Finite Group Databasebeta

← C2×#13126015 #16734997

Subgroups — C2×#13126015 #16734997

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719184C211yesmaximal, characteristic
2#13126015C2116yesmaximal, direct product factor
3C2×#11718725C212yesmaximal, complemented
4C2×#11718729C212yesmaximal, complemented
5C2×#11718657C212yesmaximal, complemented
6C2×#11718664C212yesmaximal
7C2×#11718752C211yesmaximal, characteristic, complemented
8C2×#11718755C211yesmaximal, characteristic, complemented
9C2×#11718745C211yesmaximal, characteristic, complemented
10C2×#11718748C211yesmaximal, characteristic, complemented
11C2×#11718586C211yesmaximal, characteristic, complemented
12C2×C13×#533C211yesmaximal, characteristic, complemented
13C13×#533—24no—
14C13×#533C2218yescomplemented
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#125C2212yes—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C4×Q8×C13—21no—
21C2×C4×Q8×C13—21no—
22C2×C13×#117C2212yes—
23C22×C42×C13C2211yescharacteristic
24C2×#88184C2211yescharacteristic
25C2×#88183—21no—
26C2×C4×C22⋊D13—21no—
27C2×#88178C2211yescharacteristic
28#11719184—24no—
29#11719184C2218yes—
30C2×#88130—21no—
31C2×#88129C2211yescharacteristic
32C2×C4×D52C2211yescharacteristic
33C2×#88126—21no—
34C2×#88124C2211yescharacteristic
35C2×C4×Dic26C2211yescharacteristic
36C2×C22⋊#1055C2212yes—
37#11718755C2218yescomplemented
38#11718752C2218yescomplemented
39#11718748C2218yescomplemented
40#11718745C2218yescomplemented
41#11718729C22116yescomplemented
42#11718725C22116yescomplemented
43#11718664C22116yes—
44#11718657C22116yescomplemented
45C2×#88050C2212yes—
46C2×#88050C2212yes—
47C2×#88049C2212yes—
48C2×#88049C2212yes—
49C2×#88048C2212yes—
50C2×#88048C2212yes—
51C2×#88047C2212yes—
52C2×#88047C2212yes—
53#11718586C2218yescomplemented
54C2×C4⋊#1055C2211yescharacteristic
55C2×C4⋊#1055C2211yescharacteristic
56C2×C4×#1055C2212yes—
57C22×Q8×C13—21no—
58C22×Q8×C13—21no—
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×Dic26C2311yescharacteristic
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—22no—
68C13×C4⋊Q8C2314yes—
69C13×C4⋊Q8C2314yes—
70C13×#125—24no—
71C13×#125C2318yes—
72C13×C22⋊Q8—28no—
73C13×C22⋊Q8—28no—
74C4×Q8×C13—28no—
75C4×Q8×C13—28no—
76C13×#117—24no—
77C13×#117C2318yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C22⋊C4—22no—
85C2×C42×C13—22no—
86C2×C42×C13D411yescharacteristic
87C2×C42×C13D411yescharacteristic
88C2×C42×C13D414yes—
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2314yes—
92C2×C22⋊Dic13—21no—
93#88184—22no—
94#88184C2314yes—
95#88183—28no—
96C4×C22⋊D13—28no—
97C2×#6103—21no—
98C2×#6103—21no—
99C2×#6103—21no—
100C2×#6103—21no—
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103#88178—22no—
104#88178C2314yes—
105C2×#6101—21no—
106C2×#6101—21no—
107C2×#6101—21no—
108C2×#6101—21no—
109C2×C4×Dic13—21no—
110C22×#1055C2312yes—
111C22×#1055C2312yes—
112#88130—28no—
113#88129—22no—
114#88129C2314yes—
115C4×D52—22no—
116C4×D52C2314yes—
117#88126—28no—
118#88124—22no—
119#88124C2314yes—
120C4×Dic26—22no—
121C4×Dic26C2314yes—
122C22⋊#1055C2318yes—
123#88050C2318yes—
124#88050C2318yes—
125#88049C2318yes—
126#88049C2318yes—
127#88048C2318yes—
128#88048C2318yes—
129#88047C2318yes—
130#88047C2318yes—
131C4⋊#1055C2314yes—
132C4⋊#1055C2314yes—
133C4×#1055C2318yes—
134C2×#3233—131nomaximal, Sylow
135C24×C13C2×D411yescharacteristic
136C23×D13—21no—
137C2×Q8×C13—24no—
138C2×Q8×C13—24no—
139C2×Q8×C13—44no—
140C2×Q8×C13—44no—
141C22×C4×C13—24no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—42no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D414yes—
153C22×C4×C13C2×D414yes—
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2412yes—
156C22×C4×C13C2411yescharacteristic
157C2×C22⋊D13—24no—
158C2×C22⋊D13—44no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C2×D52—22no—
163C2×D52—22no—
164C2×D52—21no—
165C2×D52C2412yes—
166C2×C4×D13—24no—
167C2×C4×D13—44no—
168C2×Dic26—22no—
169C2×Dic26—22no—
170C2×Dic26—21no—
171C2×Dic26C2412yes—
172C13×C4⋊C4—28no—
173C13×C4⋊C4—28no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—24no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4C2414yes—
179C13×C4⋊C4C2414yes—
180C13×C22⋊C4—28no—
181C42×C13—28no—
182C42×C13C2×D412yes—
183C42×C13C2×D412yes—
184C42×C13C2×D414yes—
185C42×C13C2×D414yes—
186C42×C13C2412yes—
187C42×C13C2412yes—
188C22⋊Dic13—24no—
189#6103—24no—
190#6103—24no—
191#6103—24no—
192#6103—24no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C2412yes—
196C4⋊Dic13C2412yes—
197#6101—24no—
198#6101—24no—
199#6101—24no—
200#6101—24no—
201C4×Dic13—24no—
202C2×#1055—24no—
203C2×#1055—24no—
204C2×#1055C2414yes—
205C2×#1055C2414yes—
206C2×#533D1311yescharacteristic, complemented
207C2×#529—131no—
208#3233—1316no—
209C2×#499—132no—
210C2×#488—132no—
211C2×#485—132no—
212C2×#482—132no—
213C2×#477—131no—
214C2×#475—131no—
215C2×#476—131no—
216C2×#474—131no—
217C2×#431—131no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13C22×D412yes—
222C23×C13C22×D411yescharacteristic
223C22×D13—22no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—42no—
227Q8×C13—48no—
228Q8×C13—48no—
229C2×C4×C13—22no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—24no—
234C2×C4×C13—28no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—24no—
238C2×C4×C13—24no—
239C2×C4×C13—44no—
240C2×C4×C13—44no—
241C2×C4×C13—44no—
242C2×C4×C13#13514yes—
243C2×C4×C13C22×D412yes—
244C2×C4×C13C22×D412yes—
245C2×C4×C13C22×D412yes—
246C2×C4×C13C22×D412yes—
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C22×D412yes—
249C2×C4×C132−1+412yes—
250C2×C4×C132−1+412yes—
251C2×C4×C13C2511yescharacteristic
252C22⋊D13—48no—
253C2×Dic13—22no—
254C2×Dic13—22no—
255C2×Dic13—22no—
256C2×Dic13—42no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259D52—22no—
260D52—22no—
261D52—42no—
262C4×D13—48no—
263Dic26—22no—
264Dic26—22no—
265Dic26—42no—
266#1055—24no—
267#1055—24no—
268#533—24no—
269#533C2×D1318yescomplemented
270C2×C4⋊Q8C2×D1311yescharacteristic
271C2×C4⋊Q8C2×D1311yescharacteristic
272#529—138no—
273#529—264no—
274C2×#126—261no—
275C2×#125—131no—
276C2×#125C2×D1312yes—
277C2×#124—131no—
278C2×#123—261no—
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8—131no—
282C2×#121—131no—
283C2×C4×Q8—21no—
284C2×C4×Q8—21no—
285C2×C4×Q8—131no—
286C2×C4×D4—131no—
287C2×C4×D4—261no—
288C2×#117—261no—
289C2×#117C2×D1312yes—
290C22×C42C2×D1311yescharacteristic
291#499—1316no—
292#488—1316no—
293#485—1316no—
294#482—1316no—
295#477—138no—
296#476—138no—
297#475—138no—
298#474—138no—
299#431—138no—
300C2×#107—132no—
301C2×#107—132no—
302C2×#106—132no—
303C2×#106—132no—
304C2×C4⋊C8—131no—
305C2×C4⋊C8—131no—
306C2×#103—132no—
307C2×#103—132no—
308C2×#102—132no—
309C2×#102—132no—
310C2×C22⋊C8—132no—
311C2×C4×C8—132no—
312C22×C13—22no—
313C22×C13—22no—
314C22×C13—22no—
315C22×C13—44no—
316C22×C13#53612yes—
317C22×C13C2×#13512yes—
318C22×C13#57512yes—
319C22×C13C23×D411yescharacteristic
320C2×D13—42no—
321C2×D13—42no—
322C2×D13—42no—
323C2×D13—84no—
324C4×C13—22no—
325C4×C13—22no—
326C4×C13—22no—
327C4×C13—22no—
328C4×C13—44no—
329C4×C13—44no—
330C4×C13#53612yes—
331C4×C13C2×#13514yes—
332C4×C13C2×2−1+411yescharacteristic
333C4×C13C2×2−1+411yescharacteristic
334Dic13—42no—
335Dic13—42no—
336Dic13—42no—
337C22×Q8—21no—
338C22×Q8—21no—
339C22×Q8—131no—
340C22×D4—131no—
341C22×D4—261no—
342C23×C4—261no—
343C23×C4C22⋊D1311yescharacteristic
344C23×C4C22⋊D1311yescharacteristic
345C23×C4C22×D1311yescharacteristic
346C22×C8—132no—
347C22×C8—132no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8C22×D1314yes—
351C4⋊Q8C22×D1314yes—
352#126—268no—
353#125—24no—
354#125—134no—
355#125—262no—
356#125C22×D1318yes—
357#124—134no—
358#124—262no—
359#123—268no—
360C22⋊Q8—28no—
361C22⋊Q8—28no—
362C22⋊Q8—134no—
363C22⋊Q8—262no—
364#121—134no—
365#121—262no—
366C4×Q8—28no—
367C4×Q8—28no—
368C4×Q8—134no—
369C4×Q8—262no—
370C4×D4—134no—
371C4×D4—268no—
372C4×D4—262no—
373#117—24no—
374#117—268no—
375#117C22×D1318yes—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22×D1312yes—
387C2×C4⋊C4C22×D1312yes—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—22no—
395C2×C42—261no—
396C2×C42C22⋊D1311yescharacteristic
397C2×C42C22⋊D1311yescharacteristic
398C2×C42C22⋊D1314yes—
399C2×C42C22×D1311yescharacteristic
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1314yes—
402#107—138no—
403#107—138no—
404#106—138no—
405#106—138no—
406C4⋊C8—134no—
407C4⋊C8—134no—
408#103—138no—
409#103—138no—
410#102—138no—
411#102—138no—
412C22⋊C8—138no—
413C4×C8—138no—
414C2×C13—42no—
415C2×C13#323314yescomplemented
416C2×C13C2×#53611yescharacteristic
417C2×C13C22×#13511yescharacteristic
418C2×C13C2×#57511yescharacteristic
419D13—82no—
420C24—261no—
421C24C2×C22⋊D1311yescharacteristic
422C2×Q8—24no—
423C2×Q8—24no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—132no—
427C2×Q8—261no—
428C2×Q8—262no—
429C2×Q8—262no—
430C2×D4—132no—
431C2×D4—264no—
432C2×D4—262no—
433C2×D4—262no—
434C2×D4—261no—
435C2×D4—524no—
436C22×C4—24no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—264no—
446C22×C4—524no—
447C22×C4C2×C22⋊D1312yes—
448C22×C4C2×C22⋊D1314yes—
449C22×C4C2×C22⋊D1311yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451C22×C4C2×C22⋊D1311yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1314yes—
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C23×D1312yes—
456C22×C4C23×D1311yescharacteristic
457C2×C8—134no—
458C2×C8—134no—
459C2×C8—264no—
460C2×C8—264no—
461C4⋊C4—28no—
462C4⋊C4—28no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—132no—
468C4⋊C4—132no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—264no—
474C4⋊C4—264no—
475C4⋊C4C23×D1314yes—
476C4⋊C4C23×D1314yes—
477C22⋊C4—28no—
478C22⋊C4—264no—
479C22⋊C4—264no—
480C22⋊C4—264no—
481C22⋊C4—264no—
482C22⋊C4—264no—
483C42—28no—
484C42—264no—
485C42C2×C22⋊D1314yes—
486C42C2×C22⋊D1312yes—
487C42C2×C22⋊D1314yes—
488C42C2×C22⋊D1312yes—
489C42C23×D1312yes—
490C42C23×D1312yes—
491C13C2×#323311yescharacteristic, complemented, Sylow
492C23—22no—
493C23—22no—
494C23—22no—
495C23—262no—
496C23—522no—
497C23—522no—
498C23—522no—
499C23C22×C22⋊D1312yes—
500C23C22×C22⋊D1311yescharacteristic
501Q8—48no—
502Q8—48no—
503Q8—262no—
504Q8—262no—
505Q8—522no—
506D4—262no—
507D4—262no—
508D4—528no—
509D4—522no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—28no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—262no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—528no—
530C2×C4#8820414yes—
531C2×C4#8825412yes—
532C2×C4#8825412yes—
533C2×C4C22×C22⋊D1312yes—
534C2×C4C22×C22⋊D1312yes—
535C2×C4C22×C22⋊D1312yes—
536C2×C4C22×C22⋊D1312yes—
537C2×C4C22×C22⋊D1311yescharacteristic
538C2×C4C22×C22⋊D1312yes—
539C2×C4C24×D1311yescharacteristic
540C8—264no—
541C8—264no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—44no—
546C22—522no—
547C22—522no—
548C22—522no—
549C22—1044no—
550C22#1171952112yes—
551C22C2×#8820412yes—
552C22#1171952712yes—
553C22C23×C22⋊D1311yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—22no—
558C4—44no—
559C4—44no—
560C4—522no—
561C4—522no—
562C4—522no—
563C4#1171952112yes—
564C4C2×#8820414yes—
565C4C2×#8825411yescharacteristic
566C4C2×#8825411yescharacteristic
567C2—42no—
568C2—1042no—
569C2#1312601514yesdirect product factor
570C2C2×#1171952111yescharacteristic
571C2C22×#8820411yescharacteristic
572C2C2×#1171952711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#533C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC2×#533D13
hypocenterC13C2×#3233
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13126015C2direct (N × H)
3. C2×#11718725C2semidirect
4. C2×#11718729C2semidirect
5. C2×#11718657C2semidirect
7. C2×#11718752C2semidirect
8. C2×#11718755C2semidirect
9. C2×#11718745C2semidirect
10. C2×#11718748C2semidirect
11. C2×#11718586C2semidirect
12. C2×C13×#533C2semidirect
14. C13×#533C22semidirect
37. #11718755C22semidirect
38. #11718752C22semidirect
39. #11718748C22semidirect
40. #11718745C22semidirect
41. #11718729C22semidirect
42. #11718725C22semidirect
44. #11718657C22semidirect
53. #11718586C22semidirect
206. C2×#533D13semidirect
269. #533C2×D13semidirect
415. C2×C13#3233semidirect
491. C13C2×#3233semidirect
569. C2#13126015direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191842
#131260152
C2×#117187252
C2×#117187292
C2×#117186572
C2×#117186642
C2×#117187522
C2×#117187552
C2×#117187452
C2×#117187482
C2×#117185862
C2×C13×#5332
C2×#323313