Finite Group Databasebeta

← C131×#8571 #45694455

Subgroups — C131×#8571 #45694455

Order 33536.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C131C211yesmaximal, characteristic
2#1797×C131C211yesmaximal, characteristic, complemented
3C2×#327×C131C212yesmaximal
4C4⋊#95×C131C211yesmaximal, characteristic, complemented
5#1294×C131C212yesmaximal, complemented
6C2×#121×C131C2211yescharacteristic
7C2×C4×D4×C131—21no—
8C2×C4×D4×C131C411yescharacteristic, complemented
9C22×C4⋊C4×C131—21no—
10C22×C42×C131C2211yescharacteristic
11C2×C4⋊C8×C131—21no—
12C2×C22⋊C8×C131C2212yes—
13#390×C131C411yescharacteristic, complemented
14#389×C131C411yescharacteristic, complemented
15#388×C131—21no—
16#386×C131—21no—
17#380×C131C2211yescharacteristic
18C4×C4⋊C4×C131C411yescharacteristic, complemented
19C4×C22⋊C4×C131—21no—
20C2×#95×C131—21no—
21C2×#95×C131C2212yes—
22#336×C131—21no—
23#327×C131—24no—
24C22×D4×C131—21no—
25C22×D4×C131C2×C411yescharacteristic
26C23×C4×C131—22no—
27C23×C4×C131—21no—
28C23×C4×C131D411yescharacteristic
29C23×C4×C131D411yescharacteristic
30C23×C4×C131C2311yescharacteristic
31C22×C8×C131—22no—
32#121×C131—21no—
33#121×C131—21no—
34#121×C131D412yes—
35#121×C131Q812yes—
36C4×D4×C131—42no—
37C4×D4×C131—42no—
38C4×D4×C131—42no—
39C2×C4⋊C4×C131—24no—
40C2×C4⋊C4×C131—21no—
41C2×C4⋊C4×C131—42no—
42C2×C4⋊C4×C131—42no—
43C2×C4⋊C4×C131C2×C411yescharacteristic
44C2×C4⋊C4×C131C2×C411yescharacteristic
45C2×C4⋊C4×C131C2×C411yescharacteristic
46C2×C22⋊C4×C131—21no—
47C2×C22⋊C4×C131—21no—
48C2×C22⋊C4×C131—21no—
49C2×C22⋊C4×C131—21no—
50C2×C22⋊C4×C131—21no—
51C2×C42×C131—21no—
52C2×C42×C131—42no—
53C2×C42×C131C2×C411yescharacteristic
54C2×C42×C131C2×C411yescharacteristic
55C2×C42×C131D411yescharacteristic
56C2×C42×C131D411yescharacteristic
57C4⋊C8×C131—42no—
58C22⋊C8×C131—22no—
59C22⋊C8×C131—22no—
60#95×C131—21no—
61#95×C131—21no—
62#95×C131—21no—
63#95×C131—22no—
64#95×C131—22no—
65#95×C131—42no—
66C24×C131—21no—
67C24×C131C2×D411yescharacteristic
68C2×D4×C131—22no—
69C2×D4×C131—22no—
70C2×D4×C131—21no—
71C2×D4×C131—41no—
72C2×D4×C131—41no—
73C2×D4×C131—41no—
74C2×D4×C131—41no—
75C2×D4×C131—41no—
76C2×D4×C131—41no—
77C2×D4×C131C4⋊C412yescomplemented
78C22×C4×C131—22no—
79C22×C4×C131—22no—
80C22×C4×C131—21no—
81C22×C4×C131—21no—
82C22×C4×C131—21no—
83C22×C4×C131—24no—
84C22×C4×C131—21no—
85C22×C4×C131—21no—
86C22×C4×C131—41no—
87C22×C4×C131—41no—
88C22×C4×C131—41no—
89C22×C4×C131—41no—
90C22×C4×C131—42no—
91C22×C4×C131—42no—
92C22×C4×C131—42no—
93C22×C4×C131—42no—
94C22×C4×C131—42no—
95C22×C4×C131—42no—
96C22×C4×C131—42no—
97C22×C4×C131—42no—
98C22×C4×C131—42no—
99C22×C4×C131C22⋊C411yescharacteristic
100C22×C4×C131C22⋊C411yescharacteristic
101C22×C4×C131C22⋊C411yescharacteristic
102C22×C4×C131C22⋊C411yescharacteristic
103C22×C4×C131D812yes—
104C22×C4×C131SD1612yes—
105C22×C4×C131C22×C411yescharacteristic
106C22×C4×C131C2×D411yescharacteristic
107C22×C4×C131C2×D411yescharacteristic
108C22×C4×C131C2×Q811yescharacteristic
109C22×C4×C131#4111yescharacteristic
110C22×C4×C131#4111yescharacteristic
111C2×C8×C131—42no—
112C2×C8×C131—42no—
113C2×C8×C131—42no—
114C4⋊C4×C131—21no—
115C4⋊C4×C131—41no—
116C4⋊C4×C131—41no—
117C4⋊C4×C131—48no—
118C4⋊C4×C131—42no—
119C4⋊C4×C131C4⋊C412yescomplemented
120C22⋊C4×C131—22no—
121C22⋊C4×C131—22no—
122C22⋊C4×C131—42no—
123C22⋊C4×C131—42no—
124C22⋊C4×C131—41no—
125C22⋊C4×C131—41no—
126C22⋊C4×C131—42no—
127C42×C131—22no—
128C42×C131—22no—
129C42×C131—41no—
130C42×C131—41no—
131C42×C131—42no—
132C23×C131—21no—
133C23×C131—21no—
134C23×C131—21no—
135C23×C131—21no—
136C23×C131—22no—
137C23×C131—41no—
138C23×C131—41no—
139C23×C131—41no—
140C23×C131—41no—
141C23×C131—41no—
142C23×C131—41no—
143C23×C131C2×C22⋊C411yescharacteristic
144C23×C131#12111yescharacteristic
145C23×C131C22⋊Q811yescharacteristic
146C23×C131C2×D811yescharacteristic
147C23×C131C2×SD1611yescharacteristic
148C23×C131AGL(1,ℤ/8)11yescharacteristic
149C23×C131#13711yescharacteristic
150D4×C131—42no—
151D4×C131—42no—
152D4×C131—42no—
153D4×C131—42no—
154D4×C131—42no—
155D4×C131—42no—
156C2×C4×C131—21no—
157C2×C4×C131—21no—
158C2×C4×C131—21no—
159C2×C4×C131—21no—
160C2×C4×C131—21no—
161C2×C4×C131—21no—
162C2×C4×C131—24no—
163C2×C4×C131—24no—
164C2×C4×C131—22no—
165C2×C4×C131—21no—
166C2×C4×C131—21no—
167C2×C4×C131—21no—
168C2×C4×C131—21no—
169C2×C4×C131—21no—
170C2×C4×C131—21no—
171C2×C4×C131—41no—
172C2×C4×C131—41no—
173C2×C4×C131—41no—
174C2×C4×C131—41no—
175C2×C4×C131—42no—
176C2×C4×C131—42no—
177C2×C4×C131—41no—
178C2×C4×C131—41no—
179C2×C4×C131—44no—
180C2×C4×C131—44no—
181C2×C4×C131—44no—
182C2×C4×C131—41no—
183C2×C4×C131—41no—
184C2×C4×C131—41no—
185C2×C4×C131—41no—
186C2×C4×C131—41no—
187C2×C4×C131—41no—
188C2×C4×C131—82no—
189C2×C4×C131—82no—
190C2×C4×C131—82no—
191C2×C4×C131—82no—
192C2×C4×C131—84no—
193C2×C4×C131#9912yes—
194C2×C4×C131#10212yes—
195C2×C4×C131#10212yes—
196C2×C4×C131#10412yes—
197C2×C4×C131C2×C4⋊C411yescharacteristic
198C2×C4×C131#11711yescharacteristic
199C2×C4×C131#12111yescharacteristic
200C2×C4×C131C22⋊Q811yescharacteristic
201C8×C131—82no—
202C22×C131—21no—
203C22×C131—21no—
204C22×C131—21no—
205C22×C131—21no—
206C22×C131—21no—
207C22×C131—21no—
208C22×C131—21no—
209C22×C131—21no—
210C22×C131—21no—
211C22×C131—21no—
212C22×C131—21no—
213C22×C131—21no—
214C22×C131—42no—
215C22×C131—42no—
216C22×C131—42no—
217C22×C131—81no—
218C22×C131—81no—
219C22×C131—81no—
220C22×C131—81no—
221C22×C131#38011yescharacteristic
222C22×C131C2×#9911yescharacteristic
223C22×C131#41011yescharacteristic
224C22×C131C2×#10211yescharacteristic
225C22×C131#41711yescharacteristic
226C22×C131C2×#10411yescharacteristic
227C22×C131#42111yescharacteristic
228C22×C131#45911yescharacteristic
229C22×C131#46111yescharacteristic
230C22×C131#47411yescharacteristic
231C22×C131#47611yescharacteristic
232C4×C131—21no—
233C4×C131—21no—
234C4×C131—21no—
235C4×C131—21no—
236C4×C131—22no—
237C4×C131—42no—
238C4×C131—41no—
239C4×C131—41no—
240C4×C131—84no—
241C4×C131—81no—
242C4×C131—81no—
243C4×C131#32714yescomplemented
244C2×C131—21no—
245C2×C131—21no—
246C2×C131—21no—
247C2×C131—21no—
248C2×C131—82no—
249C2×C131C2×#32711yescharacteristic
250C2×C131#150911yescharacteristic
251C2×C131#151311yescharacteristic
252C2×C131#151711yescharacteristic
253C2×C131#179911yescharacteristic
254C2×C131#180211yescharacteristic
255C2×C131#180611yescharacteristic
256#8571C13111yesmaximal, characteristic, direct product factor, Sylow
257C131#857111yescharacteristic, direct product factor, Sylow
258C4×#121C2×C13111yescharacteristic
259#1797C2×C13111yescharacteristic, complemented
260C2×#327C2×C13112yes—
261C4⋊#95C2×C13111yescharacteristic, complemented
262#1294C2×C13112yescomplemented
263C2×#121C22×C13111yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C4×C13111yescharacteristic, complemented
266C22×C4⋊C4—21no—
267C22×C42C22×C13111yescharacteristic
268C2×C4⋊C8—21no—
269C2×C22⋊C8C22×C13112yes—
270#390C4×C13111yescharacteristic, complemented
271#389C4×C13111yescharacteristic, complemented
272#388—21no—
273#386—21no—
274#380C22×C13111yescharacteristic
275C4×C4⋊C4C4×C13111yescharacteristic, complemented
276C4×C22⋊C4—21no—
277C2×#95—21no—
278C2×#95C22×C13112yes—
279#336—21no—
280#327—24no—
281C22×D4—21no—
282C22×D4C2×C4×C13111yescharacteristic
283C23×C4—22no—
284C23×C4—21no—
285C23×C4D4×C13111yescharacteristic
286C23×C4D4×C13111yescharacteristic
287C23×C4C23×C13111yescharacteristic
288C22×C8—22no—
289#121—21no—
290#121—21no—
291#121D4×C13112yes—
292#121Q8×C13112yes—
293C4×D4—42no—
294C4×D4—42no—
295C4×D4—42no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4C2×C4×C13111yescharacteristic
301C2×C4⋊C4C2×C4×C13111yescharacteristic
302C2×C4⋊C4C2×C4×C13111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C42—21no—
309C2×C42—42no—
310C2×C42C2×C4×C13111yescharacteristic
311C2×C42C2×C4×C13111yescharacteristic
312C2×C42D4×C13111yescharacteristic
313C2×C42D4×C13111yescharacteristic
314C4⋊C8—42no—
315C22⋊C8—22no—
316C22⋊C8—22no—
317#95—21no—
318#95—21no—
319#95—21no—
320#95—22no—
321#95—22no—
322#95—42no—
323C24—21no—
324C24C2×D4×C13111yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—41no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4C4⋊C4×C13112yescomplemented
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—24no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4C22⋊C4×C13111yescharacteristic
357C22×C4C22⋊C4×C13111yescharacteristic
358C22×C4C22⋊C4×C13111yescharacteristic
359C22×C4C22⋊C4×C13111yescharacteristic
360C22×C4D8×C13112yes—
361C22×C4SD16×C13112yes—
362C22×C4C22×C4×C13111yescharacteristic
363C22×C4C2×D4×C13111yescharacteristic
364C22×C4C2×D4×C13111yescharacteristic
365C22×C4C2×Q8×C13111yescharacteristic
366C22×C4#41×C13111yescharacteristic
367C22×C4#41×C13111yescharacteristic
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—48no—
375C4⋊C4—42no—
376C4⋊C4C4⋊C4×C13112yescomplemented
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—42no—
380C22⋊C4—42no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—42no—
384C42—22no—
385C42—22no—
386C42—41no—
387C42—41no—
388C42—42no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—22no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23C2×C22⋊C4×C13111yescharacteristic
401C23#121×C13111yescharacteristic
402C23C22⋊Q8×C13111yescharacteristic
403C23C2×D8×C13111yescharacteristic
404C23C2×SD16×C13111yescharacteristic
405C23AGL(1,ℤ/8)×C13111yescharacteristic
406C23#137×C13111yescharacteristic
407D4—42no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—44no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4—84no—
450C2×C4#99×C13112yes—
451C2×C4#102×C13112yes—
452C2×C4#102×C13112yes—
453C2×C4#104×C13112yes—
454C2×C4C2×C4⋊C4×C13111yescharacteristic
455C2×C4#117×C13111yescharacteristic
456C2×C4#121×C13111yescharacteristic
457C2×C4C22⋊Q8×C13111yescharacteristic
458C8—82no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—42no—
472C22—42no—
473C22—42no—
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22#380×C13111yescharacteristic
479C22C2×#99×C13111yescharacteristic
480C22#410×C13111yescharacteristic
481C22C2×#102×C13111yescharacteristic
482C22#417×C13111yescharacteristic
483C22C2×#104×C13111yescharacteristic
484C22#421×C13111yescharacteristic
485C22#459×C13111yescharacteristic
486C22#461×C13111yescharacteristic
487C22#474×C13111yescharacteristic
488C22#476×C13111yescharacteristic
489C4—22no—
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—41no—
496C4—42no—
497C4—84no—
498C4—81no—
499C4—81no—
500C4#327×C13114yescomplemented
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—82no—
506C2C2×#327×C13111yescharacteristic
507C2#1509×C13111yescharacteristic
508C2#1513×C13111yescharacteristic
509C2#1517×C13111yescharacteristic
510C2#1799×C13111yescharacteristic
511C2#1802×C13111yescharacteristic
512C2#1806×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC23×C4C23×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C131C2semidirect
4. C4⋊#95×C131C2semidirect
5. #1294×C131C2semidirect
8. C2×C4×D4×C131C4semidirect
13. #390×C131C4semidirect
14. #389×C131C4semidirect
18. C4×C4⋊C4×C131C4semidirect
77. C2×D4×C131C4⋊C4semidirect
119. C4⋊C4×C131C4⋊C4semidirect
243. C4×C131#327semidirect
256. #8571C131direct (N × H)
257. C131#8571direct (N × H)
259. #1797C2×C131semidirect
261. C4⋊#95C2×C131semidirect
262. #1294C2×C131semidirect
265. C2×C4×D4C4×C131semidirect
270. #390C4×C131semidirect
271. #389C4×C131semidirect
275. C4×C4⋊C4C4×C131semidirect
334. C2×D4C4⋊C4×C131semidirect
376. C4⋊C4C4⋊C4×C131semidirect
500. C4#327×C131semidirect

Maximal subgroups

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

subgroupindex
C4×#121×C1312
#1797×C1312
C2×#327×C1312
C4⋊#95×C1312
#1294×C1312
#8571131