Finite Group Databasebeta

← C2×#13115268 #15864600

Subgroups — C2×#13115268 #15864600

Order 3328.

1966 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
1C23×#6094C211yesmaximal, characteristic
2C22×#88151C211yesmaximal, characteristic
3C22×#88056C211yesmaximal, characteristic, complemented
4C22×#88050C211yesmaximal, characteristic, complemented
5C2×#11718648C211yesmaximal, characteristic
6#13115268C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C2×C13×#340C211yesmaximal, characteristic, complemented
9C23×C4×D13C2211yescharacteristic
10C23×Dic26C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×#6103—21no—
15C22×#6103—21no—
16C22×C4⋊Dic13—21no—
17C22×C4⋊Dic13C2211yescharacteristic
18C23×#1055C2211yescharacteristic
19C22×#6094—24no—
20C22×#6094—24no—
21C22×#6094—24no—
22C22×#6094C2214yes—
23C2×#88151—22no—
24C2×#88151—24no—
25C2×#88151C418yescomplemented
26C2×#88151C2214yes—
27C2×#88071—21no—
28C2×#88056—24no—
29C2×#88056C2214yescomplemented
30#11718648—22no—
31#11718648C2214yes—
32C2×#88050—24no—
33C2×#88050C2214yescomplemented
34C13×#340C2214yescomplemented
35#11718121C2214yescomplemented
36C24×D13D411yescharacteristic
37C23×C4×C13—21no—
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C23×Dic13—21no—
42C23×Dic13D411yescharacteristic
43C22×C4×D13—22no—
44C22×C4×D13—22no—
45C22×C4×D13—22no—
46C22×C4×D13—22no—
47C22×C4×D13C2×C414yes—
48C22×C4×D13D412yes—
49C22×C4×D13D414yes—
50C22×C4×D13C2312yes—
51C22×Dic26—22no—
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—21no—
56C22×Dic26—22no—
57C22×Dic26C2×C414yes—
58C22×Dic26C2312yes—
59C22×C8×C13—22no—
60C22×C8×C13—22no—
61C22×C8×C13D414yes—
62C22×C8×C13C2312yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2×C414yes—
69C2×C13×C4⋊C4C2312yes—
70C2×C13×C4⋊C4C2312yes—
71C2×#6103—28no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—44no—
75C2×C4⋊Dic13—28no—
76C2×C4⋊Dic13—24no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13C2312yes—
81C22×#1055—22no—
82C22×#1055—22no—
83C22×#1055D414yes—
84C22×#1055C2312yes—
85C2×#6094—232no—
86C2×#6094—28no—
87C2×#6094—28no—
88C2×#6094—28no—
89#88151—216no—
90#88151—28no—
91#88151C2×C4116yescomplemented
92#88071—24no—
93#88056—28no—
94#88050—28no—
95C2×#1894—131nomaximal, Sylow
96C24×C13C2×D411yescharacteristic
97C23×D13—22no—
98C23×D13—22no—
99C23×D13—22no—
100C23×D13—22no—
101C23×D13—22no—
102C23×D13—22no—
103C23×D13C22⋊C414yes—
104C23×D13C2×D412yes—
105C22×C4×C13—24no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—42no—
109C22×C4×C13—42no—
110C22×C4×C13—42no—
111C22×C4×C13—42no—
112C22×C4×C13—42no—
113C22×C4×C13C22×C412yes—
114C22×C4×C13C2×D412yes—
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D412yes—
117C22×C4×C13C2×D412yes—
118C22×C4×C13#4112yes—
119C22×C4×C13#4112yes—
120C22×C4×C13C2411yescharacteristic
121C22×Dic13—22no—
122C22×Dic13—22no—
123C22×Dic13—24no—
124C22×Dic13—22no—
125C22×Dic13—22no—
126C22×Dic13—42no—
127C22×Dic13—42no—
128C22×Dic13—42no—
129C22×Dic13—42no—
130C22×Dic13—42no—
131C22×Dic13C22⋊C414yes—
132C22×Dic13C2×D412yes—
133C2×C4×D13—28no—
134C2×C4×D13—28no—
135C2×C4×D13—28no—
136C2×C4×D13—24no—
137C2×C4×D13—24no—
138C2×C4×D13—28no—
139C2×C4×D13—22no—
140C2×C4×D13—22no—
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13C22⋊C418yes—
144C2×C4×D13C22×C414yes—
145C2×C4×D13C2×D414yes—
146C2×Dic26—28no—
147C2×Dic26—28no—
148C2×Dic26—22no—
149C2×Dic26—22no—
150C2×Dic26—22no—
151C2×Dic26—22no—
152C2×Dic26—24no—
153C2×Dic26—22no—
154C2×Dic26—44no—
155C2×Dic26—42no—
156C2×Dic26—42no—
157C2×Dic26—44no—
158C2×Dic26C22×C414yes—
159C2×C8×C13—28no—
160C2×C8×C13—22no—
161C2×C8×C13—22no—
162C2×C8×C13C2×D414yes—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4C22×C414yes—
169#6103—216no—
170#6103—48no—
171C4⋊Dic13—216no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—42no—
175C2×#1055—28no—
176C2×#1055—22no—
177C2×#1055—22no—
178C2×#1055C2×D414yes—
179#6094—232no—
180C23×M16—131no—
181C22×C22⋊Q8—131no—
182C22×#103—131no—
183C22×#103—131no—
184C2×#380—131no—
185#1894—138no—
186C2×#340—131no—
187C2×#340D1311yescharacteristic, complemented
188C23×C13C2×C22⋊C412yes—
189C23×C13#12112yes—
190C23×C13#12112yes—
191C23×C13AGL(1,ℤ/8)12yes—
192C23×C13#13712yes—
193C23×C13#13712yes—
194C23×C13#13712yes—
195C23×C13C22×D411yescharacteristic
196C22×D13—22no—
197C22×D13—22no—
198C22×D13—22no—
199C22×D13—22no—
200C22×D13—22no—
201C22×D13—22no—
202C22×D13—28no—
203C22×D13—28no—
204C22×D13—28no—
205C22×D13—44no—
206C22×D13—44no—
207C22×D13—44no—
208C22×D13—44no—
209C22×D13C2×C22⋊C414yes—
210C2×C4×C13—24no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—48no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—42no—
217C2×C4×C13—84no—
218C2×C4×C13C2×C22⋊C412yes—
219C2×C4×C13C4×D414yes—
220C2×C4×C13C4×D414yes—
221C2×C4×C13#12014yes—
222C2×C4×C13#12112yes—
223C2×C4×C13#12112yes—
224C2×C4×C13#12314yes—
225C2×C4×C13C23×C411yescharacteristic
226C2×C4×C13C22×D411yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C2×C4×C13C22×D411yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×Dic13—22no—
232C2×Dic13—22no—
233C2×Dic13—28no—
234C2×Dic13—24no—
235C2×Dic13—42no—
236C2×Dic13—42no—
237C2×Dic13—48no—
238C2×Dic13—42no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241C2×Dic13—84no—
242C2×Dic13C2×C22⋊C414yes—
243C4×D13—24no—
244C4×D13—24no—
245C4×D13—24no—
246C4×D13—24no—
247C4×D13—216no—
248Dic26—24no—
249Dic26—24no—
250Dic26—42no—
251Dic26—42no—
252Dic26—48no—
253C8×C13—24no—
254#1055—24no—
255C23×Q8—131no—
256C24×C4—131no—
257C22×M16—134no—
258C22×M16—264no—
259C22×M16—264no—
260C22×M16—264no—
261C23×C8—131no—
262C23×C8C2×D1311yescharacteristic
263C2×C22⋊Q8—138no—
264C2×C22⋊Q8—134no—
265C2×C22⋊Q8—264no—
266C2×C22⋊Q8—262no—
267C22×C4⋊C4—131no—
268C22×C4⋊C4—261no—
269C22×C4⋊C4C2×D1311yescharacteristic
270C22×C4⋊C4C2×D1311yescharacteristic
271C22×C22⋊C4—261no—
272C22×C22⋊C4—261no—
273C2×#103—134no—
274C2×#103—134no—
275C2×#103—264no—
276C2×#103—264no—
277#380—134no—
278#380—262no—
279C2×#95—261no—
280#340—134no—
281#340C2×D1314yescomplemented
282C22×C13#38614yes—
283C22×C13#41714yes—
284C22×C13#41914yes—
285C22×C13#46814yes—
286C22×C13#46814yes—
287C22×C13#47014yes—
288C22×C13#47014yes—
289C22×C13C22×C22⋊C411yescharacteristic
290C22×C13C2×#12111yescharacteristic
291C22×C13C2×#12111yescharacteristic
292C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C13C2×#13711yescharacteristic
294C22×C13C2×#13711yescharacteristic
295C22×C13C2×#13711yescharacteristic
296C2×D13—24no—
297C2×D13—24no—
298C2×D13—24no—
299C2×D13—416no—
300C2×D13—42no—
301C2×D13—42no—
302C2×D13—42no—
303C2×D13—42no—
304C4×C13—44no—
305C4×C13—82no—
306C4×C13#38614yes—
307C4×C13C2×C4×D411yescharacteristic
308C4×C13C2×C4×D411yescharacteristic
309C4×C13C2×#12011yescharacteristic
310C4×C13C2×#12311yescharacteristic
311Dic13—24no—
312Dic13—44no—
313Dic13—82no—
314C25—131no—
315C22×Q8—134no—
316C22×Q8—132no—
317C22×Q8—262no—
318C22×Q8—261no—
319C22×Q8—262no—
320C22×Q8—262no—
321C22×Q8—262no—
322C22×Q8—262no—
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—131no—
326C23×C4—134no—
327C23×C4—134no—
328C23×C4—132no—
329C23×C4—132no—
330C23×C4—262no—
331C23×C4—262no—
332C23×C4—262no—
333C23×C4—262no—
334C23×C4—261no—
335C23×C4—261no—
336C23×C4C22×D1311yescharacteristic
337C2×M16—268no—
338C2×M16—268no—
339C2×M16—2632no—
340C2×M16—268no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—134no—
344C22×C8—132no—
345C22×C8—262no—
346C22×C8—262no—
347C22×C8D5214yes—
348C22×C8C22×D1312yes—
349C22⋊Q8—1316no—
350C22⋊Q8—2616no—
351C22⋊Q8—268no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—132no—
358C2×C4⋊C4—268no—
359C2×C4⋊C4—264no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4C4×D1314yes—
364C2×C4⋊C4C22×D1312yes—
365C2×C4⋊C4C22×D1312yes—
366C2×C22⋊C4—268no—
367C2×C22⋊C4—264no—
368C2×C22⋊C4—264no—
369C2×C22⋊C4—524no—
370#103—268no—
371#103—268no—
372#95—264no—
373C2×C13#189418yescomplemented
374C2×C13C2×#38611yescharacteristic
375C2×C13C2×#41911yescharacteristic
376C2×C13C2×#41711yescharacteristic
377C2×C13C2×#46811yescharacteristic
378C2×C13C2×#46811yescharacteristic
379C2×C13C2×#47011yescharacteristic
380C2×C13C2×#47011yescharacteristic
381D13—44no—
382C24—134no—
383C24—132no—
384C24—262no—
385C24—262no—
386C24—262no—
387C24—262no—
388C24—262no—
389C24—262no—
390C24D4×D1311yescharacteristic
391C2×Q8—134no—
392C2×Q8—264no—
393C2×Q8—262no—
394C2×Q8—268no—
395C2×Q8—268no—
396C2×Q8—262no—
397C2×Q8—262no—
398C2×Q8—262no—
399C2×Q8—262no—
400C2×Q8—524no—
401C2×Q8—522no—
402C2×Q8—524no—
403C2×Q8—522no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—134no—
413C22×C4—132no—
414C22×C4—138no—
415C22×C4—134no—
416C22×C4—134no—
417C22×C4—262no—
418C22×C4—262no—
419C22×C4—268no—
420C22×C4—268no—
421C22×C4—264no—
422C22×C4—268no—
423C22×C4—268no—
424C22×C4—264no—
425C22×C4—262no—
426C22×C4—262no—
427C22×C4—262no—
428C22×C4—262no—
429C22×C4—264no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—522no—
433C22×C4—522no—
434C22×C4—522no—
435C22×C4—522no—
436C22×C4—522no—
437C22×C4C2×C4×D1312yes—
438C22×C4C2×D5212yes—
439C22×C4#612712yes—
440C22×C4D4×D1311yescharacteristic
441C22×C4D4×D1312yes—
442C22×C4D4×D1312yes—
443C22×C4#613112yes—
444C22×C4C23×D1311yescharacteristic
445M16—2632no—
446C2×C8—28no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—134no—
450C2×C8—268no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8C2×D5214yes—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—42no—
459C4⋊C4—2616no—
460C4⋊C4—262no—
461C4⋊C4—262no—
462C4⋊C4—522no—
463C4⋊C4C2×C4×D1314yes—
464C22⋊C4—2616no—
465C22⋊C4—528no—
466C13C2×#189411yescharacteristic, complemented, Sylow
467C23—134no—
468C23—262no—
469C23—268no—
470C23—262no—
471C23—262no—
472C23—262no—
473C23—262no—
474C23—262no—
475C23—268no—
476C23—268no—
477C23—524no—
478C23—524no—
479C23—524no—
480C23—524no—
481C23C22⋊C4×D1312yes—
482C23#8813812yes—
483C23#8814912yes—
484C23#8816512yes—
485C23#8816912yes—
486C23#8816912yes—
487C23#8817212yes—
488C23C2×D4×D1311yescharacteristic
489Q8—264no—
490Q8—264no—
491Q8—522no—
492Q8—522no—
493Q8—528no—
494C2×C4—24no—
495C2×C4—48no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4—134no—
503C2×C4—262no—
504C2×C4—262no—
505C2×C4—268no—
506C2×C4—264no—
507C2×C4—264no—
508C2×C4—264no—
509C2×C4—264no—
510C2×C4—2616no—
511C2×C4—264no—
512C2×C4—522no—
513C2×C4—522no—
514C2×C4—528no—
515C2×C4—522no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4—1044no—
519C2×C4C4×D5214yes—
520C2×C4C22⋊C4×D1312yes—
521C2×C4#8813614yes—
522C2×C4#8813812yes—
523C2×C4#8814714yes—
524C2×C4#8814814yes—
525C2×C4#8814912yes—
526C2×C4C22×C4×D1311yescharacteristic
527C2×C4C22×D5211yescharacteristic
528C2×C4C2×#612711yescharacteristic
529C2×C4C2×D4×D1311yescharacteristic
530C2×C4C2×D4×D1311yescharacteristic
531C2×C4C2×#613111yescharacteristic
532C8—24no—
533C8—264no—
534C22—264no—
535C22—264no—
536C22—264no—
537C22—522no—
538C22—522no—
539C22—522no—
540C22—522no—
541C22—5216no—
542C22#1171832614yes—
543C22#1171843214yes—
544C22#1171844114yes—
545C22#1171846314yes—
546C22#1171847714yes—
547C22#1171852914yes—
548C22#1171854714yes—
549C22C2×C22⋊C4×D1311yescharacteristic
550C22C2×#8813811yescharacteristic
551C22C2×#8814911yescharacteristic
552C22C2×#8816511yescharacteristic
553C22C2×#8816911yescharacteristic
554C22C2×#8816911yescharacteristic
555C22C2×#8817211yescharacteristic
556C4—44no—
557C4—82no—
558C4—264no—
559C4—524no—
560C4—1042no—
561C4#1171832614yes—
562C4C2×C4×D5211yescharacteristic
563C4C2×#8813611yescharacteristic
564C4C2×#8814711yescharacteristic
565C4C2×#8814811yescharacteristic
566C2—524no—
567C2#1311526818yesdirect product factor
568C2C2×#1171832611yescharacteristic
569C2C2×#1171846311yescharacteristic
570C2C2×#1171843211yescharacteristic
571C2C2×#1171844111yescharacteristic
572C2C2×#1171854711yescharacteristic
573C2C2×#1171847711yescharacteristic
574C2C2×#1171852911yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC22×C4×C13C24
hypercenterC2×#340D13
hypocenterC13C2×#1894
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. C22×#88056C2semidirect
4. C22×#88050C2semidirect
6. #13115268C2direct (N × H)
7. C2×#11718121C2semidirect
8. C2×C13×#340C2semidirect
25. C2×#88151C4semidirect
29. C2×#88056C22semidirect
33. C2×#88050C22semidirect
34. C13×#340C22semidirect
35. #11718121C22semidirect
91. #88151C2×C4semidirect
187. C2×#340D13semidirect
281. #340C2×D13semidirect
373. C2×C13#1894semidirect
466. C13C2×#1894semidirect
567. C2#13115268direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#60942
C22×#881512
C22×#880562
C22×#880502
C2×#117186482
#131152682
C2×#117181212
C2×C13×#3402
C2×#189413