Finite Group Databasebeta

← #11771261

Subgroups — #11771261

Order 1152.

256 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 44 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#10593806C212yesmaximal
2#10592817C211yesmaximal, characteristic
3C2×C32×M16C411yescharacteristic
4C2×C4×C3⋊Dic3C2211yescharacteristic
5C2×#3748C411yescharacteristic
6C22⋊#622C414yes—
7#63777—22no—
8C4⋊#622—22no—
9#63641—22no—
10#5118—62no—
11C22×C32×C4C2×C411yescharacteristic
12C22×C3⋊Dic3C2×C412yes—
13C2×#622—24no—
14C32×M16—41no—
15C2×C32×C8—21no—
16C4×C3⋊Dic3D411yescharacteristic
17C4×C3⋊Dic3D412yes—
18C4×C3⋊Dic3Q811yescharacteristic
19#3748—41no—
20C2×C3⋊(C3⋊C8)—21no—
21#1307—91nomaximal, Sylow
22C2×C3×M16—22no—
23C2×C4×Dic3—62no—
24C2×#208—62no—
25Dic3⋊C8—68no—
26C23×C32C4211yescharacteristic
27C2×C32×C4—21no—
28C2×C32×C4—21no—
29C2×C32×C4C22⋊C411yescharacteristic
30C2×C32×C4C4⋊C411yescharacteristic
31C2×C3⋊Dic3—42no—
32C2×C3⋊Dic3C22⋊C412yes—
33C2×C3⋊Dic3C4⋊C412yes—
34#622—44no—
35C32×C8—41no—
36C3⋊(C3⋊C8)—41no—
37#432—92no—
38#423—91no—
39C22×C3×C4—22no—
40C22×Dic3—64no—
41C3×M16—44no—
42C2×C3×C8—24no—
43C4×Dic3—64no—
44C4×Dic3—62no—
45C4×Dic3—62no—
46#208—124no—
47C2×C3⋊C8—64no—
48C22×C32—21no—
49C22×C32—22no—
50C22×C32#9511yescharacteristic
51C32×C4—21no—
52C32×C4#10011yescharacteristic
53C32×C4#10111yescharacteristic
54C3⋊Dic3—22no—
55C3⋊Dic3—22no—
56C2×M16—91no—
57C2×M16#15711yescharacteristic
58C2×C42—91no—
59C4⋊C8—182no—
60C4⋊C8—182no—
61C22⋊C8—94no—
62#97—182no—
63C23×C3—22no—
64C2×C3×C4—24no—
65C2×C3×C4—24no—
66C2×C3×C4—22no—
67C2×C3×C4—22no—
68C2×Dic3—64no—
69C2×Dic3—64no—
70C2×Dic3—128no—
71C3×C8—44no—
72C3⋊C8—124no—
73C2×C32—41no—
74C2×C32#34311yescharacteristic
75C2×C32#34412yes—
76C22×C4—92no—
77C22×C4C2×#15711yescharacteristic
78M16—41no—
79M16—361no—
80C2×C8—21no—
81C2×C8—184no—
82C2×C8—181no—
83C42—91no—
84C42—91no—
85C42—92no—
86C22×C3—24no—
87C22×C3—22no—
88C22×C3—44no—
89C3×C4—24no—
90C3×C4—22no—
91C3×C4—22no—
92Dic3—68no—
93Dic3—124no—
94C32#130711yescharacteristic, complemented, Sylow
95C23C4×#15711yescharacteristic
96C2×C4—21no—
97C2×C4—21no—
98C2×C4—92no—
99C2×C4—92no—
100C2×C4—362no—
101C2×C4C4⋊#15711yescharacteristic
102C2×C4C22⋊#15711yescharacteristic
103C8—41no—
104C8—364no—
105C8—361no—
106C2×C3—22no—
107C2×C3—24no—
108C2×C3—44no—
109C22—21no—
110C22—22no—
111C22#6378111yescharacteristic
112C4—21no—
113C4—182no—
114C4—182no—
115C4#6378011yescharacteristic
116C4#6378811yescharacteristic
117C3—22no—
118C2—41no—
119C2#1059019112yes—
120C2#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#1307
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
94. C32#1307semidirect

Maximal subgroups

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

subgroupindex
#105938062
#105928172
#13079