Finite Group Databasebeta

← C131×#11447 #45697331

Subgroups — C131×#11447 #45697331

Order 33536.

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

normal subgroups only

This group has 462 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#2285×C131C211yesmaximal, characteristic
2#1458×C131C212yesmaximal
3#1325×C131C212yesmaximal, complemented
4#1324×C131C212yesmaximal, complemented
5C2×#117×C131C411yescharacteristic
6C2×#117×C131C2211yescharacteristic
7C22×C42×C131C411yescharacteristic
8#431×C131—22no—
9#384×C131C411yescharacteristic
10#384×C131C2211yescharacteristic
11#382×C131C411yescharacteristic
12#382×C131C2211yescharacteristic
13#380×C131—22no—
14C4×C4⋊C4×C131—22no—
15#324×C131C2214yes—
16#323×C131—22no—
17C23×C4×C131—21no—
18C23×C4×C131C2×C411yescharacteristic
19#117×C131—41no—
20#117×C131—41no—
21#117×C131—41no—
22#117×C131—41no—
23C2×C4⋊C4×C131—22no—
24C2×C4⋊C4×C131—22no—
25C2×C4⋊C4×C131C2×C411yescharacteristic
26C2×C4⋊C4×C131C2×C411yescharacteristic
27C2×C4⋊C4×C131C2×C411yescharacteristic
28C2×C4⋊C4×C131C2311yescharacteristic
29C2×C22⋊C4×C131—21no—
30C2×C22⋊C4×C131D412yes—
31C2×C42×C131—21no—
32C2×C42×C131—22no—
33C2×C42×C131—21no—
34C2×C42×C131C814yescomplemented
35C2×C42×C131C2×C411yescharacteristic
36C2×C42×C131C2×C411yescharacteristic
37C2×C42×C131D412yes—
38C4⋊C8×C131—42no—
39C22⋊C8×C131—24no—
40C4×C8×C131—42no—
41#95×C131—22no—
42#95×C131—22no—
43C24×C131C22⋊C411yescharacteristic
44C22×C4×C131—21no—
45C22×C4×C131—21no—
46C22×C4×C131—21no—
47C22×C4×C131—22no—
48C22×C4×C131—24no—
49C22×C4×C131—21no—
50C22×C4×C131—21no—
51C22×C4×C131—21no—
52C22×C4×C131—42no—
53C22×C4×C131—42no—
54C22×C4×C131C22⋊C412yes—
55C22×C4×C131C22⋊C411yescharacteristic
56C22×C4×C131C2×C812yes—
57C22×C4×C131M1612yes—
58C22×C4×C131C22×C411yescharacteristic
59C22×C4×C131C2×D412yes—
60C2×C8×C131—44no—
61C4⋊C4×C131—41no—
62C4⋊C4×C131—41no—
63C4⋊C4×C131—41no—
64C4⋊C4×C131—41no—
65C4⋊C4×C131—44no—
66C4⋊C4×C131—44no—
67C22⋊C4×C131—42no—
68C22⋊C4×C131—42no—
69C42×C131—24no—
70C42×C131—22no—
71C42×C131—22no—
72C42×C131—21no—
73C42×C131—21no—
74C42×C131—41no—
75C42×C131—41no—
76C42×C131C2×C812yes—
77C42×C131C2×C812yes—
78C23×C131—21no—
79C23×C131—21no—
80C23×C131—41no—
81C23×C131—41no—
82C23×C131C22⋊C812yes—
83C23×C131C2×C22⋊C411yescharacteristic
84C2×C4×C131—22no—
85C2×C4×C131—22no—
86C2×C4×C131—22no—
87C2×C4×C131—21no—
88C2×C4×C131—21no—
89C2×C4×C131—22no—
90C2×C4×C131—22no—
91C2×C4×C131—22no—
92C2×C4×C131—22no—
93C2×C4×C131—22no—
94C2×C4×C131—22no—
95C2×C4×C131—22no—
96C2×C4×C131—48no—
97C2×C4×C131—41no—
98C2×C4×C131—41no—
99C2×C4×C131—42no—
100C2×C4×C131—42no—
101C2×C4×C131—42no—
102C2×C4×C131—42no—
103C2×C4×C131—41no—
104C2×C4×C131—41no—
105C2×C4×C131C22⋊C812yes—
106C2×C4×C131#9911yescharacteristic
107C2×C4×C131#9911yescharacteristic
108C2×C4×C131#10112yes—
109C2×C4×C131C22×C811yescharacteristic
110C2×C4×C131C2×M1611yescharacteristic
111C8×C131—84no—
112C22×C131—21no—
113C22×C131—21no—
114C22×C131—22no—
115C22×C131—42no—
116C22×C131—42no—
117C22×C131—41no—
118C22×C131—41no—
119C22×C131C2×C22⋊C811yescharacteristic
120C22×C131C2×#9911yescharacteristic
121C22×C131C2×#10111yescharacteristic
122C4×C131—24no—
123C4×C131—21no—
124C4×C131—21no—
125C4×C131—42no—
126C4×C131—42no—
127C4×C131—42no—
128C4×C131—81no—
129C4×C131—81no—
130C4×C131#32412yes—
131C4×C131#32412yes—
132C2×C131—21no—
133C2×C131—21no—
134C2×C131—42no—
135C2×C131C2×#32411yescharacteristic
136C2×C131#212611yescharacteristic
137C2×C131#213211yescharacteristic
138#11447C13111yesmaximal, characteristic, direct product factor, Sylow
139C131#1144711yescharacteristic, direct product factor, Sylow
140#2285C2×C13111yescharacteristic
141#1458C2×C13112yes—
142#1325C2×C13112yescomplemented
143#1324C2×C13112yescomplemented
144C2×#117C4×C13111yescharacteristic
145C2×#117C22×C13111yescharacteristic
146C22×C42C4×C13111yescharacteristic
147#431—22no—
148#384C4×C13111yescharacteristic
149#384C22×C13111yescharacteristic
150#382C4×C13111yescharacteristic
151#382C22×C13111yescharacteristic
152#380—22no—
153C4×C4⋊C4—22no—
154#324C22×C13114yes—
155#323—22no—
156C23×C4—21no—
157C23×C4C2×C4×C13111yescharacteristic
158#117—41no—
159#117—41no—
160#117—41no—
161#117—41no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4C2×C4×C13111yescharacteristic
165C2×C4⋊C4C2×C4×C13111yescharacteristic
166C2×C4⋊C4C2×C4×C13111yescharacteristic
167C2×C4⋊C4C23×C13111yescharacteristic
168C2×C22⋊C4—21no—
169C2×C22⋊C4D4×C13112yes—
170C2×C42—21no—
171C2×C42—22no—
172C2×C42—21no—
173C2×C42C8×C13114yescomplemented
174C2×C42C2×C4×C13111yescharacteristic
175C2×C42C2×C4×C13111yescharacteristic
176C2×C42D4×C13112yes—
177C4⋊C8—42no—
178C22⋊C8—24no—
179C4×C8—42no—
180#95—22no—
181#95—22no—
182C24C22⋊C4×C13111yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
187C22×C4—24no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4C22⋊C4×C13112yes—
194C22×C4C22⋊C4×C13111yescharacteristic
195C22×C4C2×C8×C13112yes—
196C22×C4M16×C13112yes—
197C22×C4C22×C4×C13111yescharacteristic
198C22×C4C2×D4×C13112yes—
199C2×C8—44no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—44no—
205C4⋊C4—44no—
206C22⋊C4—42no—
207C22⋊C4—42no—
208C42—24no—
209C42—22no—
210C42—22no—
211C42—21no—
212C42—21no—
213C42—41no—
214C42—41no—
215C42C2×C8×C13112yes—
216C42C2×C8×C13112yes—
217C23—21no—
218C23—21no—
219C23—41no—
220C23—41no—
221C23C22⋊C8×C13112yes—
222C23C2×C22⋊C4×C13111yescharacteristic
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—48no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4C22⋊C8×C13112yes—
245C2×C4#99×C13111yescharacteristic
246C2×C4#99×C13111yescharacteristic
247C2×C4#101×C13112yes—
248C2×C4C22×C8×C13111yescharacteristic
249C2×C4C2×M16×C13111yescharacteristic
250C8—84no—
251C22—21no—
252C22—21no—
253C22—22no—
254C22—42no—
255C22—42no—
256C22—41no—
257C22—41no—
258C22C2×C22⋊C8×C13111yescharacteristic
259C22C2×#99×C13111yescharacteristic
260C22C2×#101×C13111yescharacteristic
261C4—24no—
262C4—21no—
263C4—21no—
264C4—42no—
265C4—42no—
266C4—42no—
267C4—81no—
268C4—81no—
269C4#324×C13112yes—
270C4#324×C13112yes—
271C2—21no—
272C2—21no—
273C2—42no—
274C2C2×#324×C13111yescharacteristic
275C2#2126×C13111yescharacteristic
276C2#2132×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131#99
commutatorC2×C4C22×C8×C131
Frattini, cosocleC2×C4⋊C4C23×C131
socleC22×C131C2×#99
prime radicalC24×C131C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ 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
3. #1325×C131C2semidirect
4. #1324×C131C2semidirect
34. C2×C42×C131C8semidirect
138. #11447C131direct (N × H)
139. C131#11447direct (N × H)
142. #1325C2×C131semidirect
143. #1324C2×C131semidirect
173. C2×C42C8×C131semidirect

Maximal subgroups

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

subgroupindex
#2285×C1312
#1458×C1312
#1325×C1312
#1324×C1312
#11447131