Finite Group Databasebeta

← #21460945

Subgroups — #21460945

Order 7808.

106 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 20 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#16840672C211yesmaximal, characteristic, complemented
2#16840622C211yesmaximal, characteristic, complemented
3#16839947C211yesmaximal, characteristic
4#14519844—21no—
5#14519838—21no—
6#14519825C411yescharacteristic
7#14519810—21no—
8#14519775C2211yescharacteristic
9#14519703—21no—
10#101×C61C411yescharacteristic
11C2×Q8×C61C2×C411yescharacteristic
12#11758226—41no—
13Q8×D61—41no—
14#11758222—21no—
15#11758222—41no—
16C2×Dic122D411yescharacteristic
17#11758217—41no—
18C2×#92420—41no—
19M16×C61—21no—
20#11758196—41no—
21C4×Dic61D411yescharacteristic
22Dic244—41no—
23#11758190—41no—
24Q8×C61—41no—
25C2×C4×C61—21no—
26C2×C4×C61C22⋊C411yescharacteristic
27C22⋊D61—41no—
28C2×Dic61—21no—
29C2×Dic61—21no—
30D244—21no—
31D244—41no—
32C4×D61—41no—
33C4×D61—42no—
34Dic122—21no—
35Dic122—41no—
36Dic122—41no—
37#92420—81no—
38#92420—81no—
39C8×C61—41no—
40C22×C61#9911yescharacteristic
41C2×D61—41no—
42C4×C61—21no—
43C4×C61—41no—
44Dic61—21no—
45Dic61—21no—
46Dic61—41no—
47Dic61—41no—
48#1405—611nomaximal, Sylow
49C2×C61—21no—
50C2×C61AΣL(1,𝔽16)11yescharacteristic
51D61—81no—
52#456—611no—
53#356—611no—
54#333—611no—
55C61#140511yescharacteristic, complemented, Sylow
562−1+4—611no—
57#137—1221no—
58C4⋊Q8—611no—
59C4⋊C8—1221no—
60#104—1221no—
61#101—1221no—
62#101#692311yescharacteristic
63#41—1221no—
64#41—2441no—
65#41—2441no—
66C2×Q8—611no—
67C2×Q8—2441no—
68C2×Q8C2×#692311yescharacteristic
69Q16—2441no—
70SD16—2441no—
71M16—21no—
72M16—2441no—
73C2×C8—2441no—
74C4⋊C4—2441no—
75C42—611no—
76Q8—41no—
77Q8—1221no—
78Q8—2441no—
79Q8—2441no—
80D4—1221no—
81D4—2441no—
82D4—2441no—
83C2×C4—21no—
84C2×C4—1221no—
85C2×C4—1221no—
86C2×C4—2441no—
87C2×C4—2442no—
88C2×C4C22⋊#692311yescharacteristic
89C8—41no—
90C8—4881no—
91C8—4881no—
92C22—2441no—
93C22#1451983611yescharacteristic
94C4—21no—
95C4—41no—
96C4—1221no—
97C4—1221no—
98C4—2441no—
99C4—2441no—
100C2—21no—
101C2—4881no—
102C2#1684066311yescharacteristic
subgroupG/H
centerC2#16840663
commutatorC2×Q8×C61C2×C4
FrattiniC2×Q8C2×#6923
Fitting#101×C61C4
socleC2×C61AΣL(1,𝔽16)
hypercenter#101#6923
hypocenterC61#1405
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
1. #16840672C2semidirect
2. #16840622C2semidirect
55. C61#1405semidirect