528no—
453C2×Q8C23×D1318yes—
454C2×D4—48no—
455C2×D4—44no—
456C2×D4—1316no—
457C2×D4—528no—
458C2×D4C23×D1318yes—
459C2×D4C23×D13116yes—
460C22×C4—48no—
461C22×C4—131no—
462C22×C4—1316no—
463C22×C4—134no—
464C22×C4—132no—
465C22×C4—134no—
466C22×C4—134no—
467C22×C4—1316no—
468C22×C4—134no—
469C22×C4—138no—
470C22×C4—264no—
471C22×C4—2616no—
472C22×C4—524no—
473C22×C4—528no—
474C22×C4C23×D1314yes—
475C22×C4C23×D1314yes—
476C22×C4C23×D1311yescharacteristic
477C22×C4C23×D1312yes—
478C22×C4C23×D13116yes—
479C4⋊C4—1316no—
480C4⋊C4—1316no—
481C4⋊C4—138no—
482C4⋊C4—1316no—
483C4⋊C4—1316no—
484C4⋊C4—1316no—
485C4⋊C4—1316no—
486C4⋊C4—138no—
487C4⋊C4—1316no—
488C4⋊C4—138no—
489C4⋊C4—1316no—
490C4⋊C4—1316no—
491C4⋊C4—1316no—
492C4⋊C4—1316no—
493C4⋊C4C23×D1318yes—
494C4⋊C4C23×D13116yes—
495C4⋊C4C23×D13116yes—
496C22⋊C4—1316no—
497C22⋊C4—1316no—
498C22⋊C4—1316no—
499C22⋊C4—1316no—
500C22⋊C4—1316no—
501C22⋊C4—1316no—
502C22⋊C4—1316no—
503C22⋊C4C23×D13116yes—
504C22⋊C4C23×D13116yes—
505C22⋊C4C23×D13116yes—
506C42—1316no—
507C42—138no—
508C42—1316no—
509C42—1316no—
510C42—1316no—
511C42—134no—
512C42C23×D1314yes—
513C13C2×#353111yescharacteristic, complemented, Sylow
514C23—28no—
515C23—28no—
516C23—28no—
517C23—132no—
518C23—264no—
519C23—262no—
520C23C24×D1318yes—
521C23C24×D1311yescharacteristic
522Q8—48no—
523Q8—5216no—
524Q8—5216no—
525D4—416no—
526D4—48no—
527D4—5216no—
528C2×C4—28no—
529C2×C4—28no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—416no—
533C2×C4—134no—
534C2×C4—132no—
535C2×C4—138no—
536C2×C4—134no—
537C2×C4—138no—
538C2×C4—138no—
539C2×C4—268no—
540C2×C4—2632no—
541C2×C4—268no—
542C2×C4—264no—
543C2×C4—268no—
544C2×C4—268no—
545C2×C4—528no—
546C2×C4—5216no—
547C2×C4C24×D1318yes—
548C2×C4C24×D1318yes—
549C2×C4C24×D1312yes—
550C2×C4C24×D1314yes—
551C22—28no—
552C22—28no—
553C22—28no—
554C22—416no—
555C22—262no—
556C22—264no—
557C22—524no—
558C22#1171965014yes—
559C22D13×2−1+412yes—
560C22C25×D1311yescharacteristic
561C4—22no—
562C4—28no—
563C4—28no—
564C4—24no—
565C4—134no—
566C4—268no—
567C4—268no—
568C4—264no—
569C4—268no—
570C2—48no—
571C2—522no—
572C2#1312898014yesdirect product factor
573C2C2×D13×2−1+411yescharacteristic
574C2C2×#1171965012yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#562C2
socleC23×C13C25
hypercenterC2×#562D13
hypocenterC13C2×#3531
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13128980C2direct (N × H)
2. C2×C13⋊#564C2semidirect
3. C2×#11719356C2semidirect
4. C2×#11719351C2semidirect
5. C2×#11719377C2semidirect
6. C2×#11719326C2semidirect
7. C2×#11719393C2semidirect
8. C2×#11719327C2semidirect
9. C2×#11719305C2semidirect
10. C2×#11719385C2semidirect
11. C2×#11719354C2semidirect
12. C2×C13×#562C2semidirect
13. C13×#562C22semidirect
33. #11719393C22semidirect
34. C13⋊#564C22semidirect
35. #11719385C22semidirect
36. #11719377C22semidirect
37. #11719356C22semidirect
38. #11719354C22semidirect
39. #11719351C22semidirect
40. #11719327C22semidirect
41. #11719326C22semidirect
42. #11719305C22semidirect
233. C2×#562D13semidirect
281. #562C2×D13semidirect
442. C2×C13#3531semidirect
513. C13C2×#3531semidirect
572. C2#13128980direct (N × H)

Maximal subgroups

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

subgroupindex
#131289802
C2×C13⋊#5642
C2×#117193562
C2×#117193512
C2×#117193772
C2×#117193262
C2×#117193932
C2×#117193272
C2×#117193052
C2×#117193852
C2×#117193542
C2×C13×#5622
C2×#353113