Finite Group Databasebeta

← #11773003

Subgroups — #11773003

Order 1152.

127 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 127 conjugacy classes of subgroups — too many to draw. Only its 23 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#10590240C211yesmaximal, characteristic
2#10590140C211yesmaximal, characteristic
3#10589069C211yesmaximal, characteristic
4#63802—21no—
5#63771—21no—
6C16×C3⋊D3C2211yescharacteristic
7C3×Dic24—21no—
8#63550C412yes—
9C3×C3⋊C32—21no—
10D3×Q32—61no—
11#4447—61no—
12#3797—41no—
13#3788—41no—
14C8×C3⋊D3D411yescharacteristic
15C3×Dic12—22no—
16#3718—41no—
17C32×C16D411yescharacteristic
18C3⋊(C3⋊C16)C2×C411yescharacteristic
19#1420—91nomaximal, Sylow
20D3×Q16—62no—
21C3×Q32—61no—
22#829—62no—
23Dic24—21no—
24D3×C16—61no—
25D3×C16—61no—
26C3×C32—61no—
27C3⋊C32—21no—
28C4×C3⋊D3D811yescharacteristic
29C3×Dic6—42no—
30#627—81no—
31#624—81no—
32#622—81no—
33C32×C8C22⋊C411yescharacteristic
34C3⋊(C3⋊C8)SD1611yescharacteristic
35C2×Q32—91no—
36M64—91no—
37#368—91no—
38D3×Q8—122no—
39C3×Q16—62no—
40#216—122no—
41Dic12—22no—
42D3×C8—61no—
43D3×C8—61no—
44C3×C16—21no—
45C3×C16—21no—
46C3⋊C16—61no—
47C3⋊C16—61no—
48C2×C3⋊D3SD3211yescharacteristic
49C32×C4#10211yescharacteristic
50C3⋊Dic3D1611yescharacteristic
51C3×Dic3—82no—
52C2×Q16—181no—
53Q32—61no—
54Q32—92no—
55C2×C16—91no—
56#108—181no—
57C32—61no—
58C3×Q8—122no—
59C4×D3—61no—
60C4×D3—61no—
61C4×D3—242no—
62Dic6—42no—
63Dic6—242no—
64C3×C8—21no—
65C3×C8—21no—
66C3⋊C8—61no—
67C3⋊C8—61no—
68C2×C32#35711yescharacteristic
69C3⋊D3—21no—
70C2×Q8—361no—
71Q16—62no—
72Q16—361no—
73M16—361no—
74C2×C8—91no—
75C16—91no—
76C16GO+(4,𝔽2)11yescharacteristic
77C2×D3—61no—
78C2×D3—61no—
79C3×C4—21no—
80C3×C4—21no—
81C3×C4—242no—
82Dic3—61no—
83Dic3—61no—
84Dic3—82no—
85C32#142011yescharacteristic, complemented, Sylow
86Q8—122no—
87Q8—721no—
88C2×C4—91no—
89C2×C4—721no—
90C8—91no—
91C8—721no—
92C8D32⋊C411yescharacteristic
93C2×C3—21no—
94C2×C3—21no—
95D3—62no—
96D3—121no—
97C22—91no—
98C4—91no—
99C4—242no—
100C4#6372911yescharacteristic
101C3—21no—
102C3—21no—
103C2—181no—
104C2#1059001611yescharacteristic
subgroupG/H
centerC2#10590016
commutatorC3⋊(C3⋊C16)C2×C4
Frattini, hypercenterC16GO+(4,𝔽2)
FittingC32×C16D4
socleC2×C32#357
prime radicalC2×C3⋊D3SD32
cosocleC16×C3⋊D3C22
hypocenterC32#1420
LCSG ▷ C3⋊(C3⋊C16) ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
85. C32#1420semidirect

Maximal subgroups

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

subgroupindex
#105902402
#105901402
#105890692
#14209