Finite Group Databasebeta

← #15830124

Subgroups — #15830124

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128885C211yesmaximal, characteristic
2#13123871C211yesmaximal, characteristic, complemented
3#13113359C211yesmaximal, characteristic, complemented
4#13113355C212yesmaximal, complemented
5#13113347C211yesmaximal, characteristic, complemented
6#13113338C212yesmaximal, complemented
7#13113334C211yesmaximal, characteristic, complemented
8#13113325C212yesmaximal, complemented
9#13113320C211yesmaximal, characteristic, complemented
10C2×#11718044C212yesmaximal, complemented
11C13×#2275C211yesmaximal, characteristic, complemented
12C2×C4×D4×C13—21no—
13C2×C4×D4×C13C2211yescharacteristic
14#11719511—21no—
15#11719496C2212yes—
16C2×#88178C2212yes—
17#11719269—22no—
18#11719266—21no—
19#11719260C411yescharacteristic, complemented
20#11719257C412yescomplemented
21#11719256C411yescharacteristic, complemented
22#11719251—21no—
23#11719247C411yescharacteristic, complemented
24#11719246C412yescomplemented
25D4×Dic26C411yescharacteristic, complemented
26#11719216—21no—
27#11719200—22no—
28#11719184C2211yescharacteristic
29#11719175C2211yescharacteristic
30C4×C13×C4⋊C4—21no—
31C4×C13×C4⋊C4C2211yescharacteristic
32C4×C13×C22⋊C4—22no—
33C4×C13×C22⋊C4C2212yes—
34C13×#376C2211yescharacteristic
35C2×C13×#95C2212yes—
36#11718868C2212yes—
37C2×C22⋊#1055C2212yes—
38#11718673—21no—
39#11718672—22no—
40D4×#1055—21no—
41#11718587C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718044C2212yes—
44#11718044C2212yes—
45#11718044C2211yescharacteristic
46#11718044C2212yes—
47#11718044C2212yes—
48#11718044C2211yescharacteristic
49#11718044C2212yes—
50#11718043C2212yes—
51#11718043C2211yescharacteristic
52#11718043C2211yescharacteristic
53C22×D4×C13D411yescharacteristic
54C23×C4×C13—22no—
55C23×C4×C13C2312yes—
56C2×#6129—21no—
57C2×#6127C2×C412yescomplemented
58C22×Dic26C2×C412yescomplemented
59C4×D4×C13—28no—
60C4×D4×C13C2×C411yescharacteristic
61C4×D4×C13C2×C412yes—
62C4×D4×C13C2×C411yescharacteristic
63C4×D4×C13D411yescharacteristic
64C4×D4×C13D412yes—
65C4×D4×C13D411yescharacteristic
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4D411yescharacteristic
68C2×C13×C22⋊C4—22no—
69C2×C13×C22⋊C4D412yes—
70C2×C42×C13—21no—
71C2×C42×C13—21no—
72C2×C42×C13—22no—
73C2×C42×C13C2311yescharacteristic
74#88207—22no—
75C2×C22⋊Dic13—22no—
76#88193—22no—
77#88192—21no—
78#88190—21no—
79#88189—22no—
80D4×Dic13—21no—
81#88184C2×C412yescomplemented
82#88184C2311yescharacteristic
83#88183—21no—
84#88183—22no—
85C4×C22⋊D13—21no—
86C4×C22⋊D13—22no—
87C4×C22⋊D13—22no—
88#88180—21no—
89#88180C2×C412yescomplemented
90C2×C4⋊Dic13C2×C412yescomplemented
91#88178—21no—
92#88178—22no—
93#88178—22no—
94#88178C2×C412yescomplemented
95#88178C2×C412yescomplemented
96#88178C2×C412yescomplemented
97#88178C2312yes—
98#88178C2311yescharacteristic
99C2×#6101—22no—
100C2×#6099—22no—
101C22×#1055—22no—
102#88151—21no—
103#88150—22no—
104C4⋊C4×D13—21no—
105#88143—22no—
106#88142—21no—
107#88141—21no—
108#88140—22no—
109#88139—22no—
110#88137—22no—
111#88135—22no—
112#88133—22no—
113#88133—22no—
114#88132—22no—
115#88131—22no—
116#88130—21no—
117#88129C2×C411yescharacteristic, complemented
118C4×D52C2×C411yescharacteristic, complemented
119#88126—21no—
120#88124—21no—
121#88124C2×C411yescharacteristic, complemented
122#88123C2×C411yescharacteristic, complemented
123#88123C2×C411yescharacteristic, complemented
124C4×Dic26—21no—
125C4×Dic26C2×C412yescomplemented
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#17548—131nomaximal, Sylow
142C24×C13C2×D412yes—
143C2×D4×C13—24no—
144C2×D4×C13C22⋊C412yes—
145C2×D4×C13C22⋊C411yescharacteristic
146C2×D4×C13C22⋊C411yescharacteristic
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—28no—
151C22×C4×C13—82no—
152C22×C4×C13—82no—
153C22×C4×C13—82no—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C22×C412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2411yescharacteristic
162C2×C22⋊D13—22no—
163C2×C22⋊D13—21no—
164C2×C22⋊D13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167#6129—44no—
168#6127—82no—
169C2×D52C22×C411yescharacteristic
170C2×C4×D13—21no—
171C2×C4×D13—22no—
172C2×Dic26—21no—
173C2×Dic26—22no—
174C2×Dic26—82no—
175C2×Dic26C22×C412yes—
176C2×Dic26C22×C411yescharacteristic
177C13×C4⋊C4—24no—
178C13×C4⋊C4C22⋊C411yescharacteristic
179C13×C4⋊C4C22⋊C411yescharacteristic
180C13×C4⋊C4C22⋊C412yes—
181C13×C22⋊C4—28no—
182C13×C22⋊C4C22⋊C412yes—
183C13×C22⋊C4C22⋊C412yes—
184C13×C22⋊C4C22⋊C412yes—
185C13×C22⋊C4C22⋊C412yes—
186C42×C13—24no—
187C42×C13—81no—
188C42×C13—82no—
189C42×C13C22×C411yescharacteristic
190C42×C13C22×C411yescharacteristic
191C42×C13C2×D411yescharacteristic
192C42×C13C2×D411yescharacteristic
193C22⋊Dic13—22no—
194C22⋊Dic13—22no—
195C22⋊Dic13—22no—
196C22⋊Dic13—22no—
197C22⋊Dic13—22no—
198C22⋊Dic13—21no—
199#6103—21no—
200#6103—21no—
201#6103—21no—
202#6103—22no—
203#6103—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—22no—
208C4⋊Dic13C22×C412yes—
209C4⋊Dic13C22×C411yescharacteristic
210C4⋊Dic13C22×C411yescharacteristic
211#6101—22no—
212#6101—21no—
213#6101—21no—
214#6101—21no—
215#6101—22no—
216#6101—22no—
217#6101—22no—
218#6101—22no—
219#6101—21no—
220C4×Dic13—22no—
221C4×Dic13—21no—
222C4×Dic13—22no—
223#6099—82no—
224C2×#1055—21no—
225C2×#1055—22no—
226C2×#1055—21no—
227C2×#1055—82no—
228#3520—131no—
229#2974—131no—
230#2275D1311yescharacteristic, complemented
231#1509—131no—
232#1508—132no—
233#1506—131no—
234#1504—132no—
235#1503—131no—
236#1501—132no—
237#1500—131no—
238C2×#328—132no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—24no—
242C23×C13—42no—
243C23×C13C2×C22⋊C412yes—
244C23×C13C2×C22⋊C412yes—
245C23×C13C22×D411yescharacteristic
246C22×D13—21no—
247D4×C13—24no—
248D4×C13—22no—
249D4×C13#10414yes—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—24no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—42no—
264C2×C4×C13—41no—
265C2×C4×C13—42no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—88no—
269C2×C4×C13C2×C22⋊C411yescharacteristic
270C2×C4×C13C2×C22⋊C412yes—
271C2×C4×C13C2×C22⋊C411yescharacteristic
272C2×C4×C13C2×C22⋊C411yescharacteristic
273C2×C4×C13C2×C22⋊C412yes—
274C2×C4×C13C2×C22⋊C411yescharacteristic
275C2×C4×C13C23×C411yescharacteristic
276C2×C4×C13C22×D411yescharacteristic
277C22⋊D13—41no—
278C22⋊D13—41no—
279C22⋊D13—44no—
280C22⋊D13—82no—
281C2×Dic13—21no—
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—21no—
285C2×Dic13—21no—
286C2×Dic13—44no—
287C2×Dic13—82no—
288D52—41no—
289C4×D13—42no—
290C4×D13—82no—
291Dic26—42no—
292Dic26—41no—
293Dic26—42no—
294Dic26—82no—
295#1055—41no—
296#1055—42no—
297#1055—41no—
298#556—131no—
299#554—261no—
300#552—132no—
301#551—262no—
302D4×Q8—131no—
303#548—132no—
304#547—131no—
305#547—131no—
306#546—261no—
307#542—261no—
308#539—262no—
309#533—131no—
310#529—131no—
311#525—132no—
312C2×C22⋊Q8—132no—
313#520—261no—
314C2×C4×D4—21no—
315C2×C4×D4C2×D1311yescharacteristic
316#436—261no—
317#435—262no—
318C8×D4—261no—
319#432—131no—
320#431—131no—
321#407—132no—
322C2×C22⋊C8—132no—
323C4×C4⋊C4—21no—
324C4×C4⋊C4C2×D1311yescharacteristic
325C4×C22⋊C4—22no—
326C4×C22⋊C4C2×D1312yes—
327#376C2×D1311yescharacteristic
328C2×#95C2×D1312yes—
329#328—131no—
330#328—132no—
331#328—132no—
332#328—132no—
333#328—131no—
334#328—132no—
335#328—132no—
336#327—131no—
337#327—131no—
338#327—132no—
339C22×C13—22no—
340C22×C13—21no—
341C22×C13—22no—
342C22×C13—21no—
343C22×C13—22no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—44no—
347C22×C13—44no—
348C22×C13C2×#10414yes—
349C22×C13C22×C22⋊C411yescharacteristic
350C22×C13#57711yescharacteristic
351C22×C13#57811yescharacteristic
352C2×D13—41no—
353C2×D13—41no—
354C2×D13—41no—
355C4×C13—21no—
356C4×C13—21no—
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—21no—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—42no—
363C4×C13—44no—
364C4×C13—42no—
365C4×C13C2×#10412yes—
366Dic13—41no—
367Dic13—42no—
368Dic13—41no—
369Dic13—42no—
370Dic13—41no—
371C2×#41—132no—
372C2×#41—261no—
373C22×Q8—132no—
374C22×D4C22⋊D1311yescharacteristic
375C23×C4—22no—
376C23×C4C22×D1312yes—
377C2×M16—262no—
378C22×C8—262no—
379C4⋊Q8—131no—
380C4⋊Q8—131no—
381C4⋊Q8—261no—
382#126—262no—
383#126—262no—
384#126—261no—
385#125—131no—
386#125—262no—
387#125—261no—
388#124—131no—
389#124—261no—
390#124—262no—
391#123—262no—
392#123—262no—
393#123—261no—
394#123—262no—
395#123—262no—
396C22⋊Q8—132no—
397C22⋊Q8—132no—
398C22⋊Q8—132no—
399C22⋊Q8—131no—
400C22⋊Q8—132no—
401C22⋊Q8—262no—
402C22⋊Q8—262no—
403C22⋊Q8—261no—
404C22⋊Q8—262no—
405C22⋊Q8—261no—
406C22⋊Q8—262no—
407#121—132no—
408#121—131no—
409#121—262no—
410#121—261no—
411#120—262no—
412C4×Q8—131no—
413C4×Q8—132no—
414C4×Q8—261no—
415C4×Q8—261no—
416C4×D4—28no—
417C4×D4—131no—
418C4×D4—261no—
419C4×D4—262no—
420C4×D4—262no—
421C4×D4—261no—
422C4×D4—262no—
423C4×D4C4×D1311yescharacteristic
424C4×D4C4×D1311yescharacteristic
425C4×D4C4×D1312yes—
426C4×D4D5211yescharacteristic
427C4×D4D5212yes—
428C4×D4D5211yescharacteristic
429#117—132no—
430#117—261no—
431#117—262no—
432#117—261no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—132no—
435C2×C4⋊C4—262no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4C22⋊D1311yescharacteristic
438C2×C22⋊C4—22no—
439C2×C22⋊C4—262no—
440C2×C22⋊C4C22⋊D1312yes—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—22no—
444C2×C42C22×D1311yescharacteristic
445C4⋊C8—261no—
446C4⋊C8—261no—
447C22⋊C8—131no—
448C22⋊C8—132no—
449C22⋊C8—131no—
450C22⋊C8—262no—
451C22⋊C8—262no—
452#97—261no—
453C4×C8—261no—
454#95—22no—
455#95—21no—
456#95C22×D1311yescharacteristic
457#95C22×D1312yes—
458#95C22×D1311yescharacteristic
459C2×C13—21no—
460C2×C13—21no—
461C2×C13—24no—
462C2×C13—42no—
463C2×C13#288311yescharacteristic
464C2×C13#289811yescharacteristic
465C2×C13C22×#10411yescharacteristic
466D13—81no—
467C24C2×C22⋊D1312yes—
468#41—524no—
469#41—1042no—
470C2×Q8—131no—
471C2×Q8—132no—
472C2×Q8—261no—
473C2×Q8—262no—
474C2×Q8—1042no—
475C2×D4—24no—
476C2×D4—131no—
477C2×D4—262no—
478C2×D4—261no—
479C2×D4—262no—
480C2×D4#610312yes—
481C2×D4#610311yescharacteristic
482C2×D4#610311yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—28no—
487C22×C4—82no—
488C22×C4—82no—
489C22×C4—82no—
490C22×C4—262no—
491C22×C4—262no—
492C22×C4—261no—
493C22×C4—262no—
494C22×C4C2×C4×D1312yes—
495C22×C4C2×C4×D1312yes—
496C22×C4C2×D5212yes—
497C22×C4C2×D5212yes—
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1312yes—
501C22×C4C23×D1311yescharacteristic
502M16—1042no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—262no—
506C2×C8—1042no—
507C4⋊C4—24no—
508C4⋊C4—131no—
509C4⋊C4—132no—
510C4⋊C4—131no—
511C4⋊C4—262no—
512C4⋊C4—262no—
513C4⋊C4—261no—
514C4⋊C4—262no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—262no—
519C4⋊C4—261no—
520C4⋊C4—262no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—262no—
524C4⋊C4#610311yescharacteristic
525C4⋊C4#610312yes—
526C4⋊C4#610311yescharacteristic
527C22⋊C4—28no—
528C22⋊C4—262no—
529C22⋊C4—262no—
530C22⋊C4—262no—
531C22⋊C4—262no—
532C22⋊C4—261no—
533C22⋊C4—262no—
534C22⋊C4—261no—
535C22⋊C4—261no—
536C22⋊C4—262no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C22⋊C4#610312yes—
540C22⋊C4#610312yes—
541C22⋊C4#610312yes—
542C22⋊C4#610312yes—
543C42—24no—
544C42—81no—
545C42—82no—
546C42—262no—
547C42—262no—
548C42—261no—
549C42C2×C4×D1311yescharacteristic
550C42C2×C4×D1311yescharacteristic
551C42C2×D5211yescharacteristic
552C42C2×D5211yescharacteristic
553C13#1754811yescharacteristic, complemented, Sylow
554C23—22no—
555C23—22no—
556C23—24no—
557C23—42no—
558C23—261no—
559C23C2×#610312yes—
560C23C2×#610312yes—
561C23C22×C22⋊D1311yescharacteristic
562Q8—521no—
563Q8—522no—
564Q8—522no—
565Q8—1042no—
566D4—24no—
567D4—22no—
568D4—521no—
569D4—521no—
570D4—521no—
571D4—524no—
572D4—1042no—
573D4#8804514yes—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—88no—
593C2×C4—261no—
594C2×C4—262no—
595C2×C4—261no—
596C2×C4—262no—
597C2×C4—261no—
598C2×C4—524no—
599C2×C4—522no—
600C2×C4—1042no—
601C2×C4—1042no—
602C2×C4C2×#610311yescharacteristic
603C2×C4C2×#610312yes—
604C2×C4C2×#610311yescharacteristic
605C2×C4C2×#610311yescharacteristic
606C2×C4C2×#610312yes—
607C2×C4C2×#610311yescharacteristic
608C2×C4C22×C4×D1311yescharacteristic
609C2×C4C22×D5211yescharacteristic
610C8—521no—
611C8—522no—
612C8—521no—
613C22—22no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—44no—
621C22—44no—
622C22—521no—
623C22—521no—
624C22—521no—
625C22C2×#8804514yes—
626C22C22×#610311yescharacteristic
627C22#1171954111yescharacteristic
628C22#1171954311yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—22no—
635C4—22no—
636C4—42no—
637C4—44no—
638C4—42no—
639C4—521no—
640C4—521no—
641C4—522no—
642C4—522no—
643C4—521no—
644C4C2×#8804512yes—
645C2—21no—
646C2—21no—
647C2—24no—
648C2—42no—
649C2—1041no—
650C2#1312329611yescharacteristic
651C2#1312336611yescharacteristic
652C2C22×#8804511yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2275C2
socleC22×C13C22×C22⋊C4
prime radical#13128885C2
cosocleC22×C4×C13C24
hypercenter#2275D13
hypocenterC13#17548
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. #13113355C2semidirect
5. #13113347C2semidirect
6. #13113338C2semidirect
7. #13113334C2semidirect
8. #13113325C2semidirect
9. #13113320C2semidirect
10. C2×#11718044C2semidirect
11. C13×#2275C2semidirect
19. #11719260C4semidirect
20. #11719257C4semidirect
21. #11719256C4semidirect
23. #11719247C4semidirect
24. #11719246C4semidirect
25. D4×Dic26C4semidirect
57. C2×#6127C2×C4semidirect
58. C22×Dic26C2×C4semidirect
81. #88184C2×C4semidirect
89. #88180C2×C4semidirect
90. C2×C4⋊Dic13C2×C4semidirect
94. #88178C2×C4semidirect
95. #88178C2×C4semidirect
96. #88178C2×C4semidirect
117. #88129C2×C4semidirect
118. C4×D52C2×C4semidirect
121. #88124C2×C4semidirect
122. #88123C2×C4semidirect
123. #88123C2×C4semidirect
125. C4×Dic26C2×C4semidirect
126. C4×Dic26C2×C4semidirect
230. #2275D13semidirect
553. C13#17548semidirect

Maximal subgroups

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

subgroupindex
#131288852
#131238712
#131133592
#131133552
#131133472
#131133382
#131133342
#131133252
#131133202
C2×#117180442
C13×#22752
#1754813