Finite Group Databasebeta

← #11920993

Subgroups — #11920993

Order 1152.

224 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 43 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#10593632C212yesmaximal
2C3×A4×C16C211yesmaximal, characteristic
3#73037—33nomaximal
4#71416—31nomaximal
5#64259—22no—
6C3×C8×A4C2211yescharacteristic
7#63628—41nomaximal
8#5398—36no—
9C22×C3×C16D311yescharacteristic
10#5116—32no—
11C2×Dic24—31no—
12A4×C16D313yes—
13#4504—31no—
14#4503—32no—
15C3×C4×A4D411yescharacteristic
16C3⋊SL(2,ℤ/4)—42no—
17#3746—42no—
18C32×C16—41no—
19#2216—91noSylow
20A4⋊Q8—66no—
21C22×C3×C8C2×D311yescharacteristic
22#924—62no—
23C2×Dic12—32no—
24C8×A4C2×D313yes—
25C2×C3×C16—31no—
26C2×C3×C16—31no—
27#818—32no—
28#816—62no—
29Dic24—61no—
30Dic24—61no—
31Dic24—123no—
32C2×C3×A4D811yescharacteristic
33#634—82no—
34C32×C8—41no—
35C2×Q32—91no—
36C22×C16C3⋊D311yescharacteristic
37#467—92no—
38#366—91no—
39#358—92no—
40C22×C3×C4D1211yescharacteristic
41C2×Dic6—62no—
42C4×A4D1213yes—
43SL(2,ℤ/4)—126no—
44C2×C3×C8—31no—
45C2×C3×C8—31no—
46#217—122no—
47C4⋊Dic3—62no—
48Dic3⋊C4—122no—
49Dic12—62no—
50Dic12—62no—
51Dic12—126no—
52C3×C16—31no—
53C3×C16—43no—
54C3×C16S411yescharacteristic
55C3×A4Q3211yescharacteristic, complemented
56C32×C4—41no—
57C3⋊Dic3—162no—
58C2×Q16—92no—
59C22×C8C2×C3⋊D311yescharacteristic
60C22⋊Q8—182no—
61Q32—181no—
62Q32—181no—
63C2×C16—31no—
64C2×C16—31no—
65#107—92no—
66#103—182no—
67C23×C3D2411yescharacteristic
68C2×A4D2413yes—
69C2×C3×C4—31no—
70C2×C3×C4—31no—
71C2×Dic3—122no—
72C2×Dic3—122no—
73Dic6—122no—
74Dic6—122no—
75Dic6—246no—
76C3×C8—31no—
77C3×C8—43no—
78C3×C8C2×S411yescharacteristic
79C2×C32—41no—
80C2×Q8—182no—
81C22×C4C4⋊(C3⋊D3)11yescharacteristic
82Q16—182no—
83Q16—182no—
84C2×C8—31no—
85C2×C8—31no—
86C4⋊C4—182no—
87C4⋊C4—362no—
88C22⋊C4—362no—
89C16—31no—
90C16C3⋊S411yescharacteristic
91C22×C3—31no—
92C22×C3—31no—
93C22×C3Dic2411yescharacteristic, complemented
94A4Dic2413yescomplemented
95C3×C4—31no—
96C3×C4—43no—
97C3×C4C4⋊S411yescharacteristic
98Dic3—242no—
99Dic3—242no—
100Dic3—486no—
101C32—41noSylow
102C23#374511yescharacteristic
103Q8—362no—
104Q8—362no—
105C2×C4—31no—
106C2×C4—31no—
107C2×C4—362no—
108C2×C4—362no—
109C8—31no—
110C8C2×C3⋊S411yescharacteristic
111C2×C3—31no—
112C2×C3—31no—
113C2×C3—43no—
114C2×C3#540211yescharacteristic
115C22—31no—
116C22—31no—
117C22#6362811yescharacteristic, complemented
118C4—31no—
119C4—722no—
120C4—722no—
121C4C4⋊(C3⋊S4)11yescharacteristic
122C3—43no—
123C3#7303711yescharacteristic, complemented
124C2—31no—
125C2—31no—
126C2#1059363611yescharacteristic
subgroupG/H
centerC2#10593636
commutator, cosocleC3×C8×A4C22
FrattiniC8C2×C3⋊S4
FittingC22×C3×C16D3
socleC23×C3D24
prime radicalC2×C3×A4D8
hypercenterC16C3⋊S4
hypocenterC3×A4Q32
LCSG ▷ C3×C8×A4 ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16

Complements

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

NH ≅ G/Ntype
55. C3×A4Q32semidirect
93. C22×C3Dic24semidirect
94. A4Dic24semidirect
117. C22#63628semidirect
123. C3#73037semidirect

Maximal subgroups

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

subgroupindex
#105936322
C3×A4×C162
#730373
#714163
#636284