Finite Group Databasebeta

← C131×#25660 #45711544

Subgroups — C131×#25660 #45711544

Order 33536.

1092 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C131C211yesmaximal, characteristic
2C2×#489×C131C211yesmaximal, characteristic, complemented
3C2×#474×C131C211yesmaximal, characteristic, complemented
4#2567×C131C211yesmaximal, characteristic, complemented
5#2042×C131C212yesmaximal, complemented
6#2041×C131C212yesmaximal
7#1985×C131C211yesmaximal, characteristic, complemented
8#1983×C131C211yesmaximal, characteristic, complemented
9#1863×C131C212yesmaximal, complemented
10#1862×C131C212yesmaximal, complemented
11#1762×C131C211yesmaximal, characteristic, complemented
12#559×C131—24no—
13#559×C131—24no—
14C2×C4⋊Q8×C131C2211yescharacteristic
15C2×#127×C131C2211yescharacteristic
16C2×#124×C131—21no—
17C2×#124×C131C2211yescharacteristic
18C2×#124×C131C2211yescharacteristic
19C2×#123×C131—21no—
20C2×#123×C131—21no—
21C2×C4×Q8×C131C2211yescharacteristic
22C2×C4×Q8×C131C2211yescharacteristic
23C2×C4×D4×C131—21no—
24C2×C4×D4×C131C2211yescharacteristic
25C2×C4×D4×C131C2211yescharacteristic
26#489×C131—24no—
27#474×C131—24no—
28C2×#107×C131C2212yes—
29C2×C4⋊C8×C131C2211yescharacteristic
30C2×#103×C131C2212yes—
31C2×#103×C131C2212yes—
32C2×#102×C131C2212yes—
33C2×#102×C131C2212yes—
34C2×#102×C131C2212yes—
35C2×#102×C131C2212yes—
36C2×#97×C131C2211yescharacteristic
37#395×C131—21no—
38#395×C131—21no—
39#391×C131—21no—
40#389×C131C2212yes—
41#389×C131C2212yes—
42#384×C131—21no—
43C4×C4⋊C4×C131C2211yescharacteristic
44#340×C131C2212yes—
45#336×C131C2212yes—
46#336×C131C2212yes—
47C22×Q8×C131—21no—
48C22×Q8×C131D411yescharacteristic
49C22×Q8×C131C2311yescharacteristic
50C22×D4×C131—21no—
51C22×D4×C131—21no—
52C22×D4×C131C2311yescharacteristic
53C22×D4×C131C2311yescharacteristic
54C23×C4×C131—21no—
55C23×C4×C131—21no—
56C22×C8×C131C2312yes—
57C22×C8×C131C2312yes—
58C4⋊Q8×C131—22no—
59C4⋊Q8×C131—22no—
60#127×C131—22no—
61#127×C131—22no—
62#124×C131—28no—
63#124×C131—22no—
64#124×C131—22no—
65#124×C131—22no—
66#124×C131D414yes—
67#123×C131—28no—
68#123×C131—28no—
69C4×Q8×C131—22no—
70C4×Q8×C131—22no—
71C4×Q8×C131—22no—
72C4×Q8×C131—22no—
73C4×D4×C131—28no—
74C4×D4×C131—22no—
75C4×D4×C131—22no—
76C4×D4×C131—22no—
77C4×D4×C131D414yes—
78C2×C4⋊C4×C131—21no—
79C2×C4⋊C4×C131—21no—
80C2×C4⋊C4×C131—22no—
81C2×C4⋊C4×C131—22no—
82C2×C4⋊C4×C131D411yescharacteristic
83C2×C4⋊C4×C131D411yescharacteristic
84C2×C4⋊C4×C131D411yescharacteristic
85C2×C4⋊C4×C131C2312yes—
86C2×C4⋊C4×C131C2311yescharacteristic
87C2×C4⋊C4×C131C2312yes—
88C2×C22⋊C4×C131—21no—
89C2×C22⋊C4×C131—21no—
90C2×C22⋊C4×C131—21no—
91C2×C22⋊C4×C131—21no—
92C2×C22⋊C4×C131—21no—
93C2×C22⋊C4×C131—21no—
94C2×C42×C131—21no—
95C2×C42×C131—21no—
96C2×C42×C131C2311yescharacteristic
97C2×C42×C131C2311yescharacteristic
98C2×C42×C131C2311yescharacteristic
99#107×C131—24no—
100C4⋊C8×C131—22no—
101#103×C131—24no—
102#103×C131—24no—
103#102×C131—24no—
104#102×C131—24no—
105#102×C131—24no—
106#102×C131—24no—
107#97×C131—22no—
108#95×C131—22no—
109#95×C131—22no—
110#95×C131—21no—
111C24×C131—21no—
112C24×C131—21no—
113C2×Q8×C131—22no—
114C2×Q8×C131—22no—
115C2×Q8×C131—21no—
116C2×Q8×C131—22no—
117C2×Q8×C131—22no—
118C2×Q8×C131—41no—
119C2×Q8×C131—42no—
120C2×Q8×C131—82no—
121C2×Q8×C131C2×D412yes—
122C2×D4×C131—24no—
123C2×D4×C131—24no—
124C2×D4×C131—21no—
125C2×D4×C131—21no—
126C2×D4×C131—22no—
127C2×D4×C131—22no—
128C2×D4×C131—22no—
129C2×D4×C131—22no—
130C2×D4×C131—42no—
131C2×D4×C131—42no—
132C2×D4×C131—82no—
133C2×D4×C131C2×D412yes—
134C2×D4×C131C2×D412yes—
135C22×C4×C131—22no—
136C22×C4×C131—21no—
137C22×C4×C131—21no—
138C22×C4×C131—24no—
139C22×C4×C131—24no—
140C22×C4×C131—22no—
141C22×C4×C131—82no—
142C22×C4×C131—82no—
143C22×C4×C131C2×D411yescharacteristic
144C22×C4×C131C2×D411yescharacteristic
145C22×C4×C131C2×D411yescharacteristic
146C22×C4×C131C2×D411yescharacteristic
147C22×C4×C131C2×D411yescharacteristic
148C22×C4×C131C2×D411yescharacteristic
149C22×C4×C131C2411yescharacteristic
150C2×C8×C131—22no—
151C2×C8×C131—22no—
152C2×C8×C131—22no—
153C2×C8×C131—22no—
154C2×C8×C131—22no—
155C2×C8×C131—22no—
156C4⋊C4×C131—24no—
157C4⋊C4×C131—22no—
158C4⋊C4×C131—22no—
159C4⋊C4×C131—22no—
160C4⋊C4×C131—21no—
161C4⋊C4×C131—22no—
162C4⋊C4×C131—22no—
163C4⋊C4×C131—22no—
164C4⋊C4×C131—42no—
165C4⋊C4×C131—82no—
166C4⋊C4×C131—82no—
167C4⋊C4×C131C2×D412yes—
168C4⋊C4×C131#4114yes—
169C22⋊C4×C131—24no—
170C22⋊C4×C131—24no—
171C22⋊C4×C131—24no—
172C22⋊C4×C131—24no—
173C22⋊C4×C131—24no—
174C22⋊C4×C131—24no—
175C42×C131—24no—
176C42×C131—21no—
177C42×C131—21no—
178C42×C131—21no—
179C42×C131—21no—
180C42×C131—42no—
181C42×C131C2×D412yes—
182C42×C131C2×D412yes—
183C23×C131—22no—
184C23×C131—22no—
185C23×C131—42no—
186C23×C131—42no—
187C23×C131—41no—
188C23×C131—41no—
189C23×C131—41no—
190C23×C131—41no—
191C23×C131—42no—
192C23×C131—42no—
193C23×C131C22×D411yescharacteristic
194Q8×C131—24no—
195Q8×C131—44no—
196Q8×C131—41no—
197Q8×C131—41no—
198Q8×C131—84no—
199D4×C131—22no—
200D4×C131—22no—
201D4×C131—24no—
202D4×C131—48no—
203D4×C131—41no—
204D4×C131—41no—
205D4×C131—42no—
206D4×C131—84no—
207C2×C4×C131—21no—
208C2×C4×C131—21no—
209C2×C4×C131—21no—
210C2×C4×C131—21no—
211C2×C4×C131—22no—
212C2×C4×C131—22no—
213C2×C4×C131—21no—
214C2×C4×C131—21no—
215C2×C4×C131—22no—
216C2×C4×C131—21no—
217C2×C4×C131—24no—
218C2×C4×C131—21no—
219C2×C4×C131—21no—
220C2×C4×C131—22no—
221C2×C4×C131—22no—
222C2×C4×C131—42no—
223C2×C4×C131—42no—
224C2×C4×C131—42no—
225C2×C4×C131—42no—
226C2×C4×C131—42no—
227C2×C4×C131—42no—
228C2×C4×C131—42no—
229C2×C4×C131—84no—
230C2×C4×C131—84no—
231C2×C4×C131#12012yes—
232C2×C4×C131#12012yes—
233C2×C4×C131#13712yes—
234C2×C4×C131C22×D411yescharacteristic
235C2×C4×C131C22×D411yescharacteristic
236C2×C4×C131C2×#4112yes—
237C2×C4×C1312−1+412yes—
238C8×C131—42no—
239C8×C131—42no—
240C22×C131—42no—
241C22×C131—42no—
242C22×C131—42no—
243C22×C131—42no—
244C22×C131—42no—
245C22×C131—42no—
246C22×C131—82no—
247C22×C131—82no—
248C22×C131—82no—
249C22×C131—82no—
250C22×C131C2×#12011yescharacteristic
251C22×C131#54812yes—
252C22×C131C2×#13711yescharacteristic
253C22×C131#57511yescharacteristic
254C22×C131#57612yes—
255C4×C131—22no—
256C4×C131—22no—
257C4×C131—22no—
258C4×C131—44no—
259C4×C131—42no—
260C4×C131—41no—
261C4×C131—41no—
262C4×C131—41no—
263C4×C131—42no—
264C4×C131—82no—
265C4×C131#53211yescharacteristic
266C4×C131#53611yescharacteristic
267C4×C131#54712yes—
268C2×C131—82no—
269C2×C131—82no—
270C2×C131#243211yescharacteristic
271C2×C131#300711yescharacteristic
272C2×C131#300811yescharacteristic
273C2×C131#337012yes—
274C2×C131#337512yes—
275#25660C13111yesmaximal, characteristic, direct product factor, Sylow
276C131#2566011yescharacteristic, direct product factor, Sylow
277C2×#559C2×C13111yescharacteristic
278C2×#489C2×C13111yescharacteristic, complemented
279C2×#474C2×C13111yescharacteristic, complemented
280#2567C2×C13111yescharacteristic, complemented
281#2042C2×C13112yescomplemented
282#2041C2×C13112yes—
283#1985C2×C13111yescharacteristic, complemented
284#1983C2×C13111yescharacteristic, complemented
285#1863C2×C13112yescomplemented
286#1862C2×C13112yescomplemented
287#1762C2×C13111yescharacteristic, complemented
288#559—24no—
289#559—24no—
290C2×C4⋊Q8C22×C13111yescharacteristic
291C2×#127C22×C13111yescharacteristic
292C2×#124—21no—
293C2×#124C22×C13111yescharacteristic
294C2×#124C22×C13111yescharacteristic
295C2×#123—21no—
296C2×#123—21no—
297C2×C4×Q8C22×C13111yescharacteristic
298C2×C4×Q8C22×C13111yescharacteristic
299C2×C4×D4—21no—
300C2×C4×D4C22×C13111yescharacteristic
301C2×C4×D4C22×C13111yescharacteristic
302#489—24no—
303#474—24no—
304C2×#107C22×C13112yes—
305C2×C4⋊C8C22×C13111yescharacteristic
306C2×#103C22×C13112yes—
307C2×#103C22×C13112yes—
308C2×#102C22×C13112yes—
309C2×#102C22×C13112yes—
310C2×#102C22×C13112yes—
311C2×#102C22×C13112yes—
312C2×#97C22×C13111yescharacteristic
313#395—21no—
314#395—21no—
315#391—21no—
316#389C22×C13112yes—
317#389C22×C13112yes—
318#384—21no—
319C4×C4⋊C4C22×C13111yescharacteristic
320#340C22×C13112yes—
321#336C22×C13112yes—
322#336C22×C13112yes—
323C22×Q8—21no—
324C22×Q8D4×C13111yescharacteristic
325C22×Q8C23×C13111yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4C23×C13111yescharacteristic
329C22×D4C23×C13111yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C22×C8C23×C13112yes—
333C22×C8C23×C13112yes—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336#127—22no—
337#127—22no—
338#124—28no—
339#124—22no—
340#124—22no—
341#124—22no—
342#124D4×C13114yes—
343#123—28no—
344#123—28no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—28no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4D4×C13114yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4D4×C13111yescharacteristic
359C2×C4⋊C4D4×C13111yescharacteristic
360C2×C4⋊C4D4×C13111yescharacteristic
361C2×C4⋊C4C23×C13112yes—
362C2×C4⋊C4C23×C13111yescharacteristic
363C2×C4⋊C4C23×C13112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C42—21no—
371C2×C42—21no—
372C2×C42C23×C13111yescharacteristic
373C2×C42C23×C13111yescharacteristic
374C2×C42C23×C13111yescharacteristic
375#107—24no—
376C4⋊C8—22no—
377#103—24no—
378#103—24no—
379#102—24no—
380#102—24no—
381#102—24no—
382#102—24no—
383#97—22no—
384#95—21no—
385#95—22no—
386#95—22no—
387C24—21no—
388C24—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—21no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—41no—
395C2×Q8—42no—
396C2×Q8—82no—
397C2×Q8C2×D4×C13112yes—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—82no—
409C2×D4C2×D4×C13112yes—
410C2×D4C2×D4×C13112yes—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4C2×D4×C13111yescharacteristic
420C22×C4C2×D4×C13111yescharacteristic
421C22×C4C2×D4×C13111yescharacteristic
422C22×C4C2×D4×C13111yescharacteristic
423C22×C4C2×D4×C13111yescharacteristic
424C22×C4C2×D4×C13111yescharacteristic
425C22×C4C24×C13111yescharacteristic
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C4⋊C4—24no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—42no—
441C4⋊C4—82no—
442C4⋊C4—82no—
443C4⋊C4C2×D4×C13112yes—
444C4⋊C4#41×C13114yes—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C42—24no—
452C42—21no—
453C42—21no—
454C42—21no—
455C42—21no—
456C42—42no—
457C42C2×D4×C13112yes—
458C42C2×D4×C13112yes—
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—42no—
468C23—42no—
469C23C22×D4×C13111yescharacteristic
470Q8—24no—
471Q8—44no—
472Q8—41no—
473Q8—41no—
474Q8—84no—
475D4—22no—
476D4—22no—
477D4—24no—
478D4—48no—
479D4—41no—
480D4—41no—
481D4—42no—
482D4—84no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—84no—
506C2×C4—84no—
507C2×C4#120×C13112yes—
508C2×C4#120×C13112yes—
509C2×C4#137×C13112yes—
510C2×C4C22×D4×C13111yescharacteristic
511C2×C4C22×D4×C13111yescharacteristic
512C2×C4C2×#41×C13112yes—
513C2×C42−1+4×C13112yes—
514C8—42no—
515C8—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22—82no—
526C22C2×#120×C13111yescharacteristic
527C22#548×C13112yes—
528C22C2×#137×C13111yescharacteristic
529C22#575×C13111yescharacteristic
530C22#576×C13112yes—
531C4—22no—
532C4—22no—
533C4—22no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—42no—
538C4—44no—
539C4—42no—
540C4—82no—
541C4#532×C13111yescharacteristic
542C4#536×C13111yescharacteristic
543C4#547×C13112yes—
544C2—82no—
545C2—82no—
546C2#2432×C13111yescharacteristic
547C2#3007×C13111yescharacteristic
548C2#3008×C13111yescharacteristic
549C2#3370×C13112yes—
550C2#3375×C13112yes—
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#127×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#489×C131C2semidirect
3. C2×#474×C131C2semidirect
4. #2567×C131C2semidirect
5. #2042×C131C2semidirect
7. #1985×C131C2semidirect
8. #1983×C131C2semidirect
9. #1863×C131C2semidirect
10. #1862×C131C2semidirect
11. #1762×C131C2semidirect
275. #25660C131direct (N × H)
276. C131#25660direct (N × H)
278. C2×#489C2×C131semidirect
279. C2×#474C2×C131semidirect
280. #2567C2×C131semidirect
281. #2042C2×C131semidirect
283. #1985C2×C131semidirect
284. #1983C2×C131semidirect
285. #1863C2×C131semidirect
286. #1862C2×C131semidirect
287. #1762C2×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1312
C2×#489×C1312
C2×#474×C1312
#2567×C1312
#2042×C1312
#2041×C1312
#1985×C1312
#1983×C1312
#1863×C1312
#1862×C1312
#1762×C1312
#25660131