Finite Group Databasebeta

← C131×#29914 #45715798

Subgroups — C131×#29914 #45715798

Order 33536.

768 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C131C211yesmaximal, characteristic
2#2285×C131C211yesmaximal, characteristic, complemented
3#2100×C131C211yesmaximal, characteristic, complemented
4#2099×C131C211yesmaximal, characteristic, complemented
5#2094×C131C211yesmaximal, characteristic, complemented
6#2093×C131C211yesmaximal, characteristic, complemented
7#2085×C131C212yesmaximal, complemented
8#2073×C131C212yesmaximal, complemented
9#1875×C131C212yesmaximal
10#1854×C131C212yesmaximal, complemented
11#1817×C131C211yesmaximal, characteristic, complemented
12C2×#123×C131—21no—
13C2×#121×C131C2211yescharacteristic
14C2×#117×C131C2212yes—
15C22×C42×C131C2211yescharacteristic
16C2×#107×C131C2212yes—
17C2×#106×C131C2212yes—
18C2×#102×C131C2212yes—
19C2×#102×C131C2212yes—
20C2×C22⋊C8×C131C2212yes—
21#390×C131C2211yescharacteristic
22#390×C131C2211yescharacteristic
23#389×C131C2211yescharacteristic
24#389×C131C2211yescharacteristic
25#388×C131—21no—
26#388×C131—21no—
27#386×C131—21no—
28#384×C131C2211yescharacteristic
29#384×C131C2211yescharacteristic
30#382×C131C2212yes—
31#380×C131—21no—
32#380×C131—21no—
33#380×C131C2211yescharacteristic
34C4×C4⋊C4×C131—21no—
35C4×C4⋊C4×C131—21no—
36#340×C131C2212yes—
37#340×C131C2212yes—
38#340×C131C2212yes—
39#340×C131C2212yes—
40#336×C131C2212yes—
41#336×C131C2211yescharacteristic
42#336×C131C2211yescharacteristic
43C22×D4×C131—21no—
44C22×D4×C131C2311yescharacteristic
45C23×C4×C131D411yescharacteristic
46C23×C4×C131D411yescharacteristic
47C23×C4×C131C2311yescharacteristic
48C22×C8×C131C2312yes—
49C22×C8×C131C2312yes—
50#123×C131—44no—
51#121×C131—24no—
52#117×C131—42no—
53#117×C131—42no—
54C2×C4⋊C4×C131—21no—
55C2×C4⋊C4×C131—21no—
56C2×C4⋊C4×C131—21no—
57C2×C4⋊C4×C131—21no—
58C2×C4⋊C4×C131—21no—
59C2×C4⋊C4×C131—21no—
60C2×C4⋊C4×C131C2311yescharacteristic
61C2×C4⋊C4×C131C2311yescharacteristic
62C2×C4⋊C4×C131C2311yescharacteristic
63C2×C4⋊C4×C131C2312yes—
64C2×C4⋊C4×C131C2312yes—
65C2×C22⋊C4×C131—22no—
66C2×C22⋊C4×C131—21no—
67C2×C22⋊C4×C131—21no—
68C2×C22⋊C4×C131—21no—
69C2×C22⋊C4×C131—21no—
70C2×C22⋊C4×C131—21no—
71C2×C22⋊C4×C131—21no—
72C2×C42×C131—24no—
73C2×C42×C131—22no—
74C2×C42×C131D411yescharacteristic
75C2×C42×C131D411yescharacteristic
76C2×C42×C131C2311yescharacteristic
77C2×C42×C131C2311yescharacteristic
78#107×C131—42no—
79#106×C131—42no—
80#102×C131—42no—
81#102×C131—42no—
82C22⋊C8×C131—24no—
83#95×C131—21no—
84#95×C131—21no—
85#95×C131—21no—
86#95×C131—22no—
87#95×C131—22no—
88C24×C131—21no—
89C24×C131C2×D411yescharacteristic
90C2×D4×C131—22no—
91C2×D4×C131—22no—
92C2×D4×C131—21no—
93C2×D4×C131—21no—
94C2×D4×C131—42no—
95C2×D4×C131—42no—
96C2×D4×C131—42no—
97C22×C4×C131—22no—
98C22×C4×C131—21no—
99C22×C4×C131—21no—
100C22×C4×C131—22no—
101C22×C4×C131—22no—
102C22×C4×C131—22no—
103C22×C4×C131—22no—
104C22×C4×C131—22no—
105C22×C4×C131—22no—
106C22×C4×C131—21no—
107C22×C4×C131—21no—
108C22×C4×C131—21no—
109C22×C4×C131—41no—
110C22×C4×C131—41no—
111C22×C4×C131C2×D411yescharacteristic
112C22×C4×C131C2×D411yescharacteristic
113C22×C4×C131C2×D411yescharacteristic
114C22×C4×C131C2×D411yescharacteristic
115C22×C4×C131C2×D411yescharacteristic
116C22×C4×C131#4114yes—
117C22×C4×C131C2411yescharacteristic
118C2×C8×C131—22no—
119C2×C8×C131—22no—
120C2×C8×C131—22no—
121C2×C8×C131—22no—
122C2×C8×C131—22no—
123C2×C8×C131—22no—
124C4⋊C4×C131—22no—
125C4⋊C4×C131—22no—
126C4⋊C4×C131—22no—
127C4⋊C4×C131—22no—
128C4⋊C4×C131—22no—
129C4⋊C4×C131—22no—
130C4⋊C4×C131—21no—
131C4⋊C4×C131—21no—
132C4⋊C4×C131—42no—
133C4⋊C4×C131—42no—
134C4⋊C4×C131—42no—
135C4⋊C4×C131—42no—
136C4⋊C4×C131—42no—
137C4⋊C4×C131—42no—
138C22⋊C4×C131—42no—
139C22⋊C4×C131—42no—
140C22⋊C4×C131—44no—
141C22⋊C4×C131—42no—
142C22⋊C4×C131—42no—
143C22⋊C4×C131—42no—
144C22⋊C4×C131—42no—
145C42×C131—22no—
146C42×C131—22no—
147C42×C131—22no—
148C42×C131—22no—
149C42×C131—44no—
150C23×C131—21no—
151C23×C131—21no—
152C23×C131—21no—
153C23×C131—21no—
154C23×C131—21no—
155C23×C131—21no—
156C23×C131—41no—
157C23×C131—41no—
158C23×C131—41no—
159C23×C131—41no—
160C23×C131—41no—
161C23×C131—41no—
162C23×C131—41no—
163C23×C131#12312yes—
164C23×C131C22×D411yescharacteristic
165D4×C131—42no—
166D4×C131—42no—
167D4×C131—84no—
168C2×C4×C131—21no—
169C2×C4×C131—21no—
170C2×C4×C131—21no—
171C2×C4×C131—21no—
172C2×C4×C131—21no—
173C2×C4×C131—21no—
174C2×C4×C131—24no—
175C2×C4×C131—24no—
176C2×C4×C131—21no—
177C2×C4×C131—21no—
178C2×C4×C131—21no—
179C2×C4×C131—21no—
180C2×C4×C131—21no—
181C2×C4×C131—21no—
182C2×C4×C131—44no—
183C2×C4×C131—44no—
184C2×C4×C131—41no—
185C2×C4×C131—42no—
186C2×C4×C131—42no—
187C2×C4×C131—41no—
188C2×C4×C131—41no—
189C2×C4×C131—41no—
190C2×C4×C131—42no—
191C2×C4×C131—41no—
192C2×C4×C131—41no—
193C2×C4×C131—41no—
194C2×C4×C131—42no—
195C2×C4×C131—41no—
196C2×C4×C131—42no—
197C2×C4×C131—42no—
198C2×C4×C131—41no—
199C2×C4×C131#12312yes—
200C2×C4×C131#13512yes—
201C2×C4×C131AGL(1,ℤ/8)12yes—
202C2×C4×C131C2×#4112yes—
203C2×C4×C131H(5,𝔽2)12yes—
204C2×C4×C1312−1+411yescharacteristic
205C2×C4×C1312−1+411yescharacteristic
206C8×C131—42no—
207C8×C131—42no—
208C22×C131—22no—
209C22×C131—22no—
210C22×C131—22no—
211C22×C131—41no—
212C22×C131—41no—
213C22×C131—41no—
214C22×C131—41no—
215C22×C131—81no—
216C22×C131—81no—
217C22×C131—81no—
218C22×C131—81no—
219C22×C131—81no—
220C22×C131—81no—
221C22×C131—81no—
222C22×C131C2×#12311yescharacteristic
223C22×C131#53511yescharacteristic
224C22×C131#53611yescharacteristic
225C22×C131C2×#13511yescharacteristic
226C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
227C22×C131#57511yescharacteristic
228C22×C131#57511yescharacteristic
229C4×C131—22no—
230C4×C131—22no—
231C4×C131—22no—
232C4×C131—41no—
233C4×C131—41no—
234C4×C131—81no—
235C4×C131—82no—
236C4×C131—81no—
237C4×C131—82no—
238C4×C131—81no—
239C4×C131#53912yes—
240C4×C131#53912yes—
241C2×C131—42no—
242C2×C131—161no—
243C2×C131#262311yescharacteristic
244C2×C131#309111yescharacteristic
245C2×C131#309411yescharacteristic
246C2×C131#320711yescharacteristic
247C2×C131#321911yescharacteristic
248C2×C131#323311yescharacteristic
249C2×C131#323511yescharacteristic
250#29914C13111yesmaximal, characteristic, direct product factor, Sylow
251C131#2991411yescharacteristic, direct product factor, Sylow
252#2854C2×C13111yescharacteristic
253#2285C2×C13111yescharacteristic, complemented
254#2100C2×C13111yescharacteristic, complemented
255#2099C2×C13111yescharacteristic, complemented
256#2094C2×C13111yescharacteristic, complemented
257#2093C2×C13111yescharacteristic, complemented
258#2085C2×C13112yescomplemented
259#2073C2×C13112yescomplemented
260#1875C2×C13112yes—
261#1854C2×C13112yescomplemented
262#1817C2×C13111yescharacteristic, complemented
263C2×#123—21no—
264C2×#121C22×C13111yescharacteristic
265C2×#117C22×C13112yes—
266C22×C42C22×C13111yescharacteristic
267C2×#107C22×C13112yes—
268C2×#106C22×C13112yes—
269C2×#102C22×C13112yes—
270C2×#102C22×C13112yes—
271C2×C22⋊C8C22×C13112yes—
272#390C22×C13111yescharacteristic
273#390C22×C13111yescharacteristic
274#389C22×C13111yescharacteristic
275#389C22×C13111yescharacteristic
276#388—21no—
277#388—21no—
278#386—21no—
279#384C22×C13111yescharacteristic
280#384C22×C13111yescharacteristic
281#382C22×C13112yes—
282#380—21no—
283#380—21no—
284#380C22×C13111yescharacteristic
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287#340C22×C13112yes—
288#340C22×C13112yes—
289#340C22×C13112yes—
290#340C22×C13112yes—
291#336C22×C13112yes—
292#336C22×C13111yescharacteristic
293#336C22×C13111yescharacteristic
294C22×D4—21no—
295C22×D4C23×C13111yescharacteristic
296C23×C4D4×C13111yescharacteristic
297C23×C4D4×C13111yescharacteristic
298C23×C4C23×C13111yescharacteristic
299C22×C8C23×C13112yes—
300C22×C8C23×C13112yes—
301#123—44no—
302#121—24no—
303#117—42no—
304#117—42no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4C23×C13112yes—
312C2×C4⋊C4C23×C13112yes—
313C2×C4⋊C4C23×C13111yescharacteristic
314C2×C4⋊C4C23×C13111yescharacteristic
315C2×C4⋊C4C23×C13111yescharacteristic
316C2×C22⋊C4—22no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C42—24no—
324C2×C42—22no—
325C2×C42D4×C13111yescharacteristic
326C2×C42D4×C13111yescharacteristic
327C2×C42C23×C13111yescharacteristic
328C2×C42C23×C13111yescharacteristic
329#107—42no—
330#106—42no—
331#102—42no—
332#102—42no—
333C22⋊C8—24no—
334#95—22no—
335#95—22no—
336#95—21no—
337#95—21no—
338#95—21no—
339C24—21no—
340C24C2×D4×C13111yescharacteristic
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—42no—
346C2×D4—42no—
347C2×D4—42no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4C2×D4×C13111yescharacteristic
363C22×C4C2×D4×C13111yescharacteristic
364C22×C4C2×D4×C13111yescharacteristic
365C22×C4C2×D4×C13111yescharacteristic
366C22×C4C2×D4×C13111yescharacteristic
367C22×C4#41×C13114yes—
368C22×C4C24×C13111yescharacteristic
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C4⋊C4—22no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—42no—
391C22⋊C4—44no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C42—22no—
397C42—22no—
398C42—22no—
399C42—22no—
400C42—44no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—41no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23#123×C13112yes—
415C23C22×D4×C13111yescharacteristic
416D4—42no—
417D4—42no—
418D4—84no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—41no—
450C2×C4#123×C13112yes—
451C2×C4#135×C13112yes—
452C2×C4AGL(1,ℤ/8)×C13112yes—
453C2×C4C2×#41×C13112yes—
454C2×C4H(5,𝔽2)×C13112yes—
455C2×C42−1+4×C13111yescharacteristic
456C2×C42−1+4×C13111yescharacteristic
457C8—42no—
458C8—42no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C2×#123×C13111yescharacteristic
474C22#535×C13111yescharacteristic
475C22#536×C13111yescharacteristic
476C22C2×#135×C13111yescharacteristic
477C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
478C22#575×C13111yescharacteristic
479C22#575×C13111yescharacteristic
480C4—22no—
481C4—22no—
482C4—22no—
483C4—41no—
484C4—41no—
485C4—81no—
486C4—82no—
487C4—81no—
488C4—82no—
489C4—81no—
490C4#539×C13112yes—
491C4#539×C13112yes—
492C2—42no—
493C2—161no—
494C2#2623×C13111yescharacteristic
495C2#3091×C13111yescharacteristic
496C2#3094×C13111yescharacteristic
497C2#3207×C13111yescharacteristic
498C2#3219×C13111yescharacteristic
499C2#3233×C13111yescharacteristic
500C2#3235×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×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. #2285×C131C2semidirect
3. #2100×C131C2semidirect
4. #2099×C131C2semidirect
5. #2094×C131C2semidirect
6. #2093×C131C2semidirect
7. #2085×C131C2semidirect
8. #2073×C131C2semidirect
10. #1854×C131C2semidirect
11. #1817×C131C2semidirect
250. #29914C131direct (N × H)
251. C131#29914direct (N × H)
253. #2285C2×C131semidirect
254. #2100C2×C131semidirect
255. #2099C2×C131semidirect
256. #2094C2×C131semidirect
257. #2093C2×C131semidirect
258. #2085C2×C131semidirect
259. #2073C2×C131semidirect
261. #1854C2×C131semidirect
262. #1817C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2854×C1312
#2285×C1312
#2100×C1312
#2099×C1312
#2094×C1312
#2093×C1312
#2085×C1312
#2073×C1312
#1875×C1312
#1854×C1312
#1817×C1312
#29914131