Finite Group Databasebeta

← #21460818

Subgroups — #21460818

Order 7808.

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

normal subgroups only

This group has 116 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#16840642C211yesmaximal, characteristic
2#16840608C211yesmaximal, characteristic
3#16839700C211yesmaximal, characteristic
4C2×#11758217—21no—
5C22⋊#92420—21no—
6C2×#11758196C2211yescharacteristic
7#14519684—21no—
8#14519684—21no—
9#14519684C411yescharacteristic
10C2×C4⋊C4×C61C411yescharacteristic
11C22×C4×C61—21no—
12C22×C4×C61C2×C411yescharacteristic
13C22×Dic61—21no—
14C22×Dic61D411yescharacteristic
15C22×Dic61D411yescharacteristic
16#11758217—22no—
17#11758217—41no—
18C2×#92420—41no—
19C2×#92420—41no—
20C4⋊C4×C61—41no—
21#11758196—41no—
22C23×C61C22⋊C411yescharacteristic
23C2×C4×C61—21no—
24C2×C4×C61—41no—
25C2×C4×C61—42no—
26C2×C4×C61—41no—
27C2×Dic61—21no—
28C2×Dic61—21no—
29C2×Dic61—21no—
30C2×Dic61—41no—
31C2×Dic61—41no—
32C2×Dic61—41no—
33C2×Dic61—41no—
34C2×Dic61SD1611yescharacteristic
35C2×Dic61Q1611yescharacteristic
36#92420—42no—
37#92420—81no—
38C22×C61—21no—
39C22×C61—21no—
40C22×C61#9911yescharacteristic
41C22×C61#10311yescharacteristic
42C22×C61#10411yescharacteristic
43C4×C61—41no—
44C4×C61—81no—
45Dic61—21no—
46Dic61—21no—
47Dic61—41no—
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#343—611no—
57#324—611no—
58C61#135311yescharacteristic, complemented, Sylow
59C2×M16—1221no—
60C2×C4⋊C4—611no—
61C2×C4⋊C4#692311yescharacteristic
62C22⋊C8—1221no—
63#95—611no—
64#95—1221no—
65#95—1221no—
66C22×C4—21no—
67C22×C4—611no—
68C22×C4—611no—
69C22×C4—1221no—
70C22×C4C2×#692311yescharacteristic
71M16—1222no—
72M16—2441no—
73C2×C8—2441no—
74C2×C8—2441no—
75C4⋊C4—41no—
76C4⋊C4—2441no—
77C23C22⋊#692311yescharacteristic
78C2×C4—21no—
79C2×C4—41no—
80C2×C4—42no—
81C2×C4—41no—
82C2×C4—611no—
83C2×C4—611no—
84C2×C4—1221no—
85C2×C4—1221no—
86C2×C4—1221no—
87C2×C4—2441no—
88C2×C4—2441no—
89C2×C4—2441no—
90C2×C4—2441no—
91C8—4881no—
92C8—2442no—
93C22—21no—
94C22—21no—
95C22#1451983511yescharacteristic
96C22#1451984011yescharacteristic
97C22#1451984211yescharacteristic
98C4—41no—
99C4—81no—
100C4—1221no—
101C4—1221no—
102C4—4881no—
103C4—2441no—
104C2—21no—
105C2—21no—
106C2#1684061611yescharacteristic
107C2#1684066411yescharacteristic
108C2#1684067011yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC22×C4×C61C2×C4
FrattiniC22×C4C2×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61#99
hypercenterC2×C4⋊C4#6923
hypocenterC61#1353
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
58. C61#1353semidirect