Finite Group Databasebeta

← #11772916

Subgroups — #11772916

Order 1152.

180 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 26 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#10590138C211yesmaximal, characteristic, complemented
3#10590132C211yesmaximal, characteristic, complemented
4D8×C3⋊D3—21no—
5#63769—21no—
6C32×D16C411yescharacteristic, complemented
7#63653—21no—
8#63626C411yescharacteristic, complemented
9C16×C3⋊D3C2211yescharacteristic
10#63540—21no—
11D3×D16—62no—
12D4×C3⋊D3—41no—
13C4⋊#157—41no—
14C32×D8—21no—
15#3753—41no—
16#3745—21no—
17C8×C3⋊D3D411yescharacteristic
18C32×C16C2×C411yescharacteristic
19C3⋊(C3⋊C16)D411yescharacteristic
20#1415—91nomaximal, Sylow
21D3×D8—64no—
22C3×D16—22no—
23#826—64no—
24D48—62no—
25D3×C16—62no—
26C22×C3⋊D3—81no—
27C2×#157—81no—
28C32×D4—41no—
29#638—81no—
30C4⋊(C3⋊D3)—41no—
31C4×C3⋊D3D811yescharacteristic
32C32×C8C22⋊C411yescharacteristic
33C3⋊(C3⋊C8)SD1611yescharacteristic
34C2×D16—91no—
35C2×C32—91no—
36#366—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—161no—
47C2×C3⋊D3—161no—
48C2×C3⋊D3D1611yescharacteristic
49#157—161no—
50C32×C4#10211yescharacteristic
51C3⋊Dic3SD3211yescharacteristic
52C2×D8—181no—
53D16—91no—
54D16—181no—
55D16#15711yescharacteristic, complemented
56C2×C16—91no—
57#107—181no—
58C32—181no—
59C22×D3—244no—
60C3×D4—44no—
61#67—244no—
62D12—124no—
63C4×D3—62no—
64C3×C8—22no—
65C3⋊C8—62no—
66C2×C32—161no—
67C2×C32#35711yescharacteristic
68C3⋊D3—161no—
69C3⋊D3D3211yescharacteristic
70C3⋊D3SD6411yescharacteristic
71C2×D4—361no—
72D8—21no—
73D8—181no—
74D8—361no—
75C2×C8—91no—
76C4⋊C4—361no—
77C16—91no—
78C16C2×#15711yescharacteristic
79C22×C3—84no—
80C2×D3—62no—
81C2×D3—244no—
82C2×D3—484no—
83C2×D3—484no—
84C3×C4—22no—
85Dic3—62no—
86C32#141511yescharacteristic, complemented, Sylow
87C23—721no—
88D4—41no—
89D4—361no—
90D4—721no—
91C2×C4—91no—
92C2×C4—721no—
93C8—91no—
94C8C22⋊#15711yescharacteristic
95C2×C3—22no—
96C2×C3—164no—
97D3—62no—
98D3—62no—
99D3—484no—
100C22—81no—
101C22—91no—
102C22—721no—
103C22—1441no—
104C22—1441no—
105C4—91no—
106C4—1441no—
107C4#6378211yescharacteristic
108C3—22no—
109C2—91no—
110C2—91no—
111C2—161no—
112C2—1441no—
113C2#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#1415
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. #10590138C2semidirect
3. #10590132C2semidirect
6. C32×D16C4semidirect
8. #63626C4semidirect
55. D16#157semidirect
86. C32#1415semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×D162
#105901382
#105901322
#14159