Finite Group Databasebeta

← #11920992

Subgroups — #11920992

Order 1152.

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

normal subgroups only

This group has 260 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#10593636C212yesmaximal, complemented
2C3×A4×C16C211yesmaximal, characteristic, complemented
3#73035—33nomaximal
4#71413—31nomaximal
5C4⋊(C3⋊S4)—22no—
6C3×C8×A4C2211yescharacteristic
7#63626—41nomaximal
8#5402—36no—
9C22×C3×C16D311yescharacteristic, complemented
10#5115—32no—
11C2×D48—31no—
12A4×C16D313yescomplemented
13#4509—32no—
14#4504—31no—
15C2×C3⋊S4—42no—
16C3×C4×A4D411yescharacteristic
17#3745—42no—
18C32×C16—41no—
19#2215—91noSylow
20C4⋊S4—66no—
21C22×C3×C8C2×D311yescharacteristic
22#930—62no—
23C2×D24—32no—
24C8×A4C2×D313yes—
25C2×C3×C16—31no—
26C2×C3×C16—31no—
27#821—62no—
28#818—32no—
29D48—61no—
30D48—61no—
31D48—123no—
32C2×C3×A4D811yescharacteristic
33C3⋊S4—82no—
34C4⋊(C3⋊D3)—82no—
35C32×C8—41no—
36C2×D16—91no—
37C22×C16C3⋊D311yescharacteristic, complemented
38#466—92no—
39#366—91no—
40#357—92no—
41C2×S4—126no—
42C22×C3×C4D1211yescharacteristic
43C2×#67—122no—
44C2×D12—62no—
45C4×A4D1213yes—
46C2×C3×C8—31no—
47C2×C3×C8—31no—
48(C2×D3)⋊C4—122no—
49C4⋊Dic3—62no—
50D24—62no—
51D24—62no—
52D24—126no—
53C3×C16—31no—
54C3×C16—43no—
55C3×C16S411yescharacteristic, complemented
56C2×C3⋊D3—162no—
57C3×A4D1611yescharacteristic, complemented
58C32×C4—41no—
59C2×D8—92no—
60C22×C8C2×C3⋊D311yescharacteristic
61#121—182no—
62D16—181no—
63D16—181no—
64C2×C16—31no—
65C2×C16—31no—
66#107—92no—
67#102—182no—
68C23×C3D2411yescharacteristic
69C22×D3—122no—
70C2×A4D2413yes—
71S4—246no—
72C2×C3×C4—31no—
73C2×C3×C4—31no—
74#67—242no—
75#67—242no—
76C2×Dic3—122no—
77D12—122no—
78D12—122no—
79D12—246no—
80C3×C8—31no—
81C3×C8—43no—
82C3×C8C2×S411yescharacteristic
83C2×C32—41no—
84C3⋊D3—322no—
85C2×D4—182no—
86C2×D4—362no—
87C22×C4C4⋊(C3⋊D3)11yescharacteristic
88D8—182no—
89D8—182no—
90C2×C8—31no—
91C2×C8—31no—
92C4⋊C4—182no—
93C22⋊C4—362no—
94C16—31no—
95C16C3⋊S411yescharacteristic, complemented
96C22×C3—31no—
97C22×C3—31no—
98C22×C3D4811yescharacteristic, complemented
99C2×D3—242no—
100C2×D3—242no—
101C2×D3—242no—
102C2×D3—486no—
103A4D4813yescomplemented
104C3×C4—31no—
105C3×C4—43no—
106C3×C4C4⋊S411yescharacteristic
107Dic3—242no—
108C32—41noSylow
109C23—362no—
110C23#374511yescharacteristic
111D4—362no—
112D4—362no—
113D4—722no—
114D4—722no—
115C2×C4—31no—
116C2×C4—31no—
117C2×C4—362no—
118C8—31no—
119C8C2×C3⋊S411yescharacteristic
120C2×C3—31no—
121C2×C3—31no—
122C2×C3—43no—
123C2×C3#540211yescharacteristic
124D3—482no—
125D3—966no—
126C22—31no—
127C22—31no—
128C22—722no—
129C22—722no—
130C22—722no—
131C22#6362611yescharacteristic, complemented
132C4—31no—
133C4—722no—
134C4C4⋊(C3⋊S4)11yescharacteristic
135C3—43no—
136C3#7303511yescharacteristic, complemented
137C2—31no—
138C2—31no—
139C2—1442no—
140C2#1059363611yescharacteristic
subgroupG/H
centerC2#10593636
commutator, cosocleC3×C8×A4C22
FrattiniC8C2×C3⋊S4
FittingC22×C3×C16D3
socleC23×C3D24
hypercenterC16C3⋊S4
hypocenterC3×A4D16
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
1. #10593636C2semidirect
2. C3×A4×C16C2semidirect
9. C22×C3×C16D3semidirect
12. A4×C16D3semidirect
37. C22×C16C3⋊D3semidirect
55. C3×C16S4semidirect
57. C3×A4D16semidirect
95. C16C3⋊S4semidirect
98. C22×C3D48semidirect
103. A4D48semidirect
131. C22#63626semidirect
136. C3#73035semidirect

Maximal subgroups

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

subgroupindex
#105936362
C3×A4×C162
#730353
#714133
#636264