Finite Group Databasebeta

← C131×#7669 #45693553

Subgroups — C131×#7669 #45693553

Order 33536.

384 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2863×C131C211yesmaximal, characteristic
2#1831×C131C211yesmaximal, characteristic
3#1744×C131C211yesmaximal, characteristic
4#1272×C131C212yesmaximal
5#1271×C131C212yesmaximal
6C2×C4⋊C8×C131—21no—
7C2×C4×C8×C131—21no—
8#391×C131C411yescharacteristic
9#391×C131C411yescharacteristic
10#391×C131C2211yescharacteristic
11#389×C131C411yescharacteristic
12#389×C131C411yescharacteristic
13#389×C131C2211yescharacteristic
14#387×C131—21no—
15#387×C131—21no—
16#387×C131—21no—
17#383×C131—21no—
18C43×C131C2211yescharacteristic
19#336×C131—21no—
20#336×C131—21no—
21#336×C131C2212yes—
22#336×C131C2212yes—
23C22×Q8×C131C2×C411yescharacteristic
24C22×C8×C131—22no—
25C22×C8×C131—22no—
26C2×C4⋊C4×C131—21no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131—21no—
29C2×C4⋊C4×C131C2×C411yescharacteristic
30C2×C4⋊C4×C131C2×C411yescharacteristic
31C2×C4⋊C4×C131C2×C411yescharacteristic
32C2×C42×C131C2×C411yescharacteristic
33C2×C42×C131C2×C411yescharacteristic
34C2×C42×C131D411yescharacteristic
35C2×C42×C131D411yescharacteristic
36C2×C42×C131D411yescharacteristic
37C2×C42×C131D411yescharacteristic
38C2×C42×C131C2311yescharacteristic
39C4⋊C8×C131—42no—
40C4×C8×C131—24no—
41#95×C131—21no—
42#95×C131—21no—
43#95×C131—21no—
44#95×C131—21no—
45#95×C131—21no—
46#95×C131—21no—
47#95×C131—21no—
48#95×C131—21no—
49#95×C131—21no—
50C2×Q8×C131—22no—
51C2×Q8×C131—41no—
52C2×Q8×C131—41no—
53C22×C4×C131—21no—
54C22×C4×C131—21no—
55C22×C4×C131—21no—
56C22×C4×C131—21no—
57C22×C4×C131C22⋊C411yescharacteristic
58C22×C4×C131C22⋊C411yescharacteristic
59C22×C4×C131C22⋊C411yescharacteristic
60C22×C4×C131C22⋊C411yescharacteristic
61C22×C4×C131C22×C411yescharacteristic
62C22×C4×C131C2×D411yescharacteristic
63C22×C4×C131C2×D411yescharacteristic
64C2×C8×C131—24no—
65C2×C8×C131—42no—
66C2×C8×C131—42no—
67C2×C8×C131—42no—
68C2×C8×C131—42no—
69C2×C8×C131—42no—
70C4⋊C4×C131—22no—
71C4⋊C4×C131—41no—
72C4⋊C4×C131—41no—
73C4⋊C4×C131—42no—
74C4⋊C4×C131—42no—
75C4⋊C4×C131—42no—
76C42×C131—22no—
77C42×C131—22no—
78C42×C131—22no—
79C42×C131—41no—
80C42×C131—41no—
81C42×C131—41no—
82C42×C131SD1612yes—
83C42×C131Q1612yes—
84C23×C131C2×C22⋊C411yescharacteristic
85Q8×C131—82no—
86C2×C4×C131—21no—
87C2×C4×C131—21no—
88C2×C4×C131—21no—
89C2×C4×C131—21no—
90C2×C4×C131—21no—
91C2×C4×C131—21no—
92C2×C4×C131—21no—
93C2×C4×C131—21no—
94C2×C4×C131—21no—
95C2×C4×C131—21no—
96C2×C4×C131—21no—
97C2×C4×C131—21no—
98C2×C4×C131—21no—
99C2×C4×C131—21no—
100C2×C4×C131—21no—
101C2×C4×C131—41no—
102C2×C4×C131—41no—
103C2×C4×C131—41no—
104C2×C4×C131—41no—
105C2×C4×C131—41no—
106C2×C4×C131—41no—
107C2×C4×C131—41no—
108C2×C4×C131—41no—
109C2×C4×C131—41no—
110C2×C4×C131—41no—
111C2×C4×C131—41no—
112C2×C4×C131—41no—
113C2×C4×C131#10312yes—
114C2×C4×C131#10312yes—
115C2×C4×C131#10412yes—
116C2×C4×C131#13112yes—
117C2×C4×C131C2×SD1611yescharacteristic
118C2×C4×C131C2×Q1611yescharacteristic
119C2×C4×C131#13512yes—
120C8×C131—44no—
121C8×C131—82no—
122C22×C131#40811yescharacteristic
123C22×C131#41011yescharacteristic
124C22×C131#41311yescharacteristic
125C22×C131C2×#10311yescharacteristic
126C22×C131#41611yescharacteristic
127C22×C131C2×#10411yescharacteristic
128C22×C131#42111yescharacteristic
129C4×C131—22no—
130C4×C131—22no—
131C4×C131—22no—
132C4×C131—22no—
133C4×C131—21no—
134C4×C131—21no—
135C4×C131—22no—
136C4×C131—41no—
137C4×C131—81no—
138C4×C131—81no—
139C4×C131—81no—
140C4×C131—81no—
141C2×C131#147311yescharacteristic
142C2×C131#148211yescharacteristic
143C2×C131#149311yescharacteristic
144C2×C131#150011yescharacteristic
145C2×C131#151811yescharacteristic
146C2×C131#153211yescharacteristic
147C2×C131#154211yescharacteristic
148#7669C13111yesmaximal, characteristic, direct product factor, Sylow
149C131#766911yescharacteristic, direct product factor, Sylow
150#2863C2×C13111yescharacteristic
151#1831C2×C13111yescharacteristic
152#1744C2×C13111yescharacteristic
153#1272C2×C13112yes—
154#1271C2×C13112yes—
155C2×C4⋊C8—21no—
156C2×C4×C8—21no—
157#391C4×C13111yescharacteristic
158#391C4×C13111yescharacteristic
159#391C22×C13111yescharacteristic
160#389C4×C13111yescharacteristic
161#389C4×C13111yescharacteristic
162#389C22×C13111yescharacteristic
163#387—21no—
164#387—21no—
165#387—21no—
166#383—21no—
167C43C22×C13111yescharacteristic
168#336—21no—
169#336—21no—
170#336C22×C13112yes—
171#336C22×C13112yes—
172C22×Q8C2×C4×C13111yescharacteristic
173C22×C8—22no—
174C22×C8—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×C4×C13111yescharacteristic
179C2×C4⋊C4C2×C4×C13111yescharacteristic
180C2×C4⋊C4C2×C4×C13111yescharacteristic
181C2×C42C2×C4×C13111yescharacteristic
182C2×C42C2×C4×C13111yescharacteristic
183C2×C42D4×C13111yescharacteristic
184C2×C42D4×C13111yescharacteristic
185C2×C42D4×C13111yescharacteristic
186C2×C42D4×C13111yescharacteristic
187C2×C42C23×C13111yescharacteristic
188C4⋊C8—42no—
189C4×C8—24no—
190#95—21no—
191#95—21no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199C2×Q8—22no—
200C2×Q8—41no—
201C2×Q8—41no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4C22⋊C4×C13111yescharacteristic
207C22×C4C22⋊C4×C13111yescharacteristic
208C22×C4C22⋊C4×C13111yescharacteristic
209C22×C4C22⋊C4×C13111yescharacteristic
210C22×C4C22×C4×C13111yescharacteristic
211C22×C4C2×D4×C13111yescharacteristic
212C22×C4C2×D4×C13111yescharacteristic
213C2×C8—24no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C2×C8—42no—
219C4⋊C4—22no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C42—22no—
226C42—22no—
227C42—22no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42SD16×C13112yes—
232C42Q16×C13112yes—
233C23C2×C22⋊C4×C13111yescharacteristic
234Q8—82no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4#103×C13112yes—
263C2×C4#103×C13112yes—
264C2×C4#104×C13112yes—
265C2×C4#131×C13112yes—
266C2×C4C2×SD16×C13111yescharacteristic
267C2×C4C2×Q16×C13111yescharacteristic
268C2×C4#135×C13112yes—
269C8—44no—
270C8—82no—
271C22#408×C13111yescharacteristic
272C22#410×C13111yescharacteristic
273C22#413×C13111yescharacteristic
274C22C2×#103×C13111yescharacteristic
275C22#416×C13111yescharacteristic
276C22C2×#104×C13111yescharacteristic
277C22#421×C13111yescharacteristic
278C4—22no—
279C4—22no—
280C4—22no—
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—81no—
289C4—81no—
290C2#1473×C13111yescharacteristic
291C2#1482×C13111yescharacteristic
292C2#1493×C13111yescharacteristic
293C2#1500×C13111yescharacteristic
294C2#1518×C13111yescharacteristic
295C2#1532×C13111yescharacteristic
296C2#1542×C13111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C131C2×C22⋊C4
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×C42C23×C131
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C131 ◁ C43×C131 ◁ G

Complements

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

NH ≅ G/Ntype
148. #7669C131direct (N × H)
149. C131#7669direct (N × H)

Maximal subgroups

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

subgroupindex
#2863×C1312
#1831×C1312
#1744×C1312
#1272×C1312
#1271×C1312
#7669131