Finite Group Databasebeta

← C131×#11524 #45697408

Subgroups — C131×#11524 #45697408

Order 33536.

288 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 98 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#2922×C131C211yesmaximal, characteristic
2#2165×C131C212yesmaximal, complemented
3#1328×C131C212yesmaximal, complemented
4#1321×C131C212yesmaximal
5C4×#41×C131C411yescharacteristic
6#433×C131—22no—
7#431×C131—22no—
8#424×C131C411yescharacteristic
9#424×C131C2211yescharacteristic
10#408×C131C411yescharacteristic
11#408×C131C2211yescharacteristic
12C4×M16×C131C2211yescharacteristic
13C2×C4×C8×C131C411yescharacteristic
14#364×C131—22no—
15#349×C131C2214yes—
16#347×C131—22no—
17C2×#41×C131C2×C411yescharacteristic
18C2×M16×C131C2×C411yescharacteristic
19C2×M16×C131C2311yescharacteristic
20C22×C8×C131C2×C411yescharacteristic
21C22×C8×C131C2×C411yescharacteristic
22C4×Q8×C131—21no—
23C4×D4×C131—21no—
24C4×D4×C131—22no—
25#117×C131—21no—
26#117×C131C2×C411yescharacteristic
27C2×C42×C131—21no—
28C2×C42×C131C2×C411yescharacteristic
29M32×C131—24no—
30C4⋊C8×C131—22no—
31C4⋊C8×C131—22no—
32C22⋊C8×C131—22no—
33C22⋊C8×C131—22no—
34#97×C131D412yes—
35C4×C8×C131—21no—
36C4×C8×C131—21no—
37C4×C8×C131D412yes—
38#41×C131—41no—
39#41×C131—41no—
40C2×Q8×C131M1611yescharacteristic
41C2×D4×C131—21no—
42C2×D4×C131M1611yescharacteristic
43C22×C4×C131—22no—
44C22×C4×C131—21no—
45C22×C4×C131—21no—
46C22×C4×C131C22×C411yescharacteristic
47M16×C131—41no—
48M16×C131—41no—
49C2×C8×C131—21no—
50C2×C8×C131—21no—
51C2×C8×C131—41no—
52C2×C8×C131—41no—
53C2×C8×C131C22⋊C412yes—
54C2×C8×C131C2×D412yes—
55C4⋊C4×C131—22no—
56C4⋊C4×C131—21no—
57C22⋊C4×C131—22no—
58C22⋊C4×C131M1612yes—
59C42×C131—22no—
60C42×C131—21no—
61C42×C131—21no—
62C42×C131C22⋊C411yescharacteristic
63C42×C131C22⋊C411yescharacteristic
64C16×C131—44no—
65C23×C131—21no—
66C23×C131C2×M1611yescharacteristic
67Q8×C131—41no—
68D4×C131—41no—
69D4×C131—42no—
70C2×C4×C131—21no—
71C2×C4×C131—21no—
72C2×C4×C131—21no—
73C2×C4×C131—22no—
74C2×C4×C131—21no—
75C2×C4×C131—21no—
76C2×C4×C131—42no—
77C2×C4×C131—44no—
78C2×C4×C131—41no—
79C2×C4×C131—41no—
80C2×C4×C131C2×C22⋊C411yescharacteristic
81C2×C4×C131C2×M1611yescharacteristic
82C8×C131—22no—
83C8×C131—22no—
84C8×C131—41no—
85C8×C131—41no—
86C22×C131—21no—
87C22×C131—41no—
88C22×C131—42no—
89C22×C131—41no—
90C22×C131#40711yescharacteristic
91C4×C131—22no—
92C4×C131—21no—
93C4×C131—42no—
94C4×C131—41no—
95C4×C131—41no—
96C4×C131#41011yescharacteristic
97C4×C131#41311yescharacteristic
98C2×C131—21no—
99C2×C131—41no—
100C2×C131—81no—
101C2×C131#146411yescharacteristic
102#11524C13111yesmaximal, characteristic, direct product factor, Sylow
103C131#1152411yescharacteristic, direct product factor, Sylow
104#2922C2×C13111yescharacteristic
105#2165C2×C13112yescomplemented
106#1328C2×C13112yescomplemented
107#1321C2×C13112yes—
108C4×#41C4×C13111yescharacteristic
109#433—22no—
110#431—22no—
111#424C4×C13111yescharacteristic
112#424C22×C13111yescharacteristic
113#408C4×C13111yescharacteristic
114#408C22×C13111yescharacteristic
115C4×M16C22×C13111yescharacteristic
116C2×C4×C8C4×C13111yescharacteristic
117#364—22no—
118#349C22×C13114yes—
119#347—22no—
120C2×#41C2×C4×C13111yescharacteristic
121C2×M16C2×C4×C13111yescharacteristic
122C2×M16C23×C13111yescharacteristic
123C22×C8C2×C4×C13111yescharacteristic
124C22×C8C2×C4×C13111yescharacteristic
125C4×Q8—21no—
126C4×D4—21no—
127C4×D4—22no—
128#117—21no—
129#117C2×C4×C13111yescharacteristic
130C2×C42—21no—
131C2×C42C2×C4×C13111yescharacteristic
132M32—24no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C22⋊C8—22no—
136C22⋊C8—22no—
137#97D4×C13112yes—
138C4×C8—21no—
139C4×C8—21no—
140C4×C8D4×C13112yes—
141#41—41no—
142#41—41no—
143C2×Q8M16×C13111yescharacteristic
144C2×D4—21no—
145C2×D4M16×C13111yescharacteristic
146C22×C4—22no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4C22×C4×C13111yescharacteristic
150M16—41no—
151M16—41no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8C22⋊C4×C13112yes—
157C2×C8C2×D4×C13112yes—
158C4⋊C4—22no—
159C4⋊C4—21no—
160C22⋊C4—22no—
161C22⋊C4M16×C13112yes—
162C42—22no—
163C42—21no—
164C42—21no—
165C42C22⋊C4×C13111yescharacteristic
166C42C22⋊C4×C13111yescharacteristic
167C16—44no—
168C23—21no—
169C23C2×M16×C13111yescharacteristic
170Q8—41no—
171D4—41no—
172D4—42no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—42no—
180C2×C4—44no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4C2×C22⋊C4×C13111yescharacteristic
184C2×C4C2×M16×C13111yescharacteristic
185C8—22no—
186C8—22no—
187C8—41no—
188C8—41no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—41no—
193C22#407×C13111yescharacteristic
194C4—22no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4#410×C13111yescharacteristic
200C4#413×C13111yescharacteristic
201C2—21no—
202C2—41no—
203C2—81no—
204C2#1464×C13111yescharacteristic
subgroupG/H
centerC4×C131#410
commutatorC22×C4C22×C4×C131
Frattini, cosocleC2×M16C23×C131
socleC2×C131#1464
prime radicalC2×#41×C131C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C131 ◁ C42×C131 ◁ C4×M16×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2165×C131C2semidirect
3. #1328×C131C2semidirect
102. #11524C131direct (N × H)
103. C131#11524direct (N × H)
105. #2165C2×C131semidirect
106. #1328C2×C131semidirect

Maximal subgroups

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

subgroupindex
#2922×C1312
#2165×C1312
#1328×C1312
#1321×C1312
#11524131