Finite Group Databasebeta

← C2×#13116022 #15890380

Subgroups — C2×#13116022 #15890380

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88048C211yesmaximal, characteristic, complemented
2C22×#88072C211yesmaximal, characteristic, complemented
3C22×#88072C211yesmaximal, characteristic, complemented
4C22×C22⋊#1055C211yesmaximal, characteristic, complemented
5C2×#11718873C211yesmaximal, characteristic, complemented
6#13116022C218yesmaximal, direct product factor
7C2×#11718121C211yesmaximal, characteristic, complemented
8C22×C13×#121C211yesmaximal, characteristic
9C23×D4×C13—21no—
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C2×C13×#121—24no—
13C2×C13×#121—22no—
14C2×C13×#121—24no—
15C2×C13×#121C2214yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C22⋊C4—21no—
18C22×C22⋊Dic13—21no—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×#88072—24no—
24C2×#88072—24no—
25C2×#88072C2214yescomplemented
26C2×#88072C2214yescomplemented
27#11718873—22no—
28#11718873C2214yescomplemented
29C2×#88071—21no—
30C2×C22⋊#1055—24no—
31C2×C22⋊#1055C2214yescomplemented
32C2×#88048—24no—
33C2×#88048C2214yescomplemented
34#11718121C2214yescomplemented
35C25×C13—21no—
36C25×C13D411yescharacteristic
37C22×D4×C13—28no—
38C22×D4×C13—24no—
39C22×D4×C13—22no—
40C22×D4×C13—21no—
41C22×D4×C13—22no—
42C22×D4×C13—22no—
43C22×D4×C13—22no—
44C22×D4×C13—22no—
45C22×D4×C13—44no—
46C22×D4×C13—44no—
47C22×D4×C13D414yes—
48C22×D4×C13C2312yes—
49C23×C4×C13—21no—
50C23×C4×C13—22no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D412yes—
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×Dic13—21no—
61C23×Dic13—21no—
62C13×#121—216no—
63C13×#121—28no—
64C13×#121—28no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—22no—
67C2×C13×C4⋊C4D414yes—
68C2×C13×C4⋊C4C2312yes—
69C2×C13×C22⋊C4—28no—
70C2×C13×C22⋊C4—24no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—44no—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13—22no—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2312yes—
80C2×C4⋊Dic13C2312yes—
81C22×#1055—22no—
82C22×#1055—22no—
83C22×#1055—22no—
84C22×#1055—22no—
85C22×#1055—22no—
86C22×#1055D414yescomplemented
87C22×#1055C2312yes—
88C22×#1055C2312yes—
89#88072—28no—
90#88072—28no—
91#88071—24no—
92C22⋊#1055—28no—
93#88048—28no—
94C2×#2034—131nomaximal, Sylow
95C24×C13—22no—
96C24×C13—22no—
97C24×C13—22no—
98C24×C13—22no—
99C24×C13—22no—
100C24×C13—22no—
101C24×C13—24no—
102C24×C13—22no—
103C24×C13—42no—
104C24×C13—42no—
105C24×C13—42no—
106C24×C13—42no—
107C24×C13—42no—
108C24×C13—42no—
109C24×C13SD1614yes—
110C24×C13C2×D412yes—
111C24×C13C2×D411yescharacteristic
112C2×D4×C13—216no—
113C2×D4×C13—24no—
114C2×D4×C13—28no—
115C2×D4×C13—28no—
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—48no—
122C2×D4×C13—432no—
123C2×D4×C13—48no—
124C2×D4×C13—44no—
125C2×D4×C13—42no—
126C2×D4×C13—42no—
127C2×D4×C13—44no—
128C2×D4×C13C2×D414yes—
129C22×C4×C13—22no—
130C22×C4×C13—24no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—24no—
136C22×C4×C13—24no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—44no—
146C22×C4×C13—44no—
147C22×C4×C13—44no—
148C22×C4×C13—44no—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—42no—
161C22×Dic13—42no—
162C22×Dic13—42no—
163C22×Dic13—42no—
164C22×Dic13—42no—
165C22×Dic13—42no—
166C13×C4⋊C4—24no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4C2×D414yes—
169C13×C22⋊C4—216no—
170C22⋊Dic13—48no—
171C4⋊Dic13—22no—
172C4⋊Dic13—22no—
173C4⋊Dic13—22no—
174C4⋊Dic13—22no—
175C4⋊Dic13—42no—
176C4⋊Dic13—42no—
177C2×#1055—28no—
178C2×#1055—22no—
179C2×#1055—22no—
180C2×#1055—22no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—44no—
184C2×#1055C2×D414yescomplemented
185C22×#121D1311yescharacteristic
186C22×#106—131no—
187C22×#102—131no—
188C22×#102—131no—
189C22×C22⋊C8—131no—
190C2×#380—131no—
191#2034—138no—
192C2×#340—131no—
193C23×C13—22no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—28no—
200C23×C13—28no—
201C23×C13—28no—
202C23×C13—24no—
203C23×C13—44no—
204C23×C13—44no—
205C23×C13—44no—
206C23×C13—44no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—42no—
212C23×C13—42no—
213C23×C13—48no—
214C23×C13—48no—
215C23×C13—48no—
216C23×C13—84no—
217C23×C13—84no—
218C23×C13—84no—
219C23×C13—84no—
220C23×C13#12012yes—
221C23×C13#12112yes—
222C23×C13#12312yes—
223C23×C13C2×SD1614yes—
224C23×C13C2×SD1612yes—
225C23×C13#13512yes—
226C23×C13AGL(1,ℤ/8)12yes—
227C23×C13AGL(1,ℤ/8)12yes—
228C23×C13C22×D411yescharacteristic
229D4×C13—24no—
230D4×C13—24no—
231D4×C13—432no—
232D4×C13—42no—
233D4×C13—42no—
234D4×C13—48no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—44no—
242C2×C4×C13—48no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—48no—
248C2×C4×C13#12012yes—
249C2×C4×C13#12114yes—
250C2×C4×C13#12114yes—
251C2×C4×C13#12112yes—
252C2×C4×C13#12314yes—
253C2×C4×C13#12312yes—
254C2×C4×C13#12414yes—
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×Dic13—42no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—84no—
268C2×Dic13—84no—
269#1055—24no—
270#1055—42no—
271C23×D4—21no—
272C23×D4C2×D1311yescharacteristic
273C24×C4C2×D1311yescharacteristic
274C23×C8—131no—
275C23×C8—131no—
276C2×#121—24no—
277C2×#121—22no—
278C2×#121—24no—
279C2×#121C2×D1314yes—
280C22×C4⋊C4—131no—
281C22×C4⋊C4—131no—
282C22×C4⋊C4C2×D1311yescharacteristic
283C22×C22⋊C4—21no—
284C22×C22⋊C4—261no—
285C2×#106—134no—
286C2×#106—264no—
287C2×#102—134no—
288C2×#102—134no—
289C2×#102—264no—
290C2×#102—264no—
291C2×C22⋊C8—134no—
292C2×C22⋊C8—264no—
293#380—134no—
294#380—262no—
295C2×#95—261no—
296#340—134no—
297C22×C13—24no—
298C22×C13—24no—
299C22×C13—24no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—416no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—82no—
309C22×C13—82no—
310C22×C13—82no—
311C22×C13—82no—
312C22×C13—816no—
313C22×C13#39414yes—
314C22×C13#44914yes—
315C22×C13#45014yes—
316C22×C13#46514yes—
317C22×C13#46914yes—
318C22×C13#48114yes—
319C22×C13#48214yes—
320C22×C13C2×#12011yescharacteristic
321C22×C13C2×#12111yescharacteristic
322C22×C13C2×#12311yescharacteristic
323C22×C13C22×SD1611yescharacteristic
324C22×C13C2×#13511yescharacteristic
325C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
326C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
327C4×C13—42no—
328C4×C13—44no—
329C4×C13#39414yes—
330C4×C13C2×#12111yescharacteristic
331C4×C13C2×#12111yescharacteristic
332C4×C13C2×#12311yescharacteristic
333C4×C13C2×#12411yescharacteristic
334Dic13—82no—
335Dic13—82no—
336C25—21no—
337C25C22⋊D1311yescharacteristic
338C22×D4—28no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4—22no—
346C22×D4—44no—
347C22×D4—44no—
348C22×D4C22⋊D1314yes—
349C22×D4C22×D1312yes—
350C23×C4—21no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—261no—
358C23×C4—261no—
359C23×C4C22⋊D1312yes—
360C23×C4C22⋊D1311yescharacteristic
361C23×C4C22×D1312yes—
362C23×C4C22×D1311yescharacteristic
363C22×C8—134no—
364C22×C8—132no—
365C22×C8—132no—
366C22×C8—262no—
367C22×C8—262no—
368C22×C8—262no—
369C22×C8—262no—
370C22×C8—262no—
371#121—216no—
372#121—28no—
373#121—28no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—132no—
377C2×C4⋊C4—132no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4C22⋊D1314yes—
385C2×C4⋊C4C22×D1312yes—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—264no—
389C2×C22⋊C4—524no—
390#106—268no—
391#102—268no—
392#102—268no—
393C22⋊C8—268no—
394#95—264no—
395C2×C13—44no—
396C2×C13—84no—
397C2×C13#203418yescomplemented
398C2×C13C2×#39411yescharacteristic
399C2×C13C2×#45011yescharacteristic
400C2×C13C2×#44911yescharacteristic
401C2×C13C2×#46511yescharacteristic
402C2×C13C2×#46911yescharacteristic
403C2×C13C2×#48211yescharacteristic
404C2×C13C2×#48111yescharacteristic
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24#610514yes—
420C24C2×C22⋊D1312yes—
421C24C2×C22⋊D1311yescharacteristic
422C2×D4—216no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—48no—
432C2×D4—432no—
433C2×D4—48no—
434C2×D4—42no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—42no—
438C2×D4C2×C22⋊D1314yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—44no—
456C22×C4—44no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—522no—
462C22×C4—522no—
463C22×C4—522no—
464C22×C4—522no—
465C22×C4—522no—
466C22×C4—522no—
467C22×C4D4×D1312yes—
468C22×C4#612912yes—
469C22×C4#612912yes—
470C22×C4#612912yes—
471C22×C4C2×C22⋊D1312yes—
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1312yes—
474C22×C4C2×C22⋊D1312yes—
475C22×C4C23×D1311yescharacteristic
476C2×C8—134no—
477C2×C8—268no—
478C2×C8—262no—
479C2×C8—262no—
480C2×C8—262no—
481C2×C8—262no—
482C2×C8—262no—
483C2×C8—524no—
484C4⋊C4—24no—
485C4⋊C4—22no—
486C4⋊C4—262no—
487C4⋊C4—262no—
488C4⋊C4—262no—
489C4⋊C4—262no—
490C4⋊C4—522no—
491C4⋊C4—522no—
492C4⋊C4C2×C22⋊D1314yes—
493C22⋊C4—216no—
494C22⋊C4—528no—
495C13C2×#203411yescharacteristic, complemented, Sylow
496C23—28no—
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—28no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—48no—
517C23—48no—
518C23—48no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—84no—
523C23#8818612yes—
524C23C2×#610514yes—
525C23C2×#610512yes—
526C23#8818912yes—
527C23#8819312yes—
528C23#8820312yes—
529C23#8820412yes—
530C23#8820712yes—
531C23C22×C22⋊D1311yescharacteristic
532D4—24no—
533D4—24no—
534D4—432no—
535D4—42no—
536D4—42no—
537D4—48no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—48no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
551C2×C4—522no—
552C2×C4—522no—
553C2×C4—522no—
554C2×C4—522no—
555C2×C4—522no—
556C2×C4—522no—
557C2×C4—1044no—
558C2×C4—1044no—
559C2×C4#8818914yes—
560C2×C4#8818912yes—
561C2×C4#8819014yes—
562C2×C4#8819214yes—
563C2×C4#8819314yes—
564C2×C4#8819312yes—
565C2×C4#8820712yes—
566C2×C4C2×D4×D1311yescharacteristic
567C2×C4C2×#612911yescharacteristic
568C2×C4C2×#612911yescharacteristic
569C2×C4C2×#612911yescharacteristic
570C2×C4C22×C22⋊D1311yescharacteristic
571C2×C4C22×C22⋊D1311yescharacteristic
572C8—264no—
573C8—522no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—416no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—816no—
589C22—82no—
590C22#1171869514yes—
591C22#1171869614yes—
592C22#1171870014yes—
593C22#1171870214yes—
594C22#1171887914yes—
595C22#1171888314yes—
596C22#1171889914yes—
597C22C2×#8818611yescharacteristic
598C22C22×#610511yescharacteristic
599C22C2×#8818911yescharacteristic
600C22C2×#8819311yescharacteristic
601C22C2×#8820311yescharacteristic
602C22C2×#8820411yescharacteristic
603C22C2×#8820711yescharacteristic
604C4—42no—
605C4—44no—
606C4—1042no—
607C4—1042no—
608C4#1171888314yes—
609C4C2×#8818911yescharacteristic
610C4C2×#8819011yescharacteristic
611C4C2×#8819211yescharacteristic
612C4C2×#8819311yescharacteristic
613C2—44no—
614C2—84no—
615C2#1311602218yesdirect product factor
616C2C2×#1171888311yescharacteristic
617C2C2×#1171887911yescharacteristic
618C2C2×#1171889911yescharacteristic
619C2C2×#1171870211yescharacteristic
620C2C2×#1171870011yescharacteristic
621C2C2×#1171869611yescharacteristic
622C2C2×#1171869511yescharacteristic
subgroupG/H
centerC24C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC22×C13×#121C2
socleC24×C13C2×D4
hypercenterC22×#121D13
hypocenterC13C2×#2034
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#88048C2semidirect
2. C22×#88072C2semidirect
3. C22×#88072C2semidirect
4. C22×C22⋊#1055C2semidirect
5. C2×#11718873C2semidirect
6. #13116022C2direct (N × H)
7. C2×#11718121C2semidirect
25. C2×#88072C22semidirect
26. C2×#88072C22semidirect
28. #11718873C22semidirect
31. C2×C22⋊#1055C22semidirect
33. C2×#88048C22semidirect
34. #11718121C22semidirect
86. C22×#1055D4semidirect
184. C2×#1055C2×D4semidirect
397. C2×C13#2034semidirect
495. C13C2×#2034semidirect
615. C2#13116022direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#880482
C22×#880722
C22×C22⋊#10552
C2×#117188732
#131160222
C2×#117181212
C22×C13×#1212
C2×#203413