Finite Group Databasebeta

← #15890396

Subgroups — #15890396

Order 3328.

1610 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718659C211yesmaximal, characteristic, complemented
2C2×#11718894C211yesmaximal, characteristic, complemented
3C2×#11718894C211yesmaximal, characteristic, complemented
4C22×C22⋊#1055C211yesmaximal, characteristic, complemented
5#13117219C211yesmaximal, characteristic, complemented
6#13116036C212yesmaximal, complemented
7#13116029C212yesmaximal, complemented
8#13116022C212yesmaximal, complemented
9#13116015C212yesmaximal, complemented
10#13114552C211yesmaximal, characteristic, complemented
11C2×C13×#525C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C13×#525—24no—
15C13×#525—24no—
16C2×C13×#123—21no—
17C2×C13×C22⋊Q8C2212yes—
18C2×C13×#121C2212yes—
19C2×C13×#120—21no—
20C2×C4×D4×C13—22no—
21C2×C13×#117C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C23×#1055C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26#11718908—21no—
27#11718894—24no—
28#11718894—24no—
29C2×#88075C2211yescharacteristic, complemented
30C2×#88075C2212yescomplemented
31C2×#88075C2211yescharacteristic, complemented
32C2×#88072C2211yescharacteristic, complemented
33C2×#88072C2212yescomplemented
34C2×#88072C2211yescharacteristic, complemented
35#11718873C2212yes—
36#11718873C2212yes—
37#11718872—21no—
38C4×C22⋊Dic13—22no—
39C2×C22⋊#1055—24no—
40C2×C22⋊#1055C2212yes—
41C2×C22⋊#1055C2212yes—
42#11718659—24no—
43C2×#88048C2212yescomplemented
44C2×#88047C2212yescomplemented
45#11718121C2212yescomplemented
46#11718121C2212yescomplemented
47C25×C13D411yescharacteristic
48C2×C13×#41—22no—
49C2×C13×#41—22no—
50C2×C13×#41—22no—
51C2×C13×#41—22no—
52C2×C13×#41—22no—
53C2×C13×#41D414yes—
54C22×Q8×C13C2311yescharacteristic
55C22×D4×C13—22no—
56C22×D4×C13—21no—
57C22×D4×C13C2311yescharacteristic
58C23×C4×C13—21no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13D412yes—
66C23×C4×C13D411yescharacteristic
67C23×C4×C13C2312yes—
68C23×C4×C13C2311yescharacteristic
69C13×#123—28no—
70C13×C22⋊Q8—24no—
71C13×C22⋊Q8—24no—
72C13×#121—24no—
73C13×#121—24no—
74C13×#120—28no—
75C4×D4×C13—216no—
76C13×#117—22no—
77C13×#117D414yes—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4C2312yes—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C42×C13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88#88180—22no—
89#88180—22no—
90#88180—22no—
91#88180—22no—
92C2×C4⋊Dic13C2312yes—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055—22no—
98C22×#1055—22no—
99C22×#1055—22no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055D414yescomplemented
103C22×#1055C2312yes—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88075—24no—
107#88075—22no—
108#88075—22no—
109#88072—24no—
110#88072—22no—
111#88072—22no—
112#88071—22no—
113#88071—22no—
114C22⋊#1055—24no—
115C22⋊#1055—24no—
116#88048—24no—
117#88047—24no—
118#23479—131nomaximal, Sylow
119C24×C13—22no—
120C24×C13—24no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—21no—
124C24×C13—42no—
125C24×C13C2×D412yes—
126C24×C13C2×D411yescharacteristic
127C13×#41—28no—
128C13×#41—28no—
129C13×#41—44no—
130C13×#41—44no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13C2×D412yes—
137C2×D4×C13—28no—
138C2×D4×C13—24no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—44no—
145C2×D4×C13—42no—
146C2×D4×C13—42no—
147C2×D4×C13—44no—
148C2×D4×C13C2×D412yes—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—21no—
154C22×C4×C13—24no—
155C22×C4×C13—24no—
156C22×C4×C13—24no—
157C22×C4×C13—24no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—44no—
165C22×C4×C13—44no—
166C22×C4×C13—42no—
167C22×C4×C13—44no—
168C22×C4×C13—42no—
169C22×C4×C13—44no—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13#4112yes—
176C22×C4×C13#4112yes—
177C22×C4×C13#4112yes—
178C22×C4×C13C2411yescharacteristic
179C22×Dic13—22no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C13×C4⋊C4—28no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4C2×D414yes—
185C13×C22⋊C4—28no—
186C13×C22⋊C4—28no—
187C13×C22⋊C4—24no—
188C42×C13—24no—
189C22⋊Dic13—44no—
190C22⋊Dic13—42no—
191C22⋊Dic13—42no—
192C22⋊Dic13—44no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—22no—
196C4⋊Dic13—22no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4×Dic13—42no—
200C4×Dic13—42no—
201C2×#1055—28no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—22no—
207C2×#1055—22no—
208C2×#1055—22no—
209C2×#1055—44no—
210C2×#1055C2×D412yes—
211C2×#1055C2×D412yes—
212C2×#525D1311yescharacteristic
213C2×#427—131no—
214C2×#416—131no—
215C2×#416—131no—
216C22×C22⋊C8—131no—
217#2280—131no—
218#2036—132no—
219#2035—132no—
220#2034—132no—
221#2033—132no—
222#1735—131no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—28no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—48no—
234C23×C13—48no—
235C23×C13—44no—
236C23×C13—44no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—42no—
240C23×C13—42no—
241C23×C13#12012yes—
242C23×C13#12112yes—
243C23×C13#12312yes—
244C23×C13#13514yes—
245C23×C13C22×D411yescharacteristic
246Q8×C13—22no—
247Q8×C13—22no—
248Q8×C13—41no—
249Q8×C13—41no—
250D4×C13—22no—
251D4×C13—22no—
252D4×C13—416no—
253D4×C13—48no—
254D4×C13—41no—
255D4×C13—41no—
256C2×C4×C13—24no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—44no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—42no—
270C2×C4×C13—48no—
271C2×C4×C13—48no—
272C2×C4×C13#12012yes—
273C2×C4×C13#12114yes—
274C2×C4×C13#12114yes—
275C2×C4×C13#12112yes—
276C2×C4×C13#12314yes—
277C2×C4×C13#12312yes—
278C2×C4×C13#12414yes—
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C22×D411yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×Dic13—42no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—42no—
289C2×Dic13—42no—
290C2×Dic13—42no—
291C2×Dic13—42no—
292#1055—22no—
293#1055—22no—
294#1055—42no—
295C22×#41C2×D1311yescharacteristic
296C24×C4C2×D1311yescharacteristic
297C23×C8—131no—
298C23×C8—131no—
299#525—24no—
300#525—24no—
301C2×#123—21no—
302C2×C22⋊Q8C2×D1312yes—
303C2×#121C2×D1312yes—
304C2×#120—21no—
305C2×C4×D4—22no—
306C2×#117—131no—
307C2×#117—131no—
308C2×#117C2×D1311yescharacteristic
309#427—264no—
310C2×#107—132no—
311C2×#106—132no—
312#416—264no—
313#416—264no—
314C2×#103—131no—
315C2×#103—132no—
316C2×#103—131no—
317C2×#102—131no—
318C2×#102—132no—
319C2×#102—131no—
320C2×C22⋊C8—132no—
321C2×C22⋊C8—132no—
322C2×C22⋊C8—264no—
323#381—261no—
324#380—132no—
325#380—132no—
326#379—261no—
327C4×C22⋊C4—262no—
328#340—132no—
329#340—132no—
330C22×C13—24no—
331C22×C13—24no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—24no—
335C22×C13—24no—
336C22×C13—24no—
337C22×C13—416no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13—42no—
341C22×C13—42no—
342C22×C13—42no—
343C22×C13—44no—
344C22×C13—82no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13#39414yes—
348C22×C13C2×#12011yescharacteristic
349C22×C13C2×#12111yescharacteristic
350C22×C13C2×#12311yescharacteristic
351C22×C13C2×#13512yes—
352C22×C13#57512yes—
353C4×C13—42no—
354C4×C13—42no—
355C4×C13—44no—
356C4×C13#39414yes—
357C4×C13C2×#12111yescharacteristic
358C4×C13C2×#12111yescharacteristic
359C4×C13C2×#12311yescharacteristic
360C4×C13C2×#12411yescharacteristic
361Dic13—82no—
362Dic13—81no—
363Dic13—81no—
364C25C22⋊D1311yescharacteristic
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41C22⋊D1314yes—
371C22×Q8C22×D1311yescharacteristic
372C22×D4—22no—
373C22×D4—21no—
374C22×D4C22×D1311yescharacteristic
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—21no—
382C23×C4C22⋊D1311yescharacteristic
383C23×C4C22⋊D1312yes—
384C23×C4C22×D1312yes—
385C23×C4C22×D1311yescharacteristic
386C22×C8—134no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—132no—
390C22×C8—262no—
391C22×C8—262no—
392C22×C8—262no—
393C22×C8—262no—
394C22×C8—262no—
395#123—28no—
396C22⋊Q8—24no—
397C22⋊Q8—24no—
398#121—24no—
399#121—24no—
400#120—28no—
401C4×D4—216no—
402#117—22no—
403#117—262no—
404#117—262no—
405#117—262no—
406#117—262no—
407#117C22⋊D1314yes—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—132no—
412C2×C4⋊C4C22×D1312yes—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C22⋊C4—262no—
419C2×C22⋊C4—262no—
420C2×C42—21no—
421C2×C42—261no—
422C2×C42—261no—
423#107—264no—
424#106—264no—
425#103—262no—
426#103—262no—
427#103—264no—
428#102—262no—
429#102—262no—
430#102—264no—
431C22⋊C8—264no—
432C22⋊C8—264no—
433#95—262no—
434#95—262no—
435C2×C13—24no—
436C2×C13—44no—
437C2×C13—82no—
438C2×C13C2×#39411yescharacteristic
439C2×C13#300212yes—
440C2×C13#305011yescharacteristic
441C2×C13#305411yescharacteristic
442C2×C13#309112yes—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—42no—
449C24C2×C22⋊D1312yes—
450C24C2×C22⋊D1311yescharacteristic
451#41—28no—
452#41—28no—
453#41—44no—
454#41—44no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C2×C22⋊D1312yes—
461C2×D4—28no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—44no—
472C2×D4C2×C22⋊D1312yes—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—42no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—262no—
497C22×C4D4×D1312yes—
498C22×C4#612912yes—
499C22×C4#612912yes—
500C22×C4#612912yes—
501C22×C4C2×C22⋊D1312yes—
502C22×C4C2×C22⋊D1312yes—
503C22×C4C2×C22⋊D1312yes—
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C23×D1311yescharacteristic
506C2×C8—132no—
507C2×C8—132no—
508C2×C8—268no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—262no—
514C2×C8—262no—
515C2×C8—262no—
516C2×C8—524no—
517C4⋊C4—28no—
518C4⋊C4—22no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—262no—
524C4⋊C4—262no—
525C4⋊C4C2×C22⋊D1314yes—
526C22⋊C4—28no—
527C22⋊C4—28no—
528C22⋊C4—24no—
529C22⋊C4—524no—
530C22⋊C4—522no—
531C22⋊C4—524no—
532C22⋊C4—522no—
533C42—24no—
534C42—522no—
535C42—522no—
536C13#2347911yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—28no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—48no—
548C23—48no—
549C23—44no—
550C23—44no—
551C23—41no—
552C23—41no—
553C23—42no—
554C23—42no—
555C23#8818912yes—
556C23#8819312yes—
557C23#8820414yes—
558C23#8820712yes—
559C23C22×C22⋊D1311yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564D4—22no—
565D4—22no—
566D4—416no—
567D4—48no—
568D4—41no—
569D4—41no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—44no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—48no—
585C2×C4—48no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—522no—
589C2×C4—522no—
590C2×C4—522no—
591C2×C4—522no—
592C2×C4—522no—
593C2×C4#8818914yes—
594C2×C4#8818912yes—
595C2×C4#8819014yes—
596C2×C4#8819214yes—
597C2×C4#8819314yes—
598C2×C4#8819312yes—
599C2×C4#8820712yes—
600C2×C4C2×D4×D1311yescharacteristic
601C2×C4C2×#612911yescharacteristic
602C2×C4C2×#612911yescharacteristic
603C2×C4C2×#612911yescharacteristic
604C2×C4C22×C22⋊D1311yescharacteristic
605C2×C4C22×C22⋊D1311yescharacteristic
606C8—262no—
607C8—262no—
608C8—522no—
609C22—22no—
610C22—22no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—416no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—44no—
623C22—81no—
624C22—81no—
625C22—82no—
626C22#1171888314yes—
627C22C2×#8818911yescharacteristic
628C22C2×#8819311yescharacteristic
629C22C2×#8820412yes—
630C22#1171952712yes—
631C22C2×#8820711yescharacteristic
632C4—42no—
633C4—42no—
634C4—44no—
635C4—1041no—
636C4—1041no—
637C4—1042no—
638C4#1171888314yes—
639C4C2×#8818911yescharacteristic
640C4C2×#8819011yescharacteristic
641C4C2×#8819211yescharacteristic
642C4C2×#8819311yescharacteristic
643C2—24no—
644C2—44no—
645C2—82no—
646C2C2×#1171888311yescharacteristic
647C2#1312405412yes—
648C2#1312441411yescharacteristic
649C2#1312444211yescharacteristic
650C2#1312474512yes—
subgroupG/H
centerC22×C4C2×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#525C2
socleC23×C13C22×D4
hypercenterC2×#525D13
hypocenterC13#23479
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#11718659C2semidirect
2. C2×#11718894C2semidirect
3. C2×#11718894C2semidirect
4. C22×C22⋊#1055C2semidirect
5. #13117219C2semidirect
6. #13116036C2semidirect
7. #13116029C2semidirect
8. #13116022C2semidirect
9. #13116015C2semidirect
10. #13114552C2semidirect
29. C2×#88075C22semidirect
30. C2×#88075C22semidirect
31. C2×#88075C22semidirect
32. C2×#88072C22semidirect
33. C2×#88072C22semidirect
34. C2×#88072C22semidirect
43. C2×#88048C22semidirect
44. C2×#88047C22semidirect
45. #11718121C22semidirect
46. #11718121C22semidirect
102. C22×#1055D4semidirect
536. C13#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#117186592
C2×#117188942
C22×C22⋊#10552
#131172192
#131160362
#131160292
#131160222
#131160152
#131145522
C2×C13×#5252
#2347913