Finite Group Databasebeta

← #1444⋊C3 #68010

Subgroups — #1444⋊C3 #68010

Order 384.

133 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#95⋊C3C211yesmaximal, characteristic
2#1444C311yesmaximal, characteristic, complemented, Sylow
3C2×C4×A4—41nomaximal
4#95⋊C3C411yescharacteristic, complemented
5C22×C4⋊C4—31no—
6C2×#95—31no—
7C2×#95C2×C311yescharacteristic
8C22×A4—41no—
9C4×A4—42no—
10C23×C4—31no—
11C23×C4—31no—
12C23×C4A411yescharacteristic
13C2×C4⋊C4—62no—
14C2×C4⋊C4—64no—
15#95—31no—
16#95—62no—
17#95C3×C411yescharacteristic, complemented
18C2×A4—41no—
19C2×A4—41no—
20C2×A4—41no—
21C2×C3×C4—161no—
22C24C2×A411yescharacteristic
23C22×C4—32no—
24C22×C4—32no—
25C22×C4—31no—
26C22×C4—31no—
27C22×C4—32no—
28C22×C4—61no—
29C22×C4—62no—
30C22×C4—62no—
31C22×C4—61no—
32C22×C4—62no—
33C22×C4—62no—
34C22×C4—61no—
35C22×C4—61no—
36C22×C4SL(2,𝔽3)12yes—
37C4⋊C4—68no—
38C22×C3—161no—
39A4—41no—
40C3×C4—162no—
41C23—31no—
42C23—31no—
43C23—31no—
44C23—31no—
45C23C4×A411yescharacteristic
46C23C2×SL(2,𝔽3)11yescharacteristic
47C23#41⋊C311yescharacteristic
48C2×C4—32no—
49C2×C4—32no—
50C2×C4—41no—
51C2×C4—62no—
52C2×C4—62no—
53C2×C4—62no—
54C2×C4—62no—
55C2×C4—64no—
56C2×C4—62no—
57C2×C4—64no—
58C2×C4—62no—
59C2×C4—121no—
60C2×C4—121no—
61C2×C4—122no—
62C2×C4—121no—
63C2×C3—161no—
64C2×C3—161no—
65C2×C3—161no—
66C22—31no—
67C22—31no—
68C22—31no—
69C22—32no—
70C22—31no—
71C22—31no—
72C22—31no—
73C22—31no—
74C22—31no—
75C22—31no—
76C22C4×SL(2,𝔽3)11yescharacteristic
77C22#127⋊C311yescharacteristic
78C4—42no—
79C4—62no—
80C4—62no—
81C4—122no—
82C3—161noSylow
83C2—31no—
84C2—31no—
85C2—31no—
86C2—31no—
87C2#384⋊C311yescharacteristic
88C2#392⋊C311yescharacteristic
89C2#399⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22#127⋊C3
commutator, hypocenter#95C3×C4
Frattini, socleC24C2×A4
Fitting#1444C3
prime radicalC2×#95⋊C3C2
cosocleC2×#95C2×C3
LCSG ▷ #95
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #1444C3semidirect
4. #95⋊C3C4semidirect
17. #95C3×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#95⋊C32
#14443
C2×C4×A44