Finite Group Databasebeta

← #11771265

Subgroups — #11771265

Order 1152.

240 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 41 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#10593729C211yesmaximal, characteristic
2#10590299C212yesmaximal
3C2×#3788C412yes—
4C42×C3⋊D3C2211yescharacteristic
5#63779—22no—
6C3×#803—22no—
7#63572—22no—
8#63557C414yes—
9#4705—62no—
10C2×C4×C3⋊D3C2×C411yescharacteristic
11C2×C4×C3⋊D3C2×C412yes—
12C2×#622—22no—
13#3788—42no—
14C32×C42D411yescharacteristic
15C4×C3⋊Dic3D412yes—
16C4×C3⋊Dic3Q811yescharacteristic
17C2×C3×C3⋊C8—24no—
18#1307—91nomaximal, Sylow
19C42×D3—62no—
20C3×#97—62no—
21(C2×D3)⋊C8—64no—
22Dic3⋊C8—64no—
23#803—22no—
24C22×C3⋊D3C4211yescharacteristic
25C2×C32×C4C22⋊C412yes—
26C2×C32×C4C4⋊C411yescharacteristic
27C2×C3⋊Dic3C22⋊C411yescharacteristic
28C2×C3⋊Dic3C4⋊C412yes—
29C4×C3⋊D3—21no—
30C4×C3⋊D3—21no—
31C4×C3⋊D3—42no—
32#622—42no—
33C3×C3⋊C8—44no—
34#432—92no—
35#423—91no—
36C2×C4×D3—62no—
37C2×C4×D3—62no—
38C2×C4×D3—62no—
39C2×C3×C8—64no—
40C3×C42—22no—
41C4×Dic3—62no—
42C4×Dic3—62no—
43C4×Dic3—62no—
44C2×C3⋊C8—24no—
45C22×C32#9511yescharacteristic
46C2×C3⋊D3—22no—
47C2×C3⋊D3—21no—
48C32×C4—22no—
49C32×C4—21no—
50C3⋊Dic3—22no—
51C3⋊Dic3#10011yescharacteristic
52C3⋊Dic3#10111yescharacteristic
53C2×M16—92no—
54C2×C42—91no—
55C4⋊C8—182no—
56C4⋊C8—182no—
57C22⋊C8—94no—
58#97—62no—
59C22×D3—62no—
60C2×C3×C4—22no—
61C2×C3×C4—22no—
62C2×C3×C4—22no—
63C2×Dic3—62no—
64C2×Dic3—62no—
65C2×Dic3—62no—
66C4×D3—122no—
67C4×D3—122no—
68C4×D3—124no—
69C4×D3—124no—
70C3×C8—124no—
71C3⋊C8—44no—
72C2×C32#34311yescharacteristic
73C2×C32#34412yes—
74C3⋊D3—41no—
75C22×C4—91no—
76C22×C4—92no—
77M16—362no—
78C2×C8—64no—
79C2×C8—182no—
80C42—92no—
81C42—91no—
82C42GO+(4,𝔽2)11yescharacteristic
83C22×C3—22no—
84C2×D3—64no—
85C2×D3—122no—
86C2×D3—122no—
87C3×C4—24no—
88C3×C4—42no—
89C3×C4—42no—
90Dic3—62no—
91Dic3—62no—
92Dic3—122no—
93Dic3—122no—
94C32#130711yescharacteristic, complemented, Sylow
95C23—91no—
96C2×C4—91no—
97C2×C4—92no—
98C2×C4—181no—
99C2×C4—181no—
100C2×C4—362no—
101C2×C4D32⋊C412yes—
102C2×C4#377311yescharacteristic
103C8—124no—
104C8—362no—
105C2×C3—22no—
106C2×C3—22no—
107C2×C3—22no—
108D3—124no—
109C22—181no—
110C22—182no—
111C22#6373711yescharacteristic
112C4—21no—
113C4—22no—
114C4—91no—
115C4—91no—
116C4—182no—
117C3—22no—
118C2—361no—
119C2#1059005311yescharacteristic
120C2#1059005412yes—
subgroupG/H
centerC22#63737
commutator, prime radicalC22×C3⋊D3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
cosocleC42×C3⋊D3C22
hypocenterC32#1307
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

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
#105937292
#105902992
#13079