Finite Group Databasebeta

← C131×#8491 #45694375

Subgroups — C131×#8491 #45694375

Order 33536.

820 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3549×C131C211yesmaximal, characteristic
2#1963×C131C211yesmaximal, characteristic, complemented
3#1557×C131C212yesmaximal, complemented
4#1536×C131C211yesmaximal, characteristic, complemented
5#1505×C131C212yesmaximal, complemented
6H(3,𝔽4)×C131—22no—
7#555×C131—22no—
8#555×C131C412yescomplemented
9D42×C131—22no—
10D42×C131C412yescomplemented
11#535×C131—22no—
12#535×C131—24no—
13#532×C131C2211yescharacteristic
14#532×C131C2212yes—
15#432×C131C2212yescomplemented
16#423×C131C2211yescharacteristic, complemented
17C2×#104×C131—22no—
18#376×C131C2211yescharacteristic, complemented
19#332×C131—22no—
20#331×C131—22no—
21#329×C131—22no—
22#327×C131—24no—
23C2×#41×C131—22no—
24C2×#41×C131D412yes—
25C22×D4×C131—22no—
26C22×D4×C131—24no—
27C2×M16×C131—21no—
28C4⋊Q8×C131C2×C411yescharacteristic
29C4⋊Q8×C131D412yes—
30#127×C131—24no—
31#127×C131C2×C411yescharacteristic
32#127×C131D412yes—
33#124×C131—28no—
34#124×C131—24no—
35#124×C131—22no—
36#124×C131D412yes—
37#121×C131—24no—
38#121×C131—24no—
39#121×C131—22no—
40#121×C131—22no—
41#121×C131—24no—
42#121×C131D414yes—
43#120×C131—24no—
44#120×C131—28no—
45#120×C131—24no—
46C4×D4×C131—22no—
47C4×D4×C131—22no—
48C4×D4×C131C2×C414yes—
49#117×C131—22no—
50#117×C131—24no—
51C2×C42×C131—21no—
52C2×C42×C131C2311yescharacteristic
53C4⋊C8×C131—22no—
54C4⋊C8×C131—22no—
55#104×C131—44no—
56C22⋊C8×C131—22no—
57#97×C131—22no—
58#95×C131—22no—
59C24×C131—24no—
60#41×C131—42no—
61#41×C131—42no—
62#41×C131—84no—
63C2×Q8×C131—22no—
64C2×Q8×C131C22⋊C412yes—
65C2×D4×C131—24no—
66C2×D4×C131—28no—
67C2×D4×C131—22no—
68C2×D4×C131—24no—
69C2×D4×C131—22no—
70C2×D4×C131—22no—
71C2×D4×C131—22no—
72C2×D4×C131—88no—
73C2×D4×C131—82no—
74C2×D4×C131—82no—
75C2×D4×C131C22⋊C414yes—
76C2×D4×C131C22⋊C412yes—
77C22×C4×C131—24no—
78C22×C4×C131—22no—
79C22×C4×C131—41no—
80C22×C4×C131C2×D411yescharacteristic
81C22×C4×C131C2×D412yes—
82M16×C131—42no—
83C2×C8×C131—42no—
84C2×C8×C131—41no—
85C4⋊C4×C131—22no—
86C4⋊C4×C131—22no—
87C4⋊C4×C131C22⋊C414yes—
88C22⋊C4×C131—28no—
89C22⋊C4×C131—24no—
90C22⋊C4×C131—24no—
91C22⋊C4×C131—24no—
92C22⋊C4×C131—24no—
93C42×C131—24no—
94C42×C131—22no—
95C42×C131—41no—
96C42×C131C22×C411yescharacteristic
97C42×C131C2×D411yescharacteristic
98C42×C131C2×D412yes—
99C23×C131—22no—
100C23×C131—24no—
101C23×C131—84no—
102C23×C131—88no—
103C23×C131#12011yescharacteristic
104Q8×C131—42no—
105Q8×C131—82no—
106D4×C131—44no—
107D4×C131—42no—
108D4×C131—44no—
109D4×C131—42no—
110D4×C131—42no—
111D4×C131—82no—
112D4×C131—82no—
113D4×C131—84no—
114D4×C131—84no—
115D4×C131—88no—
116C2×C4×C131—21no—
117C2×C4×C131—21no—
118C2×C4×C131—22no—
119C2×C4×C131—24no—
120C2×C4×C131—42no—
121C2×C4×C131—48no—
122C2×C4×C131—42no—
123C2×C4×C131—42no—
124C2×C4×C131—42no—
125C2×C4×C131—82no—
126C2×C4×C131C2×C22⋊C411yescharacteristic
127C2×C4×C131C2×C22⋊C412yes—
128C2×C4×C131#12012yes—
129C2×C4×C131#12011yescharacteristic
130C8×C131—82no—
131C8×C131—81no—
132C22×C131—21no—
133C22×C131—22no—
134C22×C131—42no—
135C22×C131—44no—
136C22×C131—44no—
137C22×C131—44no—
138C22×C131—44no—
139C22×C131—168no—
140C22×C131#37911yescharacteristic
141C4×C131—21no—
142C4×C131—22no—
143C4×C131—22no—
144C4×C131—42no—
145C4×C131—44no—
146C4×C131—82no—
147C4×C131#45311yescharacteristic
148C4×C131#45511yescharacteristic
149C2×C131—41no—
150C2×C131—82no—
151C2×C131—84no—
152C2×C131#179211yescharacteristic
153C2×C131#179512yes—
154#8491C13111yesmaximal, characteristic, direct product factor, Sylow
155C131#849111yescharacteristic, direct product factor, Sylow
156#3549C2×C13111yescharacteristic
157#1963C2×C13111yescharacteristic, complemented
158#1557C2×C13112yescomplemented
159#1536C2×C13111yescharacteristic, complemented
160#1505C2×C13112yescomplemented
161H(3,𝔽4)—22no—
162#555—22no—
163#555C4×C13112yescomplemented
164D42—22no—
165D42C4×C13112yescomplemented
166#535—22no—
167#535—24no—
168#532C22×C13111yescharacteristic
169#532C22×C13112yes—
170#432C22×C13112yescomplemented
171#423C22×C13111yescharacteristic, complemented
172C2×#104—22no—
173#376C22×C13111yescharacteristic, complemented
174#332—22no—
175#331—22no—
176#329—22no—
177#327—24no—
178C2×#41—22no—
179C2×#41D4×C13112yes—
180C22×D4—22no—
181C22×D4—24no—
182C2×M16—21no—
183C4⋊Q8C2×C4×C13111yescharacteristic
184C4⋊Q8D4×C13112yes—
185#127—24no—
186#127C2×C4×C13111yescharacteristic
187#127D4×C13112yes—
188#124—28no—
189#124—24no—
190#124—22no—
191#124D4×C13112yes—
192#121—24no—
193#121—24no—
194#121—22no—
195#121—22no—
196#121—24no—
197#121D4×C13114yes—
198#120—24no—
199#120—28no—
200#120—24no—
201C4×D4—22no—
202C4×D4—22no—
203C4×D4C2×C4×C13114yes—
204#117—22no—
205#117—24no—
206C2×C42—21no—
207C2×C42C23×C13111yescharacteristic
208C4⋊C8—22no—
209C4⋊C8—22no—
210#104—44no—
211C22⋊C8—22no—
212#97—22no—
213#95—22no—
214C24—24no—
215#41—42no—
216#41—42no—
217#41—84no—
218C2×Q8—22no—
219C2×Q8C22⋊C4×C13112yes—
220C2×D4—24no—
221C2×D4—28no—
222C2×D4—22no—
223C2×D4—24no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—88no—
228C2×D4—82no—
229C2×D4—82no—
230C2×D4C22⋊C4×C13114yes—
231C2×D4C22⋊C4×C13112yes—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4C2×D4×C13111yescharacteristic
236C22×C4C2×D4×C13112yes—
237M16—42no—
238C2×C8—42no—
239C2×C8—41no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4C22⋊C4×C13114yes—
243C22⋊C4—28no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—24no—
248C42—24no—
249C42—22no—
250C42—41no—
251C42C22×C4×C13111yescharacteristic
252C42C2×D4×C13111yescharacteristic
253C42C2×D4×C13112yes—
254C23—22no—
255C23—24no—
256C23—84no—
257C23—88no—
258C23#120×C13111yescharacteristic
259Q8—42no—
260Q8—82no—
261D4—44no—
262D4—42no—
263D4—44no—
264D4—42no—
265D4—42no—
266D4—82no—
267D4—82no—
268D4—84no—
269D4—84no—
270D4—88no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—42no—
276C2×C4—48no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4C2×C22⋊C4×C13111yescharacteristic
282C2×C4C2×C22⋊C4×C13112yes—
283C2×C4#120×C13112yes—
284C2×C4#120×C13111yescharacteristic
285C8—82no—
286C8—81no—
287C22—21no—
288C22—22no—
289C22—42no—
290C22—44no—
291C22—44no—
292C22—44no—
293C22—44no—
294C22—168no—
295C22#379×C13111yescharacteristic
296C4—21no—
297C4—22no—
298C4—22no—
299C4—42no—
300C4—44no—
301C4—82no—
302C4#453×C13111yescharacteristic
303C4#455×C13111yescharacteristic
304C2—41no—
305C2—82no—
306C2—84no—
307C2#1792×C13111yescharacteristic
308C2#1795×C13112yes—
subgroupG/H
center, socleC22×C131#379
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
prime radical#3549×C131C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1963×C131C2semidirect
3. #1557×C131C2semidirect
4. #1536×C131C2semidirect
5. #1505×C131C2semidirect
8. #555×C131C4semidirect
10. D42×C131C4semidirect
15. #432×C131C22semidirect
16. #423×C131C22semidirect
18. #376×C131C22semidirect
154. #8491C131direct (N × H)
155. C131#8491direct (N × H)
157. #1963C2×C131semidirect
158. #1557C2×C131semidirect
159. #1536C2×C131semidirect
160. #1505C2×C131semidirect
163. #555C4×C131semidirect
165. D42C4×C131semidirect
170. #432C22×C131semidirect
171. #423C22×C131semidirect
173. #376C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3549×C1312
#1963×C1312
#1557×C1312
#1536×C1312
#1505×C1312
#8491131