Finite Group Databasebeta

← #21460764

Subgroups — #21460764

Order 7808.

158 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 34 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#16840605C211yesmaximal, characteristic
2#16840605C211yesmaximal, characteristic
3#16839635C211yesmaximal, characteristic
4C22⋊#92420—21no—
5C22⋊#92420—21no—
6C2×#11758196—21no—
7C2×C22⋊Dic61C411yescharacteristic
8C2×C22⋊Dic61C2211yescharacteristic
9#14519684—21no—
10C23×C4×C61C411yescharacteristic
11C24×C61C2×C411yescharacteristic
12C22×C4×C61—21no—
13C22×C4×C61—42no—
14C22×C4×C61—41no—
15C22×Dic61—21no—
16C22×Dic61D411yescharacteristic
17C22×Dic61D411yescharacteristic
18C2×#92420—41no—
19C2×#92420—41no—
20C22⋊Dic61—21no—
21C22⋊Dic61—41no—
22C22⋊Dic61C812yescomplemented
23#11758196—42no—
24C23×C61—21no—
25C23×C61—21no—
26C23×C61—41no—
27C23×C61—41no—
28C23×C61C22⋊C411yescharacteristic
29C23×C61C2×C811yescharacteristic
30C23×C61M1611yescharacteristic
31C2×C4×C61—22no—
32C2×C4×C61—41no—
33C2×C4×C61—42no—
34C2×C4×C61—41no—
35C2×C4×C61—42no—
36C2×Dic61—22no—
37C2×Dic61—21no—
38C2×Dic61—21no—
39C2×Dic61—41no—
40C2×Dic61—41no—
41C2×Dic61—41no—
42C2×Dic61—41no—
43#92420—81no—
44#92420—81no—
45C22×C61—21no—
46C22×C61—21no—
47C22×C61—21no—
48C22×C61—21no—
49C22×C61—41no—
50C22×C61—41no—
51C22×C61—42no—
52C22×C61—41no—
53C22×C61—41no—
54C22×C61C22⋊C811yescharacteristic
55C22×C61#9911yescharacteristic
56C22×C61#10111yescharacteristic
57C4×C61—42no—
58Dic61—42no—
59Dic61—41no—
60Dic61—41no—
61#1326—611nomaximal, Sylow
62C2×C61—21no—
63C2×C61—21no—
64C2×C61—41no—
65C2×C61—41no—
66C2×C61#32411yescharacteristic
67C2×C61AΣL(1,𝔽16)11yescharacteristic
68C2×C61#35211yescharacteristic
69#385—611no—
70#323—611no—
71#323—611no—
72C61#132611yescharacteristic, complemented, Sylow
73C23×C4#692311yescharacteristic
74C2×C4⋊C4—1221no—
75C2×C22⋊C4—611no—
76C2×C22⋊C4—611no—
77C22⋊C8—1221no—
78C22⋊C8—1221no—
79#95—1221no—
80C24C2×#692311yescharacteristic
81C22×C4—21no—
82C22×C4—42no—
83C22×C4—41no—
84C22×C4—611no—
85C22×C4—611no—
86C22×C4—1221no—
87C2×C8—2441no—
88C2×C8—2441no—
89C4⋊C4—2442no—
90C22⋊C4—612no—
91C22⋊C4—1221no—
92C22⋊C4—2441no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23D61⋊C811yescharacteristic
98C23#1175821311yescharacteristic
99C23C22⋊#692311yescharacteristic
100C2×C4—22no—
101C2×C4—41no—
102C2×C4—42no—
103C2×C4—41no—
104C2×C4—42no—
105C2×C4—1222no—
106C2×C4—1221no—
107C2×C4—1221no—
108C2×C4—2441no—
109C2×C4—2441no—
110C2×C4—2441no—
111C2×C4—2441no—
112C8—4881no—
113C8—4881no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22#1451983411yescharacteristic
124C22#1451983511yescharacteristic
125C22#1451983811yescharacteristic
126C4—42no—
127C4—2442no—
128C4—2441no—
129C4—2441no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#1684060811yescharacteristic
135C2#1684066211yescharacteristic
136C2#1684066411yescharacteristic
subgroupG/H
centerC22#14519835
commutatorC23×C61C2×C8
FrattiniC24C2×#6923
FittingC23×C4×C61C4
socleC22×C61#99
hypercenterC23×C4#6923
hypocenterC61#1326
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
22. C22⋊Dic61C8semidirect
72. C61#1326semidirect