Finite Group Databasebeta

← C131×#9388 #45695272

Subgroups — C131×#9388 #45695272

Order 33536.

532 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2873×C131C211yesmaximal, characteristic
2#2611×C131C211yesmaximal, characteristic
3#1528×C131C212yesmaximal, complemented
4#1464×C131C211yesmaximal, characteristic
5#1300×C131C212yesmaximal, complemented
6C22×M16×C131—21no—
7C2×#125×C131C2211yescharacteristic
8C2×#117×C131C2211yescharacteristic
9#432×C131C2212yes—
10#405×C131—24no—
11C4×M16×C131—21no—
12C4×M16×C131C2212yes—
13#400×C131C411yescharacteristic
14#399×C131C411yescharacteristic
15#398×C131C411yescharacteristic
16#397×C131C411yescharacteristic
17#389×C131—21no—
18#388×C131—21no—
19#387×C131—21no—
20#385×C131—21no—
21#376×C131C2211yescharacteristic
22#330×C131—24no—
23#324×C131—21no—
24#323×C131—21no—
25C23×C4×C131D411yescharacteristic
26C2×M16×C131—22no—
27C2×M16×C131—24no—
28C2×M16×C131—24no—
29C2×M16×C131—22no—
30C22×C8×C131—22no—
31#125×C131—22no—
32#125×C131—22no—
33#117×C131—22no—
34#117×C131—22no—
35C2×C4⋊C4×C131—21no—
36C2×C4⋊C4×C131—21no—
37C2×C4⋊C4×C131—21no—
38C2×C4⋊C4×C131—21no—
39C2×C4⋊C4×C131C2×C411yescharacteristic
40C2×C4⋊C4×C131C2×C411yescharacteristic
41C2×C4⋊C4×C131C2×C411yescharacteristic
42C2×C4⋊C4×C131D411yescharacteristic
43C2×C22⋊C4×C131—21no—
44C2×C22⋊C4×C131—21no—
45C2×C22⋊C4×C131C2×C411yescharacteristic
46C2×C22⋊C4×C131D411yescharacteristic
47C2×C42×C131—21no—
48C2×C42×C131D411yescharacteristic
49C2×C42×C131C2311yescharacteristic
50C4⋊C8×C131—22no—
51C22⋊C8×C131—22no—
52#97×C131—22no—
53#97×C131—22no—
54#97×C131D414yes—
55C4×C8×C131—22no—
56C4×C8×C131—22no—
57#95×C131—21no—
58#95×C131—21no—
59#95×C131—21no—
60#95×C131—21no—
61#95×C131—21no—
62#95×C131C2×C411yescharacteristic
63#95×C131C2×C411yescharacteristic
64C24×C131C22⋊C411yescharacteristic
65C22×C4×C131—22no—
66C22×C4×C131—22no—
67C22×C4×C131—21no—
68C22×C4×C131—21no—
69C22×C4×C131—21no—
70C22×C4×C131—21no—
71C22×C4×C131—21no—
72C22×C4×C131—21no—
73C22×C4×C131C22⋊C411yescharacteristic
74C22×C4×C131C22⋊C411yescharacteristic
75C22×C4×C131C22⋊C411yescharacteristic
76C22×C4×C131C22×C411yescharacteristic
77C22×C4×C131C2×D411yescharacteristic
78C22×C4×C131C2×D411yescharacteristic
79M16×C131—28no—
80M16×C131—24no—
81M16×C131—24no—
82C2×C8×C131—28no—
83C2×C8×C131—24no—
84C2×C8×C131—42no—
85C4⋊C4×C131—22no—
86C4⋊C4×C131—22no—
87C4⋊C4×C131—22no—
88C4⋊C4×C131—22no—
89C4⋊C4×C131—42no—
90C4⋊C4×C131—42no—
91C4⋊C4×C131—41no—
92C4⋊C4×C131—42no—
93C4⋊C4×C131—41no—
94C22⋊C4×C131—22no—
95C22⋊C4×C131—22no—
96C22⋊C4×C131—42no—
97C22⋊C4×C131—42no—
98C42×C131—21no—
99C42×C131—21no—
100C42×C131—42no—
101C42×C131C2×D412yes—
102C42×C131#4112yes—
103C23×C131—21no—
104C23×C131—21no—
105C23×C131—41no—
106C23×C131—41no—
107C23×C131#10412yes—
108C23×C131C2×C22⋊C411yescharacteristic
109C2×C4×C131—22no—
110C2×C4×C131—22no—
111C2×C4×C131—24no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—21no—
115C2×C4×C131—21no—
116C2×C4×C131—22no—
117C2×C4×C131—21no—
118C2×C4×C131—21no—
119C2×C4×C131—41no—
120C2×C4×C131—41no—
121C2×C4×C131—41no—
122C2×C4×C131—41no—
123C2×C4×C131—41no—
124C2×C4×C131—41no—
125C2×C4×C131—41no—
126C2×C4×C131—41no—
127C2×C4×C131—41no—
128C2×C4×C131—41no—
129C2×C4×C131—41no—
130C2×C4×C131—41no—
131C2×C4×C131—41no—
132C2×C4×C131—41no—
133C2×C4×C131—41no—
134C2×C4×C131#10412yes—
135C2×C4×C131C4×D412yes—
136C2×C4×C131#12011yescharacteristic
137C2×C4×C131#12112yes—
138C2×C4×C131#12311yescharacteristic
139C8×C131—28no—
140C8×C131—82no—
141C22×C131—21no—
142C22×C131—21no—
143C22×C131—22no—
144C22×C131—42no—
145C22×C131—41no—
146C22×C131—41no—
147C22×C131—81no—
148C22×C131#38611yescharacteristic
149C22×C131C2×#10411yescharacteristic
150C22×C131C2×#10411yescharacteristic
151C4×C131—22no—
152C4×C131—21no—
153C4×C131—22no—
154C4×C131—21no—
155C4×C131—22no—
156C4×C131—42no—
157C4×C131—41no—
158C4×C131—41no—
159C4×C131—81no—
160C4×C131—81no—
161C4×C131—81no—
162C2×C131—21no—
163C2×C131—21no—
164C2×C131—42no—
165C2×C131#188411yescharacteristic
166C2×C131#189611yescharacteristic
167C2×C131#191511yescharacteristic
168#9388C13111yesmaximal, characteristic, direct product factor, Sylow
169C131#938811yescharacteristic, direct product factor, Sylow
170#2873C2×C13111yescharacteristic
171#2611C2×C13111yescharacteristic
172#1528C2×C13112yescomplemented
173#1464C2×C13111yescharacteristic
174#1300C2×C13112yescomplemented
175C22×M16—21no—
176C2×#125C22×C13111yescharacteristic
177C2×#117C22×C13111yescharacteristic
178#432C22×C13112yes—
179#405—24no—
180C4×M16—21no—
181C4×M16C22×C13112yes—
182#400C4×C13111yescharacteristic
183#399C4×C13111yescharacteristic
184#398C4×C13111yescharacteristic
185#397C4×C13111yescharacteristic
186#389—21no—
187#388—21no—
188#387—21no—
189#385—21no—
190#376C22×C13111yescharacteristic
191#330—24no—
192#324—21no—
193#323—21no—
194C23×C4D4×C13111yescharacteristic
195C2×M16—22no—
196C2×M16—24no—
197C2×M16—24no—
198C2×M16—22no—
199C22×C8—22no—
200#125—22no—
201#125—22no—
202#117—22no—
203#117—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×C4×C13111yescharacteristic
209C2×C4⋊C4C2×C4×C13111yescharacteristic
210C2×C4⋊C4C2×C4×C13111yescharacteristic
211C2×C4⋊C4D4×C13111yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4C2×C4×C13111yescharacteristic
215C2×C22⋊C4D4×C13111yescharacteristic
216C2×C42—21no—
217C2×C42D4×C13111yescharacteristic
218C2×C42C23×C13111yescharacteristic
219C4⋊C8—22no—
220C22⋊C8—22no—
221#97—22no—
222#97—22no—
223#97D4×C13114yes—
224C4×C8—22no—
225C4×C8—22no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95C2×C4×C13111yescharacteristic
232#95C2×C4×C13111yescharacteristic
233C24C22⋊C4×C13111yescharacteristic
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C22⋊C4×C13111yescharacteristic
243C22×C4C22⋊C4×C13111yescharacteristic
244C22×C4C22⋊C4×C13111yescharacteristic
245C22×C4C22×C4×C13111yescharacteristic
246C22×C4C2×D4×C13111yescharacteristic
247C22×C4C2×D4×C13111yescharacteristic
248M16—28no—
249M16—24no—
250M16—24no—
251C2×C8—28no—
252C2×C8—24no—
253C2×C8—42no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C22⋊C4—22no—
264C22⋊C4—22no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C42—21no—
268C42—21no—
269C42—42no—
270C42C2×D4×C13112yes—
271C42#41×C13112yes—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23#104×C13112yes—
277C23C2×C22⋊C4×C13111yescharacteristic
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4#104×C13112yes—
304C2×C4C4×D4×C13112yes—
305C2×C4#120×C13111yescharacteristic
306C2×C4#121×C13112yes—
307C2×C4#123×C13111yescharacteristic
308C8—28no—
309C8—82no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22#386×C13111yescharacteristic
318C22C2×#104×C13111yescharacteristic
319C22C2×#104×C13111yescharacteristic
320C4—22no—
321C4—21no—
322C4—22no—
323C4—21no—
324C4—22no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—21no—
332C2—21no—
333C2—42no—
334C2#1884×C13111yescharacteristic
335C2#1896×C13111yescharacteristic
336C2#1915×C13111yescharacteristic
subgroupG/H
center, socleC22×C131#386
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1528×C131C2semidirect
5. #1300×C131C2semidirect
168. #9388C131direct (N × H)
169. C131#9388direct (N × H)
172. #1528C2×C131semidirect
174. #1300C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2873×C1312
#2611×C1312
#1528×C1312
#1464×C1312
#1300×C1312
#9388131