Finite Group Databasebeta

← C131×#23587 #45709471

Subgroups — C131×#23587 #45709471

Order 33536.

1274 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3460×C131C211yesmaximal, characteristic, complemented
2C4×AGL(1,ℤ/8)×C131C212yesmaximal, complemented
3C4×#127×C131C211yesmaximal, characteristic, complemented
4#2060×C131C211yesmaximal, characteristic, complemented
5#2039×C131C211yesmaximal, characteristic, complemented
6#2037×C131C212yesmaximal, complemented
7#2027×C131C211yesmaximal, characteristic, complemented
8#2006×C131C211yesmaximal, characteristic, complemented
9#2002×C131C212yesmaximal, complemented
10C4×#104×C131C212yesmaximal, complemented
11C4×#100×C131C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C131C2212yes—
13#544×C131C2211yescharacteristic
14#542×C131—22no—
15#540×C131—22no—
16#538×C131—22no—
17#537×C131C2211yescharacteristic
18#535×C131C2212yes—
19#532×C131—22no—
20C2×#127×C131C2211yescharacteristic
21#529×C131—22no—
22#525×C131—22no—
23C4×#41×C131C2212yes—
24C2×C4×D4×C131—22no—
25C2×C4×D4×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27#442×C131—22no—
28#440×C131—22no—
29C4×SD16×C131—22no—
30C4×D8×C131—22no—
31#428×C131C2212yes—
32C2×#104×C131C2212yes—
33C2×#104×C131C2212yes—
34#418×C131C2212yes—
35#417×C131C2212yes—
36C2×#100×C131C2212yes—
37C4×M16×C131C2212yes—
38#390×C131—22no—
39#390×C131C2211yescharacteristic
40#390×C131C2211yescharacteristic
41#384×C131C2211yescharacteristic
42C43×C131C2211yescharacteristic
43#343×C131C2211yescharacteristic
44#343×C131C2211yescharacteristic
45#339×C131C2212yes—
46#339×C131C2212yes—
47C2×#41×C131—22no—
48C2×#41×C131C2312yes—
49C22×D4×C131—22no—
50C22×D4×C131C2311yescharacteristic
51C22×D4×C131C2311yescharacteristic
52C23×C4×C131—21no—
53C23×C4×C131D412yes—
54AGL(1,ℤ/8)×C131—24no—
55AGL(1,ℤ/8)×C131—24no—
56C2×SD16×C131—22no—
57C2×D8×C131—22no—
58C2×M16×C131C2312yes—
59C2×M16×C131C2312yes—
60C4⋊Q8×C131—22no—
61#127×C131—22no—
62#127×C131—22no—
63#127×C131—22no—
64#126×C131—24no—
65#125×C131—22no—
66#124×C131—24no—
67#124×C131—22no—
68#123×C131—24no—
69#123×C131—24no—
70C22⋊Q8×C131—22no—
71C22⋊Q8×C131—22no—
72C22⋊Q8×C131—22no—
73#121×C131—22no—
74#121×C131—24no—
75#121×C131—22no—
76#121×C131—22no—
77#121×C131—22no—
78#121×C131—22no—
79#120×C131—24no—
80C4×Q8×C131D412yescomplemented
81C4×Q8×C131D412yescomplemented
82C4×D4×C131—24no—
83C4×D4×C131—22no—
84C4×D4×C131—22no—
85C4×D4×C131—22no—
86C4×D4×C131—22no—
87C4×D4×C131—22no—
88C4×D4×C131—22no—
89C4×D4×C131—48no—
90C4×D4×C131D412yescomplemented
91C4×D4×C131D412yescomplemented
92#117×C131—22no—
93#117×C131—22no—
94#117×C131C2312yes—
95C2×C4⋊C4×C131—22no—
96C2×C4⋊C4×C131C2311yescharacteristic
97C2×C4⋊C4×C131C2311yescharacteristic
98C2×C22⋊C4×C131—22no—
99C2×C22⋊C4×C131—21no—
100C2×C22⋊C4×C131—22no—
101C2×C22⋊C4×C131D412yes—
102C2×C42×C131—21no—
103C2×C42×C131—22no—
104C2×C42×C131—21no—
105C2×C42×C131C2311yescharacteristic
106C2×C42×C131C2311yescharacteristic
107C2×C42×C131C2311yescharacteristic
108#107×C131—22no—
109#106×C131—22no—
110#104×C131—24no—
111#104×C131—24no—
112#103×C131—22no—
113#102×C131—22no—
114#102×C131—22no—
115#102×C131—22no—
116#100×C131—24no—
117#97×C131—22no—
118C4×C8×C131—22no—
119C24×C131—21no—
120C24×C131C2×D412yes—
121#41×C131—22no—
122#41×C131—22no—
123#41×C131—22no—
124#41×C131—22no—
125#41×C131—84no—
126C2×Q8×C131—22no—
127C2×Q8×C131C2×D412yes—
128C2×D4×C131—28no—
129C2×D4×C131—22no—
130C2×D4×C131—24no—
131C2×D4×C131—24no—
132C2×D4×C131—22no—
133C2×D4×C131—22no—
134C2×D4×C131—22no—
135C2×D4×C131—22no—
136C2×D4×C131—22no—
137C2×D4×C131—21no—
138C2×D4×C131—21no—
139C2×D4×C131—21no—
140C2×D4×C131—44no—
141C2×D4×C131—44no—
142C2×D4×C131C2×D412yes—
143C2×D4×C131#4112yescomplemented
144C22×C4×C131—21no—
145C22×C4×C131—21no—
146C22×C4×C131—22no—
147C22×C4×C131—22no—
148C22×C4×C131—22no—
149C22×C4×C131—22no—
150C22×C4×C131—22no—
151C22×C4×C131—21no—
152C22×C4×C131—44no—
153C22×C4×C131—44no—
154C22×C4×C131—41no—
155C22×C4×C131—41no—
156C22×C4×C131C2×D411yescharacteristic
157C22×C4×C131C2×D412yes—
158C22×C4×C131C2×D411yescharacteristic
159C22×C4×C131C2411yescharacteristic
160SD16×C131—28no—
161D8×C131—28no—
162M16×C131—22no—
163M16×C131—22no—
164M16×C131—22no—
165M16×C131#4114yescomplemented
166C2×C8×C131—22no—
167C2×C8×C131—22no—
168C4⋊C4×C131—22no—
169C4⋊C4×C131—22no—
170C4⋊C4×C131—24no—
171C4⋊C4×C131—22no—
172C4⋊C4×C131—22no—
173C4⋊C4×C131—22no—
174C4⋊C4×C131—22no—
175C4⋊C4×C131—44no—
176C4⋊C4×C131C2×D412yes—
177C4⋊C4×C131C2×D412yes—
178C22⋊C4×C131—24no—
179C22⋊C4×C131—24no—
180C22⋊C4×C131—24no—
181C22⋊C4×C131—22no—
182C22⋊C4×C131—24no—
183C22⋊C4×C131—22no—
184C22⋊C4×C131—22no—
185C22⋊C4×C131—44no—
186C22⋊C4×C131—44no—
187C22⋊C4×C131—42no—
188C42×C131—24no—
189C42×C131—22no—
190C42×C131—22no—
191C42×C131—22no—
192C42×C131—21no—
193C42×C131—22no—
194C42×C131—42no—
195C42×C131C2×D412yes—
196C42×C131C2×D412yes—
197C42×C131#4112yescomplemented
198C23×C131—22no—
199C23×C131—22no—
200C23×C131—22no—
201C23×C131—22no—
202C23×C131—22no—
203C23×C131—42no—
204C23×C131—42no—
205C23×C131—42no—
206C23×C131—42no—
207C23×C131—41no—
208C23×C131—41no—
209C23×C131C22×D411yescharacteristic
210Q8×C131—22no—
211Q8×C131—22no—
212Q8×C131—82no—
213D4×C131—22no—
214D4×C131—24no—
215D4×C131—22no—
216D4×C131—416no—
217D4×C131—42no—
218D4×C131—42no—
219D4×C131—42no—
220D4×C131—42no—
221D4×C131—42no—
222D4×C131—84no—
223D4×C131—82no—
224D4×C131—84no—
225C2×C4×C131—22no—
226C2×C4×C131—22no—
227C2×C4×C131—22no—
228C2×C4×C131—22no—
229C2×C4×C131—22no—
230C2×C4×C131—22no—
231C2×C4×C131—22no—
232C2×C4×C131—22no—
233C2×C4×C131—22no—
234C2×C4×C131—41no—
235C2×C4×C131—41no—
236C2×C4×C131—41no—
237C2×C4×C131—42no—
238C2×C4×C131—42no—
239C2×C4×C131—44no—
240C2×C4×C131—44no—
241C2×C4×C131—42no—
242C2×C4×C131—42no—
243C2×C4×C131—41no—
244C2×C4×C131—82no—
245C2×C4×C131—82no—
246C2×C4×C131—82no—
247C2×C4×C131—82no—
248C2×C4×C131#12012yes—
249C2×C4×C131#12011yescharacteristic
250C2×C4×C131#12011yescharacteristic
251C2×C4×C131C22×D412yes—
252C2×C4×C131C2×#4111yescharacteristic
253C2×C4×C131C2×#4112yes—
254C2×C4×C131C2×#4111yescharacteristic
255C8×C131—24no—
256C8×C131—42no—
257C22×C131—21no—
258C22×C131—21no—
259C22×C131—44no—
260C22×C131—44no—
261C22×C131—42no—
262C22×C131—42no—
263C22×C131—42no—
264C22×C131—42no—
265C22×C131—42no—
266C22×C131—42no—
267C22×C131—42no—
268C22×C131—82no—
269C22×C131—82no—
270C22×C131—81no—
271C22×C131—81no—
272C22×C131C2×#12011yescharacteristic
273C22×C131#52511yescharacteristic
274C22×C131#53211yescharacteristic
275C4×C131—24no—
276C4×C131—21no—
277C4×C131—22no—
278C4×C131—42no—
279C4×C131—42no—
280C4×C131—42no—
281C4×C131—42no—
282C4×C131—42no—
283C4×C131—81no—
284C4×C131#45312yes—
285C4×C131#52512yes—
286C4×C131#53212yes—
287C2×C131—21no—
288C2×C131—21no—
289C2×C131—82no—
290C2×C131—82no—
291C2×C131—82no—
292C2×C131#238811yescharacteristic
293C2×C131C2×#45311yescharacteristic
294C2×C131#301811yescharacteristic
295#23587C13111yesmaximal, characteristic, direct product factor, Sylow
296C131#2358711yescharacteristic, direct product factor, Sylow
297#3460C2×C13111yescharacteristic, complemented
298C4×AGL(1,ℤ/8)C2×C13112yescomplemented
299C4×#127C2×C13111yescharacteristic, complemented
300#2060C2×C13111yescharacteristic, complemented
301#2039C2×C13111yescharacteristic, complemented
302#2037C2×C13112yescomplemented
303#2027C2×C13111yescharacteristic, complemented
304#2006C2×C13111yescharacteristic, complemented
305#2002C2×C13112yescomplemented
306C4×#104C2×C13112yescomplemented
307C4×#100C2×C13111yescharacteristic, complemented
308C2×AGL(1,ℤ/8)C22×C13112yes—
309#544C22×C13111yescharacteristic
310#542—22no—
311#540—22no—
312#538—22no—
313#537C22×C13111yescharacteristic
314#535C22×C13112yes—
315#532—22no—
316C2×#127C22×C13111yescharacteristic
317#529—22no—
318#525—22no—
319C4×#41C22×C13112yes—
320C2×C4×D4—22no—
321C2×C4×D4C22×C13111yescharacteristic
322C2×C4×D4C22×C13111yescharacteristic
323#442—22no—
324#440—22no—
325C4×SD16—22no—
326C4×D8—22no—
327#428C22×C13112yes—
328C2×#104C22×C13112yes—
329C2×#104C22×C13112yes—
330#418C22×C13112yes—
331#417C22×C13112yes—
332C2×#100C22×C13112yes—
333C4×M16C22×C13112yes—
334#390—22no—
335#390C22×C13111yescharacteristic
336#390C22×C13111yescharacteristic
337#384C22×C13111yescharacteristic
338C43C22×C13111yescharacteristic
339#343C22×C13111yescharacteristic
340#343C22×C13111yescharacteristic
341#339C22×C13112yes—
342#339C22×C13112yes—
343C2×#41—22no—
344C2×#41C23×C13112yes—
345C22×D4—22no—
346C22×D4C23×C13111yescharacteristic
347C22×D4C23×C13111yescharacteristic
348C23×C4—21no—
349C23×C4D4×C13112yes—
350AGL(1,ℤ/8)—24no—
351AGL(1,ℤ/8)—24no—
352C2×SD16—22no—
353C2×D8—22no—
354C2×M16C23×C13112yes—
355C2×M16C23×C13112yes—
356C4⋊Q8—22no—
357#127—22no—
358#127—22no—
359#127—22no—
360#126—24no—
361#125—22no—
362#124—24no—
363#124—22no—
364#123—24no—
365#123—24no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369#121—22no—
370#121—24no—
371#121—22no—
372#121—22no—
373#121—22no—
374#121—22no—
375#120—24no—
376C4×Q8D4×C13112yescomplemented
377C4×Q8D4×C13112yescomplemented
378C4×D4—24no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—48no—
386C4×D4D4×C13112yescomplemented
387C4×D4D4×C13112yescomplemented
388#117—22no—
389#117—22no—
390#117C23×C13112yes—
391C2×C4⋊C4—22no—
392C2×C4⋊C4C23×C13111yescharacteristic
393C2×C4⋊C4C23×C13111yescharacteristic
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4D4×C13112yes—
398C2×C42—21no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42C23×C13111yescharacteristic
402C2×C42C23×C13111yescharacteristic
403C2×C42C23×C13111yescharacteristic
404#107—22no—
405#106—22no—
406#104—24no—
407#104—24no—
408#103—22no—
409#102—22no—
410#102—22no—
411#102—22no—
412#100—24no—
413#97—22no—
414C4×C8—22no—
415C24—21no—
416C24C2×D4×C13112yes—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—84no—
422C2×Q8—22no—
423C2×Q8C2×D4×C13112yes—
424C2×D4—28no—
425C2×D4—22no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4C2×D4×C13112yes—
439C2×D4#41×C13112yescomplemented
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2×D4×C13111yescharacteristic
453C22×C4C2×D4×C13112yes—
454C22×C4C2×D4×C13111yescharacteristic
455C22×C4C24×C13111yescharacteristic
456SD16—28no—
457D8—28no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16#41×C13114yescomplemented
462C2×C8—22no—
463C2×C8—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—44no—
472C4⋊C4C2×D4×C13112yes—
473C4⋊C4C2×D4×C13112yes—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—22no—
478C22⋊C4—24no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—44no—
482C22⋊C4—44no—
483C22⋊C4—42no—
484C42—24no—
485C42—22no—
486C42—22no—
487C42—22no—
488C42—21no—
489C42—22no—
490C42—42no—
491C42C2×D4×C13112yes—
492C42C2×D4×C13112yes—
493C42#41×C13112yescomplemented
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—41no—
504C23—41no—
505C23C22×D4×C13111yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—82no—
509D4—22no—
510D4—24no—
511D4—22no—
512D4—416no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—42no—
518D4—82no—
519D4—84no—
520D4—84no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—41no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4#120×C13112yes—
545C2×C4#120×C13111yescharacteristic
546C2×C4#120×C13111yescharacteristic
547C2×C4C22×D4×C13112yes—
548C2×C4C2×#41×C13111yescharacteristic
549C2×C4C2×#41×C13112yes—
550C2×C4C2×#41×C13111yescharacteristic
551C8—24no—
552C8—42no—
553C22—21no—
554C22—21no—
555C22—44no—
556C22—44no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—82no—
565C22—82no—
566C22—81no—
567C22—81no—
568C22C2×#120×C13111yescharacteristic
569C22#525×C13111yescharacteristic
570C22#532×C13111yescharacteristic
571C4—24no—
572C4—21no—
573C4—22no—
574C4—42no—
575C4—42no—
576C4—42no—
577C4—42no—
578C4—42no—
579C4—81no—
580C4#453×C13112yes—
581C4#525×C13112yes—
582C4#532×C13112yes—
583C2—21no—
584C2—21no—
585C2—82no—
586C2—82no—
587C2—82no—
588C2#2388×C13111yescharacteristic
589C2C2×#453×C13111yescharacteristic
590C2#3018×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#120
commutator, Frattini, cosocleC22×C4C24×C131
socleC22×C131C2×#120
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3460×C131C2semidirect
2. C4×AGL(1,ℤ/8)×C131C2semidirect
3. C4×#127×C131C2semidirect
4. #2060×C131C2semidirect
5. #2039×C131C2semidirect
6. #2037×C131C2semidirect
7. #2027×C131C2semidirect
8. #2006×C131C2semidirect
9. #2002×C131C2semidirect
10. C4×#104×C131C2semidirect
11. C4×#100×C131C2semidirect
80. C4×Q8×C131D4semidirect
81. C4×Q8×C131D4semidirect
90. C4×D4×C131D4semidirect
91. C4×D4×C131D4semidirect
143. C2×D4×C131#41semidirect
165. M16×C131#41semidirect
197. C42×C131#41semidirect
295. #23587C131direct (N × H)
296. C131#23587direct (N × H)
297. #3460C2×C131semidirect
298. C4×AGL(1,ℤ/8)C2×C131semidirect
299. C4×#127C2×C131semidirect
300. #2060C2×C131semidirect
301. #2039C2×C131semidirect
302. #2037C2×C131semidirect
303. #2027C2×C131semidirect
304. #2006C2×C131semidirect
305. #2002C2×C131semidirect
306. C4×#104C2×C131semidirect
307. C4×#100C2×C131semidirect
376. C4×Q8D4×C131semidirect
377. C4×Q8D4×C131semidirect
386. C4×D4D4×C131semidirect
387. C4×D4D4×C131semidirect
439. C2×D4#41×C131semidirect
461. M16#41×C131semidirect
493. C42#41×C131semidirect

Maximal subgroups

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

subgroupindex
#3460×C1312
C4×AGL(1,ℤ/8)×C1312
C4×#127×C1312
#2060×C1312
#2039×C1312
#2037×C1312
#2027×C1312
#2006×C1312
#2002×C1312
C4×#104×C1312
C4×#100×C1312
#23587131