Finite Group Databasebeta

← #20289700

Subgroups — #20289700

Order 6784.

124 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 30 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
1#16811503C211yesmaximal, characteristic
2#16811469C211yesmaximal, characteristic
3#16810555C211yesmaximal, characteristic
4C2×#11719940—21no—
5C22⋊#88324—21no—
6C2×C4⋊Dic53—21no—
7C2×C4⋊Dic53C411yescharacteristic
8C2×#11719919C2211yescharacteristic
9#13133124—21no—
10#95×C53C411yescharacteristic
11C22×C4×C53—21no—
12C22×C4×C53C2×C411yescharacteristic
13C22×Dic53—21no—
14C22×Dic53D411yescharacteristic
15C22×Dic53D411yescharacteristic
16#11719940—22no—
17#11719940—41no—
18C2×#88324—41no—
19C2×#88324—41no—
20C4⋊Dic53—41no—
21C4⋊Dic53—41no—
22C4⋊Dic53—41no—
23#11719919—41no—
24C23×C53C22⋊C411yescharacteristic
25C2×C4×C53—22no—
26C2×C4×C53—21no—
27C2×C4×C53—41no—
28C2×C4×C53—41no—
29C2×C4×C53—41no—
30C2×Dic53—21no—
31C2×Dic53—21no—
32C2×Dic53—21no—
33C2×Dic53—41no—
34C2×Dic53—41no—
35C2×Dic53—41no—
36C2×Dic53—41no—
37C2×Dic53D811yescharacteristic
38C2×Dic53SD1611yescharacteristic
39#88324—42no—
40#88324—81no—
41C22×C53—21no—
42C22×C53—21no—
43C22×C53#9911yescharacteristic
44C22×C53#10211yescharacteristic
45C22×C53#10411yescharacteristic
46C4×C53—42no—
47C4×C53—41no—
48Dic53—21no—
49Dic53—21no—
50Dic53—41no—
51Dic53—81no—
52#1346—531nomaximal, Sylow
53C2×C53—21no—
54C2×C53—21no—
55C2×C53#32711yescharacteristic
56C2×C53#35211yescharacteristic
57C2×C53#35611yescharacteristic
58#398—531no—
59#343—531no—
60#324—531no—
61C53#134611yescharacteristic, complemented, Sylow
62C2×M16—1061no—
63C2×C4⋊C4—531no—
64C2×C4⋊C4—531no—
65C2×C4⋊C4—1061no—
66C22⋊C8—1061no—
67#95—1061no—
68#95#615711yescharacteristic
69C22×C4—21no—
70C22×C4—531no—
71C22×C4—531no—
72C22×C4—1061no—
73C22×C4C2×#615711yescharacteristic
74M16—1062no—
75M16—2121no—
76C2×C8—2121no—
77C2×C8—2121no—
78C4⋊C4—2121no—
79C4⋊C4—2121no—
80C4⋊C4—2121no—
81C4⋊C4—2121no—
82C23C22⋊#615711yescharacteristic
83C2×C4—22no—
84C2×C4—21no—
85C2×C4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—531no—
89C2×C4—531no—
90C2×C4—1061no—
91C2×C4—1061no—
92C2×C4—1061no—
93C2×C4—2121no—
94C2×C4—2121no—
95C2×C4—2121no—
96C2×C4—2121no—
97C8—4241no—
98C8—2122no—
99C22—21no—
100C22—21no—
101C22#1313327611yescharacteristic
102C22#1313327911yescharacteristic
103C22#1313328211yescharacteristic
104C4—42no—
105C4—41no—
106C4—1061no—
107C4—1061no—
108C4—4241no—
109C4—2121no—
110C2—21no—
111C2—21no—
112C2#1681147511yescharacteristic
113C2#1681152611yescharacteristic
114C2#1681153411yescharacteristic
subgroupG/H
centerC22#13133276
commutatorC22×C4×C53C2×C4
FrattiniC22×C4C2×#6157
Fitting#95×C53C4
socleC22×C53#99
hypercenter#95#6157
hypocenterC53#1346
LCSG ▷ C22×C4×C53 ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
61. C53#1346semidirect