Finite Group Databasebeta

← #10593802

Subgroups — #10593802

Order 576.

426 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C22×C4×C3⋊D3C211yesmaximal, characteristic
2C2×#3792C212yesmaximal, complemented
3#63778C214yesmaximal, complemented
4C23×C3⋊D3C411yescharacteristic
5C22×C32×C4C411yescharacteristic
6C22×C3⋊Dic3C2211yescharacteristic
7C2×C4×C3⋊D3—24no—
8C2×C4×C3⋊D3C412yes—
9C2×C4×C3⋊D3C2212yes—
10#3792—24no—
11C2×#622C2214yescomplemented
12C22×C4×D3—62no—
13C23×C32C2×C411yescharacteristic
14C22×C3⋊D3—22no—
15C22×C3⋊D3—24no—
16C22×C3⋊D3C2×C412yes—
17C2×C32×C4—22no—
18C2×C32×C4C2×C412yes—
19C2×C3⋊Dic3C2×C411yescharacteristic
20C2×C3⋊Dic3D414yes—
21C2×C3⋊Dic3C2311yescharacteristic
22C4×C3⋊D3—24no—
23C4×C3⋊D3—24no—
24#622—24no—
25#407—91nomaximal, Sylow
26C23×D3—62no—
27C22×C3×C4—22no—
28C22×Dic3—62no—
29C2×C4×D3—64no—
30C2×C4×D3—64no—
31C2×C4×D3—616no—
32C22×C32—22no—
33C22×C32C22⋊C412yes—
34C22×C32C22×C411yescharacteristic
35C2×C3⋊D3—28no—
36C2×C3⋊D3—22no—
37C2×C3⋊D3—22no—
38C2×C3⋊D3M1614yescomplemented
39C32×C4—22no—
40C3⋊Dic3C22⋊C412yes—
41C3⋊Dic3C2×D412yes—
42C23×C4—91no—
43C2×M16—92no—
44C22⋊C8—94no—
45C23×C3—22no—
46C22×D3—64no—
47C22×D3—68no—
48C22×D3—616no—
49C2×C3×C4—28no—
50C2×C3×C4—24no—
51C2×Dic3—62no—
52C2×Dic3—68no—
53C2×Dic3—62no—
54C4×D3—616no—
55C4×D3—616no—
56C2×C32—22no—
57C2×C32C2×C22⋊C411yescharacteristic
58C2×C32C2×M1612yes—
59C3⋊D3—24no—
60C24—91no—
61C22×C4—91no—
62C22×C4—92no—
63C22×C4—92no—
64C22×C4—184no—
65C22×C4#15711yescharacteristic
66M16—184no—
67C2×C8—94no—
68C22×C3—28no—
69C22×C3—22no—
70C22×C3—24no—
71C2×D3—68no—
72C2×D3—68no—
73C2×D3—632no—
74C2×D3—68no—
75C3×C4—28no—
76Dic3—64no—
77Dic3—64no—
78C32#40711yescharacteristic, complemented, Sylow
79C23—92no—
80C23—184no—
81C23—182no—
82C23C2×#15711yescharacteristic
83C2×C4—22no—
84C2×C4—91no—
85C2×C4—91no—
86C2×C4—94no—
87C2×C4—184no—
88C2×C4—184no—
89C2×C4C2×#15712yes—
90C8—184no—
91C2×C3—28no—
92C2×C3—24no—
93C2×C3—22no—
94D3—616no—
95C22—22no—
96C22—94no—
97C22—188no—
98C22—182no—
99C22—182no—
100C22C22⋊#15712yes—
101C22C22×#15711yescharacteristic
102C4—22no—
103C4—92no—
104C4—92no—
105C3—22no—
106C2—22no—
107C2—184no—
108C2#6428312yes—
109C2C2×C22⋊#15711yescharacteristic
subgroupG/H
center, FrattiniC22C22×#157
commutator, socleC22×C32C22×C4
FittingC22×C32×C4C4
prime radicalC23×C3⋊D3C4
cosocleC2×C3⋊Dic3C23
hypercenterC22×C4#157
hypocenterC32#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#3792C2semidirect
3. #63778C2semidirect
11. C2×#622C22semidirect
38. C2×C3⋊D3M16semidirect
78. C32#407semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D32
C2×#37922
#637782
#4079