Finite Group Databasebeta

← C2×#13129291 #16770683

Subgroups — C2×#13129291 #16770683

Order 3328.

6566 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#13129291C2132yesmaximal, direct product factor
2C2×C13⋊#564C211yesmaximal, characteristic, complemented
3C2×#11719377C212yesmaximal, complemented
4C2×#11719341C214yesmaximal, complemented
5C2×#11719319C214yesmaximal, complemented
6C2×#11719355C214yesmaximal, complemented
7C2×#11719330C214yesmaximal, complemented
8C2×#11719307C214yesmaximal, complemented
9C2×#11719365C214yesmaximal, complemented
10C2×#11719385C212yesmaximal, complemented
11C2×D13×#125C211yesmaximal, characteristic, 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×#88192C2212yes—
23C2×#88192C2214yes—
24C2×#88189C2214yes—
25C2×#88189C2214yes—
26C2×#88189C2214yes—
27C2×D4×Dic13C2214yes—
28C2×D4×Dic13C2212yes—
29C2×C4×C22⋊D13C2214yes—
30C2×#88180C2214yes—
31C2×#88178C2214yes—
32C22×#6101C2214yes—
33D13×#125C22116yescomplemented
34C13⋊#564C22116yescomplemented
35#11719385C22132yescomplemented
36#11719377C22132yescomplemented
37#11719365C22164yescomplemented
38#11719355C22164yescomplemented
39#11719341C22164yescomplemented
40#11719330C22164yescomplemented
41#11719319C22164yescomplemented
42#11719307C22164yescomplemented
43C2×#88150C2214yes—
44C2×C4⋊C4×D13C2214yes—
45C2×C4⋊C4×D13C2212yes—
46C2×#88144C2214yes—
47C2×#88144C2214yes—
48C2×#88144C2212yes—
49C2×#88143C2214yes—
50C2×#88143C2214yes—
51C2×#88143C2214yes—
52C2×#88143C2214yes—
53C2×#88141C2214yes—
54C2×#88137C2214yes—
55C2×#88135C2214yes—
56C2×#88135C2214yes—
57C2×#88133C2214yes—
58C2×#88133C2214yes—
59C2×#88133C2214yes—
60C2×#88133C2214yes—
61C2×#88133C2214yes—
62C2×#88132C2214yes—
63C2×#88132C2214yes—
64C2×#88132C2214yes—
65C2×#88131C2214yes—
66C2×C42×D13C2211yescharacteristic
67C2×#88124C2211yescharacteristic
68C2×#88124C2212yes—
69C22×Q8×C13C2312yes—
70C22×D4×C13C2314yes—
71C22×D4×C13C2312yes—
72C23×C4×C13C2314yes—
73C22×C22⋊D13C2314yes—
74C23×Dic13C2314yes—
75C23×Dic13C2314yes—
76C22×C4×D13C2311yescharacteristic
77C22×C4×D13C2312yes—
78C22×C4×D13C2314yes—
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#88192C23132yes—
101#88192C23116yes—
102#88189C23132yes—
103#88189C23132yes—
104#88189C23132yes—
105D4×Dic13C23116yes—
106D4×Dic13C23132yes—
107C4×C22⋊D13C23132yes—
108C2×#6103C2314yes—
109#88180C23132yes—
110C2×C4⋊Dic13C2312yes—
111C2×C4⋊Dic13C2312yes—
112C2×C4⋊Dic13C2312yes—
113C2×C4⋊Dic13C2314yes—
114C2×C4⋊Dic13C2314yes—
115C2×C4⋊Dic13C2314yes—
116#88178C23132yes—
117C2×#6101C2314yes—
118C2×#6101C2314yes—
119C2×#6101C2314yes—
120C2×#6101C2314yes—
121C2×#6101C2314yes—
122C2×#6101C2314yes—
123C2×#6101C2314yes—
124C2×#6101C2314yes—
125C2×#6101C2314yes—
126C2×#6101C2314yes—
127C2×#6101C23132yes—
128C2×C4×Dic13C2311yescharacteristic
129C2×C4×Dic13C2312yes—
130C2×C4×Dic13C2314yes—
131C2×C4×Dic13C2314yes—
132C2×C4×Dic13C2314yes—
133#88150C23132yes—
134C4⋊C4×D13C23132yes—
135C4⋊C4×D13C23116yes—
136#88144C23132yes—
137#88144C23132yes—
138#88144C23116yes—
139#88143C23132yes—
140#88143C23132yes—
141#88143C23132yes—
142#88143C23132yes—
143#88141C23132yes—
144#88137C23132yes—
145#88135C23132yes—
146#88135C23132yes—
147#88133C23132yes—
148#88133C23132yes—
149#88133C23132yes—
150#88133C23132yes—
151#88133C23132yes—
152#88132C23132yes—
153#88132C23132yes—
154#88132C23132yes—
155#88131C23132yes—
156C42×D13C2318yes—
157#88124C2318yes—
158#88124C23116yes—
159C2×#3553—131nomaximal, Sylow
160C24×C13C2414yes—
161C23×D13C2411yescharacteristic
162C2×Q8×C13—44no—
163C2×Q8×C13C2418yes—
164C2×D4×C13—48no—
165C2×D4×C13—44no—
166C2×D4×C13C24116yes—
167C2×D4×C13C2418yes—
168C22×C4×C13—48no—
169C22×C4×C13C2414yes—
170C22×C4×C13C2411yescharacteristic
171C22×C4×C13C2412yes—
172C22×C4×C13C2414yes—
173C22×C4×C13C24116yes—
174C2×C22⋊D13—216no—
175C2×C22⋊D13C24116yes—
176C22×Dic13—48no—
177C22×Dic13—48no—
178C22×Dic13C2412yes—
179C22×Dic13C2414yes—
180C22×Dic13C2411yescharacteristic
181C22×Dic13C2414yes—
182C22×Dic13C2414yes—
183C22×Dic13C24116yes—
184C22×Dic13C24116yes—
185C2×C4×D13—24no—
186C2×C4×D13—48no—
187C2×C4×D13—44no—
188C2×C4×D13C2414yes—
189C2×C4×D13C2418yes—
190C2×C4×D13C24116yes—
191C2×Dic26—48no—
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—
206C4⋊Dic13C2418yes—
207C4⋊Dic13C2418yes—
208C4⋊Dic13C2418yes—
209C4⋊Dic13C24116yes—
210C4⋊Dic13C24116yes—
211C4⋊Dic13C24116yes—
212#6101C24116yes—
213#6101C24116yes—
214#6101C24116yes—
215#6101C24116yes—
216#6101C24116yes—
217#6101C24116yes—
218#6101C24116yes—
219#6101C24116yes—
220#6101C24116yes—
221#6101C24116yes—
222C4×Dic13C2414yes—
223C4×Dic13C2418yes—
224C4×Dic13C24116yes—
225C4×Dic13C24116yes—
226C4×Dic13C24116yes—
227#3553—1332no—
228C2×#564—131no—
229C2×#563—132no—
230C2×#562D1311yescharacteristic, complemented
231C2×#554—134no—
232C2×#553—134no—
233C2×#552—134no—
234C2×#541—134no—
235C2×#539—134no—
236C2×#539—134no—
237C2×#529—132no—
238C22×#125—131no—
239C23×C13—28no—
240C23×C13—28no—
241C23×C13—28no—
242C23×C13C2518yes—
243C23×C13C2511yescharacteristic
244C22×D13—24no—
245C22×D132−1+414yes—
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×C13C2512yes—
257C2×C4×C13C2514yes—
258C2×C4×C13C2518yes—
259C22⋊D13—232no—
260C2×Dic13—22no—
261C2×Dic13—28no—
262C2×Dic13—28no—
263C2×Dic13—28no—
264C2×Dic13—24no—
265C2×Dic13—416no—
266C2×Dic13—416no—
267C2×Dic13C2514yes—
268C2×Dic13C2518yes—
269C2×Dic13C2512yes—
270C2×Dic13C2518yes—
271C2×Dic13C2518yes—
272C4×D13—28no—
273C4×D13—416no—
274C4×D13—48no—
275Dic26—416no—
276#564—1316no—
277#563—1332no—
278#562C2×D13116yescomplemented
279#554—1364no—
280#553—1364no—
281#552—1364no—
282#541—1364no—
283#539—1364no—
284#539—1364no—
285C2×C4⋊Q8—134no—
286#529—1332no—
287C2×#126—134no—
288C2×#126—134no—
289C2×#126—134no—
290C2×#126—134no—
291C2×#126—134no—
292C2×#125—1316no—
293C2×#125—134no—
294C2×#125—134no—
295C2×#125—134no—
296C2×#125—134no—
297C2×#125—132no—
298C2×#125—134no—
299C2×#125—134no—
300C2×#125—131no—
301C2×#125—132no—
302C2×#125C2×D1311yescharacteristic
303C2×#124C2×D1312yes—
304C2×#123—134no—
305C2×#123—134no—
306C2×#123—134no—
307C2×#123—134no—
308C2×#123C2×D1314yes—
309C2×C22⋊Q8—132no—
310C2×C22⋊Q8—134no—
311C2×C22⋊Q8—134no—
312C2×C22⋊Q8—134no—
313C2×C22⋊Q8—134no—
314C2×C22⋊Q8—134no—
315C2×C22⋊Q8C2×D1314yes—
316C2×#121—132no—
317C2×#121—134no—
318C2×#121C2×D1314yes—
319C2×C4×Q8—132no—
320C2×C4×Q8—134no—
321C2×C4×D4—132no—
322C2×C4×D4—134no—
323C2×C4×D4—134no—
324C2×C4×D4—134no—
325C2×C4×D4—134no—
326C2×#117—134no—
327C2×#117—134no—
328C22×C4⋊C4—134no—
329C22×C4⋊C4—132no—
330C22×C4⋊C4—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—24no—
340C2×D13—28no—
341C2×D13C2×2−1+414yes—
342C4×C13—22no—
343C4×C13—28no—
344C4×C13—28no—
345C4×C13—24no—
346Dic13—22no—
347Dic13—28no—
348Dic13—28no—
349Dic13—28no—
350Dic13—24no—
351C22×Q8—134no—
352C22×Q8C22×D1312yes—
353C22×D4—134no—
354C22×D4C22×D1314yes—
355C22×D4C22×D1312yes—
356C23×C4—134no—
357C23×C4—134no—
358C23×C4—131no—
359C23×C4—134no—
360C23×C4—132no—
361C23×C4C22×D1314yes—
362C4⋊Q8—1332no—
363#126—1332no—
364#126—1332no—
365#126—1332no—
366#126—1332no—
367#126—1332no—
368#125—1332no—
369#125—1316no—
370#125—1332no—
371#125—1332no—
372#125—1332no—
373#125—1332no—
374#125—1332no—
375#125—138no—
376#125—1316no—
377#125C22×D1318yes—
378#124C22×D13116yes—
379#123—1332no—
380#123—1332no—
381#123—1332no—
382#123—1332no—
383#123C22×D13132yes—
384C22⋊Q8—1316no—
385C22⋊Q8—1332no—
386C22⋊Q8—1332no—
387C22⋊Q8—1332no—
388C22⋊Q8—1332no—
389C22⋊Q8—1332no—
390C22⋊Q8C22×D13132yes—
391#121—1316no—
392#121—1332no—
393#121C22×D13132yes—
394C4×Q8—1316no—
395C4×Q8—1332no—
396C4×D4—1316no—
397C4×D4—1332no—
398C4×D4—1332no—
399C4×D4—1332no—
400C4×D4—1332no—
401#117—1332no—
402#117—1332no—
403C2×C4⋊C4—134no—
404C2×C4⋊C4—134no—
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—1332no—
412C2×C4⋊C4—134no—
413C2×C4⋊C4—134no—
414C2×C4⋊C4—132no—
415C2×C4⋊C4—134no—
416C2×C4⋊C4—134no—
417C2×C4⋊C4—134no—
418C2×C4⋊C4—132no—
419C2×C4⋊C4—134no—
420C2×C4⋊C4—1316no—
421C2×C4⋊C4—1332no—
422C2×C4⋊C4C22×D1314yes—
423C2×C4⋊C4C22×D1312yes—
424C2×C4⋊C4C22×D1314yes—
425C2×C22⋊C4—134no—
426C2×C22⋊C4—134no—
427C2×C22⋊C4—134no—
428C2×C22⋊C4—134no—
429C2×C22⋊C4—134no—
430C2×C22⋊C4—134no—
431C2×C22⋊C4C22×D1314yes—
432C2×C22⋊C4C22×D1314yes—
433C2×C22⋊C4C22×D1314yes—
434C2×C42—131no—
435C2×C42—134no—
436C2×C42—134no—
437C2×C42—134no—
438C2×C42—132no—
439C2×C42—138no—
440C2×C42C22×D1311yescharacteristic
441C2×C13—48no—
442C2×C13#355314yescomplemented
443C2×C13C22×2−1+411yescharacteristic
444C2×C13C2×#58512yes—
445D13—24no—
446C24—131no—
447C24C23×D1314yes—
448C2×Q8—44no—
449C2×Q8—1316no—
450C2×Q8—528no—
451C2×Q8C23×D1318yes—
452C2×D4—48no—
453C2×D4—44no—
454C2×D4—1316no—
455C2×D4—2616no—
456C2×D4C23×D13116yes—
457C2×D4C23×D1318yes—
458C22×C4—48no—
459C22×C4—132no—
460C22×C4—134no—
461C22×C4—131no—
462C22×C4—134no—
463C22×C4—134no—
464C22×C4—1316no—
465C22×C4—1316no—
466C22×C4—134no—
467C22×C4—138no—
468C22×C4—1316no—
469C22×C4—264no—
470C22×C4—528no—
471C22×C4—524no—
472C22×C4—528no—
473C22×C4—528no—
474C22×C4C23×D1314yes—
475C22×C4C23×D1311yescharacteristic
476C22×C4C23×D1312yes—
477C22×C4C23×D1314yes—
478C22×C4C23×D13116yes—
479C4⋊C4—1316no—
480C4⋊C4—1316no—
481C4⋊C4—1316no—
482C4⋊C4—1316no—
483C4⋊C4—138no—
484C4⋊C4—1316no—
485C4⋊C4—1316no—
486C4⋊C4—1316no—
487C4⋊C4—1316no—
488C4⋊C4—1316no—
489C4⋊C4—138no—
490C4⋊C4—1316no—
491C4⋊C4—1316no—
492C4⋊C4—1316no—
493C4⋊C4—138no—
494C4⋊C4—1316no—
495C4⋊C4C23×D13116yes—
496C4⋊C4C23×D1318yes—
497C4⋊C4C23×D13116yes—
498C22⋊C4—1316no—
499C22⋊C4—1316no—
500C22⋊C4—1316no—
501C22⋊C4—1316no—
502C22⋊C4—1316no—
503C22⋊C4—1316no—
504C22⋊C4C23×D13116yes—
505C22⋊C4C23×D13116yes—
506C22⋊C4C23×D13116yes—
507C42—134no—
508C42—138no—
509C42—1316no—
510C42—1316no—
511C42—1316no—
512C42C23×D1314yes—
513C13C2×#355311yescharacteristic, complemented, Sylow
514C23—28no—
515C23—28no—
516C23—28no—
517C23—134no—
518C23—132no—
519C23—264no—
520C23C24×D1318yes—
521C23C24×D1311yescharacteristic
522Q8—48no—
523Q8—5216no—
524D4—416no—
525D4—48no—
526D4—2632no—
527C2×C4—28no—
528C2×C4—28no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—416no—
532C2×C4—134no—
533C2×C4—138no—
534C2×C4—132no—
535C2×C4—138no—
536C2×C4—138no—
537C2×C4—268no—
538C2×C4—264no—
539C2×C4—268no—
540C2×C4—268no—
541C2×C4—262no—
542C2×C4—268no—
543C2×C4—5216no—
544C2×C4—528no—
545C2×C4—5216no—
546C2×C4—5216no—
547C2×C4C24×D1318yes—
548C2×C4C24×D1312yes—
549C2×C4C24×D1314yes—
550C2×C4C24×D1318yes—
551C22—28no—
552C22—28no—
553C22—28no—
554C22—416no—
555C22—134no—
556C22—268no—
557C22—264no—
558C22#1171965014yes—
559C22D13×2−1+412yes—
560C22C25×D1311yescharacteristic
561C4—22no—
562C4—28no—
563C4—28no—
564C4—24no—
565C4—262no—
566C4—268no—
567C4—264no—
568C4—268no—
569C4—268no—
570C2—48no—
571C2—264no—
572C2#1312929114yesdirect 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×#3553
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13129291C2direct (N × H)
2. C2×C13⋊#564C2semidirect
3. C2×#11719377C2semidirect
4. C2×#11719341C2semidirect
5. C2×#11719319C2semidirect
6. C2×#11719355C2semidirect
7. C2×#11719330C2semidirect
8. C2×#11719307C2semidirect
9. C2×#11719365C2semidirect
10. C2×#11719385C2semidirect
11. C2×D13×#125C2semidirect
12. C2×C13×#562C2semidirect
13. C13×#562C22semidirect
33. D13×#125C22semidirect
34. C13⋊#564C22semidirect
35. #11719385C22semidirect
36. #11719377C22semidirect
37. #11719365C22semidirect
38. #11719355C22semidirect
39. #11719341C22semidirect
40. #11719330C22semidirect
41. #11719319C22semidirect
42. #11719307C22semidirect
230. C2×#562D13semidirect
278. #562C2×D13semidirect
442. C2×C13#3553semidirect
513. C13C2×#3553semidirect
572. C2#13129291direct (N × H)

Maximal subgroups

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

subgroupindex
#131292912
C2×C13⋊#5642
C2×#117193772
C2×#117193412
C2×#117193192
C2×#117193552
C2×#117193302
C2×#117193072
C2×#117193652
C2×#117193852
C2×D13×#1252
C2×C13×#5622
C2×#355313