Finite Group Databasebeta

← C131×#7359 #45693243

Subgroups — C131×#7359 #45693243

Order 33536.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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#1991×C131C211yesmaximal, characteristic
2#1324×C131C212yesmaximal
3C2×#125×C131C411yescharacteristic
4C2×C4×C8×C131C411yescharacteristic
5#382×C131C2211yescharacteristic
6#340×C131—22no—
7#324×C131—22no—
8C22×C8×C131—21no—
9#125×C131—21no—
10#125×C131—41no—
11#125×C131C812yescomplemented
12C2×C4⋊C4×C131—21no—
13C2×C4⋊C4×C131—41no—
14C2×C4⋊C4×C131D412yes—
15C2×C42×C131C2×C411yescharacteristic
16C22⋊C8×C131—42no—
17C4×C8×C131—41no—
18#95×C131—41no—
19C22×C4×C131—21no—
20C22×C4×C131—22no—
21C22×C4×C131—41no—
22C22×C4×C131C22⋊C411yescharacteristic
23C2×C8×C131—22no—
24C2×C8×C131—41no—
25C2×C8×C131—41no—
26C2×C8×C131—82no—
27C4⋊C4×C131—22no—
28C4⋊C4×C131—42no—
29C4⋊C4×C131—42no—
30C4⋊C4×C131—42no—
31C4⋊C4×C131—41no—
32C42×C131—21no—
33C42×C131C2×C811yescharacteristic
34C42×C131M1611yescharacteristic
35C23×C131#9911yescharacteristic
36C2×C4×C131—21no—
37C2×C4×C131—21no—
38C2×C4×C131—21no—
39C2×C4×C131—21no—
40C2×C4×C131—42no—
41C2×C4×C131—42no—
42C2×C4×C131—42no—
43C2×C4×C131—82no—
44C2×C4×C131—82no—
45C2×C4×C131C22⋊C811yescharacteristic
46C2×C4×C131#10011yescharacteristic
47C8×C131—42no—
48C8×C131—162no—
49C22×C131—22no—
50C22×C131#32311yescharacteristic
51C22×C131#35411yescharacteristic
52C22×C131#35611yescharacteristic
53C4×C131—21no—
54C4×C131—21no—
55C4×C131—41no—
56C4×C131—41no—
57C4×C131—82no—
58C4×C131—82no—
59C2×C131—21no—
60C2×C131—21no—
61C2×C131#131911yescharacteristic
62C2×C131#141412yes—
63#7359C13111yesmaximal, characteristic, direct product factor, Sylow
64C131#735911yescharacteristic, direct product factor, Sylow
65#1991C2×C13111yescharacteristic
66#1324C2×C13112yes—
67C2×#125C4×C13111yescharacteristic
68C2×C4×C8C4×C13111yescharacteristic
69#382C22×C13111yescharacteristic
70#340—22no—
71#324—22no—
72C22×C8—21no—
73#125—21no—
74#125—41no—
75#125C8×C13112yescomplemented
76C2×C4⋊C4—21no—
77C2×C4⋊C4—41no—
78C2×C4⋊C4D4×C13112yes—
79C2×C42C2×C4×C13111yescharacteristic
80C22⋊C8—42no—
81C4×C8—41no—
82#95—41no—
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—41no—
86C22×C4C22⋊C4×C13111yescharacteristic
87C2×C8—22no—
88C2×C8—41no—
89C2×C8—41no—
90C2×C8—82no—
91C4⋊C4—22no—
92C4⋊C4—42no—
93C4⋊C4—42no—
94C4⋊C4—42no—
95C4⋊C4—41no—
96C42—21no—
97C42C2×C8×C13111yescharacteristic
98C42M16×C13111yescharacteristic
99C23#99×C13111yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—42no—
105C2×C4—42no—
106C2×C4—42no—
107C2×C4—82no—
108C2×C4—82no—
109C2×C4C22⋊C8×C13111yescharacteristic
110C2×C4#100×C13111yescharacteristic
111C8—42no—
112C8—162no—
113C22—22no—
114C22#323×C13111yescharacteristic
115C22#354×C13111yescharacteristic
116C22#356×C13111yescharacteristic
117C4—21no—
118C4—21no—
119C4—41no—
120C4—41no—
121C4—82no—
122C4—82no—
123C2—21no—
124C2—21no—
125C2#1319×C13111yescharacteristic
126C2#1414×C13112yes—
subgroupG/H
center, socleC22×C131#354
commutatorC42C2×C8×C131
Frattini, cosocle#382C22×C131
prime radicalC23×C131#99
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C131 ◁ C22×C4×C131 ◁ #382×C131 ◁ G

Complements

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

NH ≅ G/Ntype
11. #125×C131C8semidirect
63. #7359C131direct (N × H)
64. C131#7359direct (N × H)
75. #125C8×C131semidirect

Maximal subgroups

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

subgroupindex
#1991×C1312
#1324×C1312
#7359131