Finite Group Databasebeta

← #11772982

Subgroups — #11772982

Order 1152.

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

normal subgroups only

This group has 176 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
1C3⋊D3×D16C211yesmaximal, characteristic
2#10590141C211yesmaximal, characteristic, complemented
3#10590133C211yesmaximal, characteristic, complemented
4D8×C3⋊D3—21no—
5#63771—21no—
6C32×D16C411yescharacteristic
7#63653—21no—
8#63626C411yescharacteristic
9C16×C3⋊D3C2211yescharacteristic
10#63540—21no—
11D3×D16—62no—
12D4×C3⋊D3—41no—
13#3788—41no—
14C32×D8—21no—
15#3753—41no—
16#3745—21no—
17C8×C3⋊D3D411yescharacteristic
18C32×C16C2×C411yescharacteristic
19C3⋊(C3⋊C16)D411yescharacteristic
20#1419—91nomaximal, Sylow
21D3×D8—64no—
22C3×D16—22no—
23#826—64no—
24D48—62no—
25D3×C16—62no—
26C22×C3⋊D3—81no—
27C32×D4—41no—
28#638—81no—
29C4⋊(C3⋊D3)—41no—
30C4×C3⋊D3D811yescharacteristic
31#622—81no—
32C32×C8C22⋊C411yescharacteristic
33C3⋊(C3⋊C8)SD1611yescharacteristic
34C2×D16—91no—
35M64—91no—
36#368—91no—
37D3×D4—124no—
38C3×D8—24no—
39#213—124no—
40D24—64no—
41D3×C8—62no—
42C3×C16—22no—
43C3⋊C16—62no—
44C22×C32—81no—
45C2×C3⋊D3—81no—
46C2×C3⋊D3—162no—
47C2×C3⋊D3SD3211yescharacteristic
48C32×C4#10211yescharacteristic
49C3⋊Dic3D1611yescharacteristic
50C2×D8—181no—
51D16—91no—
52D16—181no—
53D16#15711yescharacteristic
54C2×C16—91no—
55#108—181no—
56C32—181no—
57C22×D3—244no—
58C3×D4—44no—
59#67—244no—
60D12—124no—
61C4×D3—62no—
62C3×C8—22no—
63C3⋊C8—62no—
64C2×C32—161no—
65C2×C32#35711yescharacteristic
66C3⋊D3—21no—
67C3⋊D3—161no—
68C2×D4—361no—
69D8—21no—
70D8—181no—
71D8—361no—
72M16—361no—
73C2×C8—91no—
74C16—91no—
75C16C2×#15711yescharacteristic
76C22×C3—84no—
77C2×D3—62no—
78C2×D3—244no—
79C2×D3—488no—
80C3×C4—22no—
81Dic3—62no—
82C32#141911yescharacteristic, complemented, Sylow
83C23—721no—
84D4—41no—
85D4—361no—
86D4—721no—
87C2×C4—91no—
88C8—91no—
89C8—721no—
90C8C22⋊#15711yescharacteristic
91C2×C3—22no—
92C2×C3—164no—
93D3—64no—
94D3—484no—
95C22—81no—
96C22—91no—
97C22—721no—
98C22—1442no—
99C4—91no—
100C4#6378211yescharacteristic
101C3—22no—
102C2—161no—
103C2—181no—
104C2—1441no—
105C2#1059019311yescharacteristic
subgroupG/H
centerC2#10590193
commutatorC32×C16C2×C4
FrattiniC16C2×#157
FittingC32×D16C4
socleC2×C32#357
prime radicalC3⋊D3×D16C2
cosocleC16×C3⋊D3C22
hypercenterD16#157
hypocenterC32#1419
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. #10590141C2semidirect
3. #10590133C2semidirect
82. C32#1419semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×D162
#105901412
#105901332
#14199