Finite Group Databasebeta

← #11771511

Subgroups — #11771511

Order 1152.

150 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 25 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#10593728C211yesmaximal, characteristic
2#10593266C212yesmaximal
3C2×#3788C411yescharacteristic
4C2×#3788C2211yescharacteristic
5#64218—22no—
6C42×C3⋊D3C411yescharacteristic
7C4⋊#622—22no—
8C2×C4×C3⋊D3—21no—
9C2×C4×C3⋊D3C2×C411yescharacteristic
10C2×#622—21no—
11C2×#622D412yes—
12#3788—41no—
13#3788—41no—
14#3771—42no—
15C32×C42C811yescharacteristic
16C4×C3⋊Dic3—21no—
17C4×C3⋊Dic3C811yescharacteristic
18#1327—91nomaximal, Sylow
19C42×D3—121no—
20C22×C3⋊D3M1611yescharacteristic
21C2×C32×C4—21no—
22C2×C32×C4C2×C811yescharacteristic
23C2×C3⋊Dic3—21no—
24C2×C3⋊Dic3C22⋊C411yescharacteristic
25C4×C3⋊D3—21no—
26C4×C3⋊D3—21no—
27C4×C3⋊D3—42no—
28#622—22no—
29#622—41no—
30#423—91no—
31#349—92no—
32C2×C4×D3—121no—
33C2×C4×D3—122no—
34C3×C42—41no—
35C4×Dic3—121no—
36C4×Dic3—122no—
37C22×C32C22⋊C811yescharacteristic
38C2×C3⋊D3—21no—
39C2×C3⋊D3—41no—
40C32×C4—22no—
41C32×C4—21no—
42C3⋊Dic3—41no—
43C3⋊Dic3#9911yescharacteristic
44C3⋊Dic3#10111yescharacteristic
45C2×M16—91no—
46C2×M16—91no—
47C2×C42—91no—
48M32—182no—
49C4⋊C8—182no—
50C22×D3—121no—
51C2×C3×C4—42no—
52C2×C3×C4—41no—
53C2×Dic3—121no—
54C2×Dic3—122no—
55C4×D3—122no—
56C4×D3—122no—
57C4×D3—128no—
58C2×C32—21no—
59C2×C32#32411yescharacteristic
60C3⋊D3—41no—
61C22×C4—91no—
62C22×C4—181no—
63M16—361no—
64M16—361no—
65C2×C8—92no—
66C2×C8—181no—
67C42—91no—
68C42—181no—
69C42AGL(1,𝔽9)11yescharacteristic
70C16—362no—
71C22×C3—41no—
72C2×D3—122no—
73C2×D3—124no—
74C3×C4—44no—
75C3×C4—42no—
76Dic3—121no—
77Dic3—121no—
78Dic3—124no—
79C32#132711yescharacteristic, complemented, Sylow
80C23—91no—
81C2×C4—21no—
82C2×C4—91no—
83C2×C4—181no—
84C2×C4—181no—
85C2×C4—181no—
86C2×C4—362no—
87C2×C4C2×AGL(1,𝔽9)11yescharacteristic
88C8—182no—
89C8—361no—
90C2×C3—42no—
91C2×C3—41no—
92D3—124no—
93C22—181no—
94C22—361no—
95C22C22⋊AGL(1,𝔽9)11yescharacteristic
96C4—22no—
97C4—21no—
98C4—91no—
99C4—91no—
100C4—361no—
101C3—41no—
102C2—21no—
103C2—361no—
104C2#1059326011yescharacteristic
subgroupG/H
centerC2#10593260
commutatorC2×C32×C4C2×C8
FrattiniC2×C4C2×AGL(1,𝔽9)
FittingC32×C42C8
socleC2×C32#324
prime radicalC22×C3⋊D3M16
cosocleC2×#3788C22
hypercenterC42AGL(1,𝔽9)
hypocenterC32#1327
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
79. C32#1327semidirect

Maximal subgroups

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

subgroupindex
#105937282
#105932662
#13279