Finite Group Databasebeta

← C2×#13116069 #15890586

Subgroups — C2×#13116069 #15890586

Order 3328.

2230 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88194C211yesmaximal, characteristic
2C22×#88061C211yesmaximal, characteristic, complemented
3C22×#88072C211yesmaximal, characteristic, complemented
4C22×#88049C211yesmaximal, characteristic, complemented
5C2×#11718646C211yesmaximal, characteristic, complemented
6#13116069C218yesmaximal, direct product factor
7C2×#11718142C211yesmaximal, characteristic, complemented
8C22×C13×#102C211yesmaximal, characteristic, complemented
9C23×D4×C13C2211yescharacteristic
10C23×C22⋊D13—21no—
11C23×C22⋊D13—21no—
12C23×D52C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C2×#88194—24no—
16C2×#88194—24no—
17C2×#88194—22no—
18C2×#88194C2214yes—
19C22×C4⋊Dic13—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C13×#102—24no—
24C2×C13×#102C2214yescomplemented
25C2×#88072—24no—
26C2×#88072C2214yescomplemented
27C2×#88071—21no—
28C2×#88061—24no—
29C2×#88061C2214yescomplemented
30#11718646—22no—
31#11718646C2214yescomplemented
32C2×#88049—24no—
33C2×#88049C2214yescomplemented
34#11718142C2214yescomplemented
35C25×C13—21no—
36C24×D13—21no—
37C22×D4×C13—22no—
38C22×D4×C13—21no—
39C22×D4×C13—22no—
40C22×D4×C13—22no—
41C22×D4×C13—22no—
42C22×D4×C13—22no—
43C22×D4×C13D414yes—
44C22×D4×C13C2312yes—
45C23×C4×C13—21no—
46C23×C4×C13C2311yescharacteristic
47C22×C22⋊D13—28no—
48C22×C22⋊D13—28no—
49C22×C22⋊D13—24no—
50C22×C22⋊D13—24no—
51C22×C22⋊D13—44no—
52C22×C22⋊D13—44no—
53C22×C22⋊D13—44no—
54C22×C22⋊D13—44no—
55C23×Dic13—21no—
56C23×Dic13D411yescharacteristic
57C23×Dic13D411yescharacteristic
58C22×D52—22no—
59C22×D52—22no—
60C22×D52—22no—
61C22×D52—22no—
62C22×D52—22no—
63C22×D52—21no—
64C22×D52D414yes—
65C22×D52C2312yes—
66C22×C8×C13—22no—
67C22×C8×C13—22no—
68C22×C8×C13—22no—
69C22×C8×C13C2312yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4D414yescomplemented
73C2×C13×C4⋊C4C2312yes—
74#88194—216no—
75#88194—28no—
76#88194—28no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—24no—
81C2×C4⋊Dic13—44no—
82C2×C4⋊Dic13C2312yes—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13D412yes—
86C2×C4×Dic13C2312yes—
87C22×#1055—22no—
88C22×#1055—22no—
89C22×#1055—22no—
90C22×#1055C2312yes—
91C13×#102—28no—
92#88072—28no—
93#88071—24no—
94#88061—28no—
95#88049—28no—
96C2×#2041—131nomaximal, Sylow
97C24×C13—24no—
98C24×C13—22no—
99C24×C13—42no—
100C24×C13—42no—
101C24×C13—42no—
102C24×C13—42no—
103C24×C13—42no—
104C24×C13—42no—
105C24×C13C2×D411yescharacteristic
106C23×D13—24no—
107C23×D13—22no—
108C23×D13—42no—
109C23×D13—42no—
110C23×D13—42no—
111C23×D13—42no—
112C23×D13—42no—
113C23×D13—42no—
114C2×D4×C13—24no—
115C2×D4×C13—28no—
116C2×D4×C13—28no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—44no—
123C2×D4×C13—42no—
124C2×D4×C13—44no—
125C2×D4×C13—42no—
126C2×D4×C13C2×D414yes—
127C22×C4×C13—24no—
128C22×C4×C13—22no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13C2×D412yes—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D412yes—
134C22×C4×C13C2×D412yes—
135C22×C4×C13#4112yes—
136C22×C4×C13#4112yes—
137C22×C4×C13#4112yes—
138C22×C4×C13C2411yescharacteristic
139C2×C22⋊D13—216no—
140C2×C22⋊D13—216no—
141C2×C22⋊D13—48no—
142C2×C22⋊D13—48no—
143C2×C22⋊D13—432no—
144C2×C22⋊D13—432no—
145C2×C22⋊D13—48no—
146C2×C22⋊D13—48no—
147C22×Dic13—22no—
148C22×Dic13—22no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—22no—
152C22×Dic13—42no—
153C22×Dic13—42no—
154C22×Dic13—42no—
155C22×Dic13D814yes—
156C22×Dic13SD1614yes—
157C22×Dic13C2×D412yes—
158C22×Dic13C2×D412yes—
159C2×D52—28no—
160C2×D52—28no—
161C2×D52—22no—
162C2×D52—22no—
163C2×D52—22no—
164C2×D52—22no—
165C2×D52—24no—
166C2×D52—22no—
167C2×D52—44no—
168C2×D52—42no—
169C2×D52—44no—
170C2×D52—42no—
171C2×D52C2×D414yes—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13—22no—
175C2×C8×C13—44no—
176C13×C4⋊C4—24no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4C2×D414yescomplemented
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13—42no—
182C4⋊Dic13—48no—
183C4×Dic13—24no—
184C4×Dic13—22no—
185C4×Dic13—22no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—44no—
190C22×#127—131no—
191C22×#102—131no—
192C22×#102—131no—
193C22×#102—131no—
194C22×#102D1311yescharacteristic, complemented
195C2×#389—131no—
196#2041—138no—
197C2×#336—131no—
198C23×C13—24no—
199C23×C13—42no—
200C23×C13—42no—
201C23×C13—42no—
202C23×C13—42no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13—48no—
206C23×C13—48no—
207C23×C13—48no—
208C23×C13—84no—
209C23×C13—84no—
210C23×C13—84no—
211C23×C13—84no—
212C23×C13#12012yes—
213C23×C13#12112yes—
214C23×C13#12412yes—
215C23×C13C2×D812yes—
216C23×C13C2×SD1612yes—
217C23×C13AGL(1,ℤ/8)12yes—
218C23×C13AGL(1,ℤ/8)12yes—
219C23×C13C22×D411yescharacteristic
220C22×D13—24no—
221C22×D13—42no—
222C22×D13—42no—
223C22×D13—42no—
224C22×D13—42no—
225C22×D13—42no—
226C22×D13—42no—
227C22×D13—48no—
228C22×D13—48no—
229C22×D13—48no—
230C22×D13—84no—
231C22×D13—84no—
232C22×D13—84no—
233C22×D13—84no—
234D4×C13—24no—
235D4×C13—24no—
236D4×C13—42no—
237D4×C13—42no—
238D4×C13—48no—
239C2×C4×C13—24no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—48no—
243C2×C4×C13#12012yes—
244C2×C4×C13#12114yes—
245C2×C4×C13#12114yes—
246C2×C4×C13#12112yes—
247C2×C4×C13#12314yes—
248C2×C4×C13#12314yes—
249C2×C4×C13#12412yes—
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C13C2×#4111yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C22⋊D13—432no—
257C22⋊D13—432no—
258C2×Dic13—22no—
259C2×Dic13—22no—
260C2×Dic13—22no—
261C2×Dic13—22no—
262C2×Dic13—28no—
263C2×Dic13—28no—
264C2×Dic13—42no—
265C2×Dic13—42no—
266C2×Dic13—42no—
267C2×Dic13—84no—
268C2×Dic13C2×D814yes—
269C2×Dic13C2×SD1614yes—
270D52—24no—
271D52—24no—
272D52—42no—
273D52—42no—
274D52—48no—
275C8×C13—42no—
276#1055—42no—
277C23×D4—131no—
278C23×D4—261no—
279C23×D4—261no—
280C23×D4C2×D1311yescharacteristic
281C23×C8—131no—
282C23×C8C2×D1311yescharacteristic
283C2×#127—134no—
284C2×#127—262no—
285C2×#127—264no—
286C2×#127—264no—
287C22×C4⋊C4—131no—
288C22×C4⋊C4—261no—
289C22×C4⋊C4C2×D1311yescharacteristic
290C22×C42—131no—
291C2×#102—24no—
292C2×#102—134no—
293C2×#102—134no—
294C2×#102—134no—
295C2×#102—264no—
296C2×#102—264no—
297C2×#102—264no—
298C2×#102C2×D1314yescomplemented
299#389—134no—
300#389—262no—
301C2×#95—261no—
302#336—134no—
303C22×C13—44no—
304C22×C13—44no—
305C22×C13—44no—
306C22×C13—82no—
307C22×C13—82no—
308C22×C13—82no—
309C22×C13—82no—
310C22×C13—816no—
311C22×C13#39414yes—
312C22×C13#44714yes—
313C22×C13#45014yes—
314C22×C13#45914yes—
315C22×C13#46014yes—
316C22×C13#48614yes—
317C22×C13#49014yes—
318C22×C13C2×#12011yescharacteristic
319C22×C13C2×#12111yescharacteristic
320C22×C13C2×#12411yescharacteristic
321C22×C13C22×D811yescharacteristic
322C22×C13C22×SD1611yescharacteristic
323C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
325C2×D13—44no—
326C2×D13—44no—
327C2×D13—44no—
328C2×D13—82no—
329C2×D13—82no—
330C2×D13—82no—
331C2×D13—82no—
332C2×D13—816no—
333C4×C13—44no—
334C4×C13#39414yes—
335C4×C13C2×#12111yescharacteristic
336C4×C13C2×#12111yescharacteristic
337C4×C13C2×#12311yescharacteristic
338C4×C13C2×#12311yescharacteristic
339Dic13—24no—
340Dic13—24no—
341Dic13—82no—
342C25—21no—
343C25—261no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—134no—
351C22×D4—132no—
352C22×D4—264no—
353C22×D4—264no—
354C22×D4—268no—
355C22×D4—268no—
356C22×D4—262no—
357C22×D4—262no—
358C22×D4—261no—
359C22×D4—262no—
360C22×D4—262no—
361C22×D4—262no—
362C22×D4—524no—
363C22×D4—524no—
364C22×D4—524no—
365C22×D4—524no—
366C22×D4D5214yes—
367C22×D4C22×D1312yes—
368C23×C4—21no—
369C23×C4—131no—
370C23×C4—131no—
371C23×C4—261no—
372C23×C4C22×D1311yescharacteristic
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—132no—
377C22×C8—262no—
378C22×C8—262no—
379C22×C8—262no—
380C22×C8C22×D1312yes—
381#127—268no—
382#127—2616no—
383#127—268no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—132no—
387C2×C4⋊C4—262no—
388C2×C4⋊C4—262no—
389C2×C4⋊C4—264no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—524no—
392C2×C4⋊C4C22⋊D1314yescomplemented
393C2×C4⋊C4C22×D1312yes—
394C2×C42—132no—
395C2×C42—132no—
396C2×C42—262no—
397C2×C42—262no—
398#102—28no—
399#102—268no—
400#102—268no—
401#102—268no—
402#95—264no—
403C2×C13—84no—
404C2×C13#204118yescomplemented
405C2×C13C2×#39411yescharacteristic
406C2×C13C2×#44711yescharacteristic
407C2×C13C2×#45011yescharacteristic
408C2×C13C2×#45911yescharacteristic
409C2×C13C2×#46011yescharacteristic
410C2×C13C2×#48611yescharacteristic
411C2×C13C2×#49011yescharacteristic
412D13—84no—
413C24—24no—
414C24—22no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—264no—
422C24—262no—
423C24—522no—
424C24—522no—
425C24—522no—
426C24—522no—
427C24—522no—
428C24—522no—
429C24D4×D1311yescharacteristic
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—44no—
439C2×D4—42no—
440C2×D4—44no—
441C2×D4—42no—
442C2×D4—134no—
443C2×D4—2616no—
444C2×D4—2616no—
445C2×D4—264no—
446C2×D4—268no—
447C2×D4—268no—
448C2×D4—262no—
449C2×D4—262no—
450C2×D4—262no—
451C2×D4—262no—
452C2×D4—262no—
453C2×D4—528no—
454C2×D4—528no—
455C2×D4—5232no—
456C2×D4—528no—
457C2×D4—5232no—
458C2×D4—528no—
459C2×D4—522no—
460C2×D4—524no—
461C2×D4—524no—
462C2×D4—522no—
463C2×D4C2×D5214yes—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—134no—
469C22×C4—134no—
470C22×C4—132no—
471C22×C4—132no—
472C22×C4—262no—
473C22×C4—262no—
474C22×C4—262no—
475C22×C4—262no—
476C22×C4—262no—
477C22×C4—522no—
478C22×C4—522no—
479C22×C4—522no—
480C22×C4C2×D5212yes—
481C22×C4#612712yes—
482C22×C4D4×D1311yescharacteristic
483C22×C4D4×D1312yes—
484C22×C4#612912yes—
485C22×C4#612912yes—
486C22×C4C2×C22⋊D1312yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—44no—
492C2×C8—262no—
493C2×C8—262no—
494C2×C8—262no—
495C2×C8—524no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—262no—
499C4⋊C4—262no—
500C4⋊C4—528no—
501C4⋊C4—522no—
502C4⋊C4C2×C22⋊D1314yescomplemented
503C42—264no—
504C42—262no—
505C42—262no—
506C13C2×#204111yescharacteristic, complemented, Sylow
507C23—24no—
508C23—42no—
509C23—48no—
510C23—42no—
511C23—42no—
512C23—48no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—48no—
517C23—84no—
518C23—84no—
519C23—84no—
520C23—84no—
521C23—264no—
522C23—522no—
523C23—528no—
524C23—522no—
525C23—522no—
526C23—528no—
527C23—522no—
528C23—522no—
529C23—522no—
530C23—528no—
531C23—1044no—
532C23—1044no—
533C23—1044no—
534C23—1044no—
535C23#8813612yes—
536C23#8813912yes—
537C23D8×D1312yes—
538C23#8816512yes—
539C23SD16×D1312yes—
540C23#8816812yes—
541C23#8819312yes—
542C23C2×D4×D1311yescharacteristic
543D4—24no—
544D4—24no—
545D4—42no—
546D4—42no—
547D4—48no—
548D4—264no—
549D4—264no—
550D4—5232no—
551D4—5232no—
552D4—522no—
553D4—522no—
554D4—528no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—48no—
559C2×C4—134no—
560C2×C4—134no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—268no—
564C2×C4—262no—
565C2×C4—268no—
566C2×C4—262no—
567C2×C4—522no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—1044no—
571C2×C4#8813612yes—
572C2×C4#8813714yes—
573C2×C4#8813912yes—
574C2×C4#8814014yes—
575C2×C4#8818414yes—
576C2×C4#8819214yes—
577C2×C4#8819312yes—
578C2×C4C22×D5211yescharacteristic
579C2×C4C2×#612711yescharacteristic
580C2×C4C2×D4×D1311yescharacteristic
581C2×C4C2×#612911yescharacteristic
582C2×C4C2×#612911yescharacteristic
583C2×C4C22×C22⋊D1311yescharacteristic
584C8—42no—
585C8—522no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—82no—
590C22—82no—
591C22—82no—
592C22—816no—
593C22—82no—
594C22—524no—
595C22—524no—
596C22—524no—
597C22—1042no—
598C22—1042no—
599C22—1042no—
600C22—10416no—
601C22—1042no—
602C22#1171842114yes—
603C22#1171842514yes—
604C22#1171843414yes—
605C22#1171843714yes—
606C22#1171862214yes—
607C22#1171881114yes—
608C22#1171882414yes—
609C22C2×#8813611yescharacteristic
610C22C2×#8813911yescharacteristic
611C22C2×D8×D1311yescharacteristic
612C22C2×#8816511yescharacteristic
613C22C2×SD16×D1311yescharacteristic
614C22C2×#8816811yescharacteristic
615C22C2×#8819311yescharacteristic
616C4—44no—
617C4—264no—
618C4—264no—
619C4—1042no—
620C4#1171862214yes—
621C4C2×#8813711yescharacteristic
622C4C2×#8814011yescharacteristic
623C4C2×#8818411yescharacteristic
624C4C2×#8819211yescharacteristic
625C2—84no—
626C2—1044no—
627C2#1311606918yesdirect product factor
628C2C2×#1171862211yescharacteristic
629C2C2×#1171843411yescharacteristic
630C2C2×#1171843711yescharacteristic
631C2C2×#1171881111yescharacteristic
632C2C2×#1171882411yescharacteristic
633C2C2×#1171842111yescharacteristic
634C2C2×#1171842511yescharacteristic
subgroupG/H
centerC24D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC22×C13×#102C2
socleC24×C13C2×D4
prime radicalC22×#88194C2
hypercenterC22×#102D13
hypocenterC13C2×#2041
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#88061C2semidirect
3. C22×#88072C2semidirect
4. C22×#88049C2semidirect
5. C2×#11718646C2semidirect
6. #13116069C2direct (N × H)
7. C2×#11718142C2semidirect
8. C22×C13×#102C2semidirect
24. C2×C13×#102C22semidirect
26. C2×#88072C22semidirect
29. C2×#88061C22semidirect
31. #11718646C22semidirect
33. C2×#88049C22semidirect
34. #11718142C22semidirect
72. C2×C13×C4⋊C4D4semidirect
178. C13×C4⋊C4C2×D4semidirect
194. C22×#102D13semidirect
298. C2×#102C2×D13semidirect
392. C2×C4⋊C4C22⋊D13semidirect
404. C2×C13#2041semidirect
502. C4⋊C4C2×C22⋊D13semidirect
506. C13C2×#2041semidirect
627. C2#13116069direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#881942
C22×#880612
C22×#880722
C22×#880492
C2×#117186462
#131160692
C2×#117181422
C22×C13×#1022
C2×#204113