Finite Group Databasebeta

← #11772965

Subgroups — #11772965

Order 1152.

158 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 24 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#10592611C211yesmaximal, characteristic
2#10590139C211yesmaximal, characteristic, complemented
3#10590133C211yesmaximal, characteristic, complemented
4#64121—21no—
5#63769—21no—
6C32×D16C411yescharacteristic, complemented
7#63654—21no—
8#63628C411yescharacteristic, complemented
9C16×C3⋊D3C2211yescharacteristic
10#63540—21no—
11#4912—62no—
12#3830—41no—
13C4⋊#157—41no—
14C32×D8—21no—
15#3754—41no—
16#3746—21no—
17C8×C3⋊D3D411yescharacteristic
18C32×C16C2×C411yescharacteristic
19C3⋊(C3⋊C16)D411yescharacteristic
20#1418—91nomaximal, Sylow
21#912—64no—
22C3×D16—22no—
23#827—64no—
24Dic24—62no—
25D3×C16—62no—
26C2×#157—81no—
27C32×D4—41no—
28#638—81no—
29C2×C3⋊Dic3—81no—
30C4×C3⋊D3D811yescharacteristic
31#634—41no—
32C32×C8C22⋊C411yescharacteristic
33C3⋊(C3⋊C8)SD1611yescharacteristic
34#508—91no—
35M64—91no—
36#367—91no—
37#237—124no—
38C3×D8—24no—
39#214—124no—
40Dic12—64no—
41D3×C8—62no—
42C3×C16—22no—
43C3⋊C16—62no—
44C22×C32—81no—
45C2×C3⋊D3D1611yescharacteristic
46#157—161no—
47C32×C4#10211yescharacteristic
48C3⋊Dic3—81no—
49C3⋊Dic3SD3211yescharacteristic
50#135—181no—
51Q32—91no—
52SD32—181no—
53D16#15711yescharacteristic, complemented
54C2×C16—91no—
55#107—181no—
56C32—181no—
57C3×D4—44no—
58#67—244no—
59C2×Dic3—244no—
60C4×D3—62no—
61Dic6—124no—
62C3×C8—22no—
63C3⋊C8—62no—
64C2×C32—161no—
65C2×C32#35711yescharacteristic
66C3⋊D3—21no—
67#41—361no—
68Q16—181no—
69SD16—361no—
70D8—21no—
71C2×C8—91no—
72C4⋊C4—361no—
73C16—91no—
74C16C2×#15711yescharacteristic
75C22×C3—84no—
76C2×D3—62no—
77C3×C4—22no—
78Dic3—62no—
79Dic3—244no—
80C32#141811yescharacteristic, complemented, Sylow
81Q8—361no—
82D4—41no—
83D4—721no—
84C2×C4—91no—
85C2×C4—721no—
86C2×C4—721no—
87C8—91no—
88C8C22⋊#15711yescharacteristic
89C2×C3—22no—
90C2×C3—164no—
91D3—122no—
92C22—81no—
93C22—91no—
94C4—91no—
95C4—721no—
96C4—1441no—
97C4#6378211yescharacteristic
98C3—22no—
99C2—161no—
100C2—181no—
101C2#1059019311yescharacteristic
subgroupG/H
centerC2#10590193
commutatorC32×C16C2×C4
FrattiniC16C2×#157
FittingC32×D16C4
socleC2×C32#357
prime radical#10592611C2
cosocleC16×C3⋊D3C22
hypercenterD16#157
hypocenterC32#1418
LCSG ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D16

Complements

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

NH ≅ G/Ntype
2. #10590139C2semidirect
3. #10590133C2semidirect
6. C32×D16C4semidirect
8. #63628C4semidirect
53. D16#157semidirect
80. C32#1418semidirect

Maximal subgroups

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

subgroupindex
#105926112
#105901392
#105901332
#14189