Finite Group Databasebeta

← C131×#7252 #45693136

Subgroups — C131×#7252 #45693136

Order 33536.

344 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 102 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#1798×C131C211yesmaximal, characteristic
2#1740×C131C211yesmaximal, characteristic
3#1458×C131C211yesmaximal, characteristic
4C2×#117×C131—21no—
5C2×#117×C131C2211yescharacteristic
6#431×C131—21no—
7C2×C4⋊C8×C131C411yescharacteristic, complemented
8C2×C4⋊C8×C131C411yescharacteristic, complemented
9C2×C22⋊C8×C131—21no—
10#342×C131—21no—
11#342×C131C412yes—
12#336×C131—21no—
13#324×C131C412yescomplemented
14#323×C131—21no—
15C23×C4×C131D411yescharacteristic
16C22×C8×C131—21no—
17C22×C8×C131—21no—
18#117×C131—22no—
19#117×C131—22no—
20#117×C131—41no—
21#117×C131—41no—
22#117×C131—41no—
23#117×C131—41no—
24C2×C4⋊C4×C131—41no—
25C2×C4⋊C4×C131C2×C411yescharacteristic
26C2×C4⋊C4×C131Q811yescharacteristic
27C2×C22⋊C4×C131—22no—
28C2×C22⋊C4×C131C2×C411yescharacteristic
29C2×C22⋊C4×C131D411yescharacteristic
30C2×C42×C131—41no—
31C2×C42×C131C2×C411yescharacteristic
32C2×C42×C131D411yescharacteristic
33C4⋊C8×C131—41no—
34C4⋊C8×C131—41no—
35C4⋊C8×C131—41no—
36C22⋊C8×C131—22no—
37C22⋊C8×C131—41no—
38C22⋊C8×C131—41no—
39C4×C8×C131—41no—
40C24×C131C22⋊C411yescharacteristic
41C22×C4×C131—21no—
42C22×C4×C131—21no—
43C22×C4×C131—21no—
44C22×C4×C131—21no—
45C22×C4×C131—42no—
46C22×C4×C131C4211yescharacteristic
47C22×C4×C131C22⋊C411yescharacteristic
48C22×C4×C131C22⋊C411yescharacteristic
49C22×C4×C131C4⋊C411yescharacteristic
50C22×C4×C131C4⋊C411yescharacteristic
51C22×C4×C131C4⋊C411yescharacteristic
52C22×C4×C131D811yescharacteristic
53C22×C4×C131SD1611yescharacteristic
54C22×C4×C131SD1611yescharacteristic
55C22×C4×C131Q1611yescharacteristic
56C2×C8×C131—42no—
57C2×C8×C131—41no—
58C2×C8×C131—41no—
59C2×C8×C131—41no—
60C2×C8×C131—41no—
61C2×C8×C131—41no—
62C2×C8×C131—41no—
63C4⋊C4×C131—41no—
64C4⋊C4×C131—41no—
65C4⋊C4×C131—42no—
66C4⋊C4×C131—42no—
67C22⋊C4×C131—24no—
68C22⋊C4×C131—41no—
69C22⋊C4×C131—41no—
70C22⋊C4×C131—42no—
71C42×C131—21no—
72C42×C131—21no—
73C42×C131—21no—
74C42×C131—21no—
75C42×C131—42no—
76C42×C131—42no—
77C23×C131—21no—
78C23×C131—21no—
79C23×C131—41no—
80C23×C131—41no—
81C23×C131#9511yescharacteristic
82C23×C131#10211yescharacteristic
83C23×C131#10311yescharacteristic
84C2×C4×C131—21no—
85C2×C4×C131—21no—
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—41no—
99C2×C4×C131—41no—
100C2×C4×C131—41no—
101C2×C4×C131—41no—
102C2×C4×C131—44no—
103C2×C4×C131—82no—
104C2×C4×C131—82no—
105C2×C4×C131#9911yescharacteristic
106C2×C4×C131#9911yescharacteristic
107C2×C4×C131#10211yescharacteristic
108C2×C4×C131#10311yescharacteristic
109C2×C4×C131#10411yescharacteristic
110C2×C4×C131#10411yescharacteristic
111C2×C4×C131#10611yescharacteristic
112C2×C4×C131#10711yescharacteristic
113C8×C131—82no—
114C8×C131—81no—
115C8×C131—81no—
116C22×C131—21no—
117C22×C131—21no—
118C22×C131—21no—
119C22×C131—21no—
120C22×C131—41no—
121C22×C131—41no—
122C22×C131—41no—
123C22×C131—41no—
124C22×C131—81no—
125C22×C131#33911yescharacteristic
126C22×C131#34011yescharacteristic
127C22×C131#34211yescharacteristic
128C4×C131—21no—
129C4×C131—21no—
130C4×C131—41no—
131C4×C131—41no—
132C4×C131—41no—
133C4×C131—41no—
134C4×C131—84no—
135C4×C131#32711yescharacteristic
136C4×C131#32711yescharacteristic
137C4×C131#32811yescharacteristic
138C4×C131#32811yescharacteristic
139C2×C131—21no—
140C2×C131—21no—
141C2×C131—41no—
142C2×C131—41no—
143C2×C131#129411yescharacteristic
144C2×C131#139111yescharacteristic
145C2×C131#139511yescharacteristic
146#7252C13111yesmaximal, characteristic, direct product factor, Sylow
147C131#725211yescharacteristic, direct product factor, Sylow
148#1798C2×C13111yescharacteristic
149#1740C2×C13111yescharacteristic
150#1458C2×C13111yescharacteristic
151C2×#117—21no—
152C2×#117C22×C13111yescharacteristic
153#431—21no—
154C2×C4⋊C8C4×C13111yescharacteristic, complemented
155C2×C4⋊C8C4×C13111yescharacteristic, complemented
156C2×C22⋊C8—21no—
157#342—21no—
158#342C4×C13112yes—
159#336—21no—
160#324C4×C13112yescomplemented
161#323—21no—
162C23×C4D4×C13111yescharacteristic
163C22×C8—21no—
164C22×C8—21no—
165#117—22no—
166#117—22no—
167#117—41no—
168#117—41no—
169#117—41no—
170#117—41no—
171C2×C4⋊C4—41no—
172C2×C4⋊C4C2×C4×C13111yescharacteristic
173C2×C4⋊C4Q8×C13111yescharacteristic
174C2×C22⋊C4—22no—
175C2×C22⋊C4C2×C4×C13111yescharacteristic
176C2×C22⋊C4D4×C13111yescharacteristic
177C2×C42—41no—
178C2×C42C2×C4×C13111yescharacteristic
179C2×C42D4×C13111yescharacteristic
180C4⋊C8—41no—
181C4⋊C8—41no—
182C4⋊C8—41no—
183C22⋊C8—22no—
184C22⋊C8—41no—
185C22⋊C8—41no—
186C4×C8—41no—
187C24C22⋊C4×C13111yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—42no—
193C22×C4C42×C13111yescharacteristic
194C22×C4C22⋊C4×C13111yescharacteristic
195C22×C4C22⋊C4×C13111yescharacteristic
196C22×C4C4⋊C4×C13111yescharacteristic
197C22×C4C4⋊C4×C13111yescharacteristic
198C22×C4C4⋊C4×C13111yescharacteristic
199C22×C4D8×C13111yescharacteristic
200C22×C4SD16×C13111yescharacteristic
201C22×C4SD16×C13111yescharacteristic
202C22×C4Q16×C13111yescharacteristic
203C2×C8—42no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C22⋊C4—24no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—42no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—42no—
223C42—42no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23#95×C13111yescharacteristic
229C23#102×C13111yescharacteristic
230C23#103×C13111yescharacteristic
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
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—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4#99×C13111yescharacteristic
253C2×C4#99×C13111yescharacteristic
254C2×C4#102×C13111yescharacteristic
255C2×C4#103×C13111yescharacteristic
256C2×C4#104×C13111yescharacteristic
257C2×C4#104×C13111yescharacteristic
258C2×C4#106×C13111yescharacteristic
259C2×C4#107×C13111yescharacteristic
260C8—82no—
261C8—81no—
262C8—81no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—81no—
272C22#339×C13111yescharacteristic
273C22#340×C13111yescharacteristic
274C22#342×C13111yescharacteristic
275C4—21no—
276C4—21no—
277C4—41no—
278C4—41no—
279C4—41no—
280C4—41no—
281C4—84no—
282C4#327×C13111yescharacteristic
283C4#327×C13111yescharacteristic
284C4#328×C13111yescharacteristic
285C4#328×C13111yescharacteristic
286C2—21no—
287C2—21no—
288C2—41no—
289C2—41no—
290C2#1294×C13111yescharacteristic
291C2#1391×C13111yescharacteristic
292C2#1395×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#99
commutatorC22×C4C42×C131
Frattini, cosocleC2×#117C22×C131
socleC22×C131#342
prime radicalC24×C131C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4⋊C8×C131C4semidirect
8. C2×C4⋊C8×C131C4semidirect
13. #324×C131C4semidirect
146. #7252C131direct (N × H)
147. C131#7252direct (N × H)
154. C2×C4⋊C8C4×C131semidirect
155. C2×C4⋊C8C4×C131semidirect
160. #324C4×C131semidirect

Maximal subgroups

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

subgroupindex
#1798×C1312
#1740×C1312
#1458×C1312
#7252131