Finite Group Databasebeta

← C2×#13115841 #15889711

Subgroups — C2×#13115841 #15889711

Order 3328.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6095C211yesmaximal, characteristic, complemented
2C22×#88178C211yesmaximal, characteristic, complemented
3C22×#88184C211yesmaximal, characteristic
4C22×#88056C211yesmaximal, characteristic, complemented
5C22×#88061C211yesmaximal, characteristic, complemented
6#13115841C218yesmaximal, direct product factor
7C2×#11718143C211yesmaximal, characteristic, complemented
8C22×C13×C22⋊C8C211yesmaximal, characteristic, complemented
9C24×C4×C13C2211yescharacteristic
10C23×C22⋊D13—21no—
11C23×D52C2211yescharacteristic
12C23×Dic26C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C23×C8×C13C2211yescharacteristic
15C22×C22⋊Dic13—21no—
16C2×#88184—22no—
17C2×#88184—24no—
18C2×#88184—24no—
19C2×#88184C2214yes—
20C22×#6103—21no—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C2×#88178—22no—
24C2×#88178—24no—
25C2×#88178—24no—
26C2×#88178C2214yescomplemented
27C22×#6101—21no—
28C22×#6095—24no—
29C22×#6095—24no—
30C22×#6095—24no—
31C22×#6095C2214yescomplemented
32C2×C13×C22⋊C8—24no—
33C2×C13×C22⋊C8C2214yescomplemented
34C2×#88061—24no—
35C2×#88061C2214yescomplemented
36C2×#88056—24no—
37C2×#88056C2214yescomplemented
38#11718143C2214yescomplemented
39C25×C13D411yescharacteristic
40C24×D13—21no—
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13D411yescharacteristic
48C23×C4×C13D412yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C22×C22⋊D13—28no—
52C22×C22⋊D13—24no—
53C22×C22⋊D13—44no—
54C22×C22⋊D13—44no—
55C23×Dic13—21no—
56C23×Dic13—21no—
57C23×Dic13—21no—
58C22×D52—22no—
59C22×D52—22no—
60C22×D52—22no—
61C22×D52—22no—
62C22×D52—21no—
63C22×D52—22no—
64C22×D52D414yes—
65C22×D52C2312yes—
66C22×Dic26—22no—
67C22×Dic26—22no—
68C22×Dic26—22no—
69C22×Dic26—22no—
70C22×Dic26—21no—
71C22×Dic26—22no—
72C22×Dic26D414yescomplemented
73C22×Dic26C2312yes—
74C22×C8×C13—22no—
75C22×C8×C13—22no—
76C22×C8×C13—22no—
77C22×C8×C13—22no—
78C22×C8×C13—22no—
79C22×C8×C13D414yescomplemented
80C22×C8×C13C2312yes—
81C22×C8×C13C2312yes—
82C2×C22⋊Dic13—28no—
83C2×C22⋊Dic13—24no—
84#88184—216no—
85#88184—28no—
86#88184—28no—
87C2×#6103—28no—
88C2×#6103—24no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13D414yes—
94C2×C4⋊Dic13D414yescomplemented
95C2×C4⋊Dic13C2312yes—
96C2×C4⋊Dic13C2312yes—
97#88178—216no—
98#88178—28no—
99#88178—28no—
100C2×#6101—28no—
101C2×#6101—24no—
102C2×#6095—232no—
103C2×#6095—28no—
104C2×#6095—28no—
105C2×#6095—28no—
106C13×C22⋊C8—28no—
107#88061—28no—
108#88056—28no—
109C2×#2000—131nomaximal, Sylow
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13SD1614yescomplemented
117C24×C13C2×D412yes—
118C24×C13C2×D411yescharacteristic
119C23×D13—24no—
120C23×D13—22no—
121C23×D13—42no—
122C23×D13—42no—
123C23×D13—42no—
124C23×D13—42no—
125C23×D13—42no—
126C23×D13—42no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—44no—
140C22×C4×C13—44no—
141C22×C4×C13—44no—
142C22×C4×C13—44no—
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13#4112yes—
151C22×C4×C13C2411yescharacteristic
152C2×C22⋊D13—216no—
153C2×C22⋊D13—48no—
154C2×C22⋊D13—432no—
155C2×C22⋊D13—48no—
156C22×Dic13—24no—
157C22×Dic13—24no—
158C22×Dic13—24no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—22no—
162C22×Dic13—42no—
163C22×Dic13—42no—
164C22×Dic13—42no—
165C22×Dic13—42no—
166C22×Dic13—42no—
167C22×Dic13—42no—
168C2×D52—28no—
169C2×D52—28no—
170C2×D52—22no—
171C2×D52—22no—
172C2×D52—22no—
173C2×D52—22no—
174C2×D52—24no—
175C2×D52—22no—
176C2×D52—42no—
177C2×D52—44no—
178C2×D52—42no—
179C2×D52—44no—
180C2×D52C2×D414yes—
181C2×Dic26—28no—
182C2×Dic26—28no—
183C2×Dic26—22no—
184C2×Dic26—22no—
185C2×Dic26—22no—
186C2×Dic26—22no—
187C2×Dic26—24no—
188C2×Dic26—22no—
189C2×Dic26—42no—
190C2×Dic26—44no—
191C2×Dic26—42no—
192C2×Dic26—44no—
193C2×Dic26C2×D414yescomplemented
194C2×C8×C13—28no—
195C2×C8×C13—22no—
196C2×C8×C13—22no—
197C2×C8×C13—22no—
198C2×C8×C13—22no—
199C2×C8×C13—22no—
200C2×C8×C13—44no—
201C2×C8×C13C2×D414yescomplemented
202C22⋊Dic13—216no—
203#6103—216no—
204C4⋊Dic13—24no—
205C4⋊Dic13—24no—
206C4⋊Dic13—22no—
207C4⋊Dic13—22no—
208C4⋊Dic13C2×D414yes—
209C4⋊Dic13C2×D414yescomplemented
210#6101—216no—
211#6095—232no—
212C23×SD16—131no—
213C22×C22⋊Q8—131no—
214C22×#121—131no—
215C22×#103—131no—
216C22×#102—131no—
217C22×C22⋊C8D1311yescharacteristic, complemented
218#2000—138no—
219C2×#340—131no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—28no—
227C23×C13—28no—
228C23×C13—28no—
229C23×C13—44no—
230C23×C13—44no—
231C23×C13—44no—
232C23×C13—44no—
233C23×C13#12012yes—
234C23×C13#12012yes—
235C23×C13#12112yes—
236C23×C13C2×SD1612yes—
237C23×C13C2×SD1614yescomplemented
238C23×C13#13512yes—
239C23×C13AGL(1,ℤ/8)12yes—
240C23×C13#13712yes—
241C23×C13C22×D411yescharacteristic
242C22×D13—24no—
243C22×D13—42no—
244C22×D13—42no—
245C22×D13—42no—
246C22×D13—42no—
247C22×D13—42no—
248C22×D13—42no—
249C22×D13—48no—
250C22×D13—48no—
251C22×D13—48no—
252C22×D13—84no—
253C22×D13—84no—
254C22×D13—84no—
255C22×D13—84no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—44no—
260C2×C4×C13—42no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—42no—
264C2×C4×C13—48no—
265C2×C4×C13#12014yes—
266C2×C4×C13#12012yes—
267C2×C4×C13#12012yes—
268C2×C4×C13#12114yes—
269C2×C4×C13#12114yes—
270C2×C4×C13#12112yes—
271C2×C4×C13#12714yes—
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C22×D411yescharacteristic
276C2×C4×C13C22×D411yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C22⋊D13—432no—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—42no—
283C2×Dic13—42no—
284C2×Dic13—42no—
285C2×Dic13—42no—
286C2×Dic13—42no—
287C2×Dic13—42no—
288C2×Dic13—48no—
289C2×Dic13—48no—
290C2×Dic13—48no—
291D52—24no—
292D52—24no—
293D52—42no—
294D52—42no—
295D52—48no—
296Dic26—24no—
297Dic26—24no—
298Dic26—42no—
299Dic26—42no—
300Dic26—48no—
301C8×C13—24no—
302C8×C13—42no—
303C23×Q8—131no—
304C23×D4—131no—
305C23×D4—261no—
306C24×C4C2×D1311yescharacteristic
307C22×SD16—134no—
308C22×SD16—264no—
309C22×SD16—264no—
310C22×SD16—264no—
311C23×C8C2×D1311yescharacteristic
312C23×C8C2×D1311yescharacteristic
313C2×C22⋊Q8—134no—
314C2×C22⋊Q8—264no—
315C2×C22⋊Q8—264no—
316C2×C22⋊Q8—262no—
317C2×#121—134no—
318C2×#121—264no—
319C2×#121—264no—
320C2×#121—262no—
321C22×C4⋊C4—131no—
322C22×C4⋊C4—131no—
323C22×C4⋊C4—261no—
324C22×C22⋊C4—261no—
325C22×C22⋊C4—261no—
326C2×#103—134no—
327C2×#103—264no—
328C2×#102—134no—
329C2×#102—264no—
330C2×C22⋊C8—24no—
331C2×C22⋊C8C2×D1314yescomplemented
332#340—134no—
333C22×C13—24no—
334C22×C13—24no—
335C22×C13—24no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—416no—
340C22×C13—42no—
341C22×C13#39214yes—
342C22×C13#44814yes—
343C22×C13#44914yes—
344C22×C13#45014yes—
345C22×C13#45214yes—
346C22×C13#46514yes—
347C22×C13#46814yes—
348C22×C13C2×#12011yescharacteristic
349C22×C13C2×#12011yescharacteristic
350C22×C13C2×#12111yescharacteristic
351C22×C13C22×SD1611yescharacteristic
352C22×C13C2×#13511yescharacteristic
353C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C13C2×#13711yescharacteristic
355C2×D13—44no—
356C2×D13—44no—
357C2×D13—44no—
358C2×D13—82no—
359C2×D13—82no—
360C2×D13—816no—
361C2×D13—82no—
362C2×D13—82no—
363C4×C13—42no—
364C4×C13#39214yes—
365C4×C13C2×#12011yescharacteristic
366C4×C13C2×#12111yescharacteristic
367C4×C13C2×#12111yescharacteristic
368C4×C13C2×#12711yescharacteristic
369Dic13—44no—
370Dic13—44no—
371Dic13—44no—
372C25—261no—
373C25D5211yescharacteristic
374C22×Q8—134no—
375C22×Q8—132no—
376C22×Q8—261no—
377C22×Q8—262no—
378C22×Q8—262no—
379C22×Q8—262no—
380C22×Q8—262no—
381C22×Q8—262no—
382C22×D4—134no—
383C22×D4—132no—
384C22×D4—268no—
385C22×D4—264no—
386C22×D4—261no—
387C22×D4—262no—
388C22×D4—262no—
389C22×D4—262no—
390C22×D4—262no—
391C22×D4—262no—
392C22×D4—524no—
393C22×D4—524no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—261no—
401C23×C4—261no—
402C23×C4—261no—
403C23×C4D5212yes—
404C23×C4D5211yescharacteristic
405C23×C4C22×D1312yes—
406C23×C4C22×D1311yescharacteristic
407C2×SD16—268no—
408C2×SD16—268no—
409C2×SD16—2632no—
410C2×SD16—268no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8—22no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C22⋊D1314yescomplemented
417C22×C8C22×D1312yes—
418C22×C8C22×D1312yes—
419C22⋊Q8—268no—
420C22⋊Q8—268no—
421C22⋊Q8—2616no—
422#121—268no—
423#121—268no—
424#121—2616no—
425C2×C4⋊C4—134no—
426C2×C4⋊C4—134no—
427C2×C4⋊C4—132no—
428C2×C4⋊C4—132no—
429C2×C4⋊C4—268no—
430C2×C4⋊C4—261no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—264no—
433C2×C4⋊C4—262no—
434C2×C4⋊C4—262no—
435C2×C22⋊C4—268no—
436C2×C22⋊C4—268no—
437C2×C22⋊C4—264no—
438C2×C22⋊C4—264no—
439#103—268no—
440#102—268no—
441C22⋊C8—28no—
442C2×C13—44no—
443C2×C13#200018yescomplemented
444C2×C13C2×#39211yescharacteristic
445C2×C13C2×#45011yescharacteristic
446C2×C13C2×#44811yescharacteristic
447C2×C13C2×#44911yescharacteristic
448C2×C13C2×#45211yescharacteristic
449C2×C13C2×#46511yescharacteristic
450C2×C13C2×#46811yescharacteristic
451D13—84no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—264no—
459C24—262no—
460C24—522no—
461C24—522no—
462C24—522no—
463C24—522no—
464C24—522no—
465C24—522no—
466C24#609514yescomplemented
467C24C2×D5212yes—
468C24C2×D5211yescharacteristic
469C2×Q8—134no—
470C2×Q8—264no—
471C2×Q8—262no—
472C2×Q8—268no—
473C2×Q8—268no—
474C2×Q8—262no—
475C2×Q8—262no—
476C2×Q8—262no—
477C2×Q8—262no—
478C2×Q8—522no—
479C2×Q8—524no—
480C2×Q8—522no—
481C2×Q8—524no—
482C2×D4—134no—
483C2×D4—2616no—
484C2×D4—264no—
485C2×D4—268no—
486C2×D4—268no—
487C2×D4—262no—
488C2×D4—262no—
489C2×D4—262no—
490C2×D4—262no—
491C2×D4—262no—
492C2×D4—528no—
493C2×D4—5232no—
494C2×D4—528no—
495C2×D4—522no—
496C2×D4—524no—
497C2×D4—522no—
498C2×D4—524no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—264no—
516C22×C4—264no—
517C22×C4—264no—
518C22×C4—262no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4—522no—
522C22×C4—522no—
523C22×C4—522no—
524C22×C4—522no—
525C22×C4—522no—
526C22×C4—522no—
527C22×C4C2×D5212yes—
528C22×C4C2×D5211yescharacteristic
529C22×C4#612712yes—
530C22×C4D4×D1312yes—
531C22×C4D4×D1312yes—
532C22×C4D4×D1312yes—
533C22×C4D4×D1312yes—
534C22×C4C2×C22⋊D1312yes—
535C22×C4C23×D1311yescharacteristic
536SD16—2632no—
537C2×C8—28no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—44no—
544C2×C8C2×C22⋊D1314yescomplemented
545C4⋊C4—134no—
546C4⋊C4—134no—
547C4⋊C4—2616no—
548C4⋊C4—264no—
549C4⋊C4—264no—
550C4⋊C4—262no—
551C4⋊C4—262no—
552C22⋊C4—2616no—
553C22⋊C4—2616no—
554C13C2×#200011yescharacteristic, complemented, Sylow
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—28no—
562C23—28no—
563C23—28no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—264no—
569C23—522no—
570C23—522no—
571C23—522no—
572C23—522no—
573C23—522no—
574C23—522no—
575C23—528no—
576C23—528no—
577C23—528no—
578C23—1044no—
579C23—1044no—
580C23—1044no—
581C23—1044no—
582C23#8813612yes—
583C23#8813612yes—
584C23C2×#609512yes—
585C23C2×#609514yescomplemented
586C23#8815812yes—
587C23#8816212yes—
588C23#8816312yes—
589C23#8818412yes—
590C23C22×D5211yescharacteristic
591Q8—264no—
592Q8—264no—
593Q8—522no—
594Q8—522no—
595Q8—528no—
596D4—264no—
597D4—264no—
598D4—5232no—
599D4—522no—
600D4—522no—
601D4—528no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—48no—
611C2×C4—264no—
612C2×C4—264no—
613C2×C4—264no—
614C2×C4—522no—
615C2×C4—522no—
616C2×C4—522no—
617C2×C4—522no—
618C2×C4—522no—
619C2×C4—522no—
620C2×C4—528no—
621C2×C4—528no—
622C2×C4—528no—
623C2×C4#8813612yes—
624C2×C4#8813612yes—
625C2×C4#8813814yes—
626C2×C4#8813814yes—
627C2×C4#8818412yes—
628C2×C4#8819114yes—
629C2×C4#8819414yes—
630C2×C4C2×#612711yescharacteristic
631C2×C4C2×D4×D1311yescharacteristic
632C2×C4C2×D4×D1311yescharacteristic
633C2×C4C2×D4×D1311yescharacteristic
634C2×C4C2×D4×D1311yescharacteristic
635C2×C4C22×C22⋊D1311yescharacteristic
636C8—24no—
637C8—42no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—416no—
644C22—42no—
645C22—42no—
646C22—524no—
647C22—524no—
648C22—524no—
649C22—1042no—
650C22—1042no—
651C22—1042no—
652C22—10416no—
653C22—1042no—
654C22#1171839214yes—
655C22#1171839414yes—
656C22#1171839514yes—
657C22#1171839914yes—
658C22#1171862114yes—
659C22#1171877514yes—
660C22#1171879514yes—
661C22C2×#8813611yescharacteristic
662C22C2×#8813611yescharacteristic
663C22C22×#609511yescharacteristic
664C22C2×#8815811yescharacteristic
665C22C2×#8816211yescharacteristic
666C22C2×#8816311yescharacteristic
667C22C2×#8818411yescharacteristic
668C4—42no—
669C4—524no—
670C4—524no—
671C4—524no—
672C4#1171862114yes—
673C4C2×#8813811yescharacteristic
674C4C2×#8813811yescharacteristic
675C4C2×#8819111yescharacteristic
676C4C2×#8819411yescharacteristic
677C2—44no—
678C2—1044no—
679C2#1311584118yesdirect product factor
680C2C2×#1171862111yescharacteristic
681C2C2×#1171839211yescharacteristic
682C2C2×#1171839911yescharacteristic
683C2C2×#1171839511yescharacteristic
684C2C2×#1171839411yescharacteristic
685C2C2×#1171877511yescharacteristic
686C2C2×#1171879511yescharacteristic
subgroupG/H
centerC24C2×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×C22⋊C8C2
socleC24×C13C2×D4
prime radicalC22×#88184C2
hypercenterC22×C22⋊C8D13
hypocenterC13C2×#2000
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C23×#6095C2semidirect
2. C22×#88178C2semidirect
4. C22×#88056C2semidirect
5. C22×#88061C2semidirect
6. #13115841C2direct (N × H)
7. C2×#11718143C2semidirect
8. C22×C13×C22⋊C8C2semidirect
26. C2×#88178C22semidirect
31. C22×#6095C22semidirect
33. C2×C13×C22⋊C8C22semidirect
35. C2×#88061C22semidirect
37. C2×#88056C22semidirect
38. #11718143C22semidirect
72. C22×Dic26D4semidirect
79. C22×C8×C13D4semidirect
94. C2×C4⋊Dic13D4semidirect
116. C24×C13SD16semidirect
193. C2×Dic26C2×D4semidirect
201. C2×C8×C13C2×D4semidirect
209. C4⋊Dic13C2×D4semidirect
217. C22×C22⋊C8D13semidirect
237. C23×C13C2×SD16semidirect
331. C2×C22⋊C8C2×D13semidirect
416. C22×C8C22⋊D13semidirect
443. C2×C13#2000semidirect
466. C24#6095semidirect
544. C2×C8C2×C22⋊D13semidirect
554. C13C2×#2000semidirect
585. C23C2×#6095semidirect
679. C2#13115841direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#60952
C22×#881782
C22×#881842
C22×#880562
C22×#880612
#131158412
C2×#117181432
C22×C13×C22⋊C82
C2×#200013