Finite Group Databasebeta

← #15834430

Subgroups — #15834430

Order 3328.

786 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D8×D13C211yesmaximal, characteristic
2#13123572C211yesmaximal, characteristic, complemented
3D4×#6094C211yesmaximal, characteristic, complemented
4#13113748C211yesmaximal, characteristic, complemented
5#13113747C211yesmaximal, characteristic, complemented
6#13113702C211yesmaximal, characteristic, complemented
7#13113701C211yesmaximal, characteristic, complemented
8#13113699C211yesmaximal, characteristic, complemented
9#13113658C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113590C211yesmaximal, characteristic, complemented
12#13113259C211yesmaximal, characteristic, complemented
13#13113259C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1586C211yesmaximal, characteristic, complemented
16C2×D8×D13C411yescharacteristic
17C2×M16×D13—21no—
18C22×#6094—21no—
19C4×D4×D13C2211yescharacteristic
20C4×D4×D13C2211yescharacteristic
21C4×C13×D8C2211yescharacteristic
22C13×#436C2211yescharacteristic, complemented
23C8×D4×C13C2211yescharacteristic, complemented
24D8×Dic13C411yescharacteristic
25#11718788—21no—
26#11718772—21no—
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic, complemented
30D4×#1055C2211yescharacteristic, complemented
31D13×#107C411yescharacteristic
32#11718533C411yescharacteristic
33#11718499C2211yescharacteristic, complemented
34#11718498C2211yescharacteristic
35#11718498C2211yescharacteristic
36#11718495C2211yescharacteristic, complemented
37D13×#102C411yescharacteristic
38D13×#102C411yescharacteristic
39#11718417C411yescharacteristic
40#11718417C411yescharacteristic
41#11718391—21no—
42#11718389—21no—
43#11718387—21no—
44#11718387—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic, complemented
47C4×#6094C2211yescharacteristic
48C8×D52C2211yescharacteristic, complemented
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#334C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic, complemented
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic, complemented
56D4⋊#1055C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic, complemented
62#11718051C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C22×C4×D13—21no—
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×M16—21no—
73C22×C8×C13—21no—
74C4×D4×C13C2311yescharacteristic
75C4×D4×C13C2311yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77D4×Dic13C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C2×#6104C2×C411yescharacteristic
80C4×C22⋊D13—21no—
81C4×C22⋊D13—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84D8×D13—24no—
85M16×D13—44no—
86C2×D104C2×C411yescharacteristic
87C2×#6094—21no—
88C2×#6094—21no—
89C2×#6094—21no—
90C2×#6094—21no—
91C2×#6094—44no—
92C2×#6094D411yescharacteristic
93C2×#6094D411yescharacteristic
94C2×C8×D13—21no—
95C2×C8×D13—21no—
96C2×C8×D13C2×C411yescharacteristic
97C2×C8×D13C2×C411yescharacteristic
98#88147C2×C411yescharacteristic
99#88147C2×C411yescharacteristic
100C4⋊C4×D13C2×C411yescharacteristic
101C4⋊C4×D13C2×C411yescharacteristic
102#88135—21no—
103#88135—21no—
104C22⋊C4×D13—21no—
105C22⋊C4×D13—21no—
106C4×D52C2311yescharacteristic
107C4×D52C2311yescharacteristic
108C42×D13C2311yescharacteristic
109C13×#107C2×C411yescharacteristic
110C13×C4⋊C8C2311yescharacteristic
111C13×C4⋊C8C2311yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×#102C2×C411yescharacteristic
114C13×C22⋊C8—21no—
115C13×C22⋊C8—21no—
116C4×C8×C13C2311yescharacteristic
117C4×C8×C13C2311yescharacteristic
118C4×C8×C13C2311yescharacteristic
119#88072C2×C411yescharacteristic
120#88072C2×C411yescharacteristic
121C22⋊#1055—21no—
122C22⋊#1055—21no—
123#88061C2×C411yescharacteristic
124#88061C2×C411yescharacteristic
125#88060—21no—
126#88060—21no—
127#88060—21no—
128#88060—21no—
129#88060—21no—
130#88058C2×C411yescharacteristic
131#88055D411yescharacteristic
132#88055D411yescharacteristic
133#88054—21no—
134#88054—21no—
135#88054—21no—
136C8×Dic13C2×C411yescharacteristic
137C8×Dic13C2×C411yescharacteristic
138#88049C2×C411yescharacteristic
139#88049C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141#88047C2×C411yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4⋊#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146C4×#1055C2311yescharacteristic
147#18044—131nomaximal, Sylow
148C23×D13—21no—
149C23×D13—21no—
150C2×D4×C13C22×C411yescharacteristic
151C2×D4×C13C22×C411yescharacteristic
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C2×C22⋊D13—21no—
155C2×C22⋊D13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158D4×D13—22no—
159D4×D13—22no—
160D4×D13—41no—
161D4×D13—41no—
162C2×D52C22×C411yescharacteristic
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—42no—
171C2×C4×D13—42no—
172C2×C4×D13—42no—
173C2×C4×D13—42no—
174C2×C4×D13C22×C411yescharacteristic
175C2×C4×D13C2×D411yescharacteristic
176C2×C4×D13#4111yescharacteristic
177C13×D8—22no—
178C13×M16—42no—
179C2×C8×C13—21no—
180C2×C8×C13—21no—
181C2×C8×C13—21no—
182C2×C8×C13—42no—
183C2×C8×C13C22×C411yescharacteristic
184C2×C8×C13C22×C411yescharacteristic
185C2×C8×C13C2×D411yescharacteristic
186C2×C8×C13C2×D411yescharacteristic
187C13×C4⋊C4C22×C411yescharacteristic
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C42×C13C2411yescharacteristic
192C22⋊Dic13—21no—
193C22⋊Dic13—21no—
194#6104—22no—
195#6104M1614yescomplemented
196#6103—21no—
197#6103—21no—
198#6103—21no—
199#6103—21no—
200C4⋊Dic13C22×C411yescharacteristic
201C4⋊Dic13C22×C411yescharacteristic
202#6101—21no—
203#6101—21no—
204C4×Dic13C22×C411yescharacteristic
205C4×Dic13C2×D411yescharacteristic
206C4×Dic13#4111yescharacteristic
207#6099—42no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—42no—
212C2×#1055C22×C411yescharacteristic
213C2×#1055C22×C411yescharacteristic
214C2×#1055C2×D411yescharacteristic
215C2×#1055C2×D411yescharacteristic
216D104—22no—
217#6094—22no—
218#6094—22no—
219#6094—42no—
220#6094—42no—
221#6094—42no—
222#6094—42no—
223C8×D13—22no—
224C8×D13—41no—
225C8×D13—42no—
226C8×D13—42no—
227C2×C4×D8—131no—
228D4×M16—131no—
229D4×M16—131no—
230#1594—131no—
231#1594—131no—
232#1586—131no—
233#1586—131no—
234#1586—131no—
235#1586D1311yescharacteristic, complemented
236#1580—131no—
237#1580—131no—
238#1566—131no—
239#1486—131no—
240#1486—131no—
241#1451—131no—
242C23×C13—21no—
243C23×C13—21no—
244C22×D13—21no—
245C22×D13—21no—
246C22×D13—42no—
247C22×D13—42no—
248C22×D13—42no—
249C22×D13—42no—
250C22×D13—81no—
251C22×D13—81no—
252C22×D13C4×D411yescharacteristic
253D4×C13—21no—
254D4×C13—21no—
255D4×C13—21no—
256D4×C13C2×M1612yescomplemented
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13C23×C411yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C22⋊D13—42no—
267C22⋊D13—42no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—42no—
271C2×Dic13—42no—
272C2×Dic13C4×D411yescharacteristic
273C2×Dic13C4×D411yescharacteristic
274C2×Dic13C4×D411yescharacteristic
275D52—21no—
276D52—21no—
277D52—21no—
278D52C2×M1612yescomplemented
279C4×D13—21no—
280C4×D13—21no—
281C4×D13—41no—
282C4×D13—42no—
283C4×D13—42no—
284C4×D13—41no—
285C4×D13—41no—
286C4×D13—41no—
287C4×D13—41no—
288C4×D13—42no—
289C4×D13—42no—
290C4×D13AGL(1,ℤ/8)12yes—
291C4×D13AGL(1,ℤ/8)12yes—
292C8×C13—21no—
293C8×C13—21no—
294C8×C13—21no—
295C8×C13—21no—
296C8×C13—41no—
297C8×C13—41no—
298C8×C13—41no—
299#1055—21no—
300#1055—21no—
301#1055—21no—
302#1055—41no—
303#1055—41no—
304#1055—41no—
305#1055C2×M1612yescomplemented
306C22×D8—131no—
307C22×M16—261no—
308C22×M16—261no—
309C2×C4×D4—131no—
310C2×C4×D4—131no—
311C4×D8—131no—
312C4×D8—131no—
313C4×D8—131no—
314C4×D8—131no—
315C4×D8—131no—
316C4×D8—131no—
317C4×D8—131no—
318C4×D8C2×D1311yescharacteristic
319#436—131no—
320#436—131no—
321#436—131no—
322#436C2×D1311yescharacteristic, complemented
323#435—261no—
324#435—261no—
325#435—261no—
326#435—261no—
327C8×D4—131no—
328C8×D4—131no—
329C8×D4—131no—
330C8×D4C2×D1311yescharacteristic, complemented
331#431—131no—
332C2×#107—131no—
333#423—131no—
334#423—131no—
335C2×#102—131no—
336C2×#102—131no—
337#407—261no—
338#407—261no—
339C4×M16—131no—
340C2×C4×C8—131no—
341#334—131no—
342#334—131no—
343#334—131no—
344#334C2×D1311yescharacteristic, complemented
345D4⋊C8—131no—
346D4⋊C8—131no—
347D4⋊C8—131no—
348D4⋊C8—131no—
349D4⋊C8—131no—
350D4⋊C8—131no—
351D4⋊C8C2×D1311yescharacteristic, complemented
352D4⋊C8C2×D1311yescharacteristic, complemented
353#322—131no—
354#322—131no—
355#322—131no—
356#322C2×D1311yescharacteristic, complemented
357C22×C13—22no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13C2×C4×D411yescharacteristic
364C2×D13—21no—
365C2×D13—21no—
366C2×D13—22no—
367C2×D13—41no—
368C2×D13—41no—
369C2×D13—41no—
370C2×D13—41no—
371C2×D13—41no—
372C2×D13—84no—
373C2×D13—84no—
374C2×D13#44212yes—
375C4×C13—21no—
376C4×C13—41no—
377C4×C13—41no—
378C4×C13C22×M1611yescharacteristic
379C4×C13#56811yescharacteristic
380C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
381C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
382Dic13—21no—
383Dic13—21no—
384Dic13—41no—
385Dic13—41no—
386Dic13#44212yes—
387C22×D4—131no—
388C22×D4—131no—
389C23×C4—261no—
390C23×C4—261no—
391C2×D8—131no—
392C2×D8—131no—
393C2×D8—131no—
394C2×D8—264no—
395C2×D8C4×D1311yescharacteristic
396C2×M16—21no—
397C2×M16—131no—
398C2×M16—131no—
399C2×M16—261no—
400C2×M16—261no—
401C2×M16—261no—
402C2×M16—261no—
403C2×M16—261no—
404C2×M16—524no—
405C2×M16—524no—
406C22×C8—21no—
407C22×C8—131no—
408C22×C8—131no—
409C22×C8—261no—
410C22×C8—261no—
411C22×C8—261no—
412C4×D4—131no—
413C4×D4—131no—
414C4×D4—131no—
415C4×D4—131no—
416C4×D4—131no—
417C4×D4—131no—
418C4×D4—261no—
419C4×D4—261no—
420C4×D4—261no—
421C4×D4—261no—
422C4×D4C22×D1311yescharacteristic
423C4×D4C22×D1311yescharacteristic
424C2×C4⋊C4—131no—
425C2×C4⋊C4—131no—
426C2×C22⋊C4—261no—
427C2×C22⋊C4—261no—
428C2×C42—131no—
429#107—131no—
430#107—131no—
431#107—131no—
432#107C4×D1311yescharacteristic
433C4⋊C8—131no—
434C4⋊C8—131no—
435C4⋊C8—261no—
436C4⋊C8—261no—
437C4⋊C8—261no—
438C4⋊C8C22×D1311yescharacteristic
439C4⋊C8C22×D1311yescharacteristic
440#102—131no—
441#102—131no—
442#102—131no—
443#102—131no—
444#102—131no—
445#102—131no—
446#102C4×D1311yescharacteristic
447#102C4×D1311yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—261no—
451C22⋊C8—261no—
452C22⋊C8—261no—
453C22⋊C8—261no—
454C22⋊C8—261no—
455C22⋊C8—261no—
456C22⋊C8—261no—
457#97—131no—
458#97—131no—
459C4×C8—131no—
460C4×C8—131no—
461C4×C8—131no—
462C4×C8—131no—
463C4×C8—131no—
464C4×C8C22×D1311yescharacteristic
465C4×C8C22×D1311yescharacteristic
466C4×C8C22×D1311yescharacteristic
467C2×C13—42no—
468C2×C13—81no—
469C2×C13D4×M1611yescharacteristic
470C2×C13C2×#44211yescharacteristic
471C2×C13#295711yescharacteristic
472D13—22no—
473D13—42no—
474D13—81no—
475C24—261no—
476C24—261no—
477C2×D4—131no—
478C2×D4—131no—
479C2×D4—261no—
480C2×D4—261no—
481C2×D4—262no—
482C2×D4—262no—
483C2×D4—521no—
484C2×D4—521no—
485C2×D4C2×C4×D1311yescharacteristic
486C2×D4C2×C4×D1311yescharacteristic
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—131no—
490C22×C4—131no—
491C22×C4—131no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—261no—
497C22×C4—261no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—522no—
501C22×C4—522no—
502C22×C4—522no—
503C22×C4—522no—
504D8—22no—
505D8—134no—
506D8—262no—
507D8—262no—
508M16—42no—
509M16—262no—
510M16—262no—
511M16—522no—
512M16—522no—
513M16—522no—
514M16—522no—
515M16—522no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—42no—
520C2×C8—131no—
521C2×C8—131no—
522C2×C8—131no—
523C2×C8—131no—
524C2×C8—262no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—521no—
529C2×C8—522no—
530C2×C8—522no—
531C2×C8—522no—
532C2×C8C2×C4×D1311yescharacteristic
533C2×C8C2×C4×D1311yescharacteristic
534C2×C8D4×D1311yescharacteristic
535C2×C8D4×D1311yescharacteristic
536C4⋊C4—131no—
537C4⋊C4—131no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4C2×C4×D1311yescharacteristic
541C4⋊C4C2×C4×D1311yescharacteristic
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—261no—
545C22⋊C4—261no—
546C22⋊C4—261no—
547C22⋊C4—261no—
548C22⋊C4—261no—
549C22⋊C4—261no—
550C42—131no—
551C42—131no—
552C42—131no—
553C42C23×D1311yescharacteristic
554C13#1804411yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—131no—
558C23—261no—
559C23—261no—
560C23—522no—
561C23—522no—
562C23—522no—
563C23—522no—
564C23—1041no—
565C23—1041no—
566D4—21no—
567D4—21no—
568D4—21no—
569D4—132no—
570D4—261no—
571D4—261no—
572D4—261no—
573D4—522no—
574D4—522no—
575D4M16×D1312yescomplemented
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—131no—
583C2×C4—132no—
584C2×C4—132no—
585C2×C4—131no—
586C2×C4—131no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—261no—
590C2×C4—261no—
591C2×C4—521no—
592C2×C4—522no—
593C2×C4—522no—
594C2×C4—522no—
595C2×C4—522no—
596C2×C4—522no—
597C2×C4—522no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4C22×C4×D1311yescharacteristic
603C2×C4C2×D4×D1311yescharacteristic
604C2×C4#41×D1311yescharacteristic
605C8—21no—
606C8—21no—
607C8—21no—
608C8—21no—
609C8—41no—
610C8—41no—
611C8—41no—
612C8—132no—
613C8—261no—
614C8—261no—
615C8—261no—
616C8—521no—
617C8—521no—
618C8—521no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—132no—
626C22—261no—
627C22—261no—
628C22—262no—
629C22—521no—
630C22—521no—
631C22—521no—
632C22—521no—
633C22—521no—
634C22—1044no—
635C22—1044no—
636C22C4×D4×D1311yescharacteristic
637C4—21no—
638C4—41no—
639C4—41no—
640C4—132no—
641C4—261no—
642C4—261no—
643C4—521no—
644C4—521no—
645C4C2×M16×D1311yescharacteristic
646C4#1171945511yescharacteristic
647C4D13×AGL(1,ℤ/8)11yescharacteristic
648C4D13×AGL(1,ℤ/8)11yescharacteristic
649C2—42no—
650C2—81no—
651C2—262no—
652C2—522no—
653C2—1041no—
654C2#1312356911yescharacteristic
655C2D13×#44211yescharacteristic
656C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1586C2
socleC22×C13C2×C4×D4
prime radicalC2×D8×D13C4
cosocleC42×C13C24
hypercenter#1586D13
hypocenterC13#18044
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #13123572C2semidirect
3. D4×#6094C2semidirect
4. #13113748C2semidirect
5. #13113747C2semidirect
6. #13113702C2semidirect
7. #13113701C2semidirect
8. #13113699C2semidirect
9. #13113658C2semidirect
10. #13113657C2semidirect
11. #13113590C2semidirect
12. #13113259C2semidirect
13. #13113259C2semidirect
14. #13113124C2semidirect
15. C13×#1586C2semidirect
22. C13×#436C22semidirect
23. C8×D4×C13C22semidirect
29. #11718673C22semidirect
30. D4×#1055C22semidirect
33. #11718499C22semidirect
36. #11718495C22semidirect
46. #11718349C22semidirect
48. C8×D52C22semidirect
51. C13×#334C22semidirect
52. C13×D4⋊C8C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
55. D4⋊#1055C22semidirect
56. D4⋊#1055C22semidirect
57. #11718075C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
61. #11718051C22semidirect
62. #11718051C22semidirect
63. #11718049C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
195. #6104M16semidirect
235. #1586D13semidirect
256. D4×C13C2×M16semidirect
278. D52C2×M16semidirect
305. #1055C2×M16semidirect
322. #436C2×D13semidirect
330. C8×D4C2×D13semidirect
344. #334C2×D13semidirect
351. D4⋊C8C2×D13semidirect
352. D4⋊C8C2×D13semidirect
356. #322C2×D13semidirect
554. C13#18044semidirect
575. D4M16×D13semidirect

Maximal subgroups

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

subgroupindex
C4×D8×D132
#131235722
D4×#60942
#131137482
#131137472
#131137022
#131137012
#131136992
#131136582
#131136572
#131135902
#131132592
#131131242
C13×#15862
#1804413