Finite Group Databasebeta

← C131×#33771 #45719655

Subgroups — C131×#33771 #45719655

Order 33536.

730 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3169×C131C211yesmaximal, characteristic, complemented
2C2×#493×C131C211yesmaximal, characteristic, complemented
3#2246×C131C212yesmaximal, complemented
4#2240×C131C212yesmaximal, complemented
5#2206×C131C214yesmaximal, complemented
6#2184×C131C214yesmaximal, complemented
7#2162×C131C211yesmaximal, characteristic, complemented
8C22×D8×C131—21no—
9C22×D8×C131C2212yes—
10#532×C131—21no—
11C2×#127×C131—21no—
12C2×D16×C131C2218yescomplemented
13#500×C131C2211yescharacteristic, complemented
14#493×C131—21no—
15#493×C131—21no—
16#493×C131C2212yes—
17#493×C131C2212yes—
18#493×C131C2211yescharacteristic, complemented
19#486×C131—21no—
20#466×C131—21no—
21#466×C131C2212yes—
22C4×D8×C131—21no—
23C4×D8×C131C2212yescomplemented
24C2×C4×C8×C131C2211yescharacteristic
25C4⋊C16×C131C2212yescomplemented
26#357×C131C2218yescomplemented
27C22⋊C16×C131C2212yes—
28C4×C16×C131C2212yescomplemented
29C2×#41×C131—41no—
30C22×D4×C131—22no—
31C22×D4×C131—41no—
32C22×D4×C131—41no—
33C2×D8×C131—21no—
34C2×D8×C131—22no—
35C2×D8×C131—22no—
36C2×D8×C131—22no—
37C2×D8×C131—44no—
38C2×D8×C131—44no—
39C2×D8×C131C2312yes—
40C2×D8×C131C2314yes—
41C22×C8×C131D411yescharacteristic
42C22×C8×C131C2311yescharacteristic
43C4⋊Q8×C131—21no—
44#127×C131—21no—
45#127×C131—22no—
46#127×C131—22no—
47#127×C131—41no—
48#127×C131—41no—
49#124×C131—41no—
50#121×C131—22no—
51#121×C131—41no—
52C4×D4×C131—22no—
53C4×D4×C131—41no—
54C2×C42×C131D411yescharacteristic
55D16×C131—48no—
56C2×C16×C131C2314yes—
57#107×C131—21no—
58#107×C131C2312yes—
59#102×C131—22no—
60#102×C131—22no—
61C4×C8×C131D411yescharacteristic
62C4×C8×C131D411yescharacteristic
63C4×C8×C131C2311yescharacteristic
64C4×C8×C131C2311yescharacteristic
65C24×C131—42no—
66#41×C131—84no—
67C2×Q8×C131—41no—
68C2×D4×C131—22no—
69C2×D4×C131—24no—
70C2×D4×C131—44no—
71C2×D4×C131—44no—
72C2×D4×C131—42no—
73C2×D4×C131—41no—
74C2×D4×C131—41no—
75C2×D4×C131—42no—
76C2×D4×C131—42no—
77C2×D4×C131—42no—
78C2×D4×C131—42no—
79C2×D4×C131—42no—
80C2×D4×C131—84no—
81C2×D4×C131—84no—
82C22×C4×C131—42no—
83C22×C4×C131D811yescharacteristic
84C22×C4×C131D811yescharacteristic
85C22×C4×C131C2×D411yescharacteristic
86D8×C131—24no—
87D8×C131—28no—
88D8×C131—44no—
89D8×C131—44no—
90D8×C131—42no—
91D8×C131—44no—
92C2×C8×C131—22no—
93C2×C8×C131—22no—
94C2×C8×C131C2×D411yescharacteristic
95C2×C8×C131C2×D411yescharacteristic
96C2×C8×C131C2×D411yescharacteristic
97C2×C8×C131C2411yescharacteristic
98C4⋊C4×C131—22no—
99C4⋊C4×C131—41no—
100C22⋊C4×C131—42no—
101C22⋊C4×C131—42no—
102C42×C131D811yescharacteristic
103C42×C131D811yescharacteristic
104C42×C131C2×D411yescharacteristic
105C42×C131C2×D411yescharacteristic
106C16×C131—24no—
107C23×C131—42no—
108C23×C131—44no—
109C23×C131—84no—
110C23×C131—84no—
111C23×C131—84no—
112C23×C131C2×D811yescharacteristic
113Q8×C131—82no—
114D4×C131—44no—
115D4×C131—42no—
116D4×C131—44no—
117D4×C131—42no—
118D4×C131—84no—
119D4×C131—84no—
120D4×C131—84no—
121D4×C131—84no—
122D4×C131—84no—
123D4×C131—82no—
124D4×C131—82no—
125D4×C131—84no—
126C2×C4×C131—21no—
127C2×C4×C131—21no—
128C2×C4×C131—22no—
129C2×C4×C131—42no—
130C2×C4×C131—84no—
131C2×C4×C131D1614yescomplemented
132C2×C4×C131C2×D811yescharacteristic
133C2×C4×C131C2×D811yescharacteristic
134C2×C4×C131C2×D811yescharacteristic
135C2×C4×C131C2×D811yescharacteristic
136C2×C4×C131C2×D811yescharacteristic
137C2×C4×C131C22×D411yescharacteristic
138C8×C131—21no—
139C8×C131—21no—
140C8×C131AGL(1,ℤ/8)12yes—
141C8×C131H(5,𝔽2)12yes—
142C22×C131—21no—
143C22×C131—21no—
144C22×C131—82no—
145C22×C131—84no—
146C22×C131—84no—
147C22×C131—82no—
148C22×C131—84no—
149C22×C131—82no—
150C22×C131—168no—
151C22×C131C2×D1612yes—
152C22×C131C22×D811yescharacteristic
153C4×C131—21no—
154C4×C131—21no—
155C4×C131—82no—
156C4×C131C2×D1612yes—
157C4×C131C2×D1612yes—
158C4×C131#50912yes—
159C4×C131#53511yescharacteristic
160C4×C131C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C131—22no—
162C2×C131—162no—
163C2×C131—164no—
164C2×C131#320511yescharacteristic
165C2×C131C22×D1611yescharacteristic
166C2×C131C2×#50911yescharacteristic
167#33771C13111yesmaximal, characteristic, direct product factor, Sylow
168C131#3377111yescharacteristic, direct product factor, Sylow
169#3169C2×C13111yescharacteristic, complemented
170C2×#493C2×C13111yescharacteristic, complemented
171#2246C2×C13112yescomplemented
172#2240C2×C13112yescomplemented
173#2206C2×C13114yescomplemented
174#2184C2×C13114yescomplemented
175#2162C2×C13111yescharacteristic, complemented
176C22×D8—21no—
177C22×D8C22×C13112yes—
178#532—21no—
179C2×#127—21no—
180C2×D16C22×C13118yescomplemented
181#500C22×C13111yescharacteristic, complemented
182#493—21no—
183#493—21no—
184#493C22×C13112yes—
185#493C22×C13112yes—
186#493C22×C13111yescharacteristic, complemented
187#486—21no—
188#466—21no—
189#466C22×C13112yes—
190C4×D8—21no—
191C4×D8C22×C13112yescomplemented
192C2×C4×C8C22×C13111yescharacteristic
193C4⋊C16C22×C13112yescomplemented
194#357C22×C13118yescomplemented
195C22⋊C16C22×C13112yes—
196C4×C16C22×C13112yescomplemented
197C2×#41—41no—
198C22×D4—22no—
199C22×D4—41no—
200C22×D4—41no—
201C2×D8—22no—
202C2×D8—22no—
203C2×D8—22no—
204C2×D8—21no—
205C2×D8—44no—
206C2×D8—44no—
207C2×D8C23×C13114yes—
208C2×D8C23×C13112yes—
209C22×C8D4×C13111yescharacteristic
210C22×C8C23×C13111yescharacteristic
211C4⋊Q8—21no—
212#127—22no—
213#127—22no—
214#127—21no—
215#127—41no—
216#127—41no—
217#124—41no—
218#121—22no—
219#121—41no—
220C4×D4—22no—
221C4×D4—41no—
222C2×C42D4×C13111yescharacteristic
223D16—48no—
224C2×C16C23×C13114yes—
225#107—21no—
226#107C23×C13112yes—
227#102—22no—
228#102—22no—
229C4×C8D4×C13111yescharacteristic
230C4×C8D4×C13111yescharacteristic
231C4×C8C23×C13111yescharacteristic
232C4×C8C23×C13111yescharacteristic
233C24—42no—
234#41—84no—
235C2×Q8—41no—
236C2×D4—22no—
237C2×D4—24no—
238C2×D4—44no—
239C2×D4—44no—
240C2×D4—42no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—84no—
249C2×D4—84no—
250C22×C4—42no—
251C22×C4D8×C13111yescharacteristic
252C22×C4D8×C13111yescharacteristic
253C22×C4C2×D4×C13111yescharacteristic
254D8—24no—
255D8—28no—
256D8—44no—
257D8—44no—
258D8—42no—
259D8—44no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8C2×D4×C13111yescharacteristic
263C2×C8C2×D4×C13111yescharacteristic
264C2×C8C2×D4×C13111yescharacteristic
265C2×C8C24×C13111yescharacteristic
266C4⋊C4—22no—
267C4⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C42D8×C13111yescharacteristic
271C42D8×C13111yescharacteristic
272C42C2×D4×C13111yescharacteristic
273C42C2×D4×C13111yescharacteristic
274C16—24no—
275C23—42no—
276C23—44no—
277C23—84no—
278C23—84no—
279C23—84no—
280C23C2×D8×C13111yescharacteristic
281Q8—82no—
282D4—44no—
283D4—42no—
284D4—44no—
285D4—42no—
286D4—84no—
287D4—84no—
288D4—84no—
289D4—84no—
290D4—84no—
291D4—82no—
292D4—84no—
293D4—82no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—42no—
298C2×C4—84no—
299C2×C4D16×C13114yescomplemented
300C2×C4C2×D8×C13111yescharacteristic
301C2×C4C2×D8×C13111yescharacteristic
302C2×C4C2×D8×C13111yescharacteristic
303C2×C4C2×D8×C13111yescharacteristic
304C2×C4C2×D8×C13111yescharacteristic
305C2×C4C22×D4×C13111yescharacteristic
306C8—21no—
307C8—21no—
308C8AGL(1,ℤ/8)×C13112yes—
309C8H(5,𝔽2)×C13112yes—
310C22—21no—
311C22—21no—
312C22—82no—
313C22—84no—
314C22—84no—
315C22—82no—
316C22—84no—
317C22—82no—
318C22—168no—
319C22C2×D16×C13112yes—
320C22C22×D8×C13111yescharacteristic
321C4—21no—
322C4—21no—
323C4—82no—
324C4C2×D16×C13112yes—
325C4C2×D16×C13112yes—
326C4#509×C13112yes—
327C4#535×C13111yescharacteristic
328C4C2×AGL(1,ℤ/8)×C13111yescharacteristic
329C2—22no—
330C2—164no—
331C2—162no—
332C2#3205×C13111yescharacteristic
333C2C22×D16×C13111yescharacteristic
334C2C2×#509×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C22×D8
commutator, Frattini, cosocleC2×C8C24×C131
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C2×C42×C131 ◁ C2×C4×C8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3169×C131C2semidirect
2. C2×#493×C131C2semidirect
3. #2246×C131C2semidirect
4. #2240×C131C2semidirect
5. #2206×C131C2semidirect
6. #2184×C131C2semidirect
7. #2162×C131C2semidirect
12. C2×D16×C131C22semidirect
13. #500×C131C22semidirect
18. #493×C131C22semidirect
23. C4×D8×C131C22semidirect
25. C4⋊C16×C131C22semidirect
26. #357×C131C22semidirect
28. C4×C16×C131C22semidirect
131. C2×C4×C131D16semidirect
167. #33771C131direct (N × H)
168. C131#33771direct (N × H)
169. #3169C2×C131semidirect
170. C2×#493C2×C131semidirect
171. #2246C2×C131semidirect
172. #2240C2×C131semidirect
173. #2206C2×C131semidirect
174. #2184C2×C131semidirect
175. #2162C2×C131semidirect
180. C2×D16C22×C131semidirect
181. #500C22×C131semidirect
186. #493C22×C131semidirect
191. C4×D8C22×C131semidirect
193. C4⋊C16C22×C131semidirect
194. #357C22×C131semidirect
196. C4×C16C22×C131semidirect
299. C2×C4D16×C131semidirect

Maximal subgroups

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

subgroupindex
#3169×C1312
C2×#493×C1312
#2246×C1312
#2240×C1312
#2206×C1312
#2184×C1312
#2162×C1312
#33771131