Finite Group Databasebeta

← #11772157

Subgroups — #11772157

Order 1152.

140 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 29 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#10590875C211yesmaximal, characteristic
2#10590178C211yesmaximal, characteristic
3#10589135C211yesmaximal, characteristic
4#63872C412yes—
5#63773—21no—
6C8×C3⋊Dic3C2211yescharacteristic
7C3×#818—21no—
8C3×#812—21no—
9#63574—21no—
10#4878—61no—
11#4511—61no—
12C2×C32×C8D411yescharacteristic
13C4×C3⋊Dic3C2×C411yescharacteristic
14C2×C3⋊(C3⋊C8)D411yescharacteristic
15C3×C4⋊Dic3—22no—
16Dic3⋊Dic3—42no—
17#3708—41no—
18C3×C3⋊C16—41no—
19#1366—91nomaximal, Sylow
20#890—62no—
21C3×M32—61no—
22C3×#107—61no—
23#818—21no—
24C8×Dic3—61no—
25C8×Dic3—61no—
26#812—21no—
27#808—62no—
28C2×C32×C4C22⋊C411yescharacteristic
29C2×C3⋊Dic3—21no—
30C2×C3×Dic3—42no—
31C32×C8SD1611yescharacteristic
32C32×C8Q1611yescharacteristic
33C3⋊(C3⋊C8)SD1611yescharacteristic
34C3⋊(C3⋊C8)Q1611yescharacteristic
35#499—91no—
36#364—91no—
37#364—91no—
38C2×C3×C8—21no—
39C2×C3×C8—21no—
40C3×C4⋊C4—62no—
41C4⋊Dic3—22no—
42C4⋊Dic3—122no—
43Dic3⋊C4—122no—
44C4×Dic3—61no—
45C4×Dic3—61no—
46C2×C3⋊C8—61no—
47C2×C3⋊C8—61no—
48C3×C16—121no—
49C3⋊C16—41no—
50C22×C32#10011yescharacteristic
51C32×C4#10311yescharacteristic
52C32×C4#10311yescharacteristic
53C3⋊Dic3—41no—
54C3×Dic3—82no—
55#125—92no—
56M32—61no—
57M32—181no—
58#107—61no—
59#106—181no—
60C4×C8—91no—
61C2×C3×C4—21no—
62C2×C3×C4—21no—
63C2×C3×C4—122no—
64C2×Dic3—42no—
65C2×Dic3—61no—
66C2×Dic3—61no—
67C2×Dic3—121no—
68C3×C8—21no—
69C3×C8—21no—
70C3×C8—21no—
71C3×C8—21no—
72C3⋊C8—61no—
73C3⋊C8—61no—
74C3⋊C8—61no—
75C3⋊C8—61no—
76C2×C32—21no—
77C2×C32#33311yescharacteristic
78C2×C8—91no—
79C2×C8GO+(4,𝔽2)11yescharacteristic
80C4⋊C4—62no—
81C4⋊C4—362no—
82C42—91no—
83C16—121no—
84C16—361no—
85C22×C3—21no—
86C22×C3—21no—
87C3×C4—21no—
88C3×C4—21no—
89C3×C4—21no—
90C3×C4—21no—
91C3×C4—242no—
92Dic3—82no—
93Dic3—121no—
94Dic3—121no—
95Dic3—122no—
96C32#136611yescharacteristic, complemented, Sylow
97C2×C4—122no—
98C2×C4—181no—
99C2×C4D32⋊C411yescharacteristic
100C8—91no—
101C8—91no—
102C8#377511yescharacteristic
103C8#377611yescharacteristic
104C2×C3—21no—
105C2×C3—21no—
106C2×C3—21no—
107C2×C3—21no—
108C2×C3—41no—
109C22#6372711yescharacteristic
110C4—242no—
111C4—361no—
112C4#6373011yescharacteristic
113C4#6374011yescharacteristic
114C3—21no—
115C3—21no—
116C2—21no—
117C2#1059004011yescharacteristic
subgroupG/H
centerC2#10590040
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#333
prime radicalC22×C32#100
cosocleC8×C3⋊Dic3C22
hypocenterC32#1366
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
96. C32#1366semidirect

Maximal subgroups

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

subgroupindex
#105908752
#105901782
#105891352
#13669