Finite Group Databasebeta

← C131×#21867 #45707751

Subgroups — C131×#21867 #45707751

Order 33536.

1234 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#529×C131C211yesmaximal, characteristic
2C2×#432×C131C211yesmaximal, characteristic, complemented
3C2×#384×C131C211yesmaximal, characteristic, complemented
4#1992×C131C212yesmaximal, complemented
5#1959×C131C212yesmaximal, complemented
6#1874×C131C212yesmaximal
7#1872×C131C212yesmaximal, complemented
8#1803×C131C212yesmaximal, complemented
9#1802×C131C212yesmaximal, complemented
10#529×C131—24no—
11#529×C131C418yescomplemented
12C2×#126×C131—21no—
13C2×#125×C131C2211yescharacteristic
14C2×#124×C131C2211yescharacteristic
15C2×#123×C131—21no—
16C2×C22⋊Q8×C131C2211yescharacteristic
17C2×#121×C131C2211yescharacteristic
18C2×C4×Q8×C131C2211yescharacteristic
19C2×C4×D4×C131—21no—
20C2×C4×D4×C131C2211yescharacteristic
21C2×#117×C131—21no—
22C22×C4⋊C4×C131—21no—
23C22×C4⋊C4×C131—21no—
24C22×C4⋊C4×C131C2212yes—
25C22×C42×C131C2211yescharacteristic
26#432×C131—24no—
27C2×C4⋊C8×C131C2212yes—
28C2×#103×C131C2214yes—
29C2×#102×C131C2214yes—
30C2×C22⋊C8×C131C2212yes—
31C2×#97×C131C2212yes—
32#384×C131—21no—
33#384×C131—21no—
34#384×C131C2212yes—
35#384×C131C2212yes—
36#340×C131C2214yes—
37#340×C131C2214yes—
38C22×Q8×C131C2311yescharacteristic
39C22×D4×C131—21no—
40C22×D4×C131C2311yescharacteristic
41C23×C4×C131—21no—
42C23×C4×C131—22no—
43C23×C4×C131D411yescharacteristic
44C23×C4×C131D411yescharacteristic
45C23×C4×C131C2311yescharacteristic
46C22×C8×C131C2314yes—
47#126×C131—28no—
48#125×C131—22no—
49#125×C131C2×C414yescomplemented
50#124×C131—22no—
51#124×C131C2×C414yescomplemented
52#123×C131—28no—
53C22⋊Q8×C131—22no—
54C22⋊Q8×C131C2×C414yes—
55#121×C131—22no—
56#121×C131C2×C414yes—
57C4×Q8×C131—22no—
58C4×Q8×C131C2×C414yescomplemented
59C4×D4×C131—28no—
60C4×D4×C131—22no—
61C4×D4×C131C2×C414yescomplemented
62#117×C131—28no—
63C2×C4⋊C4×C131—21no—
64C2×C4⋊C4×C131—21no—
65C2×C4⋊C4×C131—21no—
66C2×C4⋊C4×C131—21no—
67C2×C4⋊C4×C131—22no—
68C2×C4⋊C4×C131—22no—
69C2×C4⋊C4×C131—22no—
70C2×C4⋊C4×C131—22no—
71C2×C4⋊C4×C131—22no—
72C2×C4⋊C4×C131—44no—
73C2×C4⋊C4×C131—44no—
74C2×C4⋊C4×C131—44no—
75C2×C4⋊C4×C131C2314yes—
76C2×C4⋊C4×C131C2311yescharacteristic
77C2×C4⋊C4×C131C2311yescharacteristic
78C2×C22⋊C4×C131—21no—
79C2×C22⋊C4×C131—21no—
80C2×C22⋊C4×C131—21no—
81C2×C22⋊C4×C131—21no—
82C2×C22⋊C4×C131—21no—
83C2×C42×C131—21no—
84C2×C42×C131C2×C414yes—
85C2×C42×C131D411yescharacteristic
86C2×C42×C131D411yescharacteristic
87C2×C42×C131D414yes—
88C2×C42×C131C2311yescharacteristic
89C2×C42×C131C2311yescharacteristic
90C4⋊C8×C131—24no—
91#103×C131—44no—
92#102×C131—44no—
93C22⋊C8×C131—24no—
94#97×C131—24no—
95C24×C131—21no—
96C24×C131C2×D411yescharacteristic
97C2×Q8×C131—21no—
98C2×Q8×C131—22no—
99C2×Q8×C131—22no—
100C2×Q8×C131C22×C412yes—
101C2×D4×C131—24no—
102C2×D4×C131—21no—
103C2×D4×C131—22no—
104C2×D4×C131—22no—
105C2×D4×C131—42no—
106C2×D4×C131—42no—
107C2×D4×C131C22×C412yes—
108C22×C4×C131—22no—
109C22×C4×C131—22no—
110C22×C4×C131—22no—
111C22×C4×C131—22no—
112C22×C4×C131—22no—
113C22×C4×C131—22no—
114C22×C4×C131—21no—
115C22×C4×C131—21no—
116C22×C4×C131—21no—
117C22×C4×C131—24no—
118C22×C4×C131—24no—
119C22×C4×C131—42no—
120C22×C4×C131—42no—
121C22×C4×C131—44no—
122C22×C4×C131—44no—
123C22×C4×C131—44no—
124C22×C4×C131C22⋊C414yes—
125C22×C4×C131C22⋊C414yes—
126C22×C4×C131C22×C412yes—
127C22×C4×C131C2×D411yescharacteristic
128C22×C4×C131C2×D411yescharacteristic
129C22×C4×C131C2×D411yescharacteristic
130C22×C4×C131C2×D411yescharacteristic
131C22×C4×C131C2×D412yes—
132C22×C4×C131C2×D411yescharacteristic
133C22×C4×C131C2411yescharacteristic
134C2×C8×C131—24no—
135C2×C8×C131—24no—
136C2×C8×C131—24no—
137C4⋊C4×C131—24no—
138C4⋊C4×C131—24no—
139C4⋊C4×C131—24no—
140C4⋊C4×C131—24no—
141C4⋊C4×C131—21no—
142C4⋊C4×C131—21no—
143C4⋊C4×C131—24no—
144C4⋊C4×C131—24no—
145C4⋊C4×C131—44no—
146C4⋊C4×C131—44no—
147C4⋊C4×C131—44no—
148C4⋊C4×C131—44no—
149C4⋊C4×C131—44no—
150C4⋊C4×C131C22×C412yes—
151C4⋊C4×C131C22×C412yes—
152C22⋊C4×C131—24no—
153C22⋊C4×C131—24no—
154C22⋊C4×C131—24no—
155C22⋊C4×C131—24no—
156C22⋊C4×C131—24no—
157C42×C131—24no—
158C42×C131C22⋊C414yes—
159C42×C131C22⋊C414yes—
160C42×C131C22×C412yes—
161C42×C131C22×C412yes—
162C42×C131C2×D412yes—
163C42×C131C2×D412yes—
164C23×C131—21no—
165C23×C131—21no—
166C23×C131—21no—
167C23×C131—21no—
168C23×C131—22no—
169C23×C131—41no—
170C23×C131—41no—
171C23×C131—41no—
172C23×C131—41no—
173C23×C131—41no—
174C23×C131—41no—
175C23×C131C2×C22⋊C412yes—
176C23×C131AGL(1,ℤ/8)12yes—
177C23×C131#13712yes—
178C23×C131C22×D411yescharacteristic
179Q8×C131—24no—
180Q8×C131—42no—
181D4×C131—24no—
182D4×C131—48no—
183D4×C131—42no—
184C2×C4×C131—21no—
185C2×C4×C131—21no—
186C2×C4×C131—21no—
187C2×C4×C131—21no—
188C2×C4×C131—21no—
189C2×C4×C131—21no—
190C2×C4×C131—21no—
191C2×C4×C131—21no—
192C2×C4×C131—28no—
193C2×C4×C131—24no—
194C2×C4×C131—24no—
195C2×C4×C131—28no—
196C2×C4×C131—22no—
197C2×C4×C131—22no—
198C2×C4×C131—22no—
199C2×C4×C131—41no—
200C2×C4×C131—41no—
201C2×C4×C131—41no—
202C2×C4×C131—41no—
203C2×C4×C131—41no—
204C2×C4×C131—41no—
205C2×C4×C131—48no—
206C2×C4×C131—44no—
207C2×C4×C131—44no—
208C2×C4×C131—44no—
209C2×C4×C131—88no—
210C2×C4×C131C2×C22⋊C412yes—
211C2×C4×C131C2×C22⋊C412yes—
212C2×C4×C131C2×C22⋊C412yes—
213C2×C4×C131C2×C22⋊C412yes—
214C2×C4×C131C2×C22⋊C412yes—
215C2×C4×C131AGL(1,ℤ/8)12yes—
216C2×C4×C131#13712yes—
217C2×C4×C131C23×C411yescharacteristic
218C2×C4×C131C22×D411yescharacteristic
219C2×C4×C131H(5,𝔽2)12yes—
220C2×C4×C1312−1+412yes—
221C8×C131—44no—
222C22×C131—22no—
223C22×C131—22no—
224C22×C131—22no—
225C22×C131—22no—
226C22×C131—22no—
227C22×C131—22no—
228C22×C131—42no—
229C22×C131—42no—
230C22×C131—42no—
231C22×C131—81no—
232C22×C131—81no—
233C22×C131—81no—
234C22×C131—81no—
235C22×C131#41714yes—
236C22×C131C22×C22⋊C411yescharacteristic
237C22×C131#53511yescharacteristic
238C22×C131#53611yescharacteristic
239C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
240C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
241C22×C131C2×#13711yescharacteristic
242C22×C131C2×#13711yescharacteristic
243C4×C131—22no—
244C4×C131—22no—
245C4×C131—22no—
246C4×C131—22no—
247C4×C131—42no—
248C4×C131—42no—
249C4×C131—42no—
250C4×C131—84no—
251C4×C131#41714yes—
252C4×C131#52012yes—
253C4×C131#53712yes—
254C2×C131—24no—
255C2×C131—82no—
256C2×C131#231111yescharacteristic
257C2×C131C2×#41711yescharacteristic
258C2×C131C2×#41711yescharacteristic
259C2×C131#321711yescharacteristic
260C2×C131#321811yescharacteristic
261C2×C131#323811yescharacteristic
262C2×C131#323911yescharacteristic
263#21867C13111yesmaximal, characteristic, direct product factor, Sylow
264C131#2186711yescharacteristic, direct product factor, Sylow
265C2×#529C2×C13111yescharacteristic
266C2×#432C2×C13111yescharacteristic, complemented
267C2×#384C2×C13111yescharacteristic, complemented
268#1992C2×C13112yescomplemented
269#1959C2×C13112yescomplemented
270#1874C2×C13112yes—
271#1872C2×C13112yescomplemented
272#1803C2×C13112yescomplemented
273#1802C2×C13112yescomplemented
274#529—24no—
275#529C4×C13118yescomplemented
276C2×#126—21no—
277C2×#125C22×C13111yescharacteristic
278C2×#124C22×C13111yescharacteristic
279C2×#123—21no—
280C2×C22⋊Q8C22×C13111yescharacteristic
281C2×#121C22×C13111yescharacteristic
282C2×C4×Q8C22×C13111yescharacteristic
283C2×C4×D4—21no—
284C2×C4×D4C22×C13111yescharacteristic
285C2×#117—21no—
286C22×C4⋊C4—21no—
287C22×C4⋊C4—21no—
288C22×C4⋊C4C22×C13112yes—
289C22×C42C22×C13111yescharacteristic
290#432—24no—
291C2×C4⋊C8C22×C13112yes—
292C2×#103C22×C13114yes—
293C2×#102C22×C13114yes—
294C2×C22⋊C8C22×C13112yes—
295C2×#97C22×C13112yes—
296#384—21no—
297#384—21no—
298#384C22×C13112yes—
299#384C22×C13112yes—
300#340C22×C13114yes—
301#340C22×C13114yes—
302C22×Q8C23×C13111yescharacteristic
303C22×D4—21no—
304C22×D4C23×C13111yescharacteristic
305C23×C4—21no—
306C23×C4—22no—
307C23×C4D4×C13111yescharacteristic
308C23×C4D4×C13111yescharacteristic
309C23×C4C23×C13111yescharacteristic
310C22×C8C23×C13114yes—
311#126—28no—
312#125—22no—
313#125C2×C4×C13114yescomplemented
314#124—22no—
315#124C2×C4×C13114yescomplemented
316#123—28no—
317C22⋊Q8—22no—
318C22⋊Q8C2×C4×C13114yes—
319#121—22no—
320#121C2×C4×C13114yes—
321C4×Q8—22no—
322C4×Q8C2×C4×C13114yescomplemented
323C4×D4—28no—
324C4×D4—22no—
325C4×D4C2×C4×C13114yescomplemented
326#117—28no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C23×C13114yes—
340C2×C4⋊C4C23×C13111yescharacteristic
341C2×C4⋊C4C23×C13111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42C2×C4×C13114yes—
349C2×C42D4×C13111yescharacteristic
350C2×C42D4×C13111yescharacteristic
351C2×C42D4×C13114yes—
352C2×C42C23×C13111yescharacteristic
353C2×C42C23×C13111yescharacteristic
354C4⋊C8—24no—
355#103—44no—
356#102—44no—
357C22⋊C8—24no—
358#97—24no—
359C24—21no—
360C24C2×D4×C13111yescharacteristic
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8C22×C4×C13112yes—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4C22×C4×C13112yes—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—24no—
382C22×C4—24no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—44no—
386C22×C4—44no—
387C22×C4—44no—
388C22×C4C22⋊C4×C13114yes—
389C22×C4C22⋊C4×C13114yes—
390C22×C4C22×C4×C13112yes—
391C22×C4C2×D4×C13111yescharacteristic
392C22×C4C2×D4×C13111yescharacteristic
393C22×C4C2×D4×C13111yescharacteristic
394C22×C4C2×D4×C13111yescharacteristic
395C22×C4C2×D4×C13112yes—
396C22×C4C2×D4×C13111yescharacteristic
397C22×C4C24×C13111yescharacteristic
398C2×C8—24no—
399C2×C8—24no—
400C2×C8—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—44no—
410C4⋊C4—44no—
411C4⋊C4—44no—
412C4⋊C4—44no—
413C4⋊C4—44no—
414C4⋊C4C22×C4×C13112yes—
415C4⋊C4C22×C4×C13112yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C42—24no—
422C42C22⋊C4×C13114yes—
423C42C22⋊C4×C13114yes—
424C42C22×C4×C13112yes—
425C42C22×C4×C13112yes—
426C42C2×D4×C13112yes—
427C42C2×D4×C13112yes—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—22no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23C2×C22⋊C4×C13112yes—
440C23AGL(1,ℤ/8)×C13112yes—
441C23#137×C13112yes—
442C23C22×D4×C13111yescharacteristic
443Q8—24no—
444Q8—42no—
445D4—24no—
446D4—48no—
447D4—42no—
448C2×C4—28no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—28no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—48no—
470C2×C4—44no—
471C2×C4—44no—
472C2×C4—44no—
473C2×C4—88no—
474C2×C4C2×C22⋊C4×C13112yes—
475C2×C4C2×C22⋊C4×C13112yes—
476C2×C4C2×C22⋊C4×C13112yes—
477C2×C4C2×C22⋊C4×C13112yes—
478C2×C4C2×C22⋊C4×C13112yes—
479C2×C4AGL(1,ℤ/8)×C13112yes—
480C2×C4#137×C13112yes—
481C2×C4C23×C4×C13111yescharacteristic
482C2×C4C22×D4×C13111yescharacteristic
483C2×C4H(5,𝔽2)×C13112yes—
484C2×C42−1+4×C13112yes—
485C8—44no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22#417×C13114yes—
500C22C22×C22⋊C4×C13111yescharacteristic
501C22#535×C13111yescharacteristic
502C22#536×C13111yescharacteristic
503C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
504C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
505C22C2×#137×C13111yescharacteristic
506C22C2×#137×C13111yescharacteristic
507C4—22no—
508C4—22no—
509C4—22no—
510C4—22no—
511C4—42no—
512C4—42no—
513C4—42no—
514C4—84no—
515C4#417×C13114yes—
516C4#520×C13112yes—
517C4#537×C13112yes—
518C2—24no—
519C2—82no—
520C2#2311×C13111yescharacteristic
521C2C2×#417×C13111yescharacteristic
522C2C2×#417×C13111yescharacteristic
523C2#3217×C13111yescharacteristic
524C2#3218×C13111yescharacteristic
525C2#3238×C13111yescharacteristic
526C2#3239×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#432×C131C2semidirect
3. C2×#384×C131C2semidirect
4. #1992×C131C2semidirect
5. #1959×C131C2semidirect
7. #1872×C131C2semidirect
8. #1803×C131C2semidirect
9. #1802×C131C2semidirect
11. #529×C131C4semidirect
49. #125×C131C2×C4semidirect
51. #124×C131C2×C4semidirect
58. C4×Q8×C131C2×C4semidirect
61. C4×D4×C131C2×C4semidirect
263. #21867C131direct (N × H)
264. C131#21867direct (N × H)
266. C2×#432C2×C131semidirect
267. C2×#384C2×C131semidirect
268. #1992C2×C131semidirect
269. #1959C2×C131semidirect
271. #1872C2×C131semidirect
272. #1803C2×C131semidirect
273. #1802C2×C131semidirect
275. #529C4×C131semidirect
313. #125C2×C4×C131semidirect
315. #124C2×C4×C131semidirect
322. C4×Q8C2×C4×C131semidirect
325. C4×D4C2×C4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#529×C1312
C2×#432×C1312
C2×#384×C1312
#1992×C1312
#1959×C1312
#1874×C1312
#1872×C1312
#1803×C1312
#1802×C1312
#21867131