Finite Group Databasebeta

← C2×#13115072 #15863784

Subgroups — C2×#13115072 #15863784

Order 3328.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719209C211yesmaximal, characteristic
2C2×#11718782C211yesmaximal, characteristic, complemented
3C22×#88065C211yesmaximal, characteristic
4C2×#11718794C211yesmaximal, characteristic
5C2×#11718638C211yesmaximal, characteristic, complemented
6#13115072C218yesmaximal, direct product factor
7C2×#11718147C211yesmaximal, characteristic, complemented
8C2×C13×#343C211yesmaximal, characteristic, complemented
9C22×#6127C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C2×C4×C22⋊D13—22no—
14C2×#88180C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4×Dic13C2211yescharacteristic
17#11719209—22no—
18#11719209—22no—
19#11719209—22no—
20#11719209C2214yes—
21C2×#88147—21no—
22C2×#88146—21no—
23C2×C4⋊C4×D13—21no—
24C2×#88141—21no—
25C2×#88071—22no—
26C2×#88065C418yescomplemented
27C2×#88065C2214yes—
28#11718794—22no—
29#11718794C2214yes—
30#11718782—22no—
31#11718782C2214yescomplemented
32C2×#88061—21no—
33C2×#88058—21no—
34C2×#88057—21no—
35C2×#88056—21no—
36#11718638—22no—
37#11718638C2214yescomplemented
38C13×#343C2214yescomplemented
39#11718147C2214yescomplemented
40C23×C4×C13D412yes—
41C23×C4×C13C2311yescharacteristic
42C22×C22⋊D13—21no—
43C23×Dic13—21no—
44C23×Dic13—21no—
45C2×#6127—21no—
46C2×#6127—21no—
47C2×#6127—22no—
48C2×#6127—22no—
49C2×#6127C2×C414yes—
50C2×#6127D412yes—
51C2×#6127Q814yes—
52C2×#6127C2312yes—
53C22×D52D411yescharacteristic
54C22×C4×D13—21no—
55C22×C4×D13—22no—
56C22×Dic26D411yescharacteristic
57C2×C13×M16—21no—
58C2×C13×M16—22no—
59C2×C13×M16—21no—
60C2×C13×M16—22no—
61C2×C13×M16—22no—
62C2×C13×M16C2×C414yescomplemented
63C2×C13×M16C2312yes—
64C2×C13×M16C2312yes—
65C22×C8×C13—21no—
66C22×C8×C13—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4D412yes—
72C2×C13×C4⋊C4C2312yes—
73C2×C22⋊Dic13—21no—
74C4×C22⋊D13—28no—
75C4×C22⋊D13—28no—
76C2×#6103—22no—
77#88180—21no—
78#88180—21no—
79#88180D412yes—
80#88180C2312yes—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13D411yescharacteristic
87C2×C4⋊Dic13D411yescharacteristic
88C2×C4⋊Dic13C2312yes—
89C2×#6101—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13C2×C414yescomplemented
95C2×C4×Dic13C2312yes—
96#88147—24no—
97#88147—24no—
98#88146—24no—
99#88146—24no—
100C4⋊C4×D13—24no—
101C4⋊C4×D13—24no—
102#88141—24no—
103#88141—24no—
104#88071—28no—
105#88065C2×C4116yescomplemented
106#88061—24no—
107#88058—24no—
108#88057—24no—
109#88056—24no—
110C2×#1860—131nomaximal, Sylow
111C24×C13C2×D411yescharacteristic
112C23×D13—21no—
113C22×C4×C13—22no—
114C22×C4×C13—22no—
115C22×C4×C13—44no—
116C22×C4×C13C22×C412yes—
117C22×C4×C13C2×D414yes—
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2×Q812yes—
124C22×C4×C13#4112yes—
125C22×C4×C13#4112yes—
126C22×C4×C13C2411yescharacteristic
127C2×C22⋊D13—24no—
128C2×C22⋊D13—22no—
129C2×C22⋊D13—24no—
130C2×C22⋊D13—22no—
131C22×Dic13—21no—
132C22×Dic13—24no—
133C22×Dic13—21no—
134C22×Dic13—21no—
135C22×Dic13—22no—
136C22×Dic13—22no—
137C22×Dic13—42no—
138C22×Dic13—42no—
139C22×Dic13—44no—
140C22×Dic13—41no—
141C22×Dic13—41no—
142#6127—24no—
143#6127—24no—
144#6127—24no—
145#6127—24no—
146#6127—24no—
147#6127—22no—
148#6127—22no—
149#6127C4⋊C418yes—
150#6127C22×C414yes—
151#6127C2×Q814yes—
152C2×D52—21no—
153C2×D52—22no—
154C2×D52C4⋊C414yes—
155C2×D52C2×D412yes—
156C2×C4×D13—24no—
157C2×C4×D13—22no—
158C2×C4×D13—24no—
159C2×C4×D13—22no—
160C2×C4×D13—28no—
161C2×C4×D13—84no—
162C2×Dic26—21no—
163C2×Dic26—22no—
164C2×Dic26C4⋊C414yes—
165C2×Dic26C2×D412yes—
166C13×M16—24no—
167C13×M16—22no—
168C13×M16—22no—
169C13×M16—22no—
170C13×M16—42no—
171C13×M16C22×C414yescomplemented
172C2×C8×C13—24no—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—42no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C22⋊Dic13—22no—
181C22⋊Dic13—22no—
182#6103—28no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187C4⋊Dic13—41no—
188C4⋊Dic13—41no—
189C4⋊Dic13C2×D412yes—
190C4⋊Dic13C2×D412yes—
191#6101—28no—
192C4×Dic13—28no—
193C4×Dic13—24no—
194C4×Dic13—22no—
195C4×Dic13—22no—
196C4×Dic13—22no—
197C4×Dic13C22×C414yescomplemented
198C2×#520—131no—
199C2×#428—131no—
200C22×#104—131no—
201C2×#417—131no—
202C2×#382—131no—
203#1860—138no—
204C2×#343D1311yescharacteristic, complemented
205C2×#339—131no—
206C23×C13—22no—
207C23×C13—22no—
208C23×C13C4×D412yes—
209C23×C13#12011yescharacteristic
210C23×C13#12011yescharacteristic
211C23×C13C22⋊Q812yes—
212C23×C13C22×D411yescharacteristic
213C22×D13—22no—
214C22×D13—24no—
215C22×D13—42no—
216C22×D13—42no—
217C2×C4×C13—24no—
218C2×C4×C13—44no—
219C2×C4×C13—44no—
220C2×C4×C13—82no—
221C2×C4×C13C2×C4⋊C412yes—
222C2×C4×C13C2×C4⋊C412yes—
223C2×C4×C13C4×D412yes—
224C2×C4×C13C4×D412yes—
225C2×C4×C13C4×D412yes—
226C2×C4×C13#12011yescharacteristic
227C2×C4×C13#12011yescharacteristic
228C2×C4×C13C22⋊Q812yes—
229C2×C4×C13C22⋊Q812yes—
230C2×C4×C13C22⋊Q812yes—
231C2×C4×C13#12312yes—
232C2×C4×C13#12312yes—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C22×Q811yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C22⋊D13—24no—
240C22⋊D13—24no—
241C22⋊D13—28no—
242C2×Dic13—22no—
243C2×Dic13—24no—
244C2×Dic13—24no—
245C2×Dic13—22no—
246C2×Dic13—22no—
247C2×Dic13—48no—
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—44no—
253C2×Dic13—42no—
254C2×Dic13—82no—
255C2×Dic13—82no—
256D52—22no—
257D52—24no—
258D52C2×C4⋊C414yes—
259C4×D13—24no—
260C4×D13—24no—
261C4×D13—28no—
262C4×D13—88no—
263Dic26—22no—
264Dic26—24no—
265Dic26C2×C4⋊C414yes—
266C8×C13—24no—
267C8×C13—42no—
268C22×#41—131no—
269C22×M16C2×D1311yescharacteristic
270C22×M16C2×D1311yescharacteristic
271#520—134no—
272#520—262no—
273#520—262no—
274#520—262no—
275C2×C4×Q8—261no—
276C2×C4×D4—261no—
277C2×C4×D4—262no—
278C2×#117—131no—
279C2×#117—261no—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—261no—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C42—131no—
284#428—134no—
285#428—262no—
286C2×#107—261no—
287C2×#106—261no—
288C2×#104—138no—
289C2×#104—134no—
290#417—134no—
291#417—262no—
292C2×#103—261no—
293C2×#102—261no—
294#382—134no—
295#382—262no—
296C2×#95—262no—
297#343C2×D1314yescomplemented
298#339—134no—
299C22×C13—24no—
300C22×C13—24no—
301C22×C13—21no—
302C22×C13—21no—
303C22×C13—21no—
304C22×C13—21no—
305C22×C13#38512yes—
306C22×C13#38512yes—
307C22×C13#45412yes—
308C22×C13#45512yes—
309C22×C13C2×C4×D411yescharacteristic
310C22×C13C2×#12011yescharacteristic
311C22×C13C2×C22⋊Q811yescharacteristic
312C2×D13—24no—
313C2×D13—48no—
314C2×D13—42no—
315C2×D13—42no—
316C4×C13—44no—
317C4×C13#38512yes—
318C4×C13#38512yes—
319C4×C13C22×C4⋊C411yescharacteristic
320C4×C13C2×C4×D411yescharacteristic
321C4×C13C2×C22⋊Q811yescharacteristic
322C4×C13C2×#12311yescharacteristic
323Dic13—24no—
324Dic13—44no—
325Dic13—42no—
326Dic13—42no—
327Dic13—82no—
328C2×#41—134no—
329C2×#41—132no—
330C2×#41—134no—
331C2×#41—132no—
332C2×#41—261no—
333C2×#41—262no—
334C2×#41—261no—
335C2×#41—262no—
336C22×Q8—131no—
337C22×D4—131no—
338C22×D4—261no—
339C23×C4—262no—
340C23×C4—261no—
341C23×C4—261no—
342C23×C4—261no—
343C23×C4D5212yes—
344C23×C4C22×D1311yescharacteristic
345C2×M16—21no—
346C2×M16—22no—
347C2×M16—21no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16C4×D1314yescomplemented
351C2×M16C22×D1312yes—
352C2×M16C22×D1312yes—
353C22×C8—21no—
354C22×C8—21no—
355C4×Q8—264no—
356C4×Q8—264no—
357C4×D4—264no—
358C4×D4—264no—
359C4×D4—268no—
360C4×D4—268no—
361#117—132no—
362#117—132no—
363#117—264no—
364#117—264no—
365#117—261no—
366#117—261no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—131no—
372C2×C4⋊C4—131no—
373C2×C4⋊C4—132no—
374C2×C4⋊C4—264no—
375C2×C4⋊C4—264no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4D5212yes—
383C2×C4⋊C4C22×D1312yes—
384C2×C22⋊C4—262no—
385C2×C22⋊C4—261no—
386C2×C42—134no—
387C2×C42—132no—
388C2×C42—262no—
389C2×C42—261no—
390C2×C42—262no—
391C2×C42—261no—
392#107—264no—
393#106—264no—
394#104—1316no—
395#103—264no—
396#102—264no—
397#95—268no—
398C2×C13—21no—
399C2×C13—21no—
400C2×C13—22no—
401C2×C13#186014yescomplemented
402C2×C13C2×#38511yescharacteristic
403C2×C13C2×#45511yescharacteristic
404C2×C13C2×#45411yescharacteristic
405D13—44no—
406C24—261no—
407C24C2×D5211yescharacteristic
408#41—138no—
409#41—134no—
410#41—134no—
411#41—264no—
412#41—264no—
413#41—264no—
414#41—264no—
415#41—264no—
416#41—262no—
417#41—262no—
418C2×Q8—134no—
419C2×Q8—132no—
420C2×Q8—261no—
421C2×Q8—262no—
422C2×D4—134no—
423C2×D4—132no—
424C2×D4—264no—
425C2×D4—262no—
426C2×D4—264no—
427C2×D4—262no—
428C2×D4—261no—
429C2×D4—262no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—268no—
434C22×C4—261no—
435C22×C4—264no—
436C22×C4—262no—
437C22×C4—264no—
438C22×C4—262no—
439C22×C4—264no—
440C22×C4—261no—
441C22×C4—261no—
442C22×C4—262no—
443C22×C4—262no—
444C22×C4—522no—
445C22×C4—522no—
446C22×C4—524no—
447C22×C4—521no—
448C22×C4—521no—
449C22×C4—1044no—
450C22×C4C2×C4×D1312yes—
451C22×C4C2×D5214yes—
452C22×C4C2×D5211yescharacteristic
453C22×C4#612712yes—
454C22×C4D4×D1311yescharacteristic
455C22×C4D4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4#612912yes—
459C22×C4Q8×D1312yes—
460C22×C4C23×D1311yescharacteristic
461M16—24no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—42no—
466M16C2×C4×D1314yescomplemented
467C2×C8—24no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—42no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—132no—
476C4⋊C4—132no—
477C4⋊C4—268no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—262no—
481C4⋊C4—262no—
482C4⋊C4—521no—
483C4⋊C4—521no—
484C22⋊C4—268no—
485C22⋊C4—262no—
486C22⋊C4—262no—
487C42—134no—
488C42—268no—
489C42—264no—
490C42—262no—
491C42—262no—
492C42—262no—
493C13C2×#186011yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—262no—
497C23—264no—
498C23—522no—
499C23—522no—
500C23C4×D5212yes—
501C23#8813611yescharacteristic
502C23#8813611yescharacteristic
503C23#8815112yes—
504C23C22×D5211yescharacteristic
505Q8—134no—
506Q8—262no—
507Q8—264no—
508D4—134no—
509D4—264no—
510D4—264no—
511D4—268no—
512D4—262no—
513D4—264no—
514C2×C4—24no—
515C2×C4—44no—
516C2×C4—44no—
517C2×C4—82no—
518C2×C4—262no—
519C2×C4—264no—
520C2×C4—264no—
521C2×C4—264no—
522C2×C4—268no—
523C2×C4—264no—
524C2×C4—262no—
525C2×C4—262no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—528no—
529C2×C4—522no—
530C2×C4—522no—
531C2×C4—524no—
532C2×C4—522no—
533C2×C4—1048no—
534C2×C4—1042no—
535C2×C4—1042no—
536C2×C4C4×D5212yes—
537C2×C4#8813512yes—
538C2×C4#8813512yes—
539C2×C4#8813611yescharacteristic
540C2×C4#8813611yescharacteristic
541C2×C4#8813712yes—
542C2×C4#8813712yes—
543C2×C4C4⋊C4×D1312yes—
544C2×C4C4⋊C4×D1312yes—
545C2×C4#8815012yes—
546C2×C4#8815012yes—
547C2×C4#8815112yes—
548C2×C4C22×C4×D1311yescharacteristic
549C2×C4C2×#612711yescharacteristic
550C2×C4C2×D4×D1311yescharacteristic
551C2×C4C2×D4×D1311yescharacteristic
552C2×C4C2×#612911yescharacteristic
553C2×C4C2×Q8×D1311yescharacteristic
554C8—24no—
555C8—42no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—264no—
563C22—522no—
564C22—522no—
565C22—528no—
566C22#1171832912yes—
567C22#1171832912yes—
568C22#1171840712yes—
569C22#1171841412yes—
570C22C2×C4×D5211yescharacteristic
571C22C2×#8813611yescharacteristic
572C22C2×#8815111yescharacteristic
573C4—44no—
574C4—264no—
575C4—524no—
576C4—522no—
577C4—522no—
578C4—1042no—
579C4#1171832912yes—
580C4#1171832912yes—
581C4C2×#8813511yescharacteristic
582C4C2×#8813711yescharacteristic
583C4C2×C4⋊C4×D1311yescharacteristic
584C4C2×#8815011yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—524no—
589C2#1311507214yesdirect product factor
590C2C2×#1171832911yescharacteristic
591C2C2×#1171840711yescharacteristic
592C2C2×#1171841411yescharacteristic
subgroupG/H
centerC23#88136
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#343C2
socleC23×C13#120
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC2×#343D13
hypocenterC13C2×#1860
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C2×#11718782C2semidirect
5. C2×#11718638C2semidirect
6. #13115072C2direct (N × H)
7. C2×#11718147C2semidirect
8. C2×C13×#343C2semidirect
26. C2×#88065C4semidirect
31. #11718782C22semidirect
37. #11718638C22semidirect
38. C13×#343C22semidirect
39. #11718147C22semidirect
62. C2×C13×M16C2×C4semidirect
94. C2×C4×Dic13C2×C4semidirect
105. #88065C2×C4semidirect
171. C13×M16C22×C4semidirect
197. C4×Dic13C22×C4semidirect
204. C2×#343D13semidirect
297. #343C2×D13semidirect
350. C2×M16C4×D13semidirect
401. C2×C13#1860semidirect
466. M16C2×C4×D13semidirect
493. C13C2×#1860semidirect
589. C2#13115072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192092
C2×#117187822
C22×#880652
C2×#117187942
C2×#117186382
#131150722
C2×#117181472
C2×C13×#3432
C2×#186013