Finite Group Databasebeta

← #15832519

Subgroups — #15832519

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#6129C211yesmaximal, characteristic, complemented
2C4×#88165C211yesmaximal, characteristic
3D13×#436C211yesmaximal, characteristic, complemented
4#13113717C211yesmaximal, characteristic, complemented
5#13113713C211yesmaximal, characteristic, complemented
6#13113701C211yesmaximal, characteristic, complemented
7#13113697C211yesmaximal, characteristic, complemented
8#13113681C211yesmaximal, characteristic, complemented
9#13113677C211yesmaximal, characteristic, complemented
10#13113665C211yesmaximal, characteristic, complemented
11#13113587C211yesmaximal, characteristic, complemented
12#13113225C211yesmaximal, characteristic, complemented
13#13113220C211yesmaximal, characteristic, complemented
14#13113122C211yesmaximal, characteristic, complemented
15C13×#1581C211yesmaximal, characteristic, complemented
16C2×#88165C411yescharacteristic
17C2×M16×D13—21no—
18C4×D4×D13C2211yescharacteristic
19C4×#6129C2211yescharacteristic
20C4×C13×D8C2211yescharacteristic
21C13×#436C2211yescharacteristic
22C8×D4×C13C2211yescharacteristic, complemented
23#11718813C411yescharacteristic
24#11718789—21no—
25C8×C22⋊D13—21no—
26C2×C8×Dic13—21no—
27C4×#6105C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic
30D4×#1055C2211yescharacteristic, complemented
31#11718550C411yescharacteristic
32#11718542C411yescharacteristic
33#11718499C2211yescharacteristic
34#11718494C2211yescharacteristic
35D13×C4⋊C8C2211yescharacteristic
36#11718491C2211yescharacteristic, complemented
37#11718446C411yescharacteristic
38#11718432C411yescharacteristic
39#11718431C411yescharacteristic
40#11718418C411yescharacteristic
41#11718390—21no—
42#11718386—21no—
43D13×C22⋊C8—21no—
44#11718379—21no—
45C4×#6095C2211yescharacteristic
46#11718349C2211yescharacteristic
47C4×#6094C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50C8×Dic26C2211yescharacteristic, complemented
51C13×#335C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic, complemented
57#11718076C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic, complemented
60#11718071C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic, complemented
63#11718048C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718047C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×#6129C2×C411yescharacteristic
68C2×D4×D13C2×C411yescharacteristic
69C22×C4×D13—21no—
70C2×C13×D8C2×C411yescharacteristic
71C2×C13×M16—21no—
72C22×C8×C13—21no—
73C4×D4×C13C2311yescharacteristic
74C4×D4×C13C2311yescharacteristic
75D4×Dic13C2×C411yescharacteristic
76D4×Dic13C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C4×C22⋊D13—21no—
80C4×C22⋊D13—21no—
81C2×C4×Dic13—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84#88165—24no—
85M16×D13—44no—
86C2×#6095C2×C411yescharacteristic
87C2×#6094—21no—
88C2×#6094—21no—
89C2×#6094C2×C411yescharacteristic
90C2×#6094C2×C411yescharacteristic
91C2×C8×D13—21no—
92C2×C8×D13D411yescharacteristic
93C2×C8×D13D411yescharacteristic
94#88147C2×C411yescharacteristic
95#88146C2×C411yescharacteristic
96C4⋊C4×D13C2×C411yescharacteristic
97#88141C2×C411yescharacteristic
98#88135—21no—
99#88135—21no—
100C22⋊C4×D13—21no—
101#88131—21no—
102C4×D52C2311yescharacteristic
103C42×D13C2311yescharacteristic
104C4×Dic26C2311yescharacteristic
105C13×#107C2×C411yescharacteristic
106C13×C4⋊C8C2311yescharacteristic
107C13×C4⋊C8C2311yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×C22⋊C8—21no—
111C13×C22⋊C8—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055—21no—
119#88061C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88057C2×C411yescharacteristic
125#88056C2×C411yescharacteristic
126#88055C2×C411yescharacteristic
127#88055C2×C411yescharacteristic
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132C8×Dic13—21no—
133C8×Dic13—21no—
134C8×Dic13—21no—
135C8×Dic13D411yescharacteristic
136C8×Dic13D411yescharacteristic
137#88050C2×C411yescharacteristic
138#88049C2×C411yescharacteristic
139#88048C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146#17871—131nomaximal, Sylow
147C23×D13—21no—
148C2×D4×C13C22×C411yescharacteristic
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C2×C22⋊D13—21no—
153C2×C22⋊D13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157#6129—22no—
158#6129M1614yescomplemented
159D4×D13—22no—
160D4×D13—22no—
161C2×D52C22×C411yescharacteristic
162C2×C4×D13—21no—
163C2×C4×D13—21no—
164C2×C4×D13—21no—
165C2×C4×D13—42no—
166C2×C4×D13—42no—
167C2×C4×D13C22×C411yescharacteristic
168C2×C4×D13C2×D411yescharacteristic
169C2×C4×D13#4111yescharacteristic
170C2×Dic26C22×C411yescharacteristic
171C13×D8—22no—
172C13×M16—42no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—42no—
177C2×C8×C13C22×C411yescharacteristic
178C2×C8×C13C22×C411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C42×C13C2411yescharacteristic
186C22⋊Dic13—21no—
187C22⋊Dic13—21no—
188#6105—22no—
189#6104—22no—
190#6103—21no—
191#6103—21no—
192#6103—21no—
193C4⋊Dic13C22×C411yescharacteristic
194C4⋊Dic13C22×C411yescharacteristic
195#6101—21no—
196#6101—21no—
197#6101—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13C22×C411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203C4×Dic13#4111yescharacteristic
204#6099—42no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—42no—
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213#6095—22no—
214#6094—22no—
215#6094—22no—
216#6094—42no—
217#6094—42no—
218C8×D13—22no—
219C8×D13—41no—
220C8×D13—42no—
221C8×#41—131no—
222C4×AGL(1,ℤ/8)—131no—
223C2×#436—131no—
224#1588—131no—
225#1588—131no—
226#1586—131no—
227#1586—131no—
228#1583—131no—
229#1583—131no—
230#1581—131no—
231#1581D1311yescharacteristic, complemented
232#1565—131no—
233#1478—131no—
234#1477—131no—
235#1451—131no—
236C23×C13—21no—
237C23×C13—21no—
238C22×D13—21no—
239C22×D13—42no—
240C22×D13—42no—
241C22×D13—42no—
242C22×D13C4×D411yescharacteristic
243D4×C13—21no—
244D4×C13—21no—
245D4×C13—21no—
246D4×C13C2×M1612yescomplemented
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C22⋊D13—24no—
257C22⋊D13—42no—
258C2×Dic13—21no—
259C2×Dic13—24no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—42no—
263C2×Dic13—42no—
264C2×Dic13C4×D411yescharacteristic
265C2×Dic13C4×D411yescharacteristic
266C2×Dic13C4×D411yescharacteristic
267D52—21no—
268D52—21no—
269C4×D13—21no—
270C4×D13—21no—
271C4×D13—41no—
272C4×D13—42no—
273C4×D13—42no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13C2×M1612yes—
277C4×D13#13112yes—
278Dic26—21no—
279Dic26C2×M1612yescomplemented
280C8×C13—21no—
281C8×C13—21no—
282C8×C13—21no—
283C8×C13—41no—
284C8×C13—41no—
285C8×C13—41no—
286C8×C13AGL(1,ℤ/8)12yescomplemented
287#1055—21no—
288#1055—21no—
289#1055—21no—
290#1055—21no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C2×AGL(1,ℤ/8)—131no—
295C22×M16—261no—
296C4×#41—131no—
297C2×C4×D4—131no—
298C8×Q8—131no—
299C8×Q8—131no—
300#442—131no—
301#442—131no—
302#440—131no—
303#440—131no—
304C4×SD16—131no—
305C4×SD16—131no—
306C4×D8—131no—
307C4×D8C2×D1311yescharacteristic
308#436—131no—
309#436—131no—
310#436—131no—
311#436—261no—
312#436—261no—
313#436C2×D1311yescharacteristic
314C8×D4—131no—
315C8×D4—261no—
316C8×D4—261no—
317C8×D4C2×D1311yescharacteristic, complemented
318#431—131no—
319#431—131no—
320#431—261no—
321#428—131no—
322C2×C4⋊C8—131no—
323#418—131no—
324#417—131no—
325C2×C22⋊C8—261no—
326C4×M16—131no—
327C2×C4×C8—131no—
328C2×C4×C8—261no—
329#335—131no—
330#335C2×D1311yescharacteristic, complemented
331#334—131no—
332#334—131no—
333Q8⋊C8—131no—
334Q8⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8—131no—
337D4⋊C8—131no—
338D4⋊C8—131no—
339D4⋊C8C2×D1311yescharacteristic
340D4⋊C8C2×D1311yescharacteristic, complemented
341#322—131no—
342#322—131no—
343#322—131no—
344#322C2×D1311yescharacteristic, complemented
345C22×C13—22no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13C2×C4×D411yescharacteristic
352C2×D13—21no—
353C2×D13—21no—
354C2×D13—41no—
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—84no—
358C2×D13#43512yes—
359C4×C13—21no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13C22×M1611yescharacteristic
363C4×C13C2×#13111yescharacteristic
364C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
365C4×C13#57511yescharacteristic
366Dic13—22no—
367Dic13—21no—
368Dic13—21no—
369Dic13—41no—
370Dic13—41no—
371Dic13#43512yes—
372C2×#41—131no—
373C22×D4—131no—
374C23×C4—261no—
375AGL(1,ℤ/8)—264no—
376C2×SD16—131no—
377C2×SD16—131no—
378C2×D8—131no—
379C2×D8C4×D1311yescharacteristic
380C2×M16—21no—
381C2×M16—131no—
382C2×M16—131no—
383C2×M16—261no—
384C2×M16—261no—
385C2×M16—261no—
386C2×M16—524no—
387C22×C8—21no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—261no—
391C22×C8—261no—
392C4×Q8—131no—
393C4×Q8—131no—
394C4×D4—131no—
395C4×D4—131no—
396C4×D4—131no—
397C4×D4—131no—
398C4×D4—261no—
399C4×D4—261no—
400C4×D4—261no—
401C4×D4—261no—
402C4×D4C22×D1311yescharacteristic
403C4×D4C22×D1311yescharacteristic
404#117—131no—
405#117—261no—
406C2×C4⋊C4—131no—
407C2×C22⋊C4—261no—
408C2×C42—131no—
409C2×C42—261no—
410#107—131no—
411#107C4×D1311yescharacteristic
412#106—131no—
413#106—131no—
414C4⋊C8—131no—
415C4⋊C8—131no—
416C4⋊C8—261no—
417C4⋊C8—261no—
418C4⋊C8—261no—
419C4⋊C8—261no—
420C4⋊C8C22×D1311yescharacteristic
421C4⋊C8C22×D1311yescharacteristic
422#103—131no—
423#103—131no—
424#102—131no—
425#102—131no—
426#102—131no—
427#102—131no—
428#102C4×D1311yescharacteristic
429#102C4×D1311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—261no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438#97—131no—
439#97—131no—
440C4×C8—131no—
441C4×C8—131no—
442C4×C8—131no—
443C4×C8—131no—
444C4×C8—131no—
445C4×C8—261no—
446C4×C8—261no—
447C4×C8—261no—
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C4×C8C22×D1311yescharacteristic
451C2×C13—42no—
452C2×C13—81no—
453C2×C13C2×#43511yescharacteristic
454C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
455C2×C13#295511yescharacteristic
456D13—22no—
457D13—81no—
458C24—261no—
459#41—134no—
460#41—262no—
461C2×Q8—131no—
462C2×D4—131no—
463C2×D4—262no—
464C2×D4—262no—
465C2×D4—261no—
466C2×D4—261no—
467C2×D4C2×C4×D1311yescharacteristic
468C2×D4C2×C4×D1311yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—522no—
481C22×C4—522no—
482SD16—262no—
483SD16—262no—
484D8—22no—
485D8—262no—
486M16—42no—
487M16—262no—
488M16—262no—
489M16—522no—
490M16—522no—
491M16—522no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8—131no—
497C2×C8—131no—
498C2×C8—131no—
499C2×C8—131no—
500C2×C8—262no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—521no—
505C2×C8—522no—
506C2×C8—522no—
507C2×C8C2×C4×D1311yescharacteristic
508C2×C8C2×C4×D1311yescharacteristic
509C2×C8D4×D1311yescharacteristic
510C2×C8D4×D1311yescharacteristic
511C4⋊C4—131no—
512C4⋊C4—131no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4C2×C4×D1311yescharacteristic
517C4⋊C4C2×C4×D1311yescharacteristic
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—261no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42—131no—
526C42—131no—
527C42—131no—
528C42—261no—
529C42—261no—
530C42—261no—
531C42C23×D1311yescharacteristic
532C13#1787111yescharacteristic, complemented, Sylow
533C23—21no—
534C23—21no—
535C23—131no—
536C23—261no—
537C23—522no—
538C23—522no—
539C23—522no—
540Q8—132no—
541Q8—261no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—264no—
546D4—261no—
547D4—261no—
548D4—522no—
549D4M16×D1312yescomplemented
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—131no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—131no—
560C2×C4—131no—
561C2×C4—264no—
562C2×C4—261no—
563C2×C4—261no—
564C2×C4—261no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—521no—
568C2×C4—522no—
569C2×C4—522no—
570C2×C4—522no—
571C2×C4—522no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4C22×C4×D1311yescharacteristic
575C2×C4C2×D4×D1311yescharacteristic
576C2×C4#41×D1311yescharacteristic
577C8—21no—
578C8—21no—
579C8—21no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—261no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—521no—
588C8—521no—
589C8—521no—
590C8#8816512yescomplemented
591C22—22no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—132no—
598C22—261no—
599C22—261no—
600C22—521no—
601C22—521no—
602C22—521no—
603C22—1044no—
604C22C4×D4×D1311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—132no—
609C4—261no—
610C4—261no—
611C4—262no—
612C4—521no—
613C4—521no—
614C4C2×M16×D1311yescharacteristic
615C4D13×#13111yescharacteristic
616C4C2×#8816511yescharacteristic
617C4#1171947311yescharacteristic
618C2—42no—
619C2—81no—
620C2—262no—
621C2—1041no—
622C2D13×#43511yescharacteristic
623C2C4×#8816511yescharacteristic
624C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1581C2
socleC22×C13C2×C4×D4
prime radicalC2×#88165C4
cosocleC42×C13C24
hypercenter#1581D13
hypocenterC13#17871
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
1. C8×#6129C2semidirect
3. D13×#436C2semidirect
4. #13113717C2semidirect
5. #13113713C2semidirect
6. #13113701C2semidirect
7. #13113697C2semidirect
8. #13113681C2semidirect
9. #13113677C2semidirect
10. #13113665C2semidirect
11. #13113587C2semidirect
12. #13113225C2semidirect
13. #13113220C2semidirect
14. #13113122C2semidirect
15. C13×#1581C2semidirect
22. C8×D4×C13C22semidirect
30. D4×#1055C22semidirect
36. #11718491C22semidirect
50. C8×Dic26C22semidirect
51. C13×#335C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
56. D4⋊#1055C22semidirect
57. #11718076C22semidirect
59. #11718072C22semidirect
60. #11718071C22semidirect
62. #11718049C22semidirect
63. #11718048C22semidirect
64. #11718047C22semidirect
65. #11718047C22semidirect
66. #11718046C22semidirect
158. #6129M16semidirect
231. #1581D13semidirect
246. D4×C13C2×M16semidirect
279. Dic26C2×M16semidirect
286. C8×C13AGL(1,ℤ/8)semidirect
317. C8×D4C2×D13semidirect
330. #335C2×D13semidirect
340. D4⋊C8C2×D13semidirect
344. #322C2×D13semidirect
532. C13#17871semidirect
549. D4M16×D13semidirect
590. C8#88165semidirect

Maximal subgroups

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

subgroupindex
C8×#61292
C4×#881652
D13×#4362
#131137172
#131137132
#131137012
#131136972
#131136812
#131136772
#131136652
#131135872
#131132252
#131132202
#131131222
C13×#15812
#1787113