Finite Group Databasebeta

← #11771453

Subgroups — #11771453

Order 1152.

208 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 36 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#10592698C211yesmaximal, characteristic
2C22⋊#3708C212yesmaximal
3C32×#117C411yescharacteristic
4C2×#3748C411yescharacteristic
5C22×C3⋊(C3⋊C8)C2211yescharacteristic
6C2×#3708—22no—
7C4⋊(C3⋊(C3⋊C8))—22no—
8#4999—62no—
9C22×C32×C4C2×C411yescharacteristic
10C32×C4⋊C4C812yes—
11C32×C22⋊C4—21no—
12C32×C42—21no—
13#3748—41no—
14C2×C3⋊(C3⋊C8)—21no—
15C2×C3⋊(C3⋊C8)—41no—
16C2×C3⋊(C3⋊C8)D412yes—
17#3708—42no—
18#1323—91nomaximal, Sylow
19C3×#117—22no—
20C2×#208—62no—
21C22×C3⋊C8—62no—
22C4⋊(C3⋊C8)—68no—
23C23×C32M1611yescharacteristic
24C2×C32×C4—21no—
25C2×C32×C4—21no—
26C2×C32×C4—22no—
27C2×C32×C4C22⋊C411yescharacteristic
28C2×C32×C4C2×C811yescharacteristic
29C3⋊(C3⋊C8)—22no—
30C3⋊(C3⋊C8)—41no—
31#424—91no—
32C22⋊C16—92no—
33C22×C3×C4—22no—
34C3×C4⋊C4—24no—
35C3×C22⋊C4—24no—
36C3×C42—24no—
37#208—124no—
38C2×C3⋊C8—64no—
39C2×C3⋊C8—64no—
40C2×C3⋊C8—124no—
41C22×C32—21no—
42C22×C32—22no—
43C22×C32C22⋊C811yescharacteristic
44C32×C4—21no—
45C32×C4—42no—
46C32×C4#9911yescharacteristic
47C32×C4#10111yescharacteristic
48C2×M16—91no—
49C22×C8—91no—
50#117#15711yescharacteristic
51C2×C16—182no—
52C4⋊C8—182no—
53C23×C3—22no—
54C2×C3×C4—24no—
55C2×C3×C4—24no—
56C2×C3×C4—28no—
57C2×C3×C4—22no—
58C2×C3×C4—22no—
59C3⋊C8—124no—
60C3⋊C8—124no—
61C2×C32—41no—
62C2×C32#32411yescharacteristic
63C2×C32#35012yes—
64C22×C4C2×#15711yescharacteristic
65M16—361no—
66C2×C8—92no—
67C2×C8—181no—
68C2×C8—361no—
69C4⋊C4#62212yes—
70C22⋊C4—21no—
71C42—21no—
72C16—362no—
73C22×C3—24no—
74C22×C3—22no—
75C22×C3—44no—
76C3×C4—24no—
77C3×C4—22no—
78C3×C4—22no—
79C3×C4—48no—
80C32#132311yescharacteristic, complemented, Sylow
81C23#379211yescharacteristic
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—22no—
85C2×C4C2×#62211yescharacteristic
86C2×C4C22⋊#15711yescharacteristic
87C8—182no—
88C8—361no—
89C2×C3—24no—
90C2×C3—22no—
91C2×C3—44no—
92C22—22no—
93C22—21no—
94C22C22⋊#62211yescharacteristic
95C4—21no—
96C4—42no—
97C4#6377411yescharacteristic
98C4#6378011yescharacteristic
99C3—22no—
100C2—41no—
101C2#1059020211yescharacteristic
102C2#1059022112yes—
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C2×C8
FrattiniC22×C4C2×#157
FittingC32×#117C4
socleC22×C32C22⋊C8
prime radicalC23×C32M16
cosocleC22×C3⋊(C3⋊C8)C22
hypercenter#117#157
hypocenterC32#1323
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
80. C32#1323semidirect

Maximal subgroups

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

subgroupindex
#105926982
C22⋊#37082
#13239