Finite Group Databasebeta

← #15866583

Subgroups — #15866583

Order 3328.

1726 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719537C211yesmaximal, characteristic
2C2×#11718794C211yesmaximal, characteristic, complemented
3C2×#11718893C211yesmaximal, characteristic, complemented
4C2×#11718627C211yesmaximal, characteristic, complemented
5C2×M16×Dic13C211yesmaximal, characteristic, complemented
6C2×#11718637C211yesmaximal, characteristic, complemented
7#13115651C212yesmaximal, complemented
8#13115649C212yesmaximal, complemented
9#13115640C212yesmaximal, complemented
10#13115636C212yesmaximal, complemented
11C2×C13×#417C211yesmaximal, characteristic, complemented
12C22×C13×#41C2211yescharacteristic
13C22×#6127C2211yescharacteristic
14C22×C13×M16C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16#11719537—24no—
17#11719537C418yescomplemented
18C2×#88201C2211yescharacteristic
19C2×#88198C2211yescharacteristic
20C2×#88194C2211yescharacteristic
21C2×#88193—22no—
22C2×#88190C2211yescharacteristic
23C2×C4×C22⋊D13—22no—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101—22no—
26C22×C4×Dic13C2211yescharacteristic
27C22×#6099C2211yescharacteristic
28C13×#417—24no—
29C2×C13×#103C2212yes—
30C2×C13×#102C2212yes—
31#11718893—24no—
32C2×#88075C2212yes—
33C2×#88072C2212yes—
34#11718794—24no—
35M16×Dic13—24no—
36C2×#88061C2212yes—
37C2×#88056C2212yes—
38C2×#88055C2212yes—
39C2×C8×Dic13C2212yes—
40#11718637—22no—
41#11718637C2212yes—
42#11718637C2212yes—
43C2×#88050C2212yes—
44#11718627—24no—
45C2×#88049C2212yes—
46C2×C13×#41—22no—
47C2×C13×#41—22no—
48C2×C13×#41—22no—
49C2×C13×#41—22no—
50C2×C13×#41—22no—
51C2×C13×#41C2×C414yes—
52C22×Q8×C13C2311yescharacteristic
53C22×D4×C13—21no—
54C22×D4×C13C2311yescharacteristic
55C23×C4×C13—21no—
56C23×C4×C13—21no—
57C23×C4×C13C2311yescharacteristic
58C22×C22⋊D13—21no—
59C22×C22⋊D13—22no—
60C23×Dic13—21no—
61C23×Dic13D412yes—
62C2×#6127—22no—
63C2×#6127—22no—
64C2×#6127—22no—
65C2×#6127—22no—
66C2×#6127—22no—
67C2×#6127C2×C414yes—
68C22×D52C2311yescharacteristic
69C22×C4×D13—21no—
70C22×Dic26C2311yescharacteristic
71C2×C13×M16—22no—
72C2×C13×M16—22no—
73C2×C13×M16D414yescomplemented
74C22×C8×C13C2312yes—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4C2312yes—
79C2×C22⋊Dic13—22no—
80#88201—22no—
81#88201C2×C414yescomplemented
82#88198—22no—
83#88198C2×C414yescomplemented
84#88194—22no—
85#88194C2×C414yescomplemented
86#88193—216no—
87#88190—22no—
88#88190C2×C414yescomplemented
89C4×C22⋊D13—216no—
90C2×#6103—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2312yes—
95C2×#6101—22no—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—48no—
99C2×C4×Dic13C2×C414yes—
100C2×C4×Dic13D412yes—
101C2×C4×Dic13D414yes—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C2×#6099—22no—
105C2×#6099—22no—
106C2×#6099D414yescomplemented
107C22×#1055C2312yes—
108C13×#103—24no—
109C13×#102—24no—
110#88075—24no—
111#88072—24no—
112#88061—24no—
113#88056—24no—
114#88055—24no—
115C8×Dic13—24no—
116#88050—24no—
117#88049—24no—
118#21200—131nomaximal, Sylow
119C24×C13—21no—
120C24×C13C2×D411yescharacteristic
121C23×D13—21no—
122C13×#41—28no—
123C13×#41—28no—
124C13×#41—44no—
125C13×#41—44no—
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13C22×C412yes—
132C2×D4×C13—24no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—42no—
139C2×D4×C13—42no—
140C2×D4×C13C22×C412yes—
141C22×C4×C13—21no—
142C22×C4×C13—24no—
143C22×C4×C13—22no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—44no—
147C22×C4×C13—42no—
148C22×C4×C13C22×C412yes—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13C2411yescharacteristic
156C2×C22⋊D13—24no—
157C2×C22⋊D13—28no—
158C2×C22⋊D13—42no—
159C2×C22⋊D13—42no—
160C2×C22⋊D13—44no—
161C2×C22⋊D13—44no—
162C22×Dic13—24no—
163C22×Dic13—24no—
164C22×Dic13—21no—
165C22×Dic13—22no—
166C22×Dic13—44no—
167C22×Dic13—42no—
168C22×Dic13C22⋊C418yes—
169C22×Dic13C2×D412yes—
170C22×Dic13C2×D412yes—
171#6127—28no—
172#6127—28no—
173#6127—44no—
174#6127—44no—
175C2×D52—21no—
176C2×D52—21no—
177C2×D52—21no—
178C2×D52—21no—
179C2×D52—21no—
180C2×D52C22×C412yes—
181C2×C4×D13—24no—
182C2×C4×D13—42no—
183C2×C4×D13—42no—
184C2×Dic26—21no—
185C2×Dic26—21no—
186C2×Dic26—21no—
187C2×Dic26—21no—
188C2×Dic26—21no—
189C2×Dic26C22×C412yes—
190C13×M16—28no—
191C2×C8×C13—22no—
192C2×C8×C13—22no—
193C2×C8×C13C2×D414yes—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—42no—
197C22⋊Dic13—28no—
198#6103—28no—
199C4⋊Dic13—22no—
200C4⋊Dic13—22no—
201C4⋊Dic13—42no—
202#6101—28no—
203#6101—48no—
204#6101—48no—
205C4×Dic13C22⋊C418yes—
206C4×Dic13C22×C412yes—
207C4×Dic13C22×C412yes—
208C4×Dic13C2×D412yes—
209C4×Dic13C2×D412yes—
210#6099—28no—
211C2×#1055—22no—
212C2×#1055—22no—
213C2×#1055C2×D414yes—
214C2×#532—131no—
215C2×#417—131no—
216C2×#417—131no—
217C2×#417—131no—
218C2×#417D1311yescharacteristic, complemented
219C2×C4×M16—131no—
220C2×#384—131no—
221#1959—132no—
222#1959—132no—
223#1957—132no—
224#1956—132no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—42no—
231C23×C13—42no—
232C23×C13C2×C22⋊C412yes—
233C23×C13#12412yes—
234C23×C13#12712yes—
235C23×C13C22×D411yescharacteristic
236C22×D13—22no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—42no—
240C22×D13—42no—
241Q8×C13—22no—
242Q8×C13—22no—
243Q8×C13—41no—
244Q8×C13—41no—
245D4×C13—22no—
246D4×C13—22no—
247D4×C13—48no—
248D4×C13—41no—
249D4×C13—41no—
250C2×C4×C13—22no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—48no—
254C2×C4×C13—42no—
255C2×C4×C13—44no—
256C2×C4×C13—84no—
257C2×C4×C13C2×C22⋊C412yes—
258C2×C4×C13C4×D414yes—
259C2×C4×C13C4×D414yes—
260C2×C4×C13#12114yes—
261C2×C4×C13#12114yes—
262C2×C4×C13#12412yes—
263C2×C4×C13#12712yes—
264C2×C4×C13C23×C411yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C2×C4×C13C22×D411yescharacteristic
267C2×C4×C13C22×D411yescharacteristic
268C2×C4×C13C2×#4111yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C22⋊D13—48no—
271C22⋊D13—416no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—216no—
275C2×Dic13—22no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—42no—
279C2×Dic13—44no—
280C2×Dic13—84no—
281C2×Dic13C2×C22⋊C414yes—
282C2×Dic13C2×C22⋊C414yes—
283C2×Dic13AGL(1,ℤ/8)14yes—
284C2×Dic13#13714yes—
285D52—22no—
286D52—22no—
287D52—41no—
288D52—41no—
289C4×D13—48no—
290Dic26—22no—
291Dic26—22no—
292Dic26—41no—
293Dic26—41no—
294C8×C13—24no—
295#1055—24no—
296C22×#41—131no—
297C22×#41C2×D1311yescharacteristic
298C22×M16—131no—
299C22×M16C2×D1311yescharacteristic
300#532—138no—
301#532—264no—
302C2×C4⋊Q8—131no—
303C2×#127—131no—
304C2×#124—131no—
305C2×#124—131no—
306C2×#121—262no—
307C2×C4×D4—262no—
308C22×C4⋊C4—131no—
309C22×C4⋊C4—262no—
310C22×C4⋊C4C2×D1311yescharacteristic
311C22×C42—131no—
312#417—24no—
313#417—264no—
314#417—264no—
315#417—264no—
316C2×#103—132no—
317C2×#103—132no—
318C2×#103—132no—
319C2×#103C2×D1312yes—
320C2×#102—132no—
321C2×#102—132no—
322C2×#102—132no—
323C2×#102C2×D1312yes—
324C4×M16—264no—
325C2×#97—132no—
326C2×C4×C8—132no—
327#384—132no—
328#384—132no—
329#384—262no—
330C22×C13—24no—
331C22×C13—24no—
332C22×C13—22no—
333C22×C13—22no—
334C22×C13—44no—
335C22×C13—42no—
336C22×C13—82no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13#39014yes—
340C22×C13C22×C22⋊C411yescharacteristic
341C22×C13C2×#12411yescharacteristic
342C22×C13C2×#12711yescharacteristic
343C22×C13C2×AGL(1,ℤ/8)12yes—
344C22×C13C2×#13712yes—
345C2×D13—44no—
346C2×D13—42no—
347C2×D13—82no—
348C2×D13—81no—
349C2×D13—81no—
350C4×C13—42no—
351C4×C13—82no—
352C4×C13#39014yes—
353C4×C13C2×C4×D411yescharacteristic
354C4×C13C2×C4×D411yescharacteristic
355C4×C13C2×#12111yescharacteristic
356C4×C13C2×#12111yescharacteristic
357Dic13—24no—
358Dic13—42no—
359Dic13—82no—
360Dic13#41718yescomplemented
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—134no—
367C2×#41—262no—
368C2×#41—262no—
369C2×#41—262no—
370C2×#41—262no—
371C2×#41—262no—
372C2×#41C4×D1314yes—
373C22×Q8—131no—
374C22×Q8C22×D1311yescharacteristic
375C22×D4—21no—
376C22×D4—131no—
377C22×D4—262no—
378C22×D4—261no—
379C22×D4C22×D1311yescharacteristic
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—132no—
383C23×C4—261no—
384C23×C4—261no—
385C23×C4C22×D1311yescharacteristic
386C2×M16—22no—
387C2×M16—22no—
388C2×M16—134no—
389C2×M16—262no—
390C2×M16—262no—
391C2×M16C22⋊D1314yescomplemented
392C22×C8—132no—
393C22×C8C22×D1312yes—
394C4⋊Q8—134no—
395C4⋊Q8—262no—
396#127—134no—
397#127—262no—
398#124—134no—
399#124—134no—
400#124—262no—
401#124—262no—
402#121—2616no—
403C4×D4—2616no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—132no—
408C2×C4⋊C4—262no—
409C2×C4⋊C4—262no—
410C2×C4⋊C4—262no—
411C2×C4⋊C4—264no—
412C2×C4⋊C4—264no—
413C2×C4⋊C4—261no—
414C2×C4⋊C4—528no—
415C2×C4⋊C4C22×D1312yes—
416C2×C22⋊C4—262no—
417C2×C22⋊C4—262no—
418C2×C42—134no—
419C2×C42—132no—
420C2×C42—134no—
421C2×C42—131no—
422C2×C42—131no—
423#103—24no—
424#103—264no—
425#103—264no—
426#103—264no—
427#102—24no—
428#102—264no—
429#102—264no—
430#102—264no—
431#97—264no—
432C4×C8—264no—
433C2×C13—24no—
434C2×C13—82no—
435C2×C13C2×#39011yescharacteristic
436C2×C13C2×#41712yes—
437C2×C13#314112yes—
438C2×C13#315111yescharacteristic
439C2×C13#315211yescharacteristic
440D13—82no—
441C24—21no—
442C24—261no—
443C24D4×D1311yescharacteristic
444#41—28no—
445#41—28no—
446#41—44no—
447#41—44no—
448#41—268no—
449#41—268no—
450#41—524no—
451#41—524no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—132no—
458C2×Q8—261no—
459C2×Q8—261no—
460C2×Q8—261no—
461C2×Q8—261no—
462C2×Q8—261no—
463C2×Q8C2×C4×D1312yes—
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—132no—
473C2×D4—268no—
474C2×D4—264no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—261no—
478C2×D4—261no—
479C2×D4—261no—
480C2×D4—524no—
481C2×D4—524no—
482C2×D4—522no—
483C2×D4—522no—
484C2×D4C2×C4×D1312yes—
485C22×C4—21no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—44no—
491C22×C4—42no—
492C22×C4—132no—
493C22×C4—138no—
494C22×C4—132no—
495C22×C4—264no—
496C22×C4—264no—
497C22×C4—261no—
498C22×C4—264no—
499C22×C4—262no—
500C22×C4—522no—
501C22×C4—522no—
502C22×C4—524no—
503C22×C4—522no—
504C22×C4C2×C4×D1312yes—
505C22×C4#612712yes—
506C22×C4D4×D1311yescharacteristic
507C22×C4D4×D1312yes—
508C22×C4D4×D1312yes—
509C22×C4#612912yes—
510C22×C4C2×C22⋊D1312yes—
511C22×C4C23×D1311yescharacteristic
512M16—28no—
513M16—268no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—134no—
517C2×C8—262no—
518C2×C8—262no—
519C2×C8C2×C22⋊D1314yes—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—42no—
523C4⋊C4—268no—
524C4⋊C4—262no—
525C4⋊C4—262no—
526C4⋊C4—528no—
527C4⋊C4—528no—
528C4⋊C4—522no—
529C22⋊C4—268no—
530C22⋊C4—268no—
531C42—138no—
532C42—132no—
533C42—132no—
534C42—132no—
535C42—132no—
536C13#2120011yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—262no—
545C23—521no—
546C23—522no—
547C23—522no—
548C23—521no—
549C23C22⋊C4×D1312yes—
550C23#8813912yes—
551C23#8819412yes—
552C23C2×D4×D1311yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—262no—
558Q8—262no—
559Q8—521no—
560Q8—521no—
561D4—22no—
562D4—22no—
563D4—48no—
564D4—41no—
565D4—41no—
566D4—262no—
567D4—262no—
568D4—5216no—
569D4—528no—
570D4—521no—
571D4—521no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—48no—
576C2×C4—44no—
577C2×C4—42no—
578C2×C4—84no—
579C2×C4—134no—
580C2×C4—134no—
581C2×C4—134no—
582C2×C4—134no—
583C2×C4—2616no—
584C2×C4—262no—
585C2×C4—262no—
586C2×C4—262no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—528no—
590C2×C4—524no—
591C2×C4—522no—
592C2×C4—1044no—
593C2×C4C22⋊C4×D1312yes—
594C2×C4#8813514yes—
595C2×C4#8813814yes—
596C2×C4#8813912yes—
597C2×C4C4×C22⋊D1314yes—
598C2×C4#8819314yes—
599C2×C4#8819412yes—
600C2×C4C22×C4×D1311yescharacteristic
601C2×C4C2×#612711yescharacteristic
602C2×C4C2×D4×D1311yescharacteristic
603C2×C4C2×D4×D1311yescharacteristic
604C2×C4C2×#612911yescharacteristic
605C2×C4C22×C22⋊D1311yescharacteristic
606C8—24no—
607C8—264no—
608C22—24no—
609C22—24no—
610C22—22no—
611C22—22no—
612C22—44no—
613C22—42no—
614C22—82no—
615C22—81no—
616C22—81no—
617C22—524no—
618C22—522no—
619C22—1042no—
620C22—1041no—
621C22—1041no—
622C22#1171861814yes—
623C22C2×C22⋊C4×D1311yescharacteristic
624C22C2×#8813911yescharacteristic
625C22D13×AGL(1,ℤ/8)12yes—
626C22D13×#13712yes—
627C22C2×#8819411yescharacteristic
628C4—42no—
629C4—82no—
630C4—138no—
631C4—264no—
632C4—522no—
633C4—1042no—
634C4#1171861814yes—
635C4C2×#8813511yescharacteristic
636C4C2×#8813811yescharacteristic
637C4C2×C4×C22⋊D1311yescharacteristic
638C4C2×#8819311yescharacteristic
639C2—24no—
640C2—82no—
641C2—1042no—
642C2C2×#1171861811yescharacteristic
643C2D13×#41712yes—
644C2#1312522712yes—
645C2#1312528411yescharacteristic
646C2#1312529111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#417C2
socleC23×C13C22×D4
prime radicalC2×#11719537C2
cosocleC22×C4×C13C24
hypercenterC2×#417D13
hypocenterC13#21200
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#11718794C2semidirect
3. C2×#11718893C2semidirect
4. C2×#11718627C2semidirect
5. C2×M16×Dic13C2semidirect
6. C2×#11718637C2semidirect
7. #13115651C2semidirect
8. #13115649C2semidirect
9. #13115640C2semidirect
10. #13115636C2semidirect
11. C2×C13×#417C2semidirect
17. #11719537C4semidirect
73. C2×C13×M16D4semidirect
81. #88201C2×C4semidirect
83. #88198C2×C4semidirect
85. #88194C2×C4semidirect
88. #88190C2×C4semidirect
106. C2×#6099D4semidirect
218. C2×#417D13semidirect
360. Dic13#417semidirect
391. C2×M16C22⋊D13semidirect
536. C13#21200semidirect

Maximal subgroups

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

subgroupindex
C2×#117195372
C2×#117187942
C2×#117188932
C2×#117186272
C2×M16×Dic132
C2×#117186372
#131156512
#131156492
#131156402
#131156362
C2×C13×#4172
#2120013