Finite Group Databasebeta

← #11771481

Subgroups — #11771481

Order 1152.

188 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 27 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#10593735C211yesmaximal, characteristic
2#10593260C212yesmaximal
3C2×C4⋊#157—22no—
4C2×C4⋊#157C411yescharacteristic
5C2×C4⋊#157C2211yescharacteristic
6C22⋊AGL(1,𝔽9)—22no—
7C42×C3⋊D3C411yescharacteristic
8C22×#157—21no—
9C22×#157D412yes—
10C2×AGL(1,𝔽9)—42no—
11C2×C4×C3⋊D3—21no—
12C2×C4×C3⋊D3C2×C411yescharacteristic
13C4⋊#157—41no—
14C4⋊#157—41no—
15C4⋊#157—44no—
16C32×C42C811yescharacteristic, complemented
17C4×C3⋊Dic3—21no—
18C4×C3⋊Dic3C811yescharacteristic, complemented
19#1325—91nomaximal, Sylow
20C42×D3—121no—
21C22×C3⋊D3C22⋊C411yescharacteristic
22C2×#157—22no—
23C2×#157—42no—
24C2×#157—42no—
25C2×#157—41no—
26AGL(1,𝔽9)—82no—
27C2×C32×C4—21no—
28C2×C32×C4C2×C811yescharacteristic
29C2×C3⋊Dic3—21no—
30C2×C3⋊Dic3M1611yescharacteristic
31C4×C3⋊D3—22no—
32C4×C3⋊D3—22no—
33C4×C3⋊D3—21no—
34C4×C3⋊D3—21no—
35#384—91no—
36#324—92no—
37C2×C4×D3—121no—
38C2×C4×D3—122no—
39C3×C42—41no—
40C4×Dic3—121no—
41C4×Dic3—122no—
42C22×C32C22⋊C811yescharacteristic
43C2×C3⋊D3—21no—
44C2×C3⋊D3—21no—
45C2×C3⋊D3#9911yescharacteristic
46C2×C3⋊D3#10111yescharacteristic
47#157—42no—
48#157—81no—
49C32×C4—22no—
50C32×C4—21no—
51C3⋊Dic3—22no—
52C3⋊Dic3—21no—
53C2×C4⋊C4—91no—
54C2×C4⋊C4—91no—
55C2×C4⋊C4—182no—
56C2×C42—91no—
57C22⋊C8—182no—
58C22×D3—121no—
59C2×C3×C4—42no—
60C2×C3×C4—41no—
61C2×Dic3—121no—
62C2×Dic3—122no—
63C4×D3—122no—
64C4×D3—122no—
65C4×D3—124no—
66C4×D3—124no—
67C2×C32—21no—
68C2×C32#32411yescharacteristic
69C3⋊D3—21no—
70C3⋊D3#35311yescharacteristic
71C3⋊D3#35611yescharacteristic
72C22×C4—91no—
73C22×C4—92no—
74C22×C4—181no—
75C22×C4—181no—
76C2×C8—362no—
77C4⋊C4—361no—
78C4⋊C4—361no—
79C4⋊C4—364no—
80C42—91no—
81C42—181no—
82C42AGL(1,𝔽9)11yescharacteristic, complemented
83C22×C3—41no—
84C2×D3—121no—
85C2×D3—121no—
86C2×D3—122no—
87C2×D3—122no—
88C3×C4—44no—
89C3×C4—42no—
90Dic3—124no—
91Dic3—122no—
92C32#132511yescharacteristic, complemented, Sylow
93C23—91no—
94C2×C4—21no—
95C2×C4—91no—
96C2×C4—181no—
97C2×C4—181no—
98C2×C4—182no—
99C2×C4—182no—
100C2×C4—181no—
101C2×C4—182no—
102C2×C4—362no—
103C2×C4—361no—
104C2×C4—362no—
105C2×C4C2×AGL(1,𝔽9)11yescharacteristic
106C8—722no—
107C2×C3—42no—
108C2×C3—41no—
109D3—121no—
110D3—121no—
111D3—122no—
112C22—91no—
113C22—91no—
114C22—181no—
115C22—181no—
116C22C22⋊AGL(1,𝔽9)11yescharacteristic
117C4—22no—
118C4—21no—
119C4—182no—
120C4—181no—
121C4—362no—
122C4—721no—
123C3—41no—
124C2—21no—
125C2—91no—
126C2—91no—
127C2—181no—
128C2#1059326011yescharacteristic
subgroupG/H
centerC2#10593260
commutatorC2×C32×C4C2×C8
FrattiniC2×C4C2×AGL(1,𝔽9)
FittingC32×C42C8
socleC2×C32#324
prime radicalC22×C3⋊D3C22⋊C4
cosocleC2×C4⋊#157C22
hypercenterC42AGL(1,𝔽9)
hypocenterC32#1325
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
16. C32×C42C8semidirect
18. C4×C3⋊Dic3C8semidirect
82. C42AGL(1,𝔽9)semidirect
92. C32#1325semidirect

Maximal subgroups

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

subgroupindex
#105937352
#105932602
#13259