Finite Group Databasebeta

← C2×#13126004 #16734949

Subgroups — C2×#13126004 #16734949

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719184C211yesmaximal, characteristic
2#13126004C2116yesmaximal, direct product factor
3C2×#11718725C212yesmaximal, complemented
4C2×#11718729C212yesmaximal, complemented
5C2×#11718631C211yesmaximal, characteristic, complemented
6C2×#11718629C211yesmaximal, characteristic
7C2×#11718632C211yesmaximal, characteristic, complemented
8C2×#11718628C211yesmaximal, characteristic
9C2×#11718724C212yesmaximal, complemented
10C2×#11718727C212yesmaximal, complemented
11C2×#11718586C211yesmaximal, characteristic, complemented
12C22×C13×#125C211yesmaximal, characteristic, complemented
13C2×C13×#125—21no—
14C2×C13×#125—21no—
15C2×C13×#125—24no—
16C2×C13×#125C2212yes—
17C2×C13×#125C2212yes—
18C2×C13×#125C2218yescomplemented
19C22×C13×C4⋊C4—21no—
20C22×C13×C4⋊C4—21no—
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
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⋊#1055C2211yescharacteristic
37C2×C22⋊#1055C2211yescharacteristic
38#11718729C22116yescomplemented
39#11718727C22116yescomplemented
40#11718725C22116yescomplemented
41#11718724C22116yescomplemented
42#11718632C2218yescomplemented
43#11718631C2218yescomplemented
44C2×#88050C2212yes—
45C2×#88050C2212yes—
46#11718629C2218yes—
47#11718628C2218yes—
48C2×#88049C2212yes—
49C2×#88049C2212yes—
50C2×#88048C2212yes—
51C2×#88048C2212yes—
52C2×#88047C2212yes—
53C2×#88047C2212yes—
54#11718586C2218yescomplemented
55C2×C4⋊#1055C2212yes—
56C2×C4×#1055C2212yes—
57C23×C4×C13—21no—
58C23×C4×C13—21no—
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×Dic26C2311yescharacteristic
66C13×#125—24no—
67C13×#125—24no—
68C13×#125—28no—
69C13×#125—28no—
70C13×#125C2318yes—
71C13×#125C2318yes—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—28no—
77C2×C13×C4⋊C4—28no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4C2312yes—
83C2×C13×C4⋊C4C2312yes—
84C2×C13×C4⋊C4C2314yes—
85C2×C13×C4⋊C4C2314yes—
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⋊#1055C2314yes—
123C22⋊#1055C2314yes—
124#88050C2318yes—
125#88050C2318yes—
126#88049C2318yes—
127#88049C2318yes—
128#88048C2318yes—
129#88048C2318yes—
130#88047C2318yes—
131#88047C2318yes—
132C4⋊#1055C2318yes—
133C4×#1055C2318yes—
134C2×#3232—131nomaximal, Sylow
135C24×C13C2×D411yescharacteristic
136C23×D13—21no—
137C22×C4×C13—24no—
138C22×C4×C13—24no—
139C22×C4×C13—24no—
140C22×C4×C13—24no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—42no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13C2×D411yescharacteristic
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×C13C2412yes—
155C22×C4×C13C2411yescharacteristic
156C2×C22⋊D13—24no—
157C2×C22⋊D13—44no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C2×D52—24no—
162C2×D52—21no—
163C2×D52C2412yes—
164C2×C4×D13—24no—
165C2×C4×D13—44no—
166C2×Dic26—24no—
167C2×Dic26—21no—
168C2×Dic26C2412yes—
169C13×C4⋊C4—28no—
170C13×C4⋊C4—28no—
171C13×C4⋊C4—28no—
172C13×C4⋊C4—28no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4C2414yes—
178C13×C4⋊C4C2414yes—
179C42×C13C2×D412yes—
180C42×C13C2×D412yes—
181C42×C13C2×D414yes—
182C42×C13C2×D414yes—
183C42×C13C2412yes—
184C42×C13C2412yes—
185C22⋊Dic13—24no—
186#6103—24no—
187#6103—24no—
188#6103—24no—
189#6103—24no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C2412yes—
193C4⋊Dic13C2412yes—
194#6101—24no—
195#6101—24no—
196#6101—24no—
197#6101—24no—
198C4×Dic13—24no—
199C2×#1055—24no—
200C2×#1055—24no—
201C2×#1055C2414yes—
202C2×#1055C2414yes—
203C2×#529—131no—
204C22×#125D1311yescharacteristic, complemented
205#3232—1316no—
206C2×#499—132no—
207C2×#488—132no—
208C2×#484—131no—
209C2×#481—131no—
210C2×#483—131no—
211C2×#480—131no—
212C2×#479—132no—
213C2×#478—132no—
214C2×#431—131no—
215C23×C13—22no—
216C23×C13—22no—
217C23×C13#13514yes—
218C23×C13C22×D412yes—
219C23×C13C22×D411yescharacteristic
220C22×D13—22no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224C2×C4×C13—22no—
225C2×C4×C13—28no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—22no—
230C2×C4×C13—24no—
231C2×C4×C13—24no—
232C2×C4×C13—24no—
233C2×C4×C13—24no—
234C2×C4×C13—44no—
235C2×C4×C13—48no—
236C2×C4×C13—48no—
237C2×C4×C13—44no—
238C2×C4×C13—44no—
239C2×C4×C13C22×D412yes—
240C2×C4×C13C22×D412yes—
241C2×C4×C13C22×D412yes—
242C2×C4×C13C22×D412yes—
243C2×C4×C13C22×D412yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C132−1+414yes—
246C2×C4×C13C2511yescharacteristic
247C22⋊D13—48no—
248C2×Dic13—22no—
249C2×Dic13—22no—
250C2×Dic13—22no—
251C2×Dic13—42no—
252C2×Dic13—42no—
253C2×Dic13—42no—
254D52—24no—
255D52—42no—
256C4×D13—48no—
257Dic26—24no—
258Dic26—42no—
259#1055—24no—
260#1055—24no—
261#529—138no—
262#529—264no—
263C2×#126—261no—
264C2×#125—21no—
265C2×#125—21no—
266C2×#125—24no—
267C2×#125—131no—
268C2×#125C2×D1312yes—
269C2×#125C2×D1312yes—
270C2×#125C2×D1318yescomplemented
271C2×#124—131no—
272C2×#123—261no—
273C2×C22⋊Q8—131no—
274C2×#121—131no—
275C2×C4×Q8—131no—
276C2×C4×D4—131no—
277C2×C4×D4—261no—
278C2×#117—261no—
279C22×C4⋊C4—21no—
280C22×C4⋊C4—21no—
281C22×C4⋊C4C2×D1311yescharacteristic
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C42C2×D1311yescharacteristic
284#499—1316no—
285#488—1316no—
286#484—138no—
287#483—138no—
288#481—138no—
289#480—138no—
290#479—1316no—
291#478—1316no—
292#431—138no—
293C2×#107—132no—
294C2×#107—132no—
295C2×#106—132no—
296C2×#106—132no—
297C2×C4⋊C8—132no—
298C2×#103—132no—
299C2×#103—132no—
300C2×#102—132no—
301C2×#102—132no—
302C2×C22⋊C8—131no—
303C2×C22⋊C8—131no—
304C2×C4×C8—132no—
305C22×C13—22no—
306C22×C13—28no—
307C22×C13—22no—
308C22×C13#53612yes—
309C22×C13C2×#13514yes—
310C22×C13C2×#13512yes—
311C22×C13#57512yes—
312C22×C13C23×D411yescharacteristic
313C2×D13—42no—
314C2×D13—42no—
315C2×D13—42no—
316C2×D13—84no—
317C4×C13—22no—
318C4×C13—22no—
319C4×C13—22no—
320C4×C13—22no—
321C4×C13—22no—
322C4×C13—44no—
323C4×C13—44no—
324C4×C13#53612yes—
325C4×C13C2×2−1+412yes—
326Dic13—42no—
327Dic13—42no—
328Dic13—42no—
329C22×Q8—131no—
330C22×D4—131no—
331C22×D4—261no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—261no—
335C23×C4C22⋊D1311yescharacteristic
336C23×C4C22⋊D1311yescharacteristic
337C23×C4C22×D1311yescharacteristic
338C22×C8—132no—
339C22×C8—132no—
340#126—268no—
341#125—24no—
342#125—24no—
343#125—28no—
344#125—28no—
345#125—134no—
346#125—262no—
347#125C22×D1318yes—
348#125C22×D1318yes—
349#124—134no—
350#124—262no—
351#123—268no—
352C22⋊Q8—134no—
353C22⋊Q8—262no—
354#121—134no—
355#121—262no—
356C4×Q8—134no—
357C4×Q8—262no—
358C4×D4—134no—
359C4×D4—268no—
360C4×D4—262no—
361#117—268no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4C22×D1312yes—
379C2×C4⋊C4C22×D1312yes—
380C2×C4⋊C4C22×D1314yes—
381C2×C4⋊C4C22×D1314yes—
382C2×C22⋊C4—261no—
383C2×C22⋊C4—261no—
384C2×C22⋊C4—261no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—261no—
388C2×C42C22⋊D1311yescharacteristic
389C2×C42C22⋊D1311yescharacteristic
390C2×C42C22⋊D1314yes—
391C2×C42C22×D1311yescharacteristic
392C2×C42C22×D1311yescharacteristic
393C2×C42C22×D1314yes—
394#107—138no—
395#107—138no—
396#106—138no—
397#106—138no—
398C4⋊C8—138no—
399#103—138no—
400#103—138no—
401#102—138no—
402#102—138no—
403C22⋊C8—134no—
404C22⋊C8—134no—
405C4×C8—138no—
406C2×C13—24no—
407C2×C13#323214yescomplemented
408C2×C13C2×#53611yescharacteristic
409C2×C13C22×#13511yescharacteristic
410C2×C13C2×#57511yescharacteristic
411D13—82no—
412C24—261no—
413C24C2×C22⋊D1311yescharacteristic
414C2×Q8—132no—
415C2×Q8—261no—
416C2×Q8—264no—
417C2×D4—132no—
418C2×D4—264no—
419C2×D4—264no—
420C2×D4—261no—
421C2×D4—524no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—44no—
430C22×C4—44no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4—261no—
434C22×C4—264no—
435C22×C4—524no—
436C22×C4C2×C22⋊D1312yes—
437C22×C4C2×C22⋊D1314yes—
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C2×C22⋊D1314yes—
444C22×C4C23×D1312yes—
445C22×C4C23×D1311yescharacteristic
446C2×C8—134no—
447C2×C8—134no—
448C2×C8—264no—
449C2×C8—264no—
450C4⋊C4—28no—
451C4⋊C4—28no—
452C4⋊C4—28no—
453C4⋊C4—28no—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—132no—
459C4⋊C4—132no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—264no—
463C4⋊C4—264no—
464C4⋊C4—264no—
465C4⋊C4—264no—
466C4⋊C4C23×D1314yes—
467C4⋊C4C23×D1314yes—
468C22⋊C4—264no—
469C22⋊C4—264no—
470C22⋊C4—264no—
471C22⋊C4—264no—
472C22⋊C4—264no—
473C42—264no—
474C42C2×C22⋊D1314yes—
475C42C2×C22⋊D1312yes—
476C42C2×C22⋊D1312yes—
477C42C2×C22⋊D1314yes—
478C42C23×D1312yes—
479C42C23×D1312yes—
480C13C2×#323211yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—262no—
484C23—522no—
485C23—522no—
486C23—522no—
487C23#8820414yes—
488C23C22×C22⋊D1312yes—
489C23C22×C22⋊D1311yescharacteristic
490Q8—264no—
491Q8—522no—
492D4—264no—
493D4—528no—
494D4—522no—
495C2×C4—22no—
496C2×C4—28no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—44no—
506C2×C4—48no—
507C2×C4—48no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—528no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4—522no—
517C2×C4#8825414yes—
518C2×C4C22×C22⋊D1312yes—
519C2×C4C22×C22⋊D1312yes—
520C2×C4C22×C22⋊D1312yes—
521C2×C4C22×C22⋊D1312yes—
522C2×C4C22×C22⋊D1312yes—
523C2×C4C22×C22⋊D1311yescharacteristic
524C2×C4C24×D1311yescharacteristic
525C8—264no—
526C8—264no—
527C22—22no—
528C22—28no—
529C22—22no—
530C22—522no—
531C22—522no—
532C22—522no—
533C22—1044no—
534C22#1171952112yes—
535C22C2×#8820414yes—
536C22C2×#8820412yes—
537C22#1171952712yes—
538C22C23×C22⋊D1311yescharacteristic
539C4—22no—
540C4—22no—
541C4—22no—
542C4—22no—
543C4—22no—
544C4—44no—
545C4—44no—
546C4—522no—
547C4—522no—
548C4—522no—
549C4#1171952112yes—
550C4C2×#8825412yes—
551C2—24no—
552C2—1042no—
553C2#1312600414yesdirect product factor
554C2C2×#1171952111yescharacteristic
555C2C22×#8820411yescharacteristic
556C2C2×#1171952711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC22×C13×#125C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC22×#125D13
hypocenterC13C2×#3232
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #13126004C2direct (N × H)
3. C2×#11718725C2semidirect
4. C2×#11718729C2semidirect
5. C2×#11718631C2semidirect
7. C2×#11718632C2semidirect
9. C2×#11718724C2semidirect
10. C2×#11718727C2semidirect
11. C2×#11718586C2semidirect
12. C22×C13×#125C2semidirect
18. C2×C13×#125C22semidirect
38. #11718729C22semidirect
39. #11718727C22semidirect
40. #11718725C22semidirect
41. #11718724C22semidirect
42. #11718632C22semidirect
43. #11718631C22semidirect
54. #11718586C22semidirect
204. C22×#125D13semidirect
270. C2×#125C2×D13semidirect
407. C2×C13#3232semidirect
480. C13C2×#3232semidirect
553. C2#13126004direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117191842
#131260042
C2×#117187252
C2×#117187292
C2×#117186312
C2×#117186292
C2×#117186322
C2×#117186282
C2×#117187242
C2×#117187272
C2×#117185862
C22×C13×#1252
C2×#323213