Finite Group Databasebeta

← C131×#8668 #45694552

Subgroups — C131×#8668 #45694552

Order 33536.

432 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2965×C131C211yesmaximal, characteristic
2#1806×C131C212yesmaximal
3C4×#107×C131C211yesmaximal, characteristic, complemented
4#1566×C131C211yesmaximal, characteristic, complemented
5#1303×C131C212yesmaximal, complemented
6C4×#41×C131C2211yescharacteristic
7#446×C131C411yescharacteristic, complemented
8#446×C131C411yescharacteristic, complemented
9#436×C131C411yescharacteristic, complemented
10#436×C131C411yescharacteristic, complemented
11#435×C131—21no—
12#435×C131—21no—
13#431×C131—21no—
14#431×C131C2211yescharacteristic
15C2×#107×C131—21no—
16#423×C131C2212yes—
17C2×#104×C131—22no—
18C4×M16×C131—21no—
19C2×C4×C8×C131C2211yescharacteristic
20C4×C4⋊C4×C131C2212yes—
21#340×C131—21no—
22#339×C131—22no—
23#334×C131—21no—
24#334×C131—21no—
25C2×#41×C131D411yescharacteristic
26C2×M16×C131—21no—
27C2×M16×C131—21no—
28C2×M16×C131—22no—
29C22×C8×C131D411yescharacteristic
30C22×C8×C131D411yescharacteristic
31C4×Q8×C131C2×C411yescharacteristic
32C4×Q8×C131Q811yescharacteristic
33C4×D4×C131—21no—
34C4×D4×C131—21no—
35C4×D4×C131C2×C411yescharacteristic
36C4×D4×C131Q811yescharacteristic
37#117×C131—21no—
38#117×C131D411yescharacteristic
39C2×C4⋊C4×C131—22no—
40C2×C42×C131—21no—
41C2×C42×C131—22no—
42C2×C42×C131C2311yescharacteristic
43#107×C131—24no—
44C4⋊C8×C131—21no—
45C4⋊C8×C131—21no—
46C4⋊C8×C131—22no—
47C4⋊C8×C131—22no—
48C4⋊C8×C131C2×C411yescharacteristic
49C4⋊C8×C131C2×C411yescharacteristic
50#104×C131—44no—
51C22⋊C8×C131—21no—
52C22⋊C8×C131—21no—
53C22⋊C8×C131—21no—
54#97×C131—21no—
55#97×C131—21no—
56C4×C8×C131—21no—
57C4×C8×C131C2×C411yescharacteristic
58C4×C8×C131C2×C411yescharacteristic
59C4×C8×C131D411yescharacteristic
60C4×C8×C131D411yescharacteristic
61#95×C131—22no—
62#41×C131—22no—
63#41×C131—22no—
64C2×Q8×C131C4⋊C411yescharacteristic
65C2×D4×C131—21no—
66C2×D4×C131C4⋊C411yescharacteristic
67C22×C4×C131—21no—
68C22×C4×C131—21no—
69C22×C4×C131—21no—
70C22×C4×C131—42no—
71C22×C4×C131C2×D411yescharacteristic
72C22×C4×C131C2×D411yescharacteristic
73C22×C4×C131#4111yescharacteristic
74M16×C131—42no—
75M16×C131—42no—
76M16×C131—42no—
77M16×C131—42no—
78C2×C8×C131—22no—
79C2×C8×C131—21no—
80C2×C8×C131—21no—
81C2×C8×C131—41no—
82C2×C8×C131—42no—
83C2×C8×C131C22⋊C411yescharacteristic
84C2×C8×C131C22⋊C411yescharacteristic
85C2×C8×C131C22⋊C411yescharacteristic
86C2×C8×C131C22⋊C411yescharacteristic
87C4⋊C4×C131—21no—
88C4⋊C4×C131—21no—
89C4⋊C4×C131—24no—
90C4⋊C4×C131—42no—
91C4⋊C4×C131C4⋊C411yescharacteristic
92C4⋊C4×C131C4⋊C411yescharacteristic
93C22⋊C4×C131—21no—
94C22⋊C4×C131—21no—
95C22⋊C4×C131—21no—
96C42×C131—21no—
97C42×C131—21no—
98C42×C131—21no—
99C42×C131—42no—
100C42×C131—42no—
101C42×C131C22×C411yescharacteristic
102C42×C131C2×D411yescharacteristic
103C42×C131C2×Q811yescharacteristic
104C42×C131#4111yescharacteristic
105C23×C131—21no—
106C23×C131#12111yescharacteristic
107Q8×C131—22no—
108D4×C131—22no—
109D4×C131—41no—
110D4×C131—41no—
111C2×C4×C131—21no—
112C2×C4×C131—21no—
113C2×C4×C131—21no—
114C2×C4×C131—21no—
115C2×C4×C131—21no—
116C2×C4×C131—41no—
117C2×C4×C131—42no—
118C2×C4×C131—41no—
119C2×C4×C131—41no—
120C2×C4×C131—42no—
121C2×C4×C131—44no—
122C2×C4×C131—82no—
123C2×C4×C131—82no—
124C2×C4×C131C2×C22⋊C411yescharacteristic
125C2×C4×C131C2×C4⋊C411yescharacteristic
126C2×C4×C131#11711yescharacteristic
127C2×C4×C131#12111yescharacteristic
128C2×C4×C131C22⋊Q811yescharacteristic
129C2×C4×C131C22⋊Q811yescharacteristic
130C2×C4×C131AGL(1,ℤ/8)12yes—
131C2×C4×C131#13712yes—
132C8×C131—21no—
133C8×C131—21no—
134C8×C131—21no—
135C8×C131—41no—
136C8×C131—41no—
137C8×C131—82no—
138C8×C131#10412yescomplemented
139C22×C131—21no—
140C22×C131—21no—
141C22×C131—41no—
142C22×C131—41no—
143C22×C131—41no—
144C22×C131#38011yescharacteristic
145C22×C131#46911yescharacteristic
146C22×C131#47011yescharacteristic
147C4×C131—21no—
148C4×C131—21no—
149C4×C131—21no—
150C4×C131—41no—
151C4×C131—41no—
152C4×C131—41no—
153C4×C131—84no—
154C4×C131C2×#10411yescharacteristic
155C4×C131#42111yescharacteristic
156C4×C131#42812yes—
157C4×C131#46812yes—
158C2×C131—21no—
159C2×C131—21no—
160C2×C131—81no—
161C2×C131#180611yescharacteristic
162C2×C131#180911yescharacteristic
163C2×C131#181411yescharacteristic
164#8668C13111yesmaximal, characteristic, direct product factor, Sylow
165C131#866811yescharacteristic, direct product factor, Sylow
166#2965C2×C13111yescharacteristic
167#1806C2×C13112yes—
168C4×#107C2×C13111yescharacteristic, complemented
169#1566C2×C13111yescharacteristic, complemented
170#1303C2×C13112yescomplemented
171C4×#41C22×C13111yescharacteristic
172#446C4×C13111yescharacteristic, complemented
173#446C4×C13111yescharacteristic, complemented
174#436C4×C13111yescharacteristic, complemented
175#436C4×C13111yescharacteristic, complemented
176#435—21no—
177#435—21no—
178#431—21no—
179#431C22×C13111yescharacteristic
180C2×#107—21no—
181#423C22×C13112yes—
182C2×#104—22no—
183C4×M16—21no—
184C2×C4×C8C22×C13111yescharacteristic
185C4×C4⋊C4C22×C13112yes—
186#340—21no—
187#339—22no—
188#334—21no—
189#334—21no—
190C2×#41D4×C13111yescharacteristic
191C2×M16—21no—
192C2×M16—21no—
193C2×M16—22no—
194C22×C8D4×C13111yescharacteristic
195C22×C8D4×C13111yescharacteristic
196C4×Q8C2×C4×C13111yescharacteristic
197C4×Q8Q8×C13111yescharacteristic
198C4×D4—21no—
199C4×D4—21no—
200C4×D4C2×C4×C13111yescharacteristic
201C4×D4Q8×C13111yescharacteristic
202#117—21no—
203#117D4×C13111yescharacteristic
204C2×C4⋊C4—22no—
205C2×C42—21no—
206C2×C42—22no—
207C2×C42C23×C13111yescharacteristic
208#107—24no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—22no—
212C4⋊C8—22no—
213C4⋊C8C2×C4×C13111yescharacteristic
214C4⋊C8C2×C4×C13111yescharacteristic
215#104—44no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218C22⋊C8—21no—
219#97—21no—
220#97—21no—
221C4×C8—21no—
222C4×C8C2×C4×C13111yescharacteristic
223C4×C8C2×C4×C13111yescharacteristic
224C4×C8D4×C13111yescharacteristic
225C4×C8D4×C13111yescharacteristic
226#95—22no—
227#41—22no—
228#41—22no—
229C2×Q8C4⋊C4×C13111yescharacteristic
230C2×D4—21no—
231C2×D4C4⋊C4×C13111yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—42no—
236C22×C4C2×D4×C13111yescharacteristic
237C22×C4C2×D4×C13111yescharacteristic
238C22×C4#41×C13111yescharacteristic
239M16—42no—
240M16—42no—
241M16—42no—
242M16—42no—
243C2×C8—22no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8C22⋊C4×C13111yescharacteristic
249C2×C8C22⋊C4×C13111yescharacteristic
250C2×C8C22⋊C4×C13111yescharacteristic
251C2×C8C22⋊C4×C13111yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—24no—
255C4⋊C4—42no—
256C4⋊C4C4⋊C4×C13111yescharacteristic
257C4⋊C4C4⋊C4×C13111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C42—42no—
265C42—42no—
266C42C22×C4×C13111yescharacteristic
267C42C2×D4×C13111yescharacteristic
268C42C2×Q8×C13111yescharacteristic
269C42#41×C13111yescharacteristic
270C23—21no—
271C23#121×C13111yescharacteristic
272Q8—22no—
273D4—22no—
274D4—41no—
275D4—41no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4C2×C22⋊C4×C13111yescharacteristic
290C2×C4C2×C4⋊C4×C13111yescharacteristic
291C2×C4#117×C13111yescharacteristic
292C2×C4#121×C13111yescharacteristic
293C2×C4C22⋊Q8×C13111yescharacteristic
294C2×C4C22⋊Q8×C13111yescharacteristic
295C2×C4AGL(1,ℤ/8)×C13112yes—
296C2×C4#137×C13112yes—
297C8—21no—
298C8—21no—
299C8—21no—
300C8—41no—
301C8—41no—
302C8—82no—
303C8#104×C13112yescomplemented
304C22—21no—
305C22—21no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#380×C13111yescharacteristic
310C22#469×C13111yescharacteristic
311C22#470×C13111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—84no—
319C4C2×#104×C13111yescharacteristic
320C4#421×C13111yescharacteristic
321C4#428×C13112yes—
322C4#468×C13112yes—
323C2—21no—
324C2—21no—
325C2—81no—
326C2#1806×C13111yescharacteristic
327C2#1809×C13111yescharacteristic
328C2#1814×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#121
commutatorC42C22×C4×C131
Frattini, cosocleC2×C42C23×C131
socleC22×C131#380
prime radicalC2×#41×C131D4
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
3. C4×#107×C131C2semidirect
4. #1566×C131C2semidirect
5. #1303×C131C2semidirect
7. #446×C131C4semidirect
8. #446×C131C4semidirect
9. #436×C131C4semidirect
10. #436×C131C4semidirect
138. C8×C131#104semidirect
164. #8668C131direct (N × H)
165. C131#8668direct (N × H)
168. C4×#107C2×C131semidirect
169. #1566C2×C131semidirect
170. #1303C2×C131semidirect
172. #446C4×C131semidirect
173. #446C4×C131semidirect
174. #436C4×C131semidirect
175. #436C4×C131semidirect
303. C8#104×C131semidirect

Maximal subgroups

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

subgroupindex
#2965×C1312
#1806×C1312
C4×#107×C1312
#1566×C1312
#1303×C1312
#8668131