Finite Group Databasebeta

← C131×#29612 #45715496

Subgroups — C131×#29612 #45715496

Order 33536.

1464 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C131C211yesmaximal, characteristic
2#3095×C131C211yesmaximal, characteristic, complemented
3#3007×C131C211yesmaximal, characteristic, complemented
4#2435×C131C211yesmaximal, characteristic, complemented
5#2037×C131C214yesmaximal, complemented
6#2004×C131C214yesmaximal, complemented
7#1826×C131C211yesmaximal, characteristic, complemented
8#1789×C131C211yesmaximal, characteristic, complemented
9#1783×C131C211yesmaximal, characteristic, complemented
10C22×#41×C131C2211yescharacteristic
11C23×D4×C131C2211yescharacteristic
12C2×#137×C131C2212yescomplemented
13#535×C131—22no—
14#535×C131—22no—
15#535×C131—22no—
16#535×C131C2214yes—
17C2×#127×C131—21no—
18C2×#124×C131—21no—
19C2×#124×C131C2212yescomplemented
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×#121×C131—21no—
22C2×#121×C131—21no—
23C2×#120×C131—22no—
24C2×#117×C131C2211yescharacteristic
25#485×C131—22no—
26#484×C131—21no—
27#483×C131—21no—
28#452×C131—22no—
29#451×C131—21no—
30#450×C131—21no—
31#428×C131C2212yescomplemented
32C2×#104×C131C2214yescomplemented
33#419×C131C2212yescomplemented
34#417×C131C2212yescomplemented
35C2×#100×C131C2214yescomplemented
36#407×C131C2211yescharacteristic
37#407×C131C2211yescharacteristic
38#394×C131—22no—
39#390×C131C2212yescomplemented
40#379×C131—22no—
41C4×C22⋊C4×C131C2211yescharacteristic
42#339×C131C2214yescomplemented
43C25×C131D412yes—
44C2×#41×C131—21no—
45C2×#41×C131—21no—
46C2×#41×C131—44no—
47C2×#41×C131D412yes—
48C2×#41×C131C2312yes—
49C22×Q8×C131D411yescharacteristic
50C22×Q8×C131C2311yescharacteristic
51C22×D4×C131—21no—
52C22×D4×C131—22no—
53C22×D4×C131—22no—
54C22×D4×C131—21no—
55C22×D4×C131—21no—
56C22×D4×C131—21no—
57C22×D4×C131—21no—
58C22×D4×C131—44no—
59C22×D4×C131D412yes—
60C22×D4×C131D411yescharacteristic
61C22×D4×C131C2312yes—
62C23×C4×C131—21no—
63C23×C4×C131C2311yescharacteristic
64#137×C131—44no—
65C2×Q16×C131—22no—
66C2×SD16×C131—22no—
67C2×M16×C131C2312yes—
68C2×M16×C131C2312yes—
69#127×C131—24no—
70#127×C131—24no—
71#124×C131—24no—
72#124×C131—24no—
73#124×C131—44no—
74C22⋊Q8×C131—21no—
75C22⋊Q8×C131—21no—
76C22⋊Q8×C131—21no—
77C22⋊Q8×C131—21no—
78#121×C131—24no—
79#121×C131—24no—
80#121×C131—24no—
81#121×C131—24no—
82#120×C131—28no—
83#120×C131—28no—
84#117×C131—21no—
85#117×C131—21no—
86#117×C131D412yes—
87#117×C131C2312yes—
88C2×C4⋊C4×C131—21no—
89C2×C4⋊C4×C131D411yescharacteristic
90C2×C4⋊C4×C131D411yescharacteristic
91C2×C4⋊C4×C131C2311yescharacteristic
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—22no—
94C2×C22⋊C4×C131—21no—
95C2×C22⋊C4×C131—24no—
96C2×C22⋊C4×C131—21no—
97C2×C22⋊C4×C131—21no—
98C2×C22⋊C4×C131—24no—
99C2×C42×C131—21no—
100C2×C42×C131C2312yes—
101#107×C131—22no—
102#106×C131—22no—
103#104×C131—44no—
104#103×C131—22no—
105#103×C131—22no—
106#103×C131—22no—
107#102×C131—22no—
108#100×C131—44no—
109C22⋊C8×C131—21no—
110C22⋊C8×C131—21no—
111C22⋊C8×C131—21no—
112C22⋊C8×C131—21no—
113#95×C131—21no—
114C24×C131—22no—
115C24×C131—21no—
116C24×C131—22no—
117C24×C131—44no—
118C24×C131—44no—
119C24×C131—82no—
120C24×C131C2×D411yescharacteristic
121C24×C131C2×D414yes—
122#41×C131—24no—
123#41×C131—24no—
124#41×C131—42no—
125#41×C131—42no—
126#41×C131—44no—
127#41×C131—44no—
128C2×Q8×C131—21no—
129C2×Q8×C131—21no—
130C2×Q8×C131—21no—
131C2×Q8×C131—24no—
132C2×Q8×C131—42no—
133C2×Q8×C131C2×D412yes—
134C2×D4×C131—22no—
135C2×D4×C131—22no—
136C2×D4×C131—28no—
137C2×D4×C131—28no—
138C2×D4×C131—22no—
139C2×D4×C131—22no—
140C2×D4×C131—21no—
141C2×D4×C131—22no—
142C2×D4×C131—22no—
143C2×D4×C131—24no—
144C2×D4×C131—24no—
145C2×D4×C131—42no—
146C2×D4×C131—44no—
147C2×D4×C131—44no—
148C2×D4×C131—44no—
149C2×D4×C131—44no—
150C2×D4×C131—44no—
151C2×D4×C131—44no—
152C2×D4×C131—84no—
153C2×D4×C131—84no—
154C2×D4×C131C2×D412yes—
155C22×C4×C131—24no—
156C22×C4×C131—21no—
157C22×C4×C131—21no—
158C22×C4×C131—21no—
159C22×C4×C131—22no—
160C22×C4×C131—22no—
161C22×C4×C131—22no—
162C22×C4×C131—21no—
163C22×C4×C131—21no—
164C22×C4×C131—44no—
165C22×C4×C131C2×D411yescharacteristic
166C22×C4×C131C2×D411yescharacteristic
167C22×C4×C131C2×D411yescharacteristic
168C22×C4×C131C2×D411yescharacteristic
169C22×C4×C131C2×D411yescharacteristic
170C22×C4×C131C2411yescharacteristic
171Q16×C131—44no—
172SD16×C131—44no—
173M16×C131—24no—
174M16×C131—24no—
175C2×C8×C131—22no—
176C2×C8×C131—22no—
177C4⋊C4×C131—21no—
178C4⋊C4×C131—21no—
179C4⋊C4×C131—21no—
180C4⋊C4×C131—21no—
181C4⋊C4×C131—41no—
182C4⋊C4×C131—41no—
183C4⋊C4×C131C2×D412yes—
184C4⋊C4×C131C2×D412yes—
185C22⋊C4×C131—28no—
186C22⋊C4×C131—28no—
187C22⋊C4×C131—22no—
188C22⋊C4×C131—22no—
189C22⋊C4×C131—42no—
190C22⋊C4×C131—48no—
191C22⋊C4×C131—41no—
192C22⋊C4×C131—41no—
193C22⋊C4×C131—84no—
194C42×C131—22no—
195C42×C131—22no—
196C42×C131—24no—
197C23×C131—22no—
198C23×C131—22no—
199C23×C131—24no—
200C23×C131—22no—
201C23×C131—24no—
202C23×C131—24no—
203C23×C131—41no—
204C23×C131—44no—
205C23×C131—44no—
206C23×C131—42no—
207C23×C131—44no—
208C23×C131—44no—
209C23×C131—42no—
210C23×C131—44no—
211C23×C131—42no—
212C23×C131—44no—
213C23×C131—82no—
214C23×C131—82no—
215C23×C131—816no—
216C23×C131#12011yescharacteristic
217C23×C131#12011yescharacteristic
218C23×C131C22×D411yescharacteristic
219Q8×C131—22no—
220Q8×C131—22no—
221Q8×C131—42no—
222Q8×C131—42no—
223Q8×C131—42no—
224D4×C131—22no—
225D4×C131—22no—
226D4×C131—44no—
227D4×C131—44no—
228D4×C131—42no—
229D4×C131—44no—
230D4×C131—44no—
231D4×C131—44no—
232D4×C131—44no—
233D4×C131—88no—
234D4×C131—88no—
235C2×C4×C131—22no—
236C2×C4×C131—22no—
237C2×C4×C131—22no—
238C2×C4×C131—22no—
239C2×C4×C131—22no—
240C2×C4×C131—22no—
241C2×C4×C131—22no—
242C2×C4×C131—22no—
243C2×C4×C131—44no—
244C2×C4×C131—42no—
245C2×C4×C131—42no—
246C2×C4×C131—42no—
247C2×C4×C131—44no—
248C2×C4×C131—42no—
249C2×C4×C131—42no—
250C2×C4×C131—42no—
251C2×C4×C131—41no—
252C2×C4×C131—41no—
253C2×C4×C131—42no—
254C2×C4×C131—42no—
255C2×C4×C131#12011yescharacteristic
256C2×C4×C131#12011yescharacteristic
257C2×C4×C131C22×D411yescharacteristic
258C2×C4×C131C22×D411yescharacteristic
259C2×C4×C131H(5,𝔽2)14yes—
260C8×C131—42no—
261C8×C131—42no—
262C22×C131—21no—
263C22×C131—21no—
264C22×C131—21no—
265C22×C131—21no—
266C22×C131—21no—
267C22×C131—21no—
268C22×C131—21no—
269C22×C131—44no—
270C22×C131—48no—
271C22×C131—42no—
272C22×C131—44no—
273C22×C131—42no—
274C22×C131—44no—
275C22×C131—42no—
276C22×C131—44no—
277C22×C131—84no—
278C22×C131—84no—
279C22×C131—88no—
280C22×C131—88no—
281C22×C131#45512yes—
282C22×C131C2×#12011yescharacteristic
283C22×C131#53412yes—
284C4×C131—21no—
285C4×C131—21no—
286C4×C131—42no—
287C4×C131—42no—
288C4×C131—42no—
289C4×C131—82no—
290C4×C131—81no—
291C4×C131—81no—
292C4×C131#53412yes—
293C4×C131#53512yes—
294C2×C131—22no—
295C2×C131—22no—
296C2×C131—41no—
297C2×C131—84no—
298C2×C131—82no—
299C2×C131#261311yescharacteristic
300C2×C131C2×#45511yescharacteristic
301C2×C131#301911yescharacteristic
302#29612C13111yesmaximal, characteristic, direct product factor, Sylow
303C131#2961211yescharacteristic, direct product factor, Sylow
304C2×#535C2×C13111yescharacteristic
305#3095C2×C13111yescharacteristic, complemented
306#3007C2×C13111yescharacteristic, complemented
307#2435C2×C13111yescharacteristic, complemented
308#2037C2×C13114yescomplemented
309#2004C2×C13114yescomplemented
310#1826C2×C13111yescharacteristic, complemented
311#1789C2×C13111yescharacteristic, complemented
312#1783C2×C13111yescharacteristic, complemented
313C22×#41C22×C13111yescharacteristic
314C23×D4C22×C13111yescharacteristic
315C2×#137C22×C13112yescomplemented
316#535—22no—
317#535—22no—
318#535—22no—
319#535C22×C13114yes—
320C2×#127—21no—
321C2×#124—21no—
322C2×#124C22×C13112yescomplemented
323C2×C22⋊Q8C22×C13111yescharacteristic
324C2×#121—21no—
325C2×#121—21no—
326C2×#120—22no—
327C2×#117C22×C13111yescharacteristic
328#485—22no—
329#484—21no—
330#483—21no—
331#452—22no—
332#451—21no—
333#450—21no—
334#428C22×C13112yescomplemented
335C2×#104C22×C13114yescomplemented
336#419C22×C13112yescomplemented
337#417C22×C13112yescomplemented
338C2×#100C22×C13114yescomplemented
339#407C22×C13111yescharacteristic
340#407C22×C13111yescharacteristic
341#394—22no—
342#390C22×C13112yescomplemented
343#379—22no—
344C4×C22⋊C4C22×C13111yescharacteristic
345#339C22×C13114yescomplemented
346C25D4×C13112yes—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—44no—
350C2×#41D4×C13112yes—
351C2×#41C23×C13112yes—
352C22×Q8D4×C13111yescharacteristic
353C22×Q8C23×C13111yescharacteristic
354C22×D4—21no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—44no—
362C22×D4D4×C13112yes—
363C22×D4D4×C13111yescharacteristic
364C22×D4C23×C13112yes—
365C23×C4—21no—
366C23×C4C23×C13111yescharacteristic
367#137—44no—
368C2×Q16—22no—
369C2×SD16—22no—
370C2×M16C23×C13112yes—
371C2×M16C23×C13112yes—
372#127—24no—
373#127—24no—
374#124—24no—
375#124—24no—
376#124—44no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381#121—24no—
382#121—24no—
383#121—24no—
384#121—24no—
385#120—28no—
386#120—28no—
387#117—21no—
388#117—21no—
389#117D4×C13112yes—
390#117C23×C13112yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4D4×C13111yescharacteristic
393C2×C4⋊C4D4×C13111yescharacteristic
394C2×C4⋊C4C23×C13111yescharacteristic
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—24no—
402C2×C42—21no—
403C2×C42C23×C13112yes—
404#107—22no—
405#106—22no—
406#104—44no—
407#103—22no—
408#103—22no—
409#103—22no—
410#102—22no—
411#100—44no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416#95—21no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—44no—
421C24—44no—
422C24—82no—
423C24C2×D4×C13111yescharacteristic
424C24C2×D4×C13114yes—
425#41—24no—
426#41—24no—
427#41—42no—
428#41—42no—
429#41—44no—
430#41—44no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—24no—
435C2×Q8—42no—
436C2×Q8C2×D4×C13112yes—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—24no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—84no—
456C2×D4—84no—
457C2×D4C2×D4×C13112yes—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—44no—
468C22×C4C2×D4×C13111yescharacteristic
469C22×C4C2×D4×C13111yescharacteristic
470C22×C4C2×D4×C13111yescharacteristic
471C22×C4C2×D4×C13111yescharacteristic
472C22×C4C2×D4×C13111yescharacteristic
473C22×C4C24×C13111yescharacteristic
474Q16—44no—
475SD16—44no—
476M16—24no—
477M16—24no—
478C2×C8—22no—
479C2×C8—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C13112yes—
487C4⋊C4C2×D4×C13112yes—
488C22⋊C4—28no—
489C22⋊C4—28no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—42no—
493C22⋊C4—48no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—84no—
497C42—22no—
498C42—22no—
499C42—24no—
500C23—22no—
501C23—22no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—41no—
507C23—44no—
508C23—44no—
509C23—42no—
510C23—44no—
511C23—44no—
512C23—42no—
513C23—44no—
514C23—42no—
515C23—44no—
516C23—82no—
517C23—82no—
518C23—816no—
519C23#120×C13111yescharacteristic
520C23#120×C13111yescharacteristic
521C23C22×D4×C13111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—42no—
525Q8—42no—
526Q8—42no—
527D4—22no—
528D4—22no—
529D4—44no—
530D4—44no—
531D4—42no—
532D4—44no—
533D4—44no—
534D4—44no—
535D4—44no—
536D4—88no—
537D4—88no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—44no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4#120×C13111yescharacteristic
559C2×C4#120×C13111yescharacteristic
560C2×C4C22×D4×C13111yescharacteristic
561C2×C4C22×D4×C13111yescharacteristic
562C2×C4H(5,𝔽2)×C13114yes—
563C8—42no—
564C8—42no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—44no—
573C22—48no—
574C22—42no—
575C22—44no—
576C22—42no—
577C22—44no—
578C22—42no—
579C22—44no—
580C22—84no—
581C22—88no—
582C22—84no—
583C22—88no—
584C22#455×C13112yes—
585C22C2×#120×C13111yescharacteristic
586C22#534×C13112yes—
587C4—21no—
588C4—21no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—82no—
593C4—81no—
594C4—81no—
595C4#534×C13112yes—
596C4#535×C13112yes—
597C2—22no—
598C2—22no—
599C2—41no—
600C2—84no—
601C2—82no—
602C2#2613×C13111yescharacteristic
603C2C2×#455×C13111yescharacteristic
604C2#3019×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#535×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3095×C131C2semidirect
3. #3007×C131C2semidirect
4. #2435×C131C2semidirect
5. #2037×C131C2semidirect
6. #2004×C131C2semidirect
7. #1826×C131C2semidirect
8. #1789×C131C2semidirect
9. #1783×C131C2semidirect
12. C2×#137×C131C22semidirect
19. C2×#124×C131C22semidirect
31. #428×C131C22semidirect
32. C2×#104×C131C22semidirect
33. #419×C131C22semidirect
34. #417×C131C22semidirect
35. C2×#100×C131C22semidirect
39. #390×C131C22semidirect
42. #339×C131C22semidirect
302. #29612C131direct (N × H)
303. C131#29612direct (N × H)
305. #3095C2×C131semidirect
306. #3007C2×C131semidirect
307. #2435C2×C131semidirect
308. #2037C2×C131semidirect
309. #2004C2×C131semidirect
310. #1826C2×C131semidirect
311. #1789C2×C131semidirect
312. #1783C2×C131semidirect
315. C2×#137C22×C131semidirect
322. C2×#124C22×C131semidirect
334. #428C22×C131semidirect
335. C2×#104C22×C131semidirect
336. #419C22×C131semidirect
337. #417C22×C131semidirect
338. C2×#100C22×C131semidirect
342. #390C22×C131semidirect
345. #339C22×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1312
#3095×C1312
#3007×C1312
#2435×C1312
#2037×C1312
#2004×C1312
#1826×C1312
#1789×C1312
#1783×C1312
#29612131