Finite Group Databasebeta

← #10593845

Subgroups — #10593845

Order 576.

426 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C23×C3⋊Dic3C211yesmaximal, characteristic
2C2×#3792C212yesmaximal, complemented
3C22⋊#622C214yesmaximal, complemented
4C24×C32C411yescharacteristic
5C22×C3⋊Dic3—24no—
6C22×C3⋊Dic3C411yescharacteristic
7C22×C3⋊Dic3C412yes—
8C22×C3⋊Dic3C2212yes—
9C22×C3⋊Dic3C2211yescharacteristic
10#3792—24no—
11C2×#622C2214yescomplemented
12C23×Dic3—62no—
13C23×C32—22no—
14C23×C32—24no—
15C23×C32C2×C411yescharacteristic
16C23×C32C2×C412yes—
17C2×C3⋊Dic3—22no—
18C2×C3⋊Dic3—24no—
19C2×C3⋊Dic3—24no—
20C2×C3⋊Dic3C2×C412yes—
21C2×C3⋊Dic3C2×C411yescharacteristic
22C2×C3⋊Dic3D414yes—
23C2×C3⋊Dic3C2311yescharacteristic
24#622—24no—
25#407—91nomaximal, Sylow
26C24×C3—22no—
27C22×Dic3—64no—
28C22×Dic3—62no—
29C22×Dic3—62no—
30C22×Dic3—64no—
31C22×Dic3—616no—
32C22×C32—28no—
33C22×C32—22no—
34C22×C32—22no—
35C22×C32—22no—
36C22×C32C22⋊C412yes—
37C22×C32M1614yescomplemented
38C22×C32C22×C411yescharacteristic
39C3⋊Dic3—22no—
40C3⋊Dic3C22⋊C412yes—
41C3⋊Dic3C2×D412yes—
42C23×C4—91no—
43C2×M16—92no—
44C22⋊C8—94no—
45C23×C3—28no—
46C23×C3—216no—
47C23×C3—24no—
48C23×C3—22no—
49C2×Dic3—62no—
50C2×Dic3—64no—
51C2×Dic3—68no—
52C2×Dic3—62no—
53C2×Dic3—616no—
54C2×Dic3—616no—
55C2×Dic3—68no—
56C2×C32—22no—
57C2×C32—24no—
58C2×C32C2×C22⋊C411yescharacteristic
59C2×C32C2×M1612yes—
60C24#15711yescharacteristic
61C22×C4—91no—
62C22×C4—92no—
63C22×C4—92no—
64C22×C4—91no—
65C22×C4—184no—
66M16—184no—
67C2×C8—94no—
68C22×C3—28no—
69C22×C3—232no—
70C22×C3—28no—
71C22×C3—28no—
72C22×C3—22no—
73C22×C3—28no—
74C22×C3—24no—
75Dic3—64no—
76Dic3—64no—
77Dic3—68no—
78C32#40711yescharacteristic, complemented, Sylow
79C23—24no—
80C23—22no—
81C23C2×#15712yes—
82C23C2×#15711yescharacteristic
83C2×C4—91no—
84C2×C4—91no—
85C2×C4—94no—
86C2×C4—92no—
87C2×C4—184no—
88C2×C4—184no—
89C2×C4—182no—
90C8—184no—
91C2×C3—216no—
92C2×C3—28no—
93C2×C3—24no—
94C2×C3—22no—
95C22—28no—
96C22—22no—
97C22—22no—
98C22—22no—
99C22#379214yescomplemented
100C22C22⋊#15712yes—
101C22C22×#15711yescharacteristic
102C4—92no—
103C4—92no—
104C4—182no—
105C3—22no—
106C2—24no—
107C2—22no—
108C2C2×#379212yes—
109C2C2×C22⋊#15711yescharacteristic
subgroupG/H
center, FrattiniC22C22×#157
commutator, socleC22×C32C22×C4
Fitting, prime radicalC24×C32C4
cosocleC2×C3⋊Dic3C23
hypercenterC24#157
hypocenterC32#407
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#3792C2semidirect
3. C22⋊#622C2semidirect
11. C2×#622C22semidirect
37. C22×C32M16semidirect
78. C32#407semidirect
99. C22#3792semidirect

Maximal subgroups

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

subgroupindex
C23×C3⋊Dic32
C2×#37922
C22⋊#6222
#4079