Finite Group Databasebeta

← #21460940

Subgroups — #21460940

Order 7808.

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

normal subgroups only

This group has 112 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#16840670C211yesmaximal, characteristic, complemented
2#16840617C211yesmaximal, characteristic, complemented
3#16839940C211yesmaximal, characteristic
4#14519838—21no—
5#14519832—21no—
6#14519807—21no—
7#14519764C2211yescharacteristic
8#14519704—21no—
9#14519694C411yescharacteristic
10H(5,𝔽2)×C61C411yescharacteristic
11#41×C61—21no—
12#41×C61—41no—
13C2×D4×C61—41no—
14C2×D4×C61—41no—
15C2×D4×C61C2×C411yescharacteristic
16C2×Dic122D411yescharacteristic
17#11758217—41no—
18C2×#92420—41no—
19C22⋊Dic61—41no—
20#11758202—41no—
21#11758200—41no—
22C4×Dic61D411yescharacteristic
23#11758194—21no—
24C23×C61—21no—
25C23×C61—41no—
26Q8×C61—21no—
27D4×C61—21no—
28D4×C61—41no—
29D4×C61—42no—
30D4×C61—41no—
31C2×C4×C61—41no—
32C2×C4×C61—41no—
33C2×C4×C61C22⋊C411yescharacteristic
34C2×Dic61—21no—
35C2×Dic61—21no—
36Dic122—41no—
37#92420—42no—
38#92420—81no—
39#92418—41no—
40C22×C61—41no—
41C22×C61—41no—
42C22×C61—81no—
43C22×C61—161no—
44C22×C61#9911yescharacteristic
45C4×C61—21no—
46C4×C61—41no—
47Dic61—41no—
48Dic61—41no—
49#1403—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—81no—
52C2×C61—81no—
53C2×C61AΣL(1,𝔽16)11yescharacteristic
54#455—611no—
55#355—611no—
56#329—611no—
57C61#140311yescharacteristic, complemented, Sylow
58H(5,𝔽2)#692311yescharacteristic
59#137—1221no—
60#124—611no—
61#104—1221no—
62#101—1221no—
63#100—611no—
64#97—1221no—
65#41—21no—
66#41—41no—
67C2×Q8—611no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#692311yescharacteristic
71Q16—2441no—
72SD16—2441no—
73M16—1221no—
74M16—2441no—
75C2×C8—2441no—
76C22⋊C4—2441no—
77C42—611no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—2441no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—1221no—
89C2×C4—1221no—
90C2×C4C22⋊#692311yescharacteristic
91C8—4881no—
92C8—2441no—
93C8—2442no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#1451983511yescharacteristic
99C4—21no—
100C4—41no—
101C4—2441no—
102C4—2441no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#1684066211yescharacteristic
subgroupG/H
centerC2#16840662
commutatorC2×D4×C61C2×C4
FrattiniC2×D4C2×#6923
FittingH(5,𝔽2)×C61C4
socleC2×C61AΣL(1,𝔽16)
hypercenterH(5,𝔽2)#6923
hypocenterC61#1403
LCSG ▷ C2×D4×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #16840670C2semidirect
2. #16840617C2semidirect
57. C61#1403semidirect