Finite Group Databasebeta

← C4×#3773 #10593409

Subgroups — C4×#3773 #10593409

Order 576.

302 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C4×#157C211yesmaximal, characteristic
2C2×#3773C212yesmaximal
3C4×#624C212yesmaximal
4#63737C212yesmaximal
5C22×#157C2211yescharacteristic
6C22×#157C2211yescharacteristic
7C2×C4×C3⋊D3C2211yescharacteristic
8C2×#624C2214yes—
9C4×#157C414yescomplemented
10#3773C418yesdirect product factor
11C3×C4×Dic3—22no—
12Dic32—22no—
13C42×D3—62no—
14C22×C3⋊D3C2311yescharacteristic
15C2×#157—22no—
16C2×#157C2×C412yes—
17C2×#157C2×C414yes—
18C2×#157C2×C412yes—
19C2×C32×C4D411yescharacteristic
20C2×C3⋊Dic3D411yescharacteristic
21C4×C3⋊D3C2×C412yes—
22C4×C3⋊D3Q812yes—
23C2×C3×Dic3—24no—
24#624—24no—
25#624C2×C418yes—
26C4×C4⋊C4—91nomaximal, Sylow
27C2×C4×D3—64no—
28C2×C4×D3—62no—
29C3×C42—62no—
30C4×Dic3—22no—
31C4×Dic3—64no—
32C22×C32C2×D411yescharacteristic
33C2×C3⋊D3C22×C411yescharacteristic
34C2×C3⋊D3C22×C412yes—
35C2×C3⋊D3C2×Q811yescharacteristic
36C2×C3⋊D3#4112yes—
37#157—22no—
38#157C4214yescomplemented
39C32×C4C4⋊C412yescomplemented
40C3⋊Dic3C4⋊C412yescomplemented
41C3×Dic3—28no—
42C2×C4⋊C4—92no—
43C2×C42—92no—
44C2×C42—91no—
45#95—92no—
46C22×D3—62no—
47C2×C3×C4—22no—
48C2×C3×C4—64no—
49C2×Dic3—24no—
50C2×Dic3—62no—
51C4×D3—68no—
52C4×D3—64no—
53C4×D3—64no—
54C4×D3—68no—
55C2×C32C2×C4⋊C411yescharacteristic
56C2×C32C4×D412yes—
57C3⋊D3C2×C4211yescharacteristic
58C3⋊D3#11711yescharacteristic
59C3⋊D3C4×Q812yes—
60C22×C4—94no—
61C22×C4—91no—
62C22×C4—91no—
63C22×C4—91no—
64C4⋊C4—98no—
65C42—62no—
66C42—94no—
67C42—182no—
68C22×C3—22no—
69C2×D3—64no—
70C2×D3—62no—
71C2×D3—62no—
72C2×D3—64no—
73C3×C4—24no—
74C3×C4—68no—
75Dic3—28no—
76Dic3—64no—
77C32C4×C4⋊C411yescharacteristic, complemented, Sylow
78C23—91no—
79C2×C4—64no—
80C2×C4—98no—
81C2×C4—92no—
82C2×C4—94no—
83C2×C4—91no—
84C2×C4—92no—
85C2×C4—92no—
86C2×C4—92no—
87C2×C4—184no—
88C2×C4—182no—
89C2×C4GO+(4,𝔽2)11yescharacteristic
90C2×C3—24no—
91C2×C3—22no—
92D3—62no—
93D3—62no—
94D3—64no—
95C22—92no—
96C22—92no—
97C22—91no—
98C22—91no—
99C22C2×GO+(4,𝔽2)11yescharacteristic
100C4—68no—
101C4—94no—
102C4—92no—
103C4—182no—
104C4#377312yesdirect product factor
105C3—22no—
106C2—91no—
107C2—91no—
108C2—92no—
109C2C4×GO+(4,𝔽2)12yes—
110C2C2×#377311yescharacteristic
subgroupG/H
center, hypercenterC2×C4GO+(4,𝔽2)
commutatorC3⋊D3C2×C42
FrattiniC22C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radical, cosocleC22×C3⋊D3C23
hypocenterC32C4×C4⋊C4
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
9. C4×#157C4semidirect
10. #3773C4direct (N × H)
38. #157C42semidirect
39. C32×C4C4⋊C4semidirect
40. C3⋊Dic3C4⋊C4semidirect
77. C32C4×C4⋊C4semidirect
104. C4#3773direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#1572
C2×#37732
C4×#6242
#637372
C4×C4⋊C49