Finite Group Databasebeta

← #11771277

Subgroups — #11771277

Order 1152.

272 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 48 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#10593805C212yesmaximal
2#10592817C211yesmaximal, characteristic
3C2×#3792C414yes—
4C2×C32×M16C411yescharacteristic
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×#3748C411yescharacteristic
7#63779—22no—
8C4⋊#622—22no—
9#63641—22no—
10#5118—62no—
11C22×C32×C4C2×C411yescharacteristic
12C22×C3⋊Dic3C2×C412yes—
13#3792—44no—
14C2×#622—24no—
15C32×M16—41no—
16C2×C32×C8—21no—
17C4×C3⋊Dic3D411yescharacteristic
18C4×C3⋊Dic3D412yes—
19C4×C3⋊Dic3Q811yescharacteristic
20#3748—41no—
21C2×C3⋊(C3⋊C8)—21no—
22#1309—91nomaximal, Sylow
23C2×C3×M16—22no—
24C2×C4×Dic3—62no—
25C2×#208—62no—
26Dic3⋊C8—68no—
27C23×C32C4211yescharacteristic
28C2×C32×C4—21no—
29C2×C32×C4—21no—
30C2×C32×C4C22⋊C411yescharacteristic
31C2×C32×C4C4⋊C411yescharacteristic
32C2×C3⋊Dic3—22no—
33C2×C3⋊Dic3—22no—
34C2×C3⋊Dic3C22⋊C412yes—
35C2×C3⋊Dic3C4⋊C412yes—
36#622—44no—
37C32×C8—41no—
38C3⋊(C3⋊C8)—41no—
39#423—92no—
40#423—91no—
41C22×C3×C4—22no—
42C22×Dic3—64no—
43C3×M16—44no—
44C2×C3×C8—24no—
45C4×Dic3—64no—
46C4×Dic3—62no—
47C4×Dic3—62no—
48#208—124no—
49C2×C3⋊C8—64no—
50C22×C32—21no—
51C22×C32—22no—
52C22×C32#9511yescharacteristic
53C32×C4—21no—
54C32×C4#10011yescharacteristic
55C32×C4#10111yescharacteristic
56C3⋊Dic3—22no—
57C3⋊Dic3#10012yes—
58C3⋊Dic3#10112yes—
59C2×M16—94no—
60C2×M16—91no—
61C2×M16#15711yescharacteristic
62C2×C42—91no—
63C4⋊C8—182no—
64C4⋊C8—182no—
65C4⋊C8—182no—
66C23×C3—22no—
67C2×C3×C4—24no—
68C2×C3×C4—24no—
69C2×C3×C4—22no—
70C2×C3×C4—22no—
71C2×Dic3—64no—
72C2×Dic3—64no—
73C2×Dic3—124no—
74C2×Dic3—124no—
75C3×C8—44no—
76C3⋊C8—124no—
77C2×C32—41no—
78C2×C32#34312yes—
79C2×C32#34311yescharacteristic
80C22×C4—92no—
81C22×C4C2×#15711yescharacteristic
82M16—41no—
83M16—361no—
84M16—364no—
85C2×C8—21no—
86C2×C8—184no—
87C2×C8—181no—
88C42—91no—
89C42—91no—
90C42—92no—
91C22×C3—24no—
92C22×C3—22no—
93C22×C3—44no—
94C3×C4—24no—
95C3×C4—22no—
96C3×C4—22no—
97Dic3—64no—
98Dic3—64no—
99Dic3—124no—
100C32#130911yescharacteristic, complemented, Sylow
101C23C4×#15711yescharacteristic
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—92no—
105C2×C4—92no—
106C2×C4—182no—
107C2×C4—182no—
108C2×C4C4⋊#15711yescharacteristic
109C2×C4C22⋊#15711yescharacteristic
110C8—41no—
111C8—364no—
112C8—361no—
113C2×C3—22no—
114C2×C3—24no—
115C2×C3—44no—
116C22—21no—
117C22—22no—
118C22#6378111yescharacteristic
119C4—21no—
120C4—92no—
121C4—92no—
122C4—182no—
123C4#6378011yescharacteristic
124C4#6378811yescharacteristic
125C3—22no—
126C2—41no—
127C2#1059018812yes—
128C2#1059020811yescharacteristic
subgroupG/H
centerC22#63781
commutator, prime radicalC23×C32C42
FrattiniC22×C4C2×#157
FittingC2×C32×M16C4
socleC22×C32#95
cosocleC2×C4×C3⋊Dic3C22
hypercenterC2×M16#157
hypocenterC32#1309
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
100. C32#1309semidirect

Maximal subgroups

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

subgroupindex
#105938052
#105928172
#13099