Finite Group Databasebeta

← C131×#32986 #45718870

Subgroups — C131×#32986 #45718870

Order 33536.

1358 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C131C211yesmaximal, characteristic, complemented
2C2×#482×C131C211yesmaximal, characteristic, complemented
3C2×#480×C131C211yesmaximal, characteristic, complemented
4#2615×C131C211yesmaximal, characteristic
5#1875×C131C212yesmaximal, complemented
6#1874×C131C212yesmaximal, complemented
7#1854×C131C212yesmaximal, complemented
8#1852×C131C212yesmaximal, complemented
9#1825×C131C211yesmaximal, characteristic, complemented
10#1824×C131C211yesmaximal, characteristic, complemented
11#1780×C131C211yesmaximal, characteristic, complemented
12C22×#41×C131C2211yescharacteristic
13C2×#121×C131C2211yescharacteristic
14C2×#121×C131C2212yes—
15#520×C131—24no—
16#520×C131—24no—
17C2×C4×Q8×C131—21no—
18C2×C4×D4×C131—22no—
19C2×C4×D4×C131—21no—
20C2×#117×C131C2212yes—
21C2×#117×C131C2211yescharacteristic
22C22×C4⋊C4×C131C2212yes—
23C22×C4⋊C4×C131C2211yescharacteristic
24#482×C131—24no—
25#480×C131—24no—
26C2×#107×C131C2212yes—
27C2×#107×C131C2211yescharacteristic
28C2×#106×C131C2211yescharacteristic
29C2×#102×C131C2212yes—
30C2×#102×C131C2211yescharacteristic
31C2×#102×C131C2211yescharacteristic
32C2×C22⋊C8×C131C2211yescharacteristic
33C2×C22⋊C8×C131C2211yescharacteristic
34C2×C22⋊C8×C131C2212yes—
35C2×C22⋊C8×C131C2212yes—
36#393×C131—21no—
37#392×C131—21no—
38#392×C131—22no—
39#380×C131C2211yescharacteristic
40#380×C131C2212yes—
41#340×C131C2212yes—
42#340×C131C2212yes—
43#340×C131C2212yes—
44#340×C131C2212yes—
45C2×#41×C131—22no—
46C2×#41×C131—22no—
47C2×#41×C131—24no—
48C2×#41×C131—24no—
49C22×Q8×C131D411yescharacteristic
50C22×D4×C131—21no—
51C22×D4×C131—22no—
52C22×D4×C131D411yescharacteristic
53C22×D4×C131D412yes—
54C22×D4×C131C2311yescharacteristic
55C23×C4×C131—22no—
56C23×C4×C131—21no—
57C23×C4×C131C2311yescharacteristic
58C23×C4×C131C2312yes—
59C22×C8×C131C2311yescharacteristic
60C22×C8×C131C2312yes—
61C22×C8×C131C2311yescharacteristic
62#121×C131—22no—
63#121×C131—22no—
64#121×C131—24no—
65#121×C131—24no—
66C4×Q8×C131—28no—
67C4×D4×C131—216no—
68C4×D4×C131—28no—
69#117×C131—22no—
70#117×C131—24no—
71#117×C131—24no—
72#117×C131D414yescomplemented
73C2×C4⋊C4×C131—22no—
74C2×C4⋊C4×C131—21no—
75C2×C4⋊C4×C131—22no—
76C2×C4⋊C4×C131—24no—
77C2×C4⋊C4×C131—24no—
78C2×C4⋊C4×C131D414yescomplemented
79C2×C4⋊C4×C131C2311yescharacteristic
80C2×C4⋊C4×C131C2312yes—
81C2×C4⋊C4×C131C2311yescharacteristic
82C2×C4⋊C4×C131C2311yescharacteristic
83C2×C4⋊C4×C131C2312yes—
84C2×C22⋊C4×C131—22no—
85C2×C22⋊C4×C131—21no—
86C2×C22⋊C4×C131—21no—
87C2×C22⋊C4×C131—22no—
88C2×C22⋊C4×C131—21no—
89C2×C22⋊C4×C131—22no—
90C2×C42×C131—22no—
91C2×C42×C131—21no—
92#107×C131—24no—
93#107×C131—22no—
94#106×C131—22no—
95#102×C131—24no—
96#102×C131—22no—
97#102×C131—22no—
98C22⋊C8×C131—22no—
99C22⋊C8×C131—22no—
100C22⋊C8×C131—24no—
101C22⋊C8×C131—24no—
102#95×C131—21no—
103#95×C131—22no—
104C24×C131—21no—
105C24×C131C2×D411yescharacteristic
106C24×C131C2×D412yes—
107#41×C131—28no—
108#41×C131—28no—
109#41×C131—216no—
110C2×Q8×C131—22no—
111C2×Q8×C131—24no—
112C2×D4×C131—24no—
113C2×D4×C131—24no—
114C2×D4×C131—24no—
115C2×D4×C131—22no—
116C2×D4×C131—24no—
117C2×D4×C131—21no—
118C2×D4×C131—21no—
119C2×D4×C131—22no—
120C2×D4×C131—22no—
121C2×D4×C131—42no—
122C2×D4×C131—44no—
123C2×D4×C131—82no—
124C2×D4×C131—82no—
125C2×D4×C131—82no—
126C22×C4×C131—22no—
127C22×C4×C131—22no—
128C22×C4×C131—22no—
129C22×C4×C131—22no—
130C22×C4×C131—22no—
131C22×C4×C131—22no—
132C22×C4×C131—21no—
133C22×C4×C131—22no—
134C22×C4×C131—21no—
135C22×C4×C131—28no—
136C22×C4×C131—24no—
137C22×C4×C131—21no—
138C22×C4×C131—22no—
139C22×C4×C131—82no—
140C22×C4×C131—82no—
141C22×C4×C131—82no—
142C22×C4×C131C2×D411yescharacteristic
143C22×C4×C131C2×D412yes—
144C22×C4×C131C2×D412yes—
145C22×C4×C131C2×D412yes—
146C22×C4×C131#4114yes—
147C22×C4×C131#4114yes—
148C22×C4×C131C2411yescharacteristic
149C2×C8×C131—21no—
150C2×C8×C131—22no—
151C2×C8×C131—21no—
152C2×C8×C131—22no—
153C2×C8×C131—22no—
154C2×C8×C131—22no—
155C2×C8×C131—22no—
156C4⋊C4×C131—28no—
157C4⋊C4×C131—24no—
158C4⋊C4×C131—22no—
159C4⋊C4×C131—21no—
160C4⋊C4×C131—21no—
161C4⋊C4×C131—21no—
162C4⋊C4×C131—21no—
163C4⋊C4×C131—22no—
164C4⋊C4×C131—22no—
165C4⋊C4×C131C2×D412yes—
166C4⋊C4×C131C2×D412yes—
167C4⋊C4×C131C2×D414yes—
168C22⋊C4×C131—28no—
169C22⋊C4×C131—24no—
170C22⋊C4×C131—42no—
171C22⋊C4×C131—44no—
172C22⋊C4×C131—82no—
173C22⋊C4×C131—81no—
174C42×C131—28no—
175C42×C131—24no—
176C23×C131—22no—
177C23×C131—22no—
178C23×C131—22no—
179C23×C131—22no—
180C23×C131—22no—
181C23×C131—22no—
182C23×C131—21no—
183C23×C131—22no—
184C23×C131—22no—
185C23×C131—21no—
186C23×C131—41no—
187C23×C131—42no—
188C23×C131—42no—
189C23×C131—41no—
190C23×C131—41no—
191C23×C131#12012yes—
192C23×C131#12314yes—
193C23×C131C22×D411yescharacteristic
194Q8×C131—28no—
195D4×C131—28no—
196D4×C131—216no—
197D4×C131—42no—
198D4×C131—41no—
199D4×C131—41no—
200D4×C131—88no—
201D4×C131—84no—
202C2×C4×C131—22no—
203C2×C4×C131—22no—
204C2×C4×C131—22no—
205C2×C4×C131—22no—
206C2×C4×C131—22no—
207C2×C4×C131—24no—
208C2×C4×C131—24no—
209C2×C4×C131—24no—
210C2×C4×C131—24no—
211C2×C4×C131—24no—
212C2×C4×C131—22no—
213C2×C4×C131—24no—
214C2×C4×C131—22no—
215C2×C4×C131—42no—
216C2×C4×C131—42no—
217C2×C4×C131—42no—
218C2×C4×C131—41no—
219C2×C4×C131—41no—
220C2×C4×C131—41no—
221C2×C4×C131—42no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—42no—
225C2×C4×C131—84no—
226C2×C4×C131—88no—
227C2×C4×C131#12012yes—
228C2×C4×C131#12314yes—
229C2×C4×C131C22×D411yescharacteristic
230C2×C4×C131C22×D411yescharacteristic
231C2×C4×C131C2×#4112yes—
232C2×C4×C131C2×#4112yes—
233C8×C131—41no—
234C8×C131—42no—
235C8×C131—41no—
236C22×C131—24no—
237C22×C131—24no—
238C22×C131—22no—
239C22×C131—24no—
240C22×C131—22no—
241C22×C131—22no—
242C22×C131—42no—
243C22×C131—42no—
244C22×C131—42no—
245C22×C131—42no—
246C22×C131—42no—
247C22×C131—42no—
248C22×C131—82no—
249C22×C131—82no—
250C22×C131—81no—
251C22×C131—81no—
252C22×C131—81no—
253C22×C131C2×#12011yescharacteristic
254C22×C131C2×#12312yes—
255C22×C131#57612yes—
256C22×C131#57711yescharacteristic
257C22×C131#57811yescharacteristic
258C4×C131—22no—
259C4×C131—24no—
260C4×C131—44no—
261C4×C131—42no—
262C4×C131—42no—
263C4×C131—82no—
264C4×C131—81no—
265C4×C131#52511yescharacteristic
266C4×C131#52511yescharacteristic
267C4×C131#52512yes—
268C2×C131—44no—
269C2×C131—42no—
270C2×C131—161no—
271C2×C131#284911yescharacteristic
272C2×C131#300811yescharacteristic
273C2×C131#301311yescharacteristic
274C2×C131#309612yes—
275C2×C131#309812yes—
276#32986C13111yesmaximal, characteristic, direct product factor, Sylow
277C131#3298611yescharacteristic, direct product factor, Sylow
278C2×#520C2×C13111yescharacteristic, complemented
279C2×#482C2×C13111yescharacteristic, complemented
280C2×#480C2×C13111yescharacteristic, complemented
281#2615C2×C13111yescharacteristic
282#1875C2×C13112yescomplemented
283#1874C2×C13112yescomplemented
284#1854C2×C13112yescomplemented
285#1852C2×C13112yescomplemented
286#1825C2×C13111yescharacteristic, complemented
287#1824C2×C13111yescharacteristic, complemented
288#1780C2×C13111yescharacteristic, complemented
289C22×#41C22×C13111yescharacteristic
290C2×#121C22×C13111yescharacteristic
291C2×#121C22×C13112yes—
292#520—24no—
293#520—24no—
294C2×C4×Q8—21no—
295C2×C4×D4—22no—
296C2×C4×D4—21no—
297C2×#117C22×C13112yes—
298C2×#117C22×C13111yescharacteristic
299C22×C4⋊C4C22×C13112yes—
300C22×C4⋊C4C22×C13111yescharacteristic
301#482—24no—
302#480—24no—
303C2×#107C22×C13112yes—
304C2×#107C22×C13111yescharacteristic
305C2×#106C22×C13111yescharacteristic
306C2×#102C22×C13112yes—
307C2×#102C22×C13111yescharacteristic
308C2×#102C22×C13111yescharacteristic
309C2×C22⋊C8C22×C13111yescharacteristic
310C2×C22⋊C8C22×C13111yescharacteristic
311C2×C22⋊C8C22×C13112yes—
312C2×C22⋊C8C22×C13112yes—
313#393—21no—
314#392—21no—
315#392—22no—
316#380C22×C13111yescharacteristic
317#380C22×C13112yes—
318#340C22×C13112yes—
319#340C22×C13112yes—
320#340C22×C13112yes—
321#340C22×C13112yes—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—24no—
325C2×#41—24no—
326C22×Q8D4×C13111yescharacteristic
327C22×D4—21no—
328C22×D4—22no—
329C22×D4D4×C13111yescharacteristic
330C22×D4D4×C13112yes—
331C22×D4C23×C13111yescharacteristic
332C23×C4—22no—
333C23×C4—21no—
334C23×C4C23×C13111yescharacteristic
335C23×C4C23×C13112yes—
336C22×C8C23×C13111yescharacteristic
337C22×C8C23×C13111yescharacteristic
338C22×C8C23×C13112yes—
339#121—22no—
340#121—22no—
341#121—24no—
342#121—24no—
343C4×Q8—28no—
344C4×D4—216no—
345C4×D4—28no—
346#117—22no—
347#117—24no—
348#117—24no—
349#117D4×C13114yescomplemented
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4D4×C13114yescomplemented
356C2×C4⋊C4C23×C13112yes—
357C2×C4⋊C4C23×C13111yescharacteristic
358C2×C4⋊C4C23×C13111yescharacteristic
359C2×C4⋊C4C23×C13112yes—
360C2×C4⋊C4C23×C13111yescharacteristic
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C42—22no—
368C2×C42—21no—
369#107—24no—
370#107—22no—
371#106—22no—
372#102—24no—
373#102—22no—
374#102—22no—
375C22⋊C8—22no—
376C22⋊C8—22no—
377C22⋊C8—24no—
378C22⋊C8—24no—
379#95—21no—
380#95—22no—
381C24—21no—
382C24C2×D4×C13111yescharacteristic
383C24C2×D4×C13112yes—
384#41—28no—
385#41—28no—
386#41—216no—
387C2×Q8—22no—
388C2×Q8—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—22no—
393C2×D4—24no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—42no—
399C2×D4—44no—
400C2×D4—82no—
401C2×D4—82no—
402C2×D4—82no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—28no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—82no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4C2×D4×C13111yescharacteristic
420C22×C4C2×D4×C13112yes—
421C22×C4C2×D4×C13112yes—
422C22×C4C2×D4×C13112yes—
423C22×C4#41×C13114yes—
424C22×C4#41×C13114yes—
425C22×C4C24×C13111yescharacteristic
426C2×C8—21no—
427C2×C8—22no—
428C2×C8—21no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C4⋊C4—28no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4C2×D4×C13112yes—
443C4⋊C4C2×D4×C13112yes—
444C4⋊C4C2×D4×C13114yes—
445C22⋊C4—28no—
446C22⋊C4—24no—
447C22⋊C4—42no—
448C22⋊C4—44no—
449C22⋊C4—82no—
450C22⋊C4—81no—
451C42—28no—
452C42—24no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—22no—
459C23—21no—
460C23—22no—
461C23—21no—
462C23—22no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—41no—
467C23—41no—
468C23#120×C13112yes—
469C23#123×C13114yes—
470C23C22×D4×C13111yescharacteristic
471Q8—28no—
472D4—28no—
473D4—216no—
474D4—42no—
475D4—41no—
476D4—41no—
477D4—84no—
478D4—88no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—84no—
503C2×C4—88no—
504C2×C4#120×C13112yes—
505C2×C4#123×C13114yes—
506C2×C4C22×D4×C13111yescharacteristic
507C2×C4C22×D4×C13111yescharacteristic
508C2×C4C2×#41×C13112yes—
509C2×C4C2×#41×C13112yes—
510C8—41no—
511C8—42no—
512C8—41no—
513C22—22no—
514C22—22no—
515C22—24no—
516C22—24no—
517C22—22no—
518C22—24no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—81no—
526C22—81no—
527C22—82no—
528C22—82no—
529C22—81no—
530C22C2×#120×C13111yescharacteristic
531C22C2×#123×C13112yes—
532C22#576×C13112yes—
533C22#577×C13111yescharacteristic
534C22#578×C13111yescharacteristic
535C4—22no—
536C4—24no—
537C4—44no—
538C4—42no—
539C4—42no—
540C4—81no—
541C4—82no—
542C4#525×C13111yescharacteristic
543C4#525×C13111yescharacteristic
544C4#525×C13112yes—
545C2—42no—
546C2—44no—
547C2—161no—
548C2#2849×C13111yescharacteristic
549C2#3008×C13111yescharacteristic
550C2#3013×C13111yescharacteristic
551C2#3096×C13112yes—
552C2#3098×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#2615×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#520×C131C2semidirect
2. C2×#482×C131C2semidirect
3. C2×#480×C131C2semidirect
5. #1875×C131C2semidirect
6. #1874×C131C2semidirect
7. #1854×C131C2semidirect
8. #1852×C131C2semidirect
9. #1825×C131C2semidirect
10. #1824×C131C2semidirect
11. #1780×C131C2semidirect
72. #117×C131D4semidirect
78. C2×C4⋊C4×C131D4semidirect
276. #32986C131direct (N × H)
277. C131#32986direct (N × H)
278. C2×#520C2×C131semidirect
279. C2×#482C2×C131semidirect
280. C2×#480C2×C131semidirect
282. #1875C2×C131semidirect
283. #1874C2×C131semidirect
284. #1854C2×C131semidirect
285. #1852C2×C131semidirect
286. #1825C2×C131semidirect
287. #1824C2×C131semidirect
288. #1780C2×C131semidirect
349. #117D4×C131semidirect
355. C2×C4⋊C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#520×C1312
C2×#482×C1312
C2×#480×C1312
#2615×C1312
#1875×C1312
#1874×C1312
#1854×C1312
#1852×C1312
#1825×C1312
#1824×C1312
#1780×C1312
#32986131