Finite Group Databasebeta

← #21443845

Subgroups — #21443845

Order 7808.

116 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 35 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#16839701C211yesmaximal, characteristic
2#16839488C211yesmaximal, characteristic
3C61×#343C211yesmaximal, characteristic
4C2×C4⋊Dic61C411yescharacteristic
5C22⋊#92418—21no—
6#14519684—21no—
7#14519684—21no—
8#14519684C411yescharacteristic
9C2×M16×C61—21no—
10C2×C4⋊C4×C61C2211yescharacteristic
11C22×C4×C61C2×C411yescharacteristic
12C22×C4×C61D411yescharacteristic
13C22×C4×C61D411yescharacteristic
14C22×Dic61—21no—
15C22×Dic61—21no—
16M16×C61—22no—
17M16×C61—41no—
18C2×C8×C61—41no—
19C4⋊C4×C61—41no—
20C4⋊Dic61—41no—
21C2×#92418—41no—
22C23×C61C22⋊C411yescharacteristic
23C2×C4×C61—21no—
24C2×C4×C61—21no—
25C2×C4×C61—21no—
26C2×C4×C61—21no—
27C2×C4×C61—41no—
28C2×C4×C61—41no—
29C2×C4×C61SD1611yescharacteristic
30C2×C4×C61Q1611yescharacteristic
31C2×Dic61—41no—
32C2×Dic61—41no—
33C2×Dic61—42no—
34C2×Dic61—41no—
35C2×Dic61—41no—
36C8×C61—42no—
37#92418—81no—
38C22×C61—21no—
39C22×C61—21no—
40C22×C61#9911yescharacteristic
41C22×C61#10311yescharacteristic
42C22×C61#10411yescharacteristic
43C4×C61—21no—
44C4×C61—21no—
45C4×C61—41no—
46C4×C61—41no—
47Dic61—81no—
48Dic61—81no—
49#1353—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—21no—
52C2×C61#32811yescharacteristic
53C2×C61#35211yescharacteristic
54C2×C61#35511yescharacteristic
55#400—611no—
56#343D6111yescharacteristic
57#324—611no—
58C61#135311yescharacteristic, complemented, Sylow
59C2×M16—21no—
60C2×C4⋊C4—611no—
61C2×C4⋊C4C2×D6111yescharacteristic
62C22⋊C8—1221no—
63#95—611no—
64#95—1221no—
65#95—1221no—
66C22×C4—1221no—
67C22×C4—1221no—
68C22×C4C4×D6111yescharacteristic
69C22×C4D24411yescharacteristic
70C22×C4C22⋊D6111yescharacteristic
71M16—22no—
72M16—41no—
73C2×C8—41no—
74C2×C8—2441no—
75C4⋊C4—41no—
76C4⋊C4—2441no—
77C23#1175819811yescharacteristic
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—2441no—
85C2×C4—2441no—
86C2×C4—2442no—
87C2×C4—2441no—
88C2×C4—2441no—
89C2×C4#1175820011yescharacteristic
90C2×C4#1175820211yescharacteristic
91C8—42no—
92C8—4881no—
93C22—21no—
94C22—21no—
95C22#1451969111yescharacteristic
96C22#1451970011yescharacteristic
97C22#1451970511yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—4881no—
103C4—4881no—
104C2—21no—
105C2—21no—
106C2#1683949811yescharacteristic
107C2#1683955311yescharacteristic
108C2#1683955811yescharacteristic
subgroupG/H
centerC22#14519691
commutatorC22×C4×C61C2×C4
FrattiniC2×C4⋊C4C2×D61
FittingC61×#343C2
socleC22×C61#99
hypercenter#343D61
hypocenterC61#1353
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
58. C61#1353semidirect