Finite Group Databasebeta

← C131×#9056 #45694940

Subgroups — C131×#9056 #45694940

Order 33536.

432 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3170×C131C211yesmaximal, characteristic
2#2962×C131C211yesmaximal, characteristic
3#1986×C131C211yesmaximal, characteristic
4#1503×C131C211yesmaximal, characteristic
5#1481×C131C211yesmaximal, characteristic
6#1279×C131C211yesmaximal, characteristic
7#1278×C131C211yesmaximal, characteristic
8#533×C131C2211yescharacteristic
9#533×C131C2211yescharacteristic
10#500×C131C411yescharacteristic, complemented
11#494×C131C411yescharacteristic, complemented
12#487×C131C411yescharacteristic, complemented
13#487×C131C411yescharacteristic, complemented
14#467×C131—22no—
15#446×C131—22no—
16#446×C131—21no—
17C8×Q8×C131—21no—
18C4×Q16×C131—22no—
19#431×C131C2211yescharacteristic
20#424×C131—21no—
21C2×C4⋊C8×C131C2211yescharacteristic
22#405×C131—21no—
23C4×M16×C131C2211yescharacteristic
24C2×C4×C8×C131C2211yescharacteristic
25C4×C4⋊C4×C131C2211yescharacteristic
26#339×C131—21no—
27#339×C131—21no—
28#328×C131—22no—
29Q8⋊C8×C131—21no—
30Q8⋊C8×C131—21no—
31C2×Q16×C131—22no—
32C2×M16×C131D411yescharacteristic
33C2×M16×C131D411yescharacteristic
34C22×C8×C131—21no—
35C22×C8×C131—21no—
36C4⋊Q8×C131C2×C411yescharacteristic
37C4⋊Q8×C131C2×C411yescharacteristic
38C4⋊Q8×C131C2×C411yescharacteristic
39C4⋊Q8×C131C2×C411yescharacteristic
40#125×C131—21no—
41#125×C131—21no—
42C22⋊Q8×C131—21no—
43C22⋊Q8×C131—21no—
44C22⋊Q8×C131—21no—
45C22⋊Q8×C131D412yes—
46C4×Q8×C131—21no—
47C4×Q8×C131—21no—
48C4×Q8×C131—21no—
49C4×Q8×C131D412yes—
50#117×C131—21no—
51#117×C131—21no—
52C2×C4⋊C4×C131—21no—
53C2×C42×C131—21no—
54C2×C42×C131C2311yescharacteristic
55#107×C131—22no—
56C4⋊C8×C131—22no—
57C4⋊C8×C131—22no—
58C4⋊C8×C131—21no—
59C4⋊C8×C131—21no—
60C4⋊C8×C131D411yescharacteristic
61C4⋊C8×C131D411yescharacteristic
62#103×C131—22no—
63#103×C131—22no—
64C22⋊C8×C131—21no—
65#97×C131—22no—
66#97×C131—21no—
67C4×C8×C131—22no—
68C4×C8×C131—21no—
69C4×C8×C131—21no—
70C4×C8×C131—21no—
71C4×C8×C131C2×C411yescharacteristic
72C4×C8×C131C2×C411yescharacteristic
73#95×C131—21no—
74C2×Q8×C131—21no—
75C2×Q8×C131—21no—
76C2×Q8×C131—21no—
77C2×Q8×C131C22⋊C412yes—
78C22×C4×C131—41no—
79C22×C4×C131C2×D411yescharacteristic
80C22×C4×C131C2×D411yescharacteristic
81C22×C4×C131#4111yescharacteristic
82Q16×C131—44no—
83M16×C131—21no—
84M16×C131—21no—
85M16×C131—21no—
86M16×C131Q1612yescomplemented
87C2×C8×C131—21no—
88C2×C8×C131—21no—
89C2×C8×C131—21no—
90C2×C8×C131—21no—
91C2×C8×C131—21no—
92C2×C8×C131—21no—
93C2×C8×C131—42no—
94C2×C8×C131—41no—
95C2×C8×C131—41no—
96C2×C8×C131—41no—
97C4⋊C4×C131—21no—
98C4⋊C4×C131—21no—
99C4⋊C4×C131—21no—
100C4⋊C4×C131—22no—
101C4⋊C4×C131—22no—
102C4⋊C4×C131—22no—
103C4⋊C4×C131—21no—
104C4⋊C4×C131—21no—
105C4⋊C4×C131—21no—
106C4⋊C4×C131—21no—
107C4⋊C4×C131—41no—
108C4⋊C4×C131—41no—
109C4⋊C4×C131—41no—
110C4⋊C4×C131C22⋊C412yes—
111C22⋊C4×C131—22no—
112C22⋊C4×C131—41no—
113C42×C131—22no—
114C42×C131—41no—
115C42×C131—41no—
116C42×C131—41no—
117C42×C131C22×C411yescharacteristic
118C42×C131C2×D411yescharacteristic
119C42×C131C2×D411yescharacteristic
120C42×C131#4111yescharacteristic
121C23×C131#12111yescharacteristic
122Q8×C131—42no—
123Q8×C131—42no—
124Q8×C131—41no—
125Q8×C131—41no—
126Q8×C131—41no—
127Q8×C131—41no—
128C2×C4×C131—21no—
129C2×C4×C131—21no—
130C2×C4×C131—22no—
131C2×C4×C131—22no—
132C2×C4×C131—41no—
133C2×C4×C131—42no—
134C2×C4×C131—41no—
135C2×C4×C131—41no—
136C2×C4×C131—81no—
137C2×C4×C131—81no—
138C2×C4×C131C2×C22⋊C411yescharacteristic
139C2×C4×C131C4×D411yescharacteristic
140C2×C4×C131C4×D411yescharacteristic
141C2×C4×C131#12011yescharacteristic
142C2×C4×C131#12111yescharacteristic
143C2×C4×C131#12311yescharacteristic
144C2×C4×C131C2×Q1611yescharacteristic
145C2×C4×C131#13511yescharacteristic
146C2×C4×C131#13711yescharacteristic
147C2×C4×C131#13711yescharacteristic
148C8×C131—22no—
149C8×C131—22no—
150C8×C131—41no—
151C8×C131—41no—
152C8×C131—41no—
153C8×C131—41no—
154C8×C131—81no—
155C22×C131—21no—
156C22×C131—21no—
157C22×C131#38611yescharacteristic
158C22×C131#46211yescharacteristic
159C22×C131#46411yescharacteristic
160C4×C131—21no—
161C4×C131—21no—
162C4×C131—21no—
163C4×C131—42no—
164C4×C131—42no—
165C4×C131—82no—
166C4×C131—81no—
167C4×C131—81no—
168C4×C131C4×Q1611yescharacteristic
169C4×C131#44111yescharacteristic
170C4×C131#44311yescharacteristic
171C4×C131#44411yescharacteristic
172C4×C131#45111yescharacteristic
173C4×C131#45211yescharacteristic
174C2×C131—21no—
175C2×C131—21no—
176C2×C131#187611yescharacteristic
177C2×C131#187811yescharacteristic
178C2×C131#188411yescharacteristic
179#9056C13111yesmaximal, characteristic, direct product factor, Sylow
180C131#905611yescharacteristic, direct product factor, Sylow
181#3170C2×C13111yescharacteristic
182#2962C2×C13111yescharacteristic
183#1986C2×C13111yescharacteristic
184#1503C2×C13111yescharacteristic
185#1481C2×C13111yescharacteristic
186#1279C2×C13111yescharacteristic
187#1278C2×C13111yescharacteristic
188#533C22×C13111yescharacteristic
189#533C22×C13111yescharacteristic
190#500C4×C13111yescharacteristic, complemented
191#494C4×C13111yescharacteristic, complemented
192#487C4×C13111yescharacteristic, complemented
193#487C4×C13111yescharacteristic, complemented
194#467—22no—
195#446—22no—
196#446—21no—
197C8×Q8—21no—
198C4×Q16—22no—
199#431C22×C13111yescharacteristic
200#424—21no—
201C2×C4⋊C8C22×C13111yescharacteristic
202#405—21no—
203C4×M16C22×C13111yescharacteristic
204C2×C4×C8C22×C13111yescharacteristic
205C4×C4⋊C4C22×C13111yescharacteristic
206#339—21no—
207#339—21no—
208#328—22no—
209Q8⋊C8—21no—
210Q8⋊C8—21no—
211C2×Q16—22no—
212C2×M16D4×C13111yescharacteristic
213C2×M16D4×C13111yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C4⋊Q8C2×C4×C13111yescharacteristic
217C4⋊Q8C2×C4×C13111yescharacteristic
218C4⋊Q8C2×C4×C13111yescharacteristic
219C4⋊Q8C2×C4×C13111yescharacteristic
220#125—21no—
221#125—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C22⋊Q8D4×C13112yes—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8D4×C13112yes—
230#117—21no—
231#117—21no—
232C2×C4⋊C4—21no—
233C2×C42—21no—
234C2×C42C23×C13111yescharacteristic
235#107—22no—
236C4⋊C8—22no—
237C4⋊C8—22no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8D4×C13111yescharacteristic
241C4⋊C8D4×C13111yescharacteristic
242#103—22no—
243#103—22no—
244C22⋊C8—21no—
245#97—22no—
246#97—21no—
247C4×C8—22no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8C2×C4×C13111yescharacteristic
252C4×C8C2×C4×C13111yescharacteristic
253#95—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8C22⋊C4×C13112yes—
258C22×C4—41no—
259C22×C4C2×D4×C13111yescharacteristic
260C22×C4C2×D4×C13111yescharacteristic
261C22×C4#41×C13111yescharacteristic
262Q16—44no—
263M16—21no—
264M16—21no—
265M16—21no—
266M16Q16×C13112yescomplemented
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—42no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C22⋊C4×C13112yes—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C42—22no—
294C42—41no—
295C42—41no—
296C42—41no—
297C42C22×C4×C13111yescharacteristic
298C42C2×D4×C13111yescharacteristic
299C42C2×D4×C13111yescharacteristic
300C42#41×C13111yescharacteristic
301C23#121×C13111yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4C2×C22⋊C4×C13111yescharacteristic
319C2×C4C4×D4×C13111yescharacteristic
320C2×C4C4×D4×C13111yescharacteristic
321C2×C4#120×C13111yescharacteristic
322C2×C4#121×C13111yescharacteristic
323C2×C4#123×C13111yescharacteristic
324C2×C4C2×Q16×C13111yescharacteristic
325C2×C4#135×C13111yescharacteristic
326C2×C4#137×C13111yescharacteristic
327C2×C4#137×C13111yescharacteristic
328C8—22no—
329C8—22no—
330C8—41no—
331C8—41no—
332C8—41no—
333C8—41no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22#386×C13111yescharacteristic
338C22#462×C13111yescharacteristic
339C22#464×C13111yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—42no—
344C4—42no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4C4×Q16×C13111yescharacteristic
349C4#441×C13111yescharacteristic
350C4#443×C13111yescharacteristic
351C4#444×C13111yescharacteristic
352C4#451×C13111yescharacteristic
353C4#452×C13111yescharacteristic
354C2—21no—
355C2—21no—
356C2#1876×C13111yescharacteristic
357C2#1878×C13111yescharacteristic
358C2#1884×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#120
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
socleC22×C131#386
prime radicalC23×C131#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
10. #500×C131C4semidirect
11. #494×C131C4semidirect
12. #487×C131C4semidirect
13. #487×C131C4semidirect
86. M16×C131Q16semidirect
179. #9056C131direct (N × H)
180. C131#9056direct (N × H)
190. #500C4×C131semidirect
191. #494C4×C131semidirect
192. #487C4×C131semidirect
193. #487C4×C131semidirect
266. M16Q16×C131semidirect

Maximal subgroups

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

subgroupindex
#3170×C1312
#2962×C1312
#1986×C1312
#1503×C1312
#1481×C1312
#1279×C1312
#1278×C1312
#9056131