Finite Group Databasebeta

← C131×#12711 #45698595

Subgroups — C131×#12711 #45698595

Order 33536.

1156 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C131C211yesmaximal, characteristic
2#2134×C131C211yesmaximal, characteristic, complemented
3#2128×C131C211yesmaximal, characteristic, complemented
4#2120×C131C212yesmaximal, complemented
5#1795×C131C212yesmaximal, complemented
6C2×H(5,𝔽2)×C131C2211yescharacteristic
7C23×D4×C131C411yescharacteristic, complemented
8#546×C131—22no—
9#546×C131—22no—
10D42×C131—22no—
11D42×C131—22no—
12#535×C131C411yescharacteristic, complemented
13#535×C131C2211yescharacteristic
14#534×C131—22no—
15#525×C131C411yescharacteristic, complemented
16#525×C131C2211yescharacteristic
17C2×#120×C131—22no—
18#518×C131C411yescharacteristic, complemented
19#421×C131—22no—
20#418×C131—22no—
21#413×C131C2212yescomplemented
22#410×C131C2212yescomplemented
23#355×C131—22no—
24#353×C131—22no—
25#352×C131—22no—
26AΣL(1,𝔽16)×C131—22no—
27C25×C131—21no—
28H(5,𝔽2)×C131—44no—
29C2×#41×C131—21no—
30C2×#41×C131C2×C411yescharacteristic
31C2×#41×C131D412yes—
32C2×#41×C131C2311yescharacteristic
33C22×D4×C131—24no—
34C22×D4×C131—22no—
35C22×D4×C131—22no—
36C22×D4×C131—22no—
37C22×D4×C131—21no—
38C22×D4×C131—21no—
39C22×D4×C131—44no—
40C22×D4×C131C2×C411yescharacteristic
41C22×D4×C131C2×C411yescharacteristic
42C22×D4×C131D412yes—
43C23×C4×C131C2×C411yescharacteristic
44C2×M16×C131—22no—
45#127×C131—21no—
46#127×C131D412yes—
47#124×C131—21no—
48#124×C131D412yes—
49#123×C131—24no—
50#123×C131—21no—
51#123×C131D412yes—
52C22⋊Q8×C131—21no—
53C22⋊Q8×C131—21no—
54#121×C131—24no—
55#121×C131—24no—
56#121×C131—21no—
57#121×C131—22no—
58#121×C131—21no—
59#121×C131—22no—
60#120×C131—24no—
61#120×C131—24no—
62#120×C131—24no—
63#120×C131—21no—
64#120×C131—22no—
65#120×C131—22no—
66#120×C131D412yes—
67C4×D4×C131—22no—
68C4×D4×C131—22no—
69C4×D4×C131—22no—
70C4×D4×C131—22no—
71#117×C131—22no—
72#117×C131C2×C411yescharacteristic
73#117×C131C2×C411yescharacteristic
74C2×C22⋊C4×C131—24no—
75C2×C22⋊C4×C131—22no—
76#104×C131—44no—
77#102×C131—44no—
78#101×C131—22no—
79#100×C131—22no—
80#99×C131—22no—
81#99×C131—22no—
82C24×C131—21no—
83C24×C131—24no—
84C24×C131—21no—
85C24×C131—22no—
86C24×C131—44no—
87C24×C131—84no—
88C24×C131C22⋊C411yescharacteristic
89#41×C131—24no—
90#41×C131—42no—
91#41×C131—42no—
92#41×C131—42no—
93#41×C131—44no—
94C2×Q8×C131C22⋊C411yescharacteristic
95C2×Q8×C131C2×D411yescharacteristic
96C2×D4×C131—24no—
97C2×D4×C131—24no—
98C2×D4×C131—22no—
99C2×D4×C131—24no—
100C2×D4×C131—21no—
101C2×D4×C131—22no—
102C2×D4×C131—22no—
103C2×D4×C131—24no—
104C2×D4×C131—24no—
105C2×D4×C131—21no—
106C2×D4×C131—21no—
107C2×D4×C131—22no—
108C2×D4×C131—42no—
109C2×D4×C131—42no—
110C2×D4×C131—48no—
111C2×D4×C131—44no—
112C2×D4×C131—44no—
113C2×D4×C131—44no—
114C2×D4×C131—48no—
115C2×D4×C131—44no—
116C2×D4×C131—88no—
117C2×D4×C131C22⋊C412yes—
118C2×D4×C131C22⋊C411yescharacteristic
119C2×D4×C131C22⋊C412yes—
120C2×D4×C131C2×D411yescharacteristic
121C2×D4×C131C2×D412yes—
122C22×C4×C131—24no—
123C22×C4×C131—21no—
124C22×C4×C131—21no—
125C22×C4×C131—21no—
126C22×C4×C131—22no—
127C22×C4×C131—42no—
128C22×C4×C131C22⋊C411yescharacteristic
129C22×C4×C131C22×C411yescharacteristic
130C22×C4×C131C2×D412yes—
131M16×C131—42no—
132M16×C131—42no—
133C2×C8×C131—42no—
134C4⋊C4×C131—22no—
135C4⋊C4×C131—21no—
136C4⋊C4×C131—21no—
137C4⋊C4×C131—22no—
138C4⋊C4×C131—42no—
139C22⋊C4×C131—22no—
140C22⋊C4×C131—24no—
141C22⋊C4×C131—24no—
142C22⋊C4×C131—22no—
143C22⋊C4×C131—21no—
144C22⋊C4×C131—22no—
145C22⋊C4×C131—22no—
146C22⋊C4×C131—24no—
147C22⋊C4×C131—42no—
148C22⋊C4×C131C22⋊C412yes—
149C42×C131—21no—
150C42×C131—42no—
151C42×C131C22⋊C412yes—
152C23×C131—24no—
153C23×C131—21no—
154C23×C131—22no—
155C23×C131—22no—
156C23×C131—21no—
157C23×C131—44no—
158C23×C131—41no—
159C23×C131—42no—
160C23×C131—42no—
161C23×C131—48no—
162C23×C131—48no—
163C23×C131—82no—
164C23×C131—82no—
165C23×C131—84no—
166C23×C131—84no—
167C23×C131—88no—
168C23×C131—88no—
169C23×C131C2×C22⋊C411yescharacteristic
170C23×C131#12012yes—
171Q8×C131—22no—
172Q8×C131—41no—
173D4×C131—24no—
174D4×C131—22no—
175D4×C131—22no—
176D4×C131—42no—
177D4×C131—41no—
178D4×C131—44no—
179D4×C131—42no—
180D4×C131—44no—
181D4×C131—48no—
182D4×C131—42no—
183D4×C131—44no—
184D4×C131—44no—
185D4×C131—42no—
186D4×C131—84no—
187D4×C131—84no—
188D4×C131#9914yes—
189C2×C4×C131—22no—
190C2×C4×C131—22no—
191C2×C4×C131—22no—
192C2×C4×C131—22no—
193C2×C4×C131—22no—
194C2×C4×C131—21no—
195C2×C4×C131—21no—
196C2×C4×C131—44no—
197C2×C4×C131—42no—
198C2×C4×C131—42no—
199C2×C4×C131—42no—
200C2×C4×C131—41no—
201C2×C4×C131—84no—
202C2×C4×C131—82no—
203C2×C4×C131C2×C22⋊C411yescharacteristic
204C2×C4×C131C2×C22⋊C411yescharacteristic
205C2×C4×C131#12012yes—
206C8×C131—82no—
207C22×C131—22no—
208C22×C131—21no—
209C22×C131—22no—
210C22×C131—24no—
211C22×C131—42no—
212C22×C131—41no—
213C22×C131—44no—
214C22×C131—41no—
215C22×C131—42no—
216C22×C131—44no—
217C22×C131—42no—
218C22×C131—42no—
219C22×C131—41no—
220C22×C131—41no—
221C22×C131—42no—
222C22×C131—84no—
223C22×C131—816no—
224C22×C131—84no—
225C22×C131—164no—
226C22×C131#37911yescharacteristic
227C4×C131—22no—
228C4×C131—21no—
229C4×C131—42no—
230C4×C131—42no—
231C4×C131—41no—
232C4×C131—41no—
233C4×C131—162no—
234C4×C131C2×#9912yes—
235C2×C131—21no—
236C2×C131—42no—
237C2×C131—42no—
238C2×C131—41no—
239C2×C131—44no—
240C2×C131—82no—
241C2×C131—81no—
242C2×C131#178111yescharacteristic
243#12711C13111yesmaximal, characteristic, direct product factor, Sylow
244C131#1271111yescharacteristic, direct product factor, Sylow
245#3484C2×C13111yescharacteristic
246#2134C2×C13111yescharacteristic, complemented
247#2128C2×C13111yescharacteristic, complemented
248#2120C2×C13112yescomplemented
249#1795C2×C13112yescomplemented
250C2×H(5,𝔽2)C22×C13111yescharacteristic
251C23×D4C4×C13111yescharacteristic, complemented
252#546—22no—
253#546—22no—
254D42—22no—
255D42—22no—
256#535C4×C13111yescharacteristic, complemented
257#535C22×C13111yescharacteristic
258#534—22no—
259#525C4×C13111yescharacteristic, complemented
260#525C22×C13111yescharacteristic
261C2×#120—22no—
262#518C4×C13111yescharacteristic, complemented
263#421—22no—
264#418—22no—
265#413C22×C13112yescomplemented
266#410C22×C13112yescomplemented
267#355—22no—
268#353—22no—
269#352—22no—
270AΣL(1,𝔽16)—22no—
271C25—21no—
272H(5,𝔽2)—44no—
273C2×#41—21no—
274C2×#41C2×C4×C13111yescharacteristic
275C2×#41D4×C13112yes—
276C2×#41C23×C13111yescharacteristic
277C22×D4—24no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—44no—
284C22×D4C2×C4×C13111yescharacteristic
285C22×D4C2×C4×C13111yescharacteristic
286C22×D4D4×C13112yes—
287C23×C4C2×C4×C13111yescharacteristic
288C2×M16—22no—
289#127—21no—
290#127D4×C13112yes—
291#124—21no—
292#124D4×C13112yes—
293#123—24no—
294#123—21no—
295#123D4×C13112yes—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298#121—24no—
299#121—24no—
300#121—21no—
301#121—22no—
302#121—21no—
303#121—22no—
304#120—24no—
305#120—24no—
306#120—24no—
307#120—21no—
308#120—22no—
309#120—22no—
310#120D4×C13112yes—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315#117—22no—
316#117C2×C4×C13111yescharacteristic
317#117C2×C4×C13111yescharacteristic
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320#104—44no—
321#102—44no—
322#101—22no—
323#100—22no—
324#99—22no—
325#99—22no—
326C24—21no—
327C24—24no—
328C24—21no—
329C24—22no—
330C24—44no—
331C24—84no—
332C24C22⋊C4×C13111yescharacteristic
333#41—24no—
334#41—42no—
335#41—42no—
336#41—42no—
337#41—44no—
338C2×Q8C22⋊C4×C13111yescharacteristic
339C2×Q8C2×D4×C13111yescharacteristic
340C2×D4—24no—
341C2×D4—24no—
342C2×D4—22no—
343C2×D4—24no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—24no—
348C2×D4—24no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—48no—
355C2×D4—44no—
356C2×D4—44no—
357C2×D4—44no—
358C2×D4—48no—
359C2×D4—44no—
360C2×D4—88no—
361C2×D4C22⋊C4×C13111yescharacteristic
362C2×D4C22⋊C4×C13112yes—
363C2×D4C22⋊C4×C13112yes—
364C2×D4C2×D4×C13111yescharacteristic
365C2×D4C2×D4×C13112yes—
366C22×C4—24no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—42no—
372C22×C4C22⋊C4×C13111yescharacteristic
373C22×C4C22×C4×C13111yescharacteristic
374C22×C4C2×D4×C13112yes—
375M16—42no—
376M16—42no—
377C2×C8—42no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C22⋊C4—22no—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—22no—
387C22⋊C4—21no—
388C22⋊C4—22no—
389C22⋊C4—22no—
390C22⋊C4—24no—
391C22⋊C4—42no—
392C22⋊C4C22⋊C4×C13112yes—
393C42—21no—
394C42—42no—
395C42C22⋊C4×C13112yes—
396C23—24no—
397C23—21no—
398C23—22no—
399C23—22no—
400C23—21no—
401C23—44no—
402C23—41no—
403C23—42no—
404C23—42no—
405C23—48no—
406C23—48no—
407C23—82no—
408C23—82no—
409C23—84no—
410C23—84no—
411C23—88no—
412C23—88no—
413C23C2×C22⋊C4×C13111yescharacteristic
414C23#120×C13112yes—
415Q8—22no—
416Q8—41no—
417D4—24no—
418D4—22no—
419D4—22no—
420D4—42no—
421D4—41no—
422D4—44no—
423D4—42no—
424D4—44no—
425D4—48no—
426D4—42no—
427D4—44no—
428D4—44no—
429D4—42no—
430D4—84no—
431D4—84no—
432D4#99×C13114yes—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—84no—
446C2×C4—82no—
447C2×C4C2×C22⋊C4×C13111yescharacteristic
448C2×C4C2×C22⋊C4×C13111yescharacteristic
449C2×C4#120×C13112yes—
450C8—82no—
451C22—22no—
452C22—21no—
453C22—22no—
454C22—24no—
455C22—42no—
456C22—41no—
457C22—44no—
458C22—41no—
459C22—42no—
460C22—44no—
461C22—42no—
462C22—42no—
463C22—41no—
464C22—41no—
465C22—42no—
466C22—84no—
467C22—816no—
468C22—84no—
469C22—164no—
470C22#379×C13111yescharacteristic
471C4—22no—
472C4—21no—
473C4—42no—
474C4—42no—
475C4—41no—
476C4—41no—
477C4—162no—
478C4C2×#99×C13112yes—
479C2—21no—
480C2—42no—
481C2—42no—
482C2—41no—
483C2—44no—
484C2—82no—
485C2—81no—
486C2#1781×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1781
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×#41C23×C131
prime radical#3484×C131C2
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×H(5,𝔽2)×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2134×C131C2semidirect
3. #2128×C131C2semidirect
4. #2120×C131C2semidirect
5. #1795×C131C2semidirect
7. C23×D4×C131C4semidirect
12. #535×C131C4semidirect
15. #525×C131C4semidirect
18. #518×C131C4semidirect
21. #413×C131C22semidirect
22. #410×C131C22semidirect
243. #12711C131direct (N × H)
244. C131#12711direct (N × H)
246. #2134C2×C131semidirect
247. #2128C2×C131semidirect
248. #2120C2×C131semidirect
249. #1795C2×C131semidirect
251. C23×D4C4×C131semidirect
256. #535C4×C131semidirect
259. #525C4×C131semidirect
262. #518C4×C131semidirect
265. #413C22×C131semidirect
266. #410C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3484×C1312
#2134×C1312
#2128×C1312
#2120×C1312
#1795×C1312
#12711131