Finite Group Databasebeta

← #21460907

Subgroups — #21460907

Order 7808.

166 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 40 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#16840741C212yesmaximal
2#16839728C211yesmaximal, characteristic
3#14519856—22no—
4#14519836—22no—
5#14519835C414yescomplemented
6C2×#11758222C2211yescharacteristic
7C2×#11758194C411yescharacteristic, complemented
8#14519689—22no—
9C22×C8×C61C411yescharacteristic, complemented
10C22×C4×C61C2×C411yescharacteristic
11C2×C22⋊D61C2×C412yes—
12#11758222—41no—
13#11758222—41no—
14C2×D244D411yescharacteristic
15C2×C4×D61D412yes—
16C2×Dic122Q811yescharacteristic
17C22⋊#6923—24no—
18C4⋊#6923—42no—
19C4×#6923—42no—
20C2×C8×C61—21no—
21C2×C8×C61—41no—
22#11758194—41no—
23C2×#92418—21no—
24C23×C61C4211yescharacteristic
25C22×D61C22⋊C412yes—
26C2×#6923—44no—
27C2×C4×C61—21no—
28C2×C4×C61—21no—
29C2×C4×C61C22⋊C411yescharacteristic
30C2×C4×C61C4⋊C411yescharacteristic
31C22⋊D61—42no—
32C2×Dic61C4⋊C412yes—
33D244—41no—
34C4×D61—22no—
35C4×D61—22no—
36Dic122—41no—
37C8×C61—41no—
38#92418—41no—
39C22×C61—21no—
40C22×C61—41no—
41C22×C61#9511yescharacteristic
42C2×D61—22no—
43C2×D61—42no—
44#6923—84no—
45C4×C61—21no—
46C4×C61#9911yescharacteristic
47C4×C61#9911yescharacteristic
48Dic61—22no—
49#1391—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—41no—
52C2×C61#34211yescharacteristic
53D61—42no—
54#410—612no—
55#408—611no—
56C61#139111yescharacteristic, complemented, Sylow
57C2×#41—611no—
58C2×M16—611no—
59C22×C8#692311yescharacteristic, complemented
60#117—1222no—
61#99—614no—
62#99—1222no—
63C22⋊C8—1222no—
64#41—2441no—
65#41—2441no—
66C2×Q8—611no—
67C2×D4—612no—
68C2×D4—611no—
69C22×C4—612no—
70C22×C4C2×#692311yescharacteristic
71M16—2441no—
72C2×C8—21no—
73C2×C8—41no—
74C2×C8—1221no—
75C4⋊C4—2442no—
76C22⋊C4—1224no—
77C42—2442no—
78C23—612no—
79C23C4×#692311yescharacteristic
80Q8—2441no—
81D4—2441no—
82D4—2442no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—612no—
86C2×C4—1222no—
87C2×C4—1222no—
88C2×C4—2444no—
89C2×C4C4⋊#692311yescharacteristic
90C2×C4C22⋊#692311yescharacteristic
91C8—41no—
92C8—2441no—
93C22—21no—
94C22—41no—
95C22—1222no—
96C22—2442no—
97C22(C2×#6923)⋊C411yescharacteristic
98C4—21no—
99C4—1222no—
100C4—4884no—
101C4#1451983511yescharacteristic
102C4#1451983611yescharacteristic
103C2—21no—
104C2—41no—
105C2—2442no—
106C2#1684064011yescharacteristic
subgroupG/H
centerC4#14519835
commutatorC23×C61C42
FrattiniC22×C4C2×#6923
FittingC22×C8×C61C4
socleC2×C61#342
hypercenterC22×C8#6923
hypocenterC61#1391
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
5. #14519835C4semidirect
7. C2×#11758194C4semidirect
9. C22×C8×C61C4semidirect
56. C61#1391semidirect
59. C22×C8#6923semidirect