Finite Group Databasebeta

← #15895066

Subgroups — #15895066

Order 3328.

1690 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718697C211yesmaximal, characteristic, complemented
2C22×#88049C211yesmaximal, characteristic, complemented
3#13118192C211yesmaximal, characteristic, complemented
4#13115969C212yesmaximal, complemented
5#13115832C212yesmaximal, complemented
6#13115265C211yesmaximal, characteristic, complemented
7#13115184C212yesmaximal, complemented
8#13115153C212yesmaximal, complemented
9#13115129C211yesmaximal, characteristic, complemented
10#13114922C211yesmaximal, characteristic, complemented
11C2×C13×#547C211yesmaximal, characteristic, complemented
12C22×C13×#41—21no—
13C23×D52C2211yescharacteristic
14C13×#547—24no—
15C13×#547—24no—
16C2×C13×C4⋊Q8C2211yescharacteristic, complemented
17C2×C13×#123—21no—
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×#121C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic, complemented
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic, complemented
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic, complemented
26C2×#88191—21no—
27C22×#6104C2212yes—
28C2×#88184C2212yes—
29C23×#1055C2211yescharacteristic
30C2×#88072C2212yescomplemented
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×C22⋊#1055C2212yescomplemented
34#11718697—24no—
35#11718652—21no—
36C2×#88049—24no—
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—
48C2×C13×#41—28no—
49C2×C13×#41—44no—
50C2×C13×#41—44no—
51C22×Q8×C13—21no—
52C22×D4×C13—21no—
53C22×D4×C13—21no—
54C22×D4×C13D411yescharacteristic
55C22×D4×C13C2311yescharacteristic
56C23×C4×C13—21no—
57C23×C4×C13—21no—
58C23×C4×C13—21no—
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—22no—
62C22×D52—22no—
63C22×D52—24no—
64C22×D52—22no—
65C22×D52—21no—
66C22×D52—42no—
67C22×D52C2312yes—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—22no—
70C13×#123—28no—
71C13×#123—28no—
72C13×C22⋊Q8—28no—
73C13×#121—22no—
74C13×#121—22no—
75C13×#121—22no—
76C13×#121D414yescomplemented
77C4×D4×C13—22no—
78C4×D4×C13—22no—
79C4×D4×C13—22no—
80C4×D4×C13—22no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4D411yescharacteristic
88C2×C13×C4⋊C4D414yescomplemented
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4D411yescharacteristic
96C2×C13×C22⋊C4D411yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C22⋊Dic13—21no—
99#88191—44no—
100C2×#6104—24no—
101C2×#6104—24no—
102C2×#6104—42no—
103#88184—24no—
104#88184—42no—
105C2×#6103—22no—
106C2×#6103—22no—
107C2×#6103—22no—
108C2×C4⋊Dic13C2312yes—
109C22×#1055—22no—
110C22×#1055—42no—
111C22×#1055C2312yes—
112C22×#1055C2312yes—
113#88072—42no—
114#88071—21no—
115C22⋊#1055—22no—
116C22⋊#1055—42no—
117#88049—24no—
118#88049—24no—
119#88049—24no—
120#23960—131nomaximal, Sylow
121C24×C13—21no—
122C24×C13C2×D411yescharacteristic
123C24×C13C2×D411yescharacteristic
124C23×D13—22no—
125C23×D13—44no—
126C23×D13—42no—
127C23×D13—42no—
128C23×D13—42no—
129C23×D13—82no—
130C13×#41—432no—
131C2×Q8×C13—24no—
132C2×Q8×C13—42no—
133C2×Q8×C13—42no—
134C2×D4×C13—22no—
135C2×D4×C13—22no—
136C2×D4×C13—24no—
137C2×D4×C13—24no—
138C2×D4×C13—21no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—42no—
142C2×D4×C13—42no—
143C2×D4×C13—42no—
144C2×D4×C13—42no—
145C2×D4×C13D814yescomplemented
146C2×D4×C13C2×D412yes—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—24no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—42no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13—42no—
163C22×C4×C13—42no—
164C22×C4×C13—42no—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2411yescharacteristic
172C2×C22⋊D13—44no—
173C2×C22⋊D13—44no—
174C2×C22⋊D13—82no—
175C22×Dic13—22no—
176C2×D52—28no—
177C2×D52—22no—
178C2×D52—22no—
179C2×D52—22no—
180C2×D52—22no—
181C2×D52—22no—
182C2×D52—48no—
183C2×D52—44no—
184C2×D52—44no—
185C2×D52—42no—
186C2×D52#4114yescomplemented
187C13×C4⋊C4—24no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4C2×D412yes—
195C13×C4⋊C4C2×D412yes—
196C13×C4⋊C4C2×D412yes—
197C13×C22⋊C4—24no—
198C13×C22⋊C4—24no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—24no—
201C13×C22⋊C4—22no—
202C42×C13—21no—
203C42×C13—21no—
204C22⋊Dic13—42no—
205#6104—48no—
206#6103—44no—
207#6103—44no—
208#6103—82no—
209C4⋊Dic13—22no—
210C4⋊Dic13—22no—
211C2×#1055—22no—
212C2×#1055—22no—
213C2×#1055—22no—
214C2×#1055—22no—
215C2×#1055—22no—
216C2×#1055—22no—
217C2×#1055—44no—
218C2×#547D1311yescharacteristic, complemented
219C2×#447—131no—
220C22×#102—131no—
221#2408—131no—
222#2023—132no—
223#1999—132no—
224#1893—131no—
225#1879—132no—
226#1874—132no—
227#1869—131no—
228#1823—131no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—21no—
232C23×C13—22no—
233C23×C13—21no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—42no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—42no—
240C23×C13#12012yes—
241C23×C13C2×D812yes—
242C23×C13C2×D812yes—
243C23×C13AGL(1,ℤ/8)12yes—
244C23×C13C22×D411yescharacteristic
245C22×D13—24no—
246C22×D13—48no—
247C22×D13—42no—
248C22×D13—42no—
249C22×D13—42no—
250C22×D13—42no—
251C22×D13—42no—
252C22×D13—42no—
253C22×D13—88no—
254C22×D13—88no—
255C22×D13—84no—
256C22×D13—84no—
257Q8×C13—48no—
258D4×C13—28no—
259D4×C13—24no—
260D4×C13—48no—
261D4×C13—48no—
262D4×C13—41no—
263D4×C13—41no—
264C2×C4×C13—21no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—24no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—48no—
278C2×C4×C13—48no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—48no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—42no—
289C2×C4×C13#12012yes—
290C2×C4×C13C2×D812yes—
291C2×C4×C13C22×D411yescharacteristic
292C2×C4×C13C22×D411yescharacteristic
293C2×C4×C13C2×#4112yes—
294C2×C4×C13H(5,𝔽2)12yes—
295C22⋊D13—88no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299D52—24no—
300D52—24no—
301D52—48no—
302D52—42no—
303D52—42no—
304#1055—42no—
305#1055—42no—
306C22×#41—21no—
307C23×D4—131no—
308C22×D8—132no—
309C23×C8—131no—
310#547—24no—
311#547—24no—
312C2×C4⋊Q8C2×D1311yescharacteristic, complemented
313C2×#123—21no—
314C2×#123—21no—
315C2×C22⋊Q8—21no—
316C2×#121—132no—
317C2×#121C2×D1311yescharacteristic
318C2×#121C2×D1311yescharacteristic, complemented
319C2×#120—261no—
320C2×C4×D4C2×D1311yescharacteristic
321C2×C4×D4C2×D1311yescharacteristic, complemented
322C22×C4⋊C4C2×D1311yescharacteristic
323C22×C4⋊C4C2×D1311yescharacteristic, complemented
324#447—264no—
325C2×#102—132no—
326C2×#102—132no—
327C2×#102—132no—
328C2×#102—132no—
329C2×#102—264no—
330C2×C22⋊C8—131no—
331C2×C22⋊C8—132no—
332#394—261no—
333#392—261no—
334#390—132no—
335#380—131no—
336#379—261no—
337#340—132no—
338#340—132no—
339#340—132no—
340#336—132no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—24no—
344C22×C13—24no—
345C22×C13—22no—
346C22×C13—24no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13—42no—
353C22×C13—82no—
354C22×C13—82no—
355C22×C13#44714yes—
356C22×C13C2×#12011yescharacteristic
357C22×C13#54612yes—
358C22×C13C22×D811yescharacteristic
359C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C13#57712yes—
361C2×D13—44no—
362C2×D13—44no—
363C2×D13—44no—
364C2×D13—816no—
365C2×D13—82no—
366C2×D13—82no—
367C2×D13—82no—
368C2×D13—82no—
369C4×C13—22no—
370C4×C13—22no—
371C4×C13—41no—
372C4×C13—42no—
373C4×C13—42no—
374C4×C13—42no—
375C4×C13—41no—
376C4×C13#52511yescharacteristic
377C4×C13#53511yescharacteristic
378C4×C13#54612yes—
379Dic13—82no—
380C25—261no—
381C2×#41—28no—
382C2×#41—44no—
383C2×#41—44no—
384C22×Q8—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—132no—
388C22×D4—264no—
389C22×D4—262no—
390C22×D4—262no—
391C22×D4—262no—
392C22×D4—261no—
393C22×D4—522no—
394C22×D4C22⋊D1311yescharacteristic
395C22×D4C22×D1311yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—21no—
399C23×C4C22×D1311yescharacteristic
400C23×C4C22×D1311yescharacteristic
401C2×D8—264no—
402C2×D8—264no—
403C2×D8—522no—
404C22×C8—132no—
405C22×C8—132no—
406C22×C8—262no—
407C22×C8—522no—
408C4⋊Q8—22no—
409C4⋊Q8—22no—
410#123—28no—
411#123—28no—
412C22⋊Q8—28no—
413#121—22no—
414#121—22no—
415#121—22no—
416#121—264no—
417#121—522no—
418#121C22⋊D1314yescomplemented
419#120—524no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—132no—
431C2×C4⋊C4C22⋊D1311yescharacteristic
432C2×C4⋊C4C22⋊D1314yescomplemented
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C4⋊C4C22×D1311yescharacteristic
435C2×C4⋊C4C22×D1311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4—262no—
441C2×C22⋊C4—262no—
442C2×C22⋊C4—262no—
443C2×C22⋊C4C22⋊D1311yescharacteristic
444C2×C22⋊C4C22⋊D1311yescharacteristic
445C2×C42C22×D1311yescharacteristic
446#102—264no—
447#102—264no—
448#102—264no—
449#102—522no—
450C22⋊C8—262no—
451C22⋊C8—522no—
452#95—261no—
453C2×C13—24no—
454C2×C13—42no—
455C2×C13—82no—
456C2×C13#240411yescharacteristic
457C2×C13C2×#44711yescharacteristic
458C2×C13#301011yescharacteristic
459C2×C13#329412yes—
460C2×C13#330612yes—
461D13—84no—
462C24—21no—
463C24—262no—
464C24—524no—
465C24—522no—
466C24—522no—
467C24—522no—
468C24—1042no—
469C24C2×C22⋊D1311yescharacteristic
470C24C2×C22⋊D1311yescharacteristic
471#41—432no—
472C2×Q8—24no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—134no—
487C2×D4—268no—
488C2×D4—262no—
489C2×D4—262no—
490C2×D4—262no—
491C2×D4—262no—
492C2×D4—262no—
493C2×D4—528no—
494C2×D4—524no—
495C2×D4—524no—
496C2×D4—524no—
497C2×D4—524no—
498C2×D4—522no—
499C2×D4—1042no—
500C2×D4#610414yescomplemented
501C2×D4C2×C22⋊D1312yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—262no—
521C22×C4C2×C22⋊D1311yescharacteristic
522C22×C4C2×C22⋊D1311yescharacteristic
523C22×C4C2×C22⋊D1311yescharacteristic
524C22×C4C2×C22⋊D1311yescharacteristic
525C22×C4C2×C22⋊D1312yes—
526C22×C4C2×C22⋊D1312yes—
527C22×C4C23×D1311yescharacteristic
528D8—528no—
529C2×C8—262no—
530C2×C8—262no—
531C2×C8—262no—
532C2×C8—262no—
533C2×C8—262no—
534C2×C8—262no—
535C2×C8—524no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—24no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—262no—
544C4⋊C4—262no—
545C4⋊C4C2×C22⋊D1312yes—
546C4⋊C4C2×C22⋊D1312yes—
547C4⋊C4C2×C22⋊D1312yes—
548C22⋊C4—24no—
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—22no—
553C22⋊C4—524no—
554C22⋊C4—522no—
555C22⋊C4—524no—
556C22⋊C4—1042no—
557C42—21no—
558C42—21no—
559C13#2396011yescharacteristic, complemented, Sylow
560C23—22no—
561C23—22no—
562C23—21no—
563C23—22no—
564C23—22no—
565C23—21no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23—264no—
572C23—528no—
573C23—522no—
574C23—522no—
575C23—522no—
576C23—522no—
577C23—522no—
578C23—522no—
579C23—1048no—
580C23—1048no—
581C23—1044no—
582C23—1044no—
583C23C2×#610412yes—
584C23C2×#610412yes—
585C23#8818612yes—
586C23#8820712yes—
587C23C22×C22⋊D1311yescharacteristic
588Q8—48no—
589D4—28no—
590D4—24no—
591D4—48no—
592D4—48no—
593D4—41no—
594D4—41no—
595D4—264no—
596D4—264no—
597D4—528no—
598D4—522no—
599D4—522no—
600D4—1048no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—48no—
615C2×C4—48no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—48no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—522no—
627C2×C4—522no—
628C2×C4—522no—
629C2×C4C2×#610412yes—
630C2×C4#8820712yes—
631C2×C4#41×D1312yes—
632C2×C4#8825612yes—
633C2×C4C22×C22⋊D1311yescharacteristic
634C2×C4C22×C22⋊D1311yescharacteristic
635C8—522no—
636C8—522no—
637C22—22no—
638C22—24no—
639C22—22no—
640C22—24no—
641C22—22no—
642C22—24no—
643C22—41no—
644C22—42no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—82no—
650C22—82no—
651C22—524no—
652C22—524no—
653C22—524no—
654C22—10416no—
655C22—1042no—
656C22—1042no—
657C22—1042no—
658C22—1042no—
659C22#1171887814yes—
660C22C22×#610411yescharacteristic
661C22C2×#8818611yescharacteristic
662C22#1171953412yes—
663C22#1171954212yes—
664C22C2×#8820711yescharacteristic
665C4—22no—
666C4—22no—
667C4—41no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—41no—
672C4—1042no—
673C4#1171953311yescharacteristic
674C4#1171953412yes—
675C4#1171953511yescharacteristic
676C2—24no—
677C2—42no—
678C2—82no—
679C2—1044no—
680C2#1311815111yescharacteristic
681C2C2×#1171887811yescharacteristic
682C2#1312412211yescharacteristic
683C2#1312664312yes—
684C2#1312679112yes—
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#547C2
socleC23×C13C22×D4
hypercenterC2×#547D13
hypocenterC13#23960
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718697C2semidirect
2. C22×#88049C2semidirect
3. #13118192C2semidirect
4. #13115969C2semidirect
5. #13115832C2semidirect
6. #13115265C2semidirect
7. #13115184C2semidirect
8. #13115153C2semidirect
9. #13115129C2semidirect
10. #13114922C2semidirect
11. C2×C13×#547C2semidirect
16. C2×C13×C4⋊Q8C22semidirect
21. C2×C13×#121C22semidirect
23. C2×C4×D4×C13C22semidirect
25. C22×C13×C4⋊C4C22semidirect
30. C2×#88072C22semidirect
33. C2×C22⋊#1055C22semidirect
43. #11718121C22semidirect
44. #11718121C22semidirect
45. #11718121C22semidirect
46. #11718116C22semidirect
76. C13×#121D4semidirect
88. C2×C13×C4⋊C4D4semidirect
145. C2×D4×C13D8semidirect
186. C2×D52#41semidirect
218. C2×#547D13semidirect
312. C2×C4⋊Q8C2×D13semidirect
318. C2×#121C2×D13semidirect
321. C2×C4×D4C2×D13semidirect
323. C22×C4⋊C4C2×D13semidirect
418. #121C22⋊D13semidirect
432. C2×C4⋊C4C22⋊D13semidirect
500. C2×D4#6104semidirect
559. C13#23960semidirect

Maximal subgroups

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

subgroupindex
C2×#117186972
C22×#880492
#131181922
#131159692
#131158322
#131152652
#131151842
#131151532
#131151292
#131149222
C2×C13×#5472
#2396013