Finite Group Databasebeta

← #15895340

Subgroups — #15895340

Order 3328.

1424 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718707C211yesmaximal, characteristic, complemented
2C2×#11718662C211yesmaximal, characteristic, complemented
3#13118192C211yesmaximal, characteristic
4#13115979C212yesmaximal, complemented
5#13115837C212yesmaximal, complemented
6#13115270C211yesmaximal, characteristic, complemented
7#13115191C212yesmaximal, complemented
8#13115153C212yesmaximal, complemented
9#13115134C211yesmaximal, characteristic, complemented
10#13114931C211yesmaximal, characteristic, complemented
11C2×C13×#552C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C13×#552—24no—
14C13×#552—24no—
15C2×C13×#126—21no—
16C2×C13×#125—21no—
17C2×C13×#125C2211yescharacteristic, complemented
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic, complemented
21C2×C4×Q8×C13C2211yescharacteristic, complemented
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#117—21no—
24C2×C13×#117C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic, complemented
26C22×#6106C2212yes—
27C2×#88191—21no—
28C2×#88184C2212yes—
29C22×#6099C2211yescharacteristic
30C2×#88075C2212yescomplemented
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yescomplemented
34#11718707—24no—
35#11718662—24no—
36#11718652—21no—
37C2×#88049C2212yes—
38C2×#88049C2212yes—
39C2×#88049C2212yes—
40#11718621—21no—
41#11718616—21no—
42#11718600C2212yes—
43#11718121C2212yescomplemented
44#11718121C2212yescomplemented
45#11718121C2212yescomplemented
46#11718116C2212yescomplemented
47C24×D13—21no—
48C22×Q8×C13C2311yescharacteristic
49C22×D4×C13D411yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C22×C22⋊D13—22no—
54C22×D52—22no—
55C22×D52—24no—
56C22×D52—22no—
57C22×D52—21no—
58C22×D52—42no—
59C22×D52C2312yes—
60C13×#126—28no—
61C13×#125—28no—
62C13×#125—22no—
63C13×#125—22no—
64C13×#123—28no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8D414yescomplemented
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C13×#117—28no—
74C13×#117—22no—
75C13×#117D414yescomplemented
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C42×C13—21no—
94C2×C42×C13—21no—
95C2×C42×C13C2311yescharacteristic
96C2×C22⋊Dic13—21no—
97C2×#6106—24no—
98C2×#6106—24no—
99C2×#6106—42no—
100#88191—44no—
101#88184—24no—
102#88184—42no—
103C2×#6103—22no—
104C2×#6103—22no—
105C2×#6103—22no—
106C2×C4⋊Dic13C2312yes—
107C2×#6099—22no—
108C2×#6099—42no—
109C22×#1055C2312yes—
110C22×#1055C2312yes—
111#88075—42no—
112#88071—21no—
113C22⋊#1055—22no—
114C22⋊#1055—42no—
115#88049—24no—
116#88049—24no—
117#88049—24no—
118#23982—131nomaximal, Sylow
119C24×C13C2×D411yescharacteristic
120C24×C13C2×D411yescharacteristic
121C23×D13—22no—
122C23×D13—44no—
123C23×D13—42no—
124C23×D13—42no—
125C23×D13—42no—
126C23×D13—82no—
127C2×Q8×C13—21no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13C2×D412yes—
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—41no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—24no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2411yescharacteristic
154C2×C22⋊D13—44no—
155C2×C22⋊D13—44no—
156C2×C22⋊D13—82no—
157C22×Dic13—22no—
158C2×D52—28no—
159C2×D52—22no—
160C2×D52—22no—
161C2×D52—22no—
162C2×D52—22no—
163C2×D52—22no—
164C2×D52—48no—
165C2×D52—44no—
166C2×D52—44no—
167C2×D52—42no—
168C2×D52#4114yes—
169C13×C4⋊C4—24no—
170C13×C4⋊C4—24no—
171C13×C4⋊C4—24no—
172C13×C4⋊C4—24no—
173C13×C4⋊C4—24no—
174C13×C4⋊C4—24no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4C2×D412yes—
180C13×C4⋊C4C2×D412yes—
181C13×C4⋊C4C2×D412yes—
182C13×C22⋊C4—24no—
183C13×C22⋊C4—24no—
184C13×C22⋊C4—24no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C42×C13—24no—
188C42×C13—24no—
189C42×C13—21no—
190C42×C13—21no—
191C22⋊Dic13—42no—
192#6106—48no—
193#6103—44no—
194#6103—44no—
195#6103—82no—
196C4⋊Dic13—22no—
197C4⋊Dic13—22no—
198#6099—44no—
199C2×#1055—22no—
200C2×#1055—22no—
201C2×#1055—22no—
202C2×#1055—22no—
203C2×#1055—22no—
204C2×#1055—22no—
205C2×#552D1311yescharacteristic, complemented
206C2×#450—131no—
207C2×#418—131no—
208#2408—131no—
209#2025—132no—
210#2000—132no—
211#1894—131no—
212#1880—132no—
213#1874—132no—
214#1870—131no—
215#1825—131no—
216C23×C13—21no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13#12012yes—
225C23×C13AGL(1,ℤ/8)12yes—
226C23×C13C22×D411yescharacteristic
227C22×D13—24no—
228C22×D13—48no—
229C22×D13—42no—
230C22×D13—42no—
231C22×D13—42no—
232C22×D13—42no—
233C22×D13—42no—
234C22×D13—42no—
235C22×D13—88no—
236C22×D13—88no—
237C22×D13—84no—
238C22×D13—84no—
239Q8×C13—24no—
240Q8×C13—41no—
241Q8×C13—41no—
242D4×C13—44no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—24no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—22no—
258C2×C4×C13—48no—
259C2×C4×C13—42no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—42no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—42no—
268C2×C4×C13#12012yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×D411yescharacteristic
271C2×C4×C13C2×#4112yes—
272C2×C4×C13H(5,𝔽2)12yes—
273C22⋊D13—88no—
274C2×Dic13—42no—
275C2×Dic13—42no—
276C2×Dic13—42no—
277D52—24no—
278D52—24no—
279D52—48no—
280D52—42no—
281D52—42no—
282#1055—42no—
283#1055—42no—
284C23×D4—131no—
285C22×SD16—132no—
286C22×M16—131no—
287#552—24no—
288#552—24no—
289C2×#126—21no—
290C2×#125—21no—
291C2×#125C2×D1311yescharacteristic, complemented
292C2×#123—21no—
293C2×C22⋊Q8C2×D1311yescharacteristic
294C2×C22⋊Q8C2×D1311yescharacteristic, complemented
295C2×#121—132no—
296C2×#120—261no—
297C2×C4×Q8C2×D1311yescharacteristic, complemented
298C2×C4×D4C2×D1311yescharacteristic
299C2×#117—21no—
300C2×#117C2×D1311yescharacteristic
301C22×C4⋊C4C2×D1311yescharacteristic, complemented
302#450—264no—
303#418—264no—
304C2×#103—132no—
305C2×#102—132no—
306C2×#102—132no—
307C2×#102—132no—
308C2×C22⋊C8—131no—
309C2×C22⋊C8—132no—
310#394—261no—
311#392—261no—
312#390—132no—
313#380—131no—
314#379—261no—
315#340—132no—
316#340—132no—
317#340—132no—
318#336—132no—
319C22×C13—22no—
320C22×C13—22no—
321C22×C13—22no—
322C22×C13—22no—
323C22×C13—24no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13—42no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13C2×#12011yescharacteristic
330C22×C13#54612yes—
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13#57511yescharacteristic
333C22×C13#57712yes—
334C2×D13—44no—
335C2×D13—44no—
336C2×D13—44no—
337C2×D13—816no—
338C2×D13—82no—
339C2×D13—82no—
340C2×D13—82no—
341C2×D13—82no—
342C4×C13—22no—
343C4×C13—41no—
344C4×C13—42no—
345C4×C13—41no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13#52511yescharacteristic
351C4×C13#53511yescharacteristic
352C4×C13#54612yes—
353Dic13—82no—
354C25—261no—
355C22×Q8C22×D1311yescharacteristic
356C22×D4—132no—
357C22×D4—264no—
358C22×D4—262no—
359C22×D4—262no—
360C22×D4—262no—
361C22×D4—261no—
362C22×D4—522no—
363C22×D4C22⋊D1311yescharacteristic
364C23×C4—21no—
365C23×C4C22×D1311yescharacteristic
366C23×C4C22×D1311yescharacteristic
367C2×SD16—264no—
368C2×SD16—264no—
369C2×SD16—522no—
370C2×M16—262no—
371C2×M16—522no—
372C22×C8—132no—
373C22×C8—132no—
374#126—28no—
375#125—28no—
376#125—22no—
377#125—22no—
378#123—28no—
379C22⋊Q8—22no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8C22⋊D1314yescomplemented
383#121—264no—
384#121—522no—
385#120—524no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×D4—22no—
389C4×D4—22no—
390#117—28no—
391#117—22no—
392#117C22⋊D1314yescomplemented
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—132no—
402C2×C4⋊C4C22⋊D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4—262no—
411C2×C22⋊C4—262no—
412C2×C22⋊C4—262no—
413C2×C22⋊C4C22⋊D1311yescharacteristic
414C2×C22⋊C4C22⋊D1311yescharacteristic
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C22×D1311yescharacteristic
418#103—522no—
419#102—264no—
420#102—264no—
421#102—264no—
422C22⋊C8—262no—
423C22⋊C8—522no—
424#95—261no—
425C2×C13—42no—
426C2×C13—42no—
427C2×C13#240411yescharacteristic
428C2×C13#300611yescharacteristic
429C2×C13#301011yescharacteristic
430C2×C13#331012yes—
431C2×C13#332312yes—
432D13—84no—
433C24—262no—
434C24—524no—
435C24—522no—
436C24—522no—
437C24—522no—
438C24—1042no—
439C24C2×C22⋊D1311yescharacteristic
440C24C2×C22⋊D1311yescharacteristic
441C2×Q8—21no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8C2×C22⋊D1312yes—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—41no—
448C2×D4—134no—
449C2×D4—268no—
450C2×D4—262no—
451C2×D4—262no—
452C2×D4—262no—
453C2×D4—262no—
454C2×D4—262no—
455C2×D4—528no—
456C2×D4—524no—
457C2×D4—524no—
458C2×D4—524no—
459C2×D4—524no—
460C2×D4—522no—
461C2×D4—1042no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4—262no—
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1312yes—
481C22×C4C2×C22⋊D1312yes—
482C22×C4C23×D1311yescharacteristic
483SD16—528no—
484M16—524no—
485C2×C8—262no—
486C2×C8—262no—
487C2×C8—262no—
488C2×C8—262no—
489C2×C8—262no—
490C2×C8—262no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—262no—
502C4⋊C4—262no—
503C4⋊C4C2×C22⋊D1312yes—
504C4⋊C4C2×C22⋊D1312yes—
505C4⋊C4C2×C22⋊D1312yes—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—524no—
512C22⋊C4—524no—
513C22⋊C4—522no—
514C22⋊C4—1042no—
515C42—24no—
516C42—24no—
517C42—21no—
518C42—21no—
519C13#2398211yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—21no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—21no—
528C23—264no—
529C23—528no—
530C23—522no—
531C23—522no—
532C23—522no—
533C23—522no—
534C23—522no—
535C23—522no—
536C23—1044no—
537C23—1044no—
538C23—1048no—
539C23—1048no—
540C23#8820312yes—
541C23#8820712yes—
542C23C22×C22⋊D1311yescharacteristic
543Q8—24no—
544Q8—41no—
545Q8—41no—
546D4—44no—
547D4—264no—
548D4—264no—
549D4—528no—
550D4—522no—
551D4—522no—
552D4—1048no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—48no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—522no—
579C2×C4—522no—
580C2×C4—522no—
581C2×C4#8820712yes—
582C2×C4#41×D1312yes—
583C2×C4#8825612yes—
584C2×C4C22×C22⋊D1311yescharacteristic
585C2×C4C22×C22⋊D1311yescharacteristic
586C8—522no—
587C8—522no—
588C22—22no—
589C22—24no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22—524no—
599C22—524no—
600C22—524no—
601C22—10416no—
602C22—1042no—
603C22—1042no—
604C22—1042no—
605C22—1042no—
606C22C2×#8820311yescharacteristic
607C22#1171952711yescharacteristic
608C22#1171953412yes—
609C22#1171954212yes—
610C22C2×#8820711yescharacteristic
611C4—22no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—42no—
618C4—42no—
619C4—1042no—
620C4#1171953311yescharacteristic
621C4#1171953412yes—
622C4#1171953511yescharacteristic
623C2—42no—
624C2—42no—
625C2—1044no—
626C2#1311815111yescharacteristic
627C2#1312408811yescharacteristic
628C2#1312412211yescharacteristic
629C2#1312685112yes—
630C2#1312704612yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radical#13118192C2
hypercenterC2×#552D13
hypocenterC13#23982
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718707C2semidirect
2. C2×#11718662C2semidirect
4. #13115979C2semidirect
5. #13115837C2semidirect
6. #13115270C2semidirect
7. #13115191C2semidirect
8. #13115153C2semidirect
9. #13115134C2semidirect
10. #13114931C2semidirect
11. C2×C13×#552C2semidirect
17. C2×C13×#125C22semidirect
20. C2×C13×C22⋊Q8C22semidirect
21. C2×C4×Q8×C13C22semidirect
25. C22×C13×C4⋊C4C22semidirect
30. C2×#88075C22semidirect
33. C2×C22⋊#1055C22semidirect
43. #11718121C22semidirect
44. #11718121C22semidirect
45. #11718121C22semidirect
46. #11718116C22semidirect
68. C13×C22⋊Q8D4semidirect
75. C13×#117D4semidirect
205. C2×#552D13semidirect
291. C2×#125C2×D13semidirect
294. C2×C22⋊Q8C2×D13semidirect
297. C2×C4×Q8C2×D13semidirect
301. C22×C4⋊C4C2×D13semidirect
382. C22⋊Q8C22⋊D13semidirect
392. #117C22⋊D13semidirect
519. C13#23982semidirect

Maximal subgroups

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

subgroupindex
C2×#117187072
C2×#117186622
#131181922
#131159792
#131158372
#131152702
#131151912
#131151532
#131151342
#131149312
C2×C13×#5522
#2398213