Finite Group Databasebeta

← #15830113

Subgroups — #15830113

Order 3328.

1166 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128868C211yesmaximal, characteristic
2#13123871C211yesmaximal, characteristic, complemented
3#13113359C211yesmaximal, characteristic, complemented
4#13113351C212yesmaximal, complemented
5#13113343C211yesmaximal, characteristic, complemented
6#13113338C212yesmaximal, complemented
7#13113330C211yesmaximal, characteristic, complemented
8#13113325C212yesmaximal, complemented
9#13113320C211yesmaximal, characteristic, complemented
10C2×#11718043C212yesmaximal, complemented
11C13×#2275C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13—21no—
13C2×C4×D4×C13C2211yescharacteristic
14D4×C22⋊D13—21no—
15#11719496C2212yes—
16C2×#88184C2212yes—
17#11719270C412yescomplemented
18#11719268C411yescharacteristic, complemented
19#11719267—21no—
20#11719265—22no—
21#11719258C411yescharacteristic, complemented
22#11719255C412yescomplemented
23D4×D52C411yescharacteristic, complemented
24#11719250—21no—
25#11719248C411yescharacteristic, complemented
26#11719219—21no—
27#11719195—22no—
28#11719184C2211yescharacteristic
29#11719182C2211yescharacteristic
30C4×C13×C4⋊C4—21no—
31C4×C13×C4⋊C4C2211yescharacteristic, complemented
32C4×C13×C22⋊C4—22no—
33C4×C13×C22⋊C4C2212yescomplemented
34C13×#376C2211yescharacteristic, complemented
35C2×C13×#95C2212yescomplemented
36#11718868C2212yescomplemented
37C2×C22⋊#1055C2212yescomplemented
38#11718673—21no—
39#11718672—22no—
40D4×#1055—21no—
41#11718587C2211yescharacteristic, complemented
42#11718586C2211yescharacteristic, complemented
43#11718044C2212yescomplemented
44#11718044C2211yescharacteristic, complemented
45#11718044C2211yescharacteristic, complemented
46#11718043C2211yescharacteristic
47#11718043C2212yes—
48#11718043C2211yescharacteristic
49#11718043C2212yescomplemented
50#11718043C2212yescomplemented
51#11718043C2212yescomplemented
52#11718043C2212yescomplemented
53C22×D4×C13D411yescharacteristic
54C23×C4×C13—22no—
55C23×C4×C13C2312yes—
56C22×C22⋊D13—22no—
57C2×D4×D13—21no—
58C2×#6127—21no—
59C2×#6127C2×C412yescomplemented
60C22×D52C2×C412yescomplemented
61C4×D4×C13—28no—
62C4×D4×C13C2×C411yescharacteristic
63C4×D4×C13C2×C412yes—
64C4×D4×C13C2×C411yescharacteristic
65C4×D4×C13D411yescharacteristic
66C4×D4×C13D412yes—
67C4×D4×C13D411yescharacteristic
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C22⋊C4—22no—
71C2×C13×C22⋊C4D412yes—
72C2×C42×C13—21no—
73C2×C42×C13—21no—
74C2×C42×C13—22no—
75C2×C42×C13C2311yescharacteristic
76#88207—22no—
77#88194—21no—
78#88193—22no—
79#88192—21no—
80#88191—22no—
81D4×Dic13—21no—
82#88184—21no—
83#88184—22no—
84#88184—22no—
85#88184C2×C412yescomplemented
86#88184C2×C412yescomplemented
87#88184C2×C412yescomplemented
88#88184C2312yes—
89#88184C2311yescharacteristic
90#88183—21no—
91#88183—22no—
92C4×C22⋊D13—21no—
93C4×C22⋊D13—22no—
94C4×C22⋊D13—22no—
95C2×#6103—22no—
96#88180C2×C412yescomplemented
97C2×C4⋊Dic13C2×C412yescomplemented
98#88178C2×C412yescomplemented
99#88178C2311yescharacteristic
100C2×#6099—22no—
101C22×#1055—22no—
102#88152—22no—
103#88149—21no—
104#88148—22no—
105#88147—21no—
106#88146—21no—
107#88144—21no—
108#88139—22no—
109#88138—22no—
110#88138—22no—
111#88137—22no—
112#88136—22no—
113#88135—22no—
114C22⋊C4×D13—22no—
115#88132—22no—
116#88130—21no—
117#88129—21no—
118#88129C2×C411yescharacteristic, complemented
119#88128C2×C411yescharacteristic, complemented
120C4×D52—21no—
121C4×D52C2×C412yescomplemented
122C4×D52C2×C411yescharacteristic, complemented
123#88126—21no—
124#88124C2×C411yescharacteristic, complemented
125#88123C2×C411yescharacteristic, complemented
126C4×Dic26C2×C411yescharacteristic, complemented
127C13×#95—21no—
128C13×#95—22no—
129C13×#95C2311yescharacteristic
130C13×#95C2312yes—
131C13×#95C2311yescharacteristic
132C22⋊#1055—22no—
133C22⋊#1055—22no—
134C22⋊#1055C2311yescharacteristic
135C22⋊#1055C2311yescharacteristic
136C22⋊#1055C2312yes—
137C4⋊#1055—21no—
138C4⋊#1055—21no—
139#88043—21no—
140C4×#1055—21no—
141#17547—131nomaximal, Sylow
142C24×C13C2×D412yes—
143C23×D13—22no—
144C2×D4×C13—24no—
145C2×D4×C13C22⋊C412yes—
146C2×D4×C13C22⋊C411yescharacteristic
147C2×D4×C13C22⋊C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—28no—
152C22×C4×C13—82no—
153C22×C4×C13—82no—
154C22×C4×C13—82no—
155C22×C4×C13C22×C412yes—
156C22×C4×C13C22×C412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2411yescharacteristic
163C2×C22⋊D13—22no—
164C2×C22⋊D13—21no—
165C2×C22⋊D13—22no—
166C2×C22⋊D13—22no—
167C2×C22⋊D13—22no—
168C2×C22⋊D13—22no—
169C2×C22⋊D13—82no—
170C2×C22⋊D13—82no—
171C22×Dic13—22no—
172D4×D13—44no—
173#6127—82no—
174#6127—81no—
175#6127—81no—
176C2×D52—21no—
177C2×D52—21no—
178C2×D52—22no—
179C2×D52—82no—
180C2×D52C22×C412yes—
181C2×D52C22×C411yescharacteristic
182C2×C4×D13—21no—
183C2×C4×D13—22no—
184C2×C4×D13—22no—
185C2×Dic26—21no—
186C2×Dic26C22×C411yescharacteristic
187C13×C4⋊C4—24no—
188C13×C4⋊C4C22⋊C411yescharacteristic
189C13×C4⋊C4C22⋊C411yescharacteristic
190C13×C4⋊C4C22⋊C412yes—
191C13×C22⋊C4—28no—
192C13×C22⋊C4C22⋊C412yes—
193C13×C22⋊C4C22⋊C412yes—
194C13×C22⋊C4C22⋊C412yes—
195C13×C22⋊C4C22⋊C412yes—
196C42×C13—24no—
197C42×C13—81no—
198C42×C13—82no—
199C42×C13C22×C411yescharacteristic
200C42×C13C22×C411yescharacteristic
201C42×C13C2×D411yescharacteristic
202C42×C13C2×D411yescharacteristic
203C22⋊Dic13—22no—
204C22⋊Dic13—22no—
205C22⋊Dic13—21no—
206#6103—21no—
207#6103—22no—
208#6103—21no—
209#6103—21no—
210#6103—22no—
211#6103—22no—
212#6103—22no—
213#6103—21no—
214#6103—22no—
215C4⋊Dic13—21no—
216C4⋊Dic13—22no—
217C4⋊Dic13C22×C411yescharacteristic
218C4⋊Dic13C22×C412yes—
219C4⋊Dic13C22×C411yescharacteristic
220#6101—21no—
221#6101—21no—
222#6101—21no—
223#6101—22no—
224#6101—21no—
225C4×Dic13—21no—
226C4×Dic13—22no—
227#6099—82no—
228C2×#1055—21no—
229C2×#1055—22no—
230C2×#1055—21no—
231C2×#1055—82no—
232#3519—131no—
233#2974—131no—
234#2275D1311yescharacteristic, complemented
235#1509—131no—
236#1507—132no—
237#1505—131no—
238#1504—132no—
239#1502—131no—
240#1501—132no—
241#1500—131no—
242C2×#327—132no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—24no—
246C23×C13—42no—
247C23×C13C2×C22⋊C412yes—
248C23×C13C2×C22⋊C412yes—
249C23×C13C22×D411yescharacteristic
250C22×D13—21no—
251C22×D13—22no—
252C22×D13—44no—
253C22×D13—82no—
254C22×D13—82no—
255D4×C13—24no—
256D4×C13—22no—
257D4×C13#10414yes—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—24no—
264C2×C4×C13—42no—
265C2×C4×C13—42no—
266C2×C4×C13—42no—
267C2×C4×C13—42no—
268C2×C4×C13—42no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—42no—
272C2×C4×C13—41no—
273C2×C4×C13—42no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—88no—
277C2×C4×C13C2×C22⋊C412yes—
278C2×C4×C13C2×C22⋊C412yes—
279C2×C4×C13C2×C22⋊C411yescharacteristic
280C2×C4×C13C2×C22⋊C411yescharacteristic
281C2×C4×C13C2×C22⋊C411yescharacteristic
282C2×C4×C13C2×C22⋊C411yescharacteristic
283C2×C4×C13C23×C411yescharacteristic
284C2×C4×C13C22×D411yescharacteristic
285C22⋊D13—42no—
286C22⋊D13—41no—
287C22⋊D13—42no—
288C22⋊D13—41no—
289C22⋊D13—44no—
290C22⋊D13—82no—
291C22⋊D13—82no—
292C22⋊D13—82no—
293C2×Dic13—21no—
294C2×Dic13—21no—
295C2×Dic13—21no—
296C2×Dic13—22no—
297C2×Dic13—82no—
298D52—41no—
299D52—42no—
300D52—42no—
301D52—82no—
302D52—81no—
303C4×D13—42no—
304C4×D13—82no—
305C4×D13—82no—
306Dic26—41no—
307Dic26—81no—
308#1055—41no—
309#1055—42no—
310#1055—41no—
311#555—131no—
312#554—131no—
313#553—132no—
314#553—261no—
315#550—131no—
316#546—132no—
317#546—262no—
318D42—131no—
319D42—261no—
320#540—261no—
321#538—262no—
322#532—131no—
323#529—131no—
324#525—132no—
325C2×#121—132no—
326#518—261no—
327C2×C4×D4—21no—
328C2×C4×D4C2×D1311yescharacteristic
329#436—261no—
330#435—262no—
331C8×D4—261no—
332#432—131no—
333#431—131no—
334#407—132no—
335C2×C22⋊C8—132no—
336C4×C4⋊C4—21no—
337C4×C4⋊C4C2×D1311yescharacteristic, complemented
338C4×C22⋊C4—22no—
339C4×C22⋊C4C2×D1312yescomplemented
340#376C2×D1311yescharacteristic, complemented
341C2×#95C2×D1312yescomplemented
342#328—131no—
343#328—131no—
344#328—132no—
345#327—131no—
346#327—132no—
347#327—131no—
348#327—132no—
349#327—132no—
350#327—132no—
351#327—132no—
352C22×C13—21no—
353C22×C13—22no—
354C22×C13—22no—
355C22×C13—21no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—44no—
360C22×C13—44no—
361C22×C13C2×#10414yes—
362C22×C13C22×C22⋊C411yescharacteristic
363C22×C13#57611yescharacteristic
364C22×C13#57711yescharacteristic
365C2×D13—42no—
366C2×D13—41no—
367C2×D13—42no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—42no—
371C2×D13—164no—
372C4×C13—21no—
373C4×C13—21no—
374C4×C13—22no—
375C4×C13—22no—
376C4×C13—21no—
377C4×C13—21no—
378C4×C13—21no—
379C4×C13—42no—
380C4×C13—44no—
381C4×C13—42no—
382C4×C13C2×#10412yes—
383Dic13—41no—
384Dic13—42no—
385Dic13—41no—
386Dic13—41no—
387C2×#41—132no—
388C2×#41—261no—
389C22×D4—132no—
390C22×D4—262no—
391C22×D4—261no—
392C22×D4C22⋊D1311yescharacteristic
393C23×C4—22no—
394C23×C4C22×D1312yes—
395C2×M16—262no—
396C22×C8—262no—
397C4⋊Q8—131no—
398#127—131no—
399#127—261no—
400#126—262no—
401#126—261no—
402#125—131no—
403#125—261no—
404#124—131no—
405#124—262no—
406#124—261no—
407#123—262no—
408#123—261no—
409#123—262no—
410#123—262no—
411C22⋊Q8—132no—
412C22⋊Q8—131no—
413C22⋊Q8—262no—
414#121—132no—
415#121—132no—
416#121—132no—
417#121—131no—
418#121—132no—
419#121—262no—
420#121—261no—
421#121—262no—
422#121—262no—
423#121—261no—
424#121—261no—
425#121—262no—
426#121—262no—
427#120—262no—
428#120—262no—
429#120—262no—
430C4×Q8—131no—
431C4×D4—28no—
432C4×D4—131no—
433C4×D4—132no—
434C4×D4—261no—
435C4×D4—262no—
436C4×D4—262no—
437C4×D4—261no—
438C4×D4—261no—
439C4×D4—262no—
440C4×D4—261no—
441C4×D4C4×D1311yescharacteristic
442C4×D4C4×D1312yes—
443C4×D4C4×D1311yescharacteristic
444C4×D4D5211yescharacteristic
445C4×D4D5212yes—
446C4×D4D5211yescharacteristic
447#117—132no—
448#117—261no—
449#117—261no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—132no—
452C2×C4⋊C4C22⋊D1311yescharacteristic
453C2×C22⋊C4—22no—
454C2×C22⋊C4—262no—
455C2×C22⋊C4—262no—
456C2×C22⋊C4C22⋊D1312yes—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—22no—
460C2×C42C22×D1311yescharacteristic
461C4⋊C8—261no—
462C4⋊C8—261no—
463C22⋊C8—131no—
464C22⋊C8—132no—
465C22⋊C8—131no—
466C22⋊C8—262no—
467C22⋊C8—262no—
468#97—261no—
469C4×C8—261no—
470#95—22no—
471#95—21no—
472#95C22×D1311yescharacteristic
473#95C22×D1312yes—
474#95C22×D1311yescharacteristic
475C2×C13—21no—
476C2×C13—21no—
477C2×C13—24no—
478C2×C13—42no—
479C2×C13#288311yescharacteristic
480C2×C13#289711yescharacteristic
481C2×C13C22×#10411yescharacteristic
482D13—82no—
483D13—81no—
484C24—262no—
485C24C2×C22⋊D1312yes—
486#41—1041no—
487#41—1041no—
488#41—1042no—
489C2×Q8—131no—
490C2×Q8—261no—
491C2×D4—24no—
492C2×D4—131no—
493C2×D4—132no—
494C2×D4—262no—
495C2×D4—262no—
496C2×D4—261no—
497C2×D4—262no—
498C2×D4—262no—
499C2×D4—262no—
500C2×D4—261no—
501C2×D4—261no—
502C2×D4—262no—
503C2×D4—524no—
504C2×D4—1042no—
505C2×D4—1042no—
506C2×D4—1042no—
507C2×D4#610312yes—
508C2×D4#610311yescharacteristic
509C2×D4#610311yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—28no—
514C22×C4—82no—
515C22×C4—82no—
516C22×C4—82no—
517C22×C4—262no—
518C22×C4—261no—
519C22×C4—262no—
520C22×C4—262no—
521C22×C4C2×C4×D1312yes—
522C22×C4C2×C4×D1312yes—
523C22×C4C2×D5212yes—
524C22×C4C2×D5212yes—
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1312yes—
528C22×C4C23×D1311yescharacteristic
529M16—1042no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—262no—
533C2×C8—1042no—
534C4⋊C4—24no—
535C4⋊C4—131no—
536C4⋊C4—132no—
537C4⋊C4—131no—
538C4⋊C4—262no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—262no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4#610311yescharacteristic
546C4⋊C4#610311yescharacteristic
547C4⋊C4#610312yes—
548C22⋊C4—28no—
549C22⋊C4—262no—
550C22⋊C4—262no—
551C22⋊C4—261no—
552C22⋊C4—262no—
553C22⋊C4—261no—
554C22⋊C4—262no—
555C22⋊C4—261no—
556C22⋊C4—262no—
557C22⋊C4—261no—
558C22⋊C4—262no—
559C22⋊C4—261no—
560C22⋊C4—262no—
561C22⋊C4#610312yes—
562C22⋊C4#610312yes—
563C22⋊C4#610312yes—
564C22⋊C4#610312yes—
565C42—24no—
566C42—81no—
567C42—82no—
568C42—262no—
569C42—261no—
570C42C2×C4×D1311yescharacteristic
571C42C2×C4×D1311yescharacteristic
572C42C2×D5211yescharacteristic
573C42C2×D5211yescharacteristic
574C13#1754711yescharacteristic, complemented, Sylow
575C23—22no—
576C23—22no—
577C23—24no—
578C23—42no—
579C23—261no—
580C23—262no—
581C23—524no—
582C23—1042no—
583C23—1042no—
584C23C2×#610312yes—
585C23C2×#610312yes—
586C23C22×C22⋊D1311yescharacteristic
587Q8—521no—
588Q8—1041no—
589D4—24no—
590D4—22no—
591D4—521no—
592D4—522no—
593D4—521no—
594D4—522no—
595D4—521no—
596D4—522no—
597D4—524no—
598D4—522no—
599D4—1042no—
600D4—1041no—
601D4—1042no—
602D4—1042no—
603D4—1042no—
604D4#8804514yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—88no—
624C2×C4—261no—
625C2×C4—262no—
626C2×C4—261no—
627C2×C4—261no—
628C2×C4—522no—
629C2×C4—1042no—
630C2×C4—1042no—
631C2×C4—1042no—
632C2×C4C2×#610312yes—
633C2×C4C2×#610311yescharacteristic
634C2×C4C2×#610311yescharacteristic
635C2×C4C2×#610311yescharacteristic
636C2×C4C2×#610312yes—
637C2×C4C2×#610311yescharacteristic
638C2×C4C22×C4×D1311yescharacteristic
639C2×C4C22×D5211yescharacteristic
640C8—521no—
641C8—522no—
642C8—521no—
643C22—22no—
644C22—21no—
645C22—21no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—44no—
651C22—44no—
652C22—522no—
653C22—521no—
654C22—521no—
655C22—522no—
656C22—522no—
657C22—521no—
658C22—2084no—
659C22C2×#8804514yes—
660C22C22×#610311yescharacteristic
661C22#1171954011yescharacteristic
662C22#1171954211yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—21no—
668C4—22no—
669C4—22no—
670C4—42no—
671C4—44no—
672C4—42no—
673C4—521no—
674C4—522no—
675C4—521no—
676C4—521no—
677C4C2×#8804512yes—
678C2—21no—
679C2—21no—
680C2—24no—
681C2—42no—
682C2—1041no—
683C2—1042no—
684C2#1312329611yescharacteristic
685C2#1312335911yescharacteristic
686C2C22×#8804511yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2275C2
socleC22×C13C22×C22⋊C4
prime radical#13128868C2
cosocleC22×C4×C13C24
hypercenter#2275D13
hypocenterC13#17547
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13123871C2semidirect
3. #13113359C2semidirect
4. #13113351C2semidirect
5. #13113343C2semidirect
6. #13113338C2semidirect
7. #13113330C2semidirect
8. #13113325C2semidirect
9. #13113320C2semidirect
10. C2×#11718043C2semidirect
11. C13×#2275C2semidirect
17. #11719270C4semidirect
18. #11719268C4semidirect
21. #11719258C4semidirect
22. #11719255C4semidirect
23. D4×D52C4semidirect
25. #11719248C4semidirect
31. C4×C13×C4⋊C4C22semidirect
33. C4×C13×C22⋊C4C22semidirect
34. C13×#376C22semidirect
35. C2×C13×#95C22semidirect
36. #11718868C22semidirect
37. C2×C22⋊#1055C22semidirect
41. #11718587C22semidirect
42. #11718586C22semidirect
43. #11718044C22semidirect
44. #11718044C22semidirect
45. #11718044C22semidirect
49. #11718043C22semidirect
50. #11718043C22semidirect
51. #11718043C22semidirect
52. #11718043C22semidirect
59. C2×#6127C2×C4semidirect
60. C22×D52C2×C4semidirect
85. #88184C2×C4semidirect
86. #88184C2×C4semidirect
87. #88184C2×C4semidirect
96. #88180C2×C4semidirect
97. C2×C4⋊Dic13C2×C4semidirect
98. #88178C2×C4semidirect
118. #88129C2×C4semidirect
119. #88128C2×C4semidirect
121. C4×D52C2×C4semidirect
122. C4×D52C2×C4semidirect
124. #88124C2×C4semidirect
125. #88123C2×C4semidirect
126. C4×Dic26C2×C4semidirect
234. #2275D13semidirect
337. C4×C4⋊C4C2×D13semidirect
339. C4×C22⋊C4C2×D13semidirect
340. #376C2×D13semidirect
341. C2×#95C2×D13semidirect
574. C13#17547semidirect

Maximal subgroups

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

subgroupindex
#131288682
#131238712
#131133592
#131133512
#131133432
#131133382
#131133302
#131133252
#131133202
C2×#117180432
C13×#22752
#1754713