Finite Group Databasebeta

← C131×#7351 #45693235

Subgroups — C131×#7351 #45693235

Order 33536.

178 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 46 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#1822×C131C211yesmaximal, characteristic
2#1320×C131C212yesmaximal
3C2×#117×C131C411yescharacteristic
4#407×C131C411yescharacteristic
5#407×C131C2211yescharacteristic
6#349×C131—22no—
7#343×C131—22no—
8C23×C4×C131C2×C411yescharacteristic
9C2×M16×C131—21no—
10C2×M16×C131D412yes—
11#117×C131—41no—
12#117×C131—41no—
13C2×C4⋊C4×C131—21no—
14C2×C22⋊C4×C131C812yes—
15C2×C42×C131—21no—
16M32×C131—42no—
17C22⋊C8×C131—41no—
18C22⋊C8×C131—41no—
19C24×C131C2×C811yescharacteristic
20C22×C4×C131—21no—
21C22×C4×C131—21no—
22C22×C4×C131—22no—
23C22×C4×C131—42no—
24C22×C4×C131C22⋊C411yescharacteristic
25C22×C4×C131M1611yescharacteristic
26M16×C131—42no—
27M16×C131—42no—
28C2×C8×C131—22no—
29C2×C8×C131—41no—
30C4⋊C4×C131—41no—
31C4⋊C4×C131—41no—
32C22⋊C4×C131—42no—
33C42×C131—42no—
34C16×C131—82no—
35C23×C131—21no—
36C23×C131—41no—
37C23×C131—81no—
38C23×C131C22⋊C811yescharacteristic
39C2×C4×C131—22no—
40C2×C4×C131—21no—
41C2×C4×C131—42no—
42C2×C4×C131—42no—
43C2×C4×C131—41no—
44C2×C4×C131—42no—
45C2×C4×C131—82no—
46C2×C4×C131#9911yescharacteristic
47C2×C4×C131#10011yescharacteristic
48C8×C131—42no—
49C8×C131—81no—
50C22×C131—21no—
51C22×C131—41no—
52C22×C131—42no—
53C22×C131—41no—
54C22×C131—82no—
55C22×C131#32311yescharacteristic
56C4×C131—21no—
57C4×C131—41no—
58C4×C131—82no—
59C4×C131#35212yes—
60C2×C131—21no—
61C2×C131—41no—
62C2×C131—81no—
63C2×C131#131711yescharacteristic
64#7351C13111yesmaximal, characteristic, direct product factor, Sylow
65C131#735111yescharacteristic, direct product factor, Sylow
66#1822C2×C13111yescharacteristic
67#1320C2×C13112yes—
68C2×#117C4×C13111yescharacteristic
69#407C4×C13111yescharacteristic
70#407C22×C13111yescharacteristic
71#349—22no—
72#343—22no—
73C23×C4C2×C4×C13111yescharacteristic
74C2×M16—21no—
75C2×M16D4×C13112yes—
76#117—41no—
77#117—41no—
78C2×C4⋊C4—21no—
79C2×C22⋊C4C8×C13112yes—
80C2×C42—21no—
81M32—42no—
82C22⋊C8—41no—
83C22⋊C8—41no—
84C24C2×C8×C13111yescharacteristic
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—22no—
88C22×C4—42no—
89C22×C4C22⋊C4×C13111yescharacteristic
90C22×C4M16×C13111yescharacteristic
91M16—42no—
92M16—42no—
93C2×C8—22no—
94C2×C8—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C22⋊C4—42no—
98C42—42no—
99C16—82no—
100C23—21no—
101C23—41no—
102C23—81no—
103C23C22⋊C8×C13111yescharacteristic
104C2×C4—22no—
105C2×C4—21no—
106C2×C4—42no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—42no—
110C2×C4—82no—
111C2×C4#99×C13111yescharacteristic
112C2×C4#100×C13111yescharacteristic
113C8—42no—
114C8—81no—
115C22—21no—
116C22—41no—
117C22—42no—
118C22—41no—
119C22—82no—
120C22#323×C13111yescharacteristic
121C4—21no—
122C4—41no—
123C4—82no—
124C4#352×C13112yes—
125C2—21no—
126C2—41no—
127C2—81no—
128C2#1317×C13111yescharacteristic
subgroupG/H
center, socleC2×C131#1317
commutatorC24C2×C8×C131
Frattini, cosocle#407C22×C131
prime radicalC24×C131C2×C8
LCSG ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C22×C4×C131 ◁ #407×C131 ◁ G

Complements

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

NH ≅ G/Ntype
64. #7351C131direct (N × H)
65. C131#7351direct (N × H)

Maximal subgroups

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

subgroupindex
#1822×C1312
#1320×C1312
#7351131