Finite Group Databasebeta

← C131×#12804 #45698688

Subgroups — C131×#12804 #45698688

Order 33536.

432 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 130 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#2327×C131C211yesmaximal, characteristic
2C2×#356×C131C212yesmaximal
3#1801×C131C212yesmaximal
4#1394×C131C212yesmaximal
5C2×C4⋊Q8×C131C2211yescharacteristic
6C2×C4×Q8×C131C411yescharacteristic
7C2×C4×Q8×C131C2211yescharacteristic
8#423×C131—22no—
9C2×#101×C131C2214yes—
10#391×C131C411yescharacteristic
11#391×C131C2211yescharacteristic
12#387×C131—22no—
13#387×C131—22no—
14#382×C131C411yescharacteristic
15#376×C131C411yescharacteristic
16#356×C131—24no—
17#343×C131—22no—
18C22×Q8×C131C2×C411yescharacteristic
19C22×Q8×C131C2311yescharacteristic
20C2×M16×C131—24no—
21C4⋊Q8×C131—22no—
22C4⋊Q8×C131D412yes—
23C4⋊Q8×C131Q812yes—
24C4×Q8×C131—42no—
25C4×Q8×C131—42no—
26C2×C4⋊C4×C131—22no—
27C2×C4⋊C4×C131—21no—
28C2×C4⋊C4×C131C2×C411yescharacteristic
29C2×C4⋊C4×C131C2×C411yescharacteristic
30C2×C4⋊C4×C131D412yes—
31C2×C42×C131—21no—
32C2×C42×C131C2×C411yescharacteristic
33C2×C42×C131C2×C411yescharacteristic
34C2×C42×C131C2×C411yescharacteristic
35C2×C42×C131D412yes—
36C4⋊C8×C131—44no—
37#101×C131—24no—
38#101×C131—24no—
39#95×C131—22no—
40#95×C131—21no—
41#95×C131—22no—
42#95×C131—21no—
43#95×C131—22no—
44C2×Q8×C131—21no—
45C2×Q8×C131—41no—
46C2×Q8×C131—41no—
47C2×Q8×C131—41no—
48C2×Q8×C131—41no—
49C2×Q8×C131C4⋊C412yes—
50C2×Q8×C131C2×D411yescharacteristic
51C2×Q8×C131C2×Q811yescharacteristic
52C2×Q8×C131#4112yes—
53C22×C4×C131—21no—
54C22×C4×C131—21no—
55C22×C4×C131—21no—
56C22×C4×C131—21no—
57C22×C4×C131C22⋊C412yes—
58C22×C4×C131C22⋊C411yescharacteristic
59C22×C4×C131C22⋊C411yescharacteristic
60C22×C4×C131C22×C411yescharacteristic
61C22×C4×C131C2×D412yes—
62M16×C131—44no—
63M16×C131—44no—
64C2×C8×C131—44no—
65C4⋊C4×C131—24no—
66C4⋊C4×C131—24no—
67C4⋊C4×C131—41no—
68C4⋊C4×C131—42no—
69C4⋊C4×C131—41no—
70C4⋊C4×C131—42no—
71C42×C131—24no—
72C42×C131—22no—
73C42×C131—21no—
74C42×C131—41no—
75C42×C131—42no—
76C42×C131C4⋊C412yes—
77C23×C131C2×C22⋊C411yescharacteristic
78Q8×C131—41no—
79Q8×C131—41no—
80Q8×C131—42no—
81Q8×C131—42no—
82Q8×C131—42no—
83C2×C4×C131—21no—
84C2×C4×C131—22no—
85C2×C4×C131—21no—
86C2×C4×C131—22no—
87C2×C4×C131—22no—
88C2×C4×C131—22no—
89C2×C4×C131—21no—
90C2×C4×C131—22no—
91C2×C4×C131—41no—
92C2×C4×C131—41no—
93C2×C4×C131—41no—
94C2×C4×C131—41no—
95C2×C4×C131—41no—
96C2×C4×C131—42no—
97C2×C4×C131—41no—
98C2×C4×C131—41no—
99C2×C4×C131—41no—
100C2×C4×C131—42no—
101C2×C4×C131—41no—
102C2×C4×C131—41no—
103C2×C4×C131#9912yes—
104C2×C4×C131C2×C4⋊C411yescharacteristic
105C2×C4×C131#11711yescharacteristic
106C2×C4×C131#12112yes—
107C2×C4×C131C22⋊Q812yes—
108C8×C131—84no—
109C22×C131—21no—
110C22×C131—21no—
111C22×C131#38011yescharacteristic
112C22×C131C2×#9911yescharacteristic
113C22×C131#41011yescharacteristic
114C4×C131—22no—
115C4×C131—21no—
116C4×C131—21no—
117C4×C131—22no—
118C4×C131—22no—
119C4×C131—42no—
120C4×C131—42no—
121C4×C131—41no—
122C4×C131—42no—
123C4×C131—81no—
124C4×C131—81no—
125C2×C131—21no—
126C2×C131—21no—
127C2×C131#179911yescharacteristic
128C2×C131#213311yescharacteristic
129C2×C131#213511yescharacteristic
130#12804C13111yesmaximal, characteristic, direct product factor, Sylow
131C131#1280411yescharacteristic, direct product factor, Sylow
132#2327C2×C13111yescharacteristic
133C2×#356C2×C13112yes—
134#1801C2×C13112yes—
135#1394C2×C13112yes—
136C2×C4⋊Q8C22×C13111yescharacteristic
137C2×C4×Q8C4×C13111yescharacteristic
138C2×C4×Q8C22×C13111yescharacteristic
139#423—22no—
140C2×#101C22×C13114yes—
141#391C4×C13111yescharacteristic
142#391C22×C13111yescharacteristic
143#387—22no—
144#387—22no—
145#382C4×C13111yescharacteristic
146#376C4×C13111yescharacteristic
147#356—24no—
148#343—22no—
149C22×Q8C2×C4×C13111yescharacteristic
150C22×Q8C23×C13111yescharacteristic
151C2×M16—24no—
152C4⋊Q8—22no—
153C4⋊Q8D4×C13112yes—
154C4⋊Q8Q8×C13112yes—
155C4×Q8—42no—
156C4×Q8—42no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×C4×C13111yescharacteristic
160C2×C4⋊C4C2×C4×C13111yescharacteristic
161C2×C4⋊C4D4×C13112yes—
162C2×C42—21no—
163C2×C42C2×C4×C13111yescharacteristic
164C2×C42C2×C4×C13111yescharacteristic
165C2×C42C2×C4×C13111yescharacteristic
166C2×C42D4×C13112yes—
167C4⋊C8—44no—
168#101—24no—
169#101—24no—
170#95—21no—
171#95—21no—
172#95—22no—
173#95—22no—
174#95—22no—
175C2×Q8—21no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8C4⋊C4×C13112yes—
181C2×Q8C2×D4×C13111yescharacteristic
182C2×Q8C2×Q8×C13111yescharacteristic
183C2×Q8#41×C13112yes—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4C22⋊C4×C13112yes—
189C22×C4C22⋊C4×C13111yescharacteristic
190C22×C4C22⋊C4×C13111yescharacteristic
191C22×C4C22×C4×C13111yescharacteristic
192C22×C4C2×D4×C13112yes—
193M16—44no—
194M16—44no—
195C2×C8—44no—
196C4⋊C4—24no—
197C4⋊C4—24no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—41no—
201C4⋊C4—42no—
202C42—24no—
203C42—22no—
204C42—21no—
205C42—41no—
206C42—42no—
207C42C4⋊C4×C13112yes—
208C23C2×C22⋊C4×C13111yescharacteristic
209Q8—41no—
210Q8—41no—
211Q8—42no—
212Q8—42no—
213Q8—42no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4#99×C13112yes—
235C2×C4C2×C4⋊C4×C13111yescharacteristic
236C2×C4#117×C13111yescharacteristic
237C2×C4#121×C13112yes—
238C2×C4C22⋊Q8×C13112yes—
239C8—84no—
240C22—21no—
241C22—21no—
242C22#380×C13111yescharacteristic
243C22C2×#99×C13111yescharacteristic
244C22#410×C13111yescharacteristic
245C4—22no—
246C4—21no—
247C4—21no—
248C4—22no—
249C4—22no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4—81no—
256C2—21no—
257C2—21no—
258C2#1799×C13111yescharacteristic
259C2#2133×C13111yescharacteristic
260C2#2135×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#99
commutatorC22×C4C22×C4×C131
Frattini, cosocleC22×Q8C23×C131
prime radicalC23×C131C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×C4×Q8×C131 ◁ G

Complements

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

NH ≅ G/Ntype
130. #12804C131direct (N × H)
131. C131#12804direct (N × H)

Maximal subgroups

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

subgroupindex
#2327×C1312
C2×#356×C1312
#1801×C1312
#1394×C1312
#12804131