Finite Group Databasebeta

← #15769295

Subgroups — #15769295

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88045C211yesmaximal, characteristic
2#13123356C211yesmaximal, characteristic
3C2×#11718667C211yesmaximal, characteristic
4C4×#88180C211yesmaximal, characteristic, complemented
5C2×#11718151C211yesmaximal, characteristic, complemented
6#13114546C211yesmaximal, characteristic, complemented
7C2×C13×#339C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15C4×C22⋊Dic13—22no—
16#11718794—22no—
17#11718792C412yescomplemented
18#11718781C412yescomplemented
19#11718774—22no—
20#11718667—22no—
21#11718667C414yescomplemented
22C2×#88046—22no—
23C4×C4⋊Dic13—22no—
24#11718593—21no—
25C42×Dic13—21no—
26C2×#88045—21no—
27C2×#88045—21no—
28C2×#88045—22no—
29C2×#88045C414yescomplemented
30C13×#339—22no—
31#11718151—22no—
32#11718115—22no—
33C23×C4×C13—21no—
34C23×C4×C13C2311yescharacteristic
35C22×C22⋊D13—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127—21no—
44C2×#6127—21no—
45C2×#6127—21no—
46C2×#6127C2×C412yes—
47C2×#6127C2×C412yes—
48C22×D52C2×C411yescharacteristic
49C22×C4×D13—21no—
50C22×Dic26C2×C411yescharacteristic
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16C2×C412yes—
57C22×C8×C13—21no—
58C13×#117—21no—
59C13×#117—21no—
60C13×#117—21no—
61C13×#117C2×C412yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C42×C13—21no—
65C2×C42×C13—21no—
66C2×C42×C13—21no—
67C2×C42×C13—21no—
68C2×C42×C13C2×C412yes—
69C2×C42×C13D411yescharacteristic
70C2×C42×C13D411yescharacteristic
71C2×C42×C13D412yes—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13D412yes—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77#88180—21no—
78#88180C2×C412yes—
79#88180C2×C412yes—
80#88180D412yes—
81#88180D412yes—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13D412yes—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—24no—
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099—21no—
91C2×#6099—21no—
92C2×#6099C2×C412yes—
93C22×#1055—21no—
94#88071—24no—
95#88061—24no—
96#88056—24no—
97#88046—28no—
98#88045—24no—
99#88045—24no—
100#10945—131nomaximal, Sylow
101C24×C13C2×D411yescharacteristic
102C23×D13—21no—
103C22×C4×C13—21no—
104C22×C4×C13—22no—
105C22×C4×C13—21no—
106C22×C4×C13—22no—
107C22×C4×C13—44no—
108C22×C4×C13—41no—
109C22×C4×C13C22×C411yescharacteristic
110C22×C4×C13C22×C411yescharacteristic
111C22×C4×C13C22×C411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13#4111yescharacteristic
118C22×C4×C13#4111yescharacteristic
119C22×C4×C13#4111yescharacteristic
120C22×C4×C13#4111yescharacteristic
121C22×C4×C13#4111yescharacteristic
122C22×C4×C13#4111yescharacteristic
123C2×C22⋊D13—22no—
124C2×C22⋊D13—22no—
125C2×C22⋊D13—41no—
126C2×C22⋊D13—41no—
127C2×C22⋊D13—41no—
128C2×C22⋊D13—41no—
129C22×Dic13—21no—
130C22×Dic13—22no—
131C22×Dic13—22no—
132#6127—22no—
133#6127—22no—
134#6127—22no—
135#6127—22no—
136#6127—22no—
137#6127—22no—
138#6127—22no—
139#6127—22no—
140#6127—41no—
141#6127—41no—
142#6127—41no—
143#6127—41no—
144#6127—41no—
145#6127—41no—
146#6127—41no—
147#6127—41no—
148C2×D52—21no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52C4212yescomplemented
154C2×C4×D13—22no—
155C2×C4×D13—22no—
156C2×C4×D13—41no—
157C2×C4×D13—41no—
158C2×C4×D13—41no—
159C2×C4×D13—41no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26C4212yescomplemented
166C13×M16—22no—
167C13×M16—22no—
168C13×M16—41no—
169C13×M16—41no—
170C2×C8×C13—22no—
171C2×C8×C13—41no—
172C2×C8×C13—41no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—41no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—41no—
177C42×C13—22no—
178C42×C13—22no—
179C42×C13—21no—
180C42×C13—21no—
181C42×C13—22no—
182C42×C13—41no—
183C42×C13C22⋊C412yes—
184C42×C13C22⋊C412yes—
185C22⋊Dic13—22no—
186C22⋊Dic13—22no—
187C22⋊Dic13—22no—
188C22⋊Dic13C22⋊C414yes—
189C4⋊Dic13—22no—
190C4⋊Dic13—22no—
191C4⋊Dic13—22no—
192C4⋊Dic13C22⋊C414yes—
193C4×Dic13—22no—
194C4×Dic13—22no—
195C4×Dic13—22no—
196C4×Dic13—22no—
197C4×Dic13—48no—
198#6099—22no—
199#6099—22no—
200#6099—41no—
201#6099—41no—
202C2×#1055—22no—
203C2×#1055—41no—
204C2×#1055—41no—
205C22×#104—131no—
206#2896—131no—
207C2×#410—131no—
208C4×#117—131no—
209C2×#344—131no—
210#1733—131no—
211C2×#339D1311yescharacteristic, complemented
212C23×C13—42no—
213C23×C13C2×C22⋊C411yescharacteristic
214C23×C13C4×D411yescharacteristic
215C23×C13C4×D411yescharacteristic
216C23×C13#12011yescharacteristic
217C23×C13#12111yescharacteristic
218C23×C13#12111yescharacteristic
219C23×C13#12311yescharacteristic
220C22×D13—22no—
221C22×D13—41no—
222C22×D13—41no—
223C22×D13—82no—
224C2×C4×C13—24no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—44no—
228C2×C4×C13—44no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—82no—
232C2×C4×C13C2×C4211yescharacteristic
233C2×C4×C13C2×C22⋊C411yescharacteristic
234C2×C4×C13C2×C22⋊C411yescharacteristic
235C2×C4×C13#11711yescharacteristic
236C2×C4×C13#11711yescharacteristic
237C2×C4×C13#11711yescharacteristic
238C2×C4×C13C4×D411yescharacteristic
239C2×C4×C13C4×D411yescharacteristic
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C4×D411yescharacteristic
247C2×C4×C13C4×D411yescharacteristic
248C2×C4×C13#12111yescharacteristic
249C2×C4×C13#12111yescharacteristic
250C2×C4×C13#12111yescharacteristic
251C2×C4×C13#12111yescharacteristic
252C2×C4×C13#12311yescharacteristic
253C2×C4×C13#12311yescharacteristic
254C2×C4×C13#12411yescharacteristic
255C2×C4×C13#12411yescharacteristic
256C2×C4×C13#12411yescharacteristic
257C2×C4×C13#12611yescharacteristic
258C2×C4×C13#12611yescharacteristic
259C2×C4×C13#12711yescharacteristic
260C22⋊D13—42no—
261C22⋊D13—42no—
262C22⋊D13—42no—
263C22⋊D13—42no—
264C2×Dic13—22no—
265C2×Dic13—24no—
266C2×Dic13—24no—
267C2×Dic13—44no—
268C2×Dic13—44no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271D52—22no—
272D52—22no—
273D52—41no—
274D52—41no—
275C4×D13—42no—
276C4×D13—42no—
277C4×D13—42no—
278C4×D13—42no—
279Dic26—22no—
280Dic26—22no—
281Dic26—41no—
282Dic26—41no—
283C8×C13—42no—
284#1055—42no—
285C22×#41—131no—
286C22×M16—131no—
287C22×M16C2×D1311yescharacteristic
288C2×#117—131no—
289C2×#117—131no—
290C2×#117C2×D1311yescharacteristic
291C22×C42C2×D1311yescharacteristic
292C2×#104—134no—
293C2×#104—261no—
294C2×#104—261no—
295C2×#104—262no—
296#419—132no—
297#418—132no—
298#417—262no—
299#416—262no—
300#410—134no—
301#410—262no—
302C2×#99—262no—
303C4×C4⋊C4—262no—
304C4×C22⋊C4—262no—
305#376—261no—
306C43—261no—
307#344—262no—
308#339—22no—
309#339—262no—
310C22×C13—22no—
311C22×C13—22no—
312C22×C13—22no—
313C22×C13—41no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—41no—
317C22×C13C4×C22⋊C411yescharacteristic
318C22×C13#38611yescharacteristic
319C22×C13#38611yescharacteristic
320C22×C13#38611yescharacteristic
321C22×C13#38811yescharacteristic
322C22×C13#38811yescharacteristic
323C22×C13#39011yescharacteristic
324C2×D13—42no—
325C2×D13—82no—
326C2×D13—82no—
327C2×D13—82no—
328C4×C13—24no—
329C4×C13—42no—
330C4×C13—82no—
331C4×C13C4×C22⋊C411yescharacteristic
332C4×C13C4×C22⋊C411yescharacteristic
333C4×C13#38811yescharacteristic
334C4×C13#38811yescharacteristic
335C4×C13#38811yescharacteristic
336C4×C13#38811yescharacteristic
337C4×C13#39011yescharacteristic
338C4×C13#39011yescharacteristic
339Dic13—44no—
340Dic13—44no—
341Dic13—42no—
342C2×#41—132no—
343C2×#41—132no—
344C2×#41—261no—
345C2×#41—261no—
346C2×#41—261no—
347C2×#41—261no—
348C2×#41—261no—
349C2×#41—261no—
350C2×#41—261no—
351C2×#41—261no—
352C2×#41—261no—
353C2×#41—261no—
354C22×Q8—131no—
355C22×D4—131no—
356C22×D4—261no—
357C23×C4—21no—
358C23×C4—261no—
359C23×C4C22×D1311yescharacteristic
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—132no—
366C2×M16—261no—
367C2×M16—261no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16—261no—
371C2×M16C4×D1312yes—
372C22×C8—21no—
373C22×C8—261no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—132no—
378#117—132no—
379#117—132no—
380#117—132no—
381#117—261no—
382#117—261no—
383#117—261no—
384#117—261no—
385#117C4×D1312yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—132no—
388C2×C4⋊C4—261no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—132no—
391C2×C22⋊C4—261no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—264no—
399C2×C42C4×D1312yes—
400C2×C42D5211yescharacteristic
401C2×C42D5211yescharacteristic
402C2×C42C22⋊D1312yes—
403#104—264no—
404#104—264no—
405#103—264no—
406#102—264no—
407#99—268no—
408#95—264no—
409C2×C13—21no—
410C2×C13—21no—
411C2×C13—21no—
412C2×C13—21no—
413C2×C13—21no—
414C2×C13—21no—
415C2×C13#143711yescharacteristic
416C2×C13#190612yes—
417D13—82no—
418C24—261no—
419C24D4×D1311yescharacteristic
420#41—262no—
421#41—262no—
422#41—262no—
423#41—262no—
424#41—262no—
425#41—262no—
426#41—262no—
427#41—262no—
428#41—521no—
429#41—521no—
430#41—521no—
431#41—521no—
432#41—521no—
433#41—521no—
434#41—521no—
435#41—521no—
436C2×Q8—132no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×Q8—261no—
440C2×Q8—261no—
441C2×Q8—261no—
442C2×D4—132no—
443C2×D4—262no—
444C2×D4—262no—
445C2×D4—261no—
446C2×D4—261no—
447C2×D4—261no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—521no—
451C2×D4—521no—
452C2×D4—521no—
453C2×D4—521no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—44no—
459C22×C4—41no—
460C22×C4—262no—
461C22×C4—262no—
462C22×C4—261no—
463C22×C4—262no—
464C22×C4—262no—
465C22×C4—521no—
466C22×C4—521no—
467C22×C4—521no—
468C22×C4—521no—
469C22×C4C2×C4×D1311yescharacteristic
470C22×C4C2×C4×D1311yescharacteristic
471C22×C4C2×C4×D1311yescharacteristic
472C22×C4C2×D5211yescharacteristic
473C22×C4#612711yescharacteristic
474C22×C4#612711yescharacteristic
475C22×C4D4×D1311yescharacteristic
476C22×C4D4×D1311yescharacteristic
477C22×C4D4×D1311yescharacteristic
478C22×C4#612911yescharacteristic
479C22×C4#612911yescharacteristic
480C22×C4#613111yescharacteristic
481C22×C4#613111yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483M16—22no—
484M16—22no—
485M16—41no—
486M16—41no—
487M16—262no—
488M16—262no—
489M16—521no—
490M16—521no—
491C2×C8—22no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—262no—
495C2×C8—521no—
496C2×C8—521no—
497C4⋊C4—22no—
498C4⋊C4—41no—
499C4⋊C4—134no—
500C4⋊C4—262no—
501C4⋊C4—262no—
502C4⋊C4—262no—
503C22⋊C4—22no—
504C22⋊C4—41no—
505C22⋊C4—134no—
506C22⋊C4—262no—
507C22⋊C4—262no—
508C22⋊C4—262no—
509C42—22no—
510C42—21no—
511C42—21no—
512C42—22no—
513C42—22no—
514C42—41no—
515C42—262no—
516C42—262no—
517C42—262no—
518C42—262no—
519C42—528no—
520C42#610312yes—
521C42#610312yes—
522C13#1094511yescharacteristic, complemented, Sylow
523C23—42no—
524C23—262no—
525C23—521no—
526C23—521no—
527C23—1042no—
528C23C22⋊C4×D1311yescharacteristic
529C23#8813511yescharacteristic
530C23#8813611yescharacteristic
531C23#8813811yescharacteristic
532C23#8814711yescharacteristic
533C23#8814811yescharacteristic
534C23#8819311yescharacteristic
535Q8—262no—
536Q8—262no—
537Q8—521no—
538Q8—521no—
539D4—262no—
540D4—262no—
541D4—522no—
542D4—522no—
543D4—522no—
544D4—522no—
545D4—521no—
546D4—521no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—44no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—82no—
555C2×C4—264no—
556C2×C4—264no—
557C2×C4—262no—
558C2×C4—524no—
559C2×C4—524no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—522no—
563C2×C4—522no—
564C2×C4—522no—
565C2×C4—522no—
566C2×C4C42×D1311yescharacteristic
567C2×C4#8812611yescharacteristic
568C2×C4C4×D5211yescharacteristic
569C2×C4C4×D5211yescharacteristic
570C2×C4C22⋊C4×D1311yescharacteristic
571C2×C4#8813511yescharacteristic
572C2×C4#8813511yescharacteristic
573C2×C4#8813511yescharacteristic
574C2×C4#8813811yescharacteristic
575C2×C4#8813911yescharacteristic
576C2×C4#8813911yescharacteristic
577C2×C4#8814011yescharacteristic
578C2×C4#8814611yescharacteristic
579C2×C4#8814611yescharacteristic
580C2×C4#8814711yescharacteristic
581C2×C4#8814711yescharacteristic
582C2×C4#8814711yescharacteristic
583C2×C4#8814811yescharacteristic
584C2×C4#8814911yescharacteristic
585C2×C4#8814911yescharacteristic
586C2×C4#8815211yescharacteristic
587C2×C4#8815211yescharacteristic
588C2×C4C2×#610311yescharacteristic
589C2×C4C4×C22⋊D1311yescharacteristic
590C2×C4C4×C22⋊D1311yescharacteristic
591C2×C4#8819311yescharacteristic
592C2×C4#8819411yescharacteristic
593C2×C4#8820111yescharacteristic
594C8—42no—
595C8—522no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—522no—
604C22—1042no—
605C22—1042no—
606C22—1042no—
607C22#1171832611yescharacteristic
608C22#1171832611yescharacteristic
609C22#1171832711yescharacteristic
610C22#1171833011yescharacteristic
611C22#1171861811yescharacteristic
612C22#1171861911yescharacteristic
613C22#1171865111yescharacteristic
614C4—24no—
615C4—42no—
616C4—82no—
617C4—524no—
618C4—524no—
619C4—522no—
620C4#1171832711yescharacteristic
621C4#1171833011yescharacteristic
622C4#1171833111yescharacteristic
623C4#1171833111yescharacteristic
624C4C4×#610311yescharacteristic
625C4#1171861811yescharacteristic
626C4#1171864911yescharacteristic
627C4#1171865111yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—1042no—
635C2#1311307211yescharacteristic
636C2#1311533612yes—
subgroupG/H
centerC2×C4#88149
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#339C2
socleC22×C13#386
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#339D13
hypocenterC13#10945
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C4×#88180C2semidirect
5. C2×#11718151C2semidirect
6. #13114546C2semidirect
7. C2×C13×#339C2semidirect
17. #11718792C4semidirect
18. #11718781C4semidirect
21. #11718667C4semidirect
29. C2×#88045C4semidirect
153. C2×D52C42semidirect
165. C2×Dic26C42semidirect
211. C2×#339D13semidirect
522. C13#10945semidirect

Maximal subgroups

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

subgroupindex
C22×#880452
#131233562
C2×#117186672
C4×#881802
C2×#117181512
#131145462
C2×C13×#3392
#1094513