Finite Group Databasebeta

← #10593836

Subgroups — #10593836

Order 576.

302 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 50 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×Q8×C3⋊D3C211yesmaximal, characteristic
2#64283C212yesmaximal
3#63780C214yesmaximal, complemented
4C2×C32×Q8C411yescharacteristic
5Q8×C3⋊D3—22no—
6Q8×C3⋊D3—22no—
7C2×C4×C3⋊D3C412yes—
8C2×C4×C3⋊D3C2211yescharacteristic
9C2×#634C411yescharacteristic
10C2×#634C2212yes—
11#3792C2214yes—
12#3788—22no—
13#3787—22no—
14C2×D3×Q8—62no—
15C22×C3⋊D3C2×C411yescharacteristic
16C32×Q8—22no—
17C2×C32×C4C2×C412yes—
18C2×C32×C4C2×C411yescharacteristic
19C2×C3⋊Dic3C2×C412yes—
20C2×C3⋊Dic3C2311yescharacteristic
21C4×C3⋊D3—22no—
22C4×C3⋊D3—22no—
23C4×C3⋊D3D412yes—
24C4×C3⋊D3D412yes—
25#634—22no—
26#634—24no—
27#622—24no—
28C2×#101—91nomaximal, Sylow
29C2×C3×Q8—22no—
30D3×Q8—68no—
31D3×Q8—68no—
32C2×C4×D3—64no—
33C2×C4×D3—62no—
34C2×Dic6—62no—
35C2×Dic6—64no—
36C22×C32C22×C411yescharacteristic
37C2×C3⋊D3—22no—
38C2×C3⋊D3C22⋊C411yescharacteristic
39C2×C3⋊D3C22⋊C411yescharacteristic
40C32×C4—22no—
41C32×C4C22⋊C412yes—
42C3⋊Dic3—22no—
43C3⋊Dic3C2×D412yes—
44C22×Q8—91no—
45C2×M16—92no—
46#101—94no—
47C22×D3—62no—
48C3×Q8—28no—
49C2×C3×C4—24no—
50C2×C3×C4—22no—
51C2×Dic3—64no—
52C2×Dic3—62no—
53C4×D3—64no—
54C4×D3—64no—
55C4×D3—68no—
56C4×D3—68no—
57Dic6—616no—
58Dic6—68no—
59C2×C32—21no—
60C2×C32C2×C22⋊C411yescharacteristic
61C3⋊D3—21no—
62C3⋊D3#10112yescomplemented
63C2×Q8—92no—
64C2×Q8—91no—
65C2×Q8—182no—
66C2×Q8—182no—
67C2×Q8#15711yescharacteristic
68C22×C4—91no—
69C22×C4—92no—
70M16—94no—
71M16—182no—
72C2×C8—182no—
73C22×C3—22no—
74C2×D3—62no—
75C2×D3—62no—
76C2×D3—68no—
77C3×C4—28no—
78C3×C4—24no—
79Dic3—64no—
80Dic3—68no—
81C32C2×#10111yescharacteristic, complemented, Sylow
82C23—91no—
83Q8—22no—
84Q8—184no—
85Q8—182no—
86C2×C4—91no—
87C2×C4—92no—
88C2×C4—92no—
89C2×C4—92no—
90C2×C4—182no—
91C2×C4—182no—
92C2×C4C2×#15712yes—
93C2×C4C2×#15711yescharacteristic
94C8—184no—
95C2×C3—24no—
96C2×C3—22no—
97D3—64no—
98D3—64no—
99C22—91no—
100C22—91no—
101C22—182no—
102C22C22×#15711yescharacteristic
103C4—22no—
104C4—92no—
105C4—182no—
106C4C22⋊#15712yes—
107C3—22no—
108C2—21no—
109C2—92no—
110C2—181no—
111C2C2×C22⋊#15711yescharacteristic
subgroupG/H
centerC2C2×C22⋊#157
commutatorC22×C32C22×C4
FrattiniC22C22×#157
FittingC2×C32×Q8C4
socleC2×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C23
hypercenterC2×Q8#157
hypocenterC32C2×#101
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
3. #63780C2semidirect
62. C3⋊D3#101semidirect
81. C32C2×#101semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊D32
#642832
#637802
C2×#1019