Finite Group Databasebeta

← #21460942

Subgroups — #21460942

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#16840668C211yesmaximal, characteristic, complemented
2#16840618C211yesmaximal, characteristic, complemented
3#16839935C211yesmaximal, characteristic
4#14519836—21no—
5#14519832—21no—
6#14519802—21no—
7#14519766C2211yescharacteristic
8#14519704—21no—
9#14519696C411yescharacteristic, complemented
102−1+4×C61C411yescharacteristic, complemented
11#41×C61—21no—
12#41×C61—41no—
13#41×C61—41no—
14C2×Q8×C61—41no—
15C2×Q8×C61C2×C411yescharacteristic
16C2×D244D411yescharacteristic
17C22⋊#6923—41no—
18C2×#92420—41no—
19#11758201—41no—
20#11758199—41no—
21#11758198—41no—
22C4×Dic61D411yescharacteristic
23#11758194—21no—
24C22×D61—21no—
25C2×#6923—81no—
26Q8×C61—21no—
27Q8×C61—41no—
28Q8×C61—41no—
29D4×C61—21no—
30D4×C61—41no—
31D4×C61—41no—
32C2×C4×C61—21no—
33C2×C4×C61—41no—
34C2×C4×C61—42no—
35C2×C4×C61C22⋊C411yescharacteristic
36C2×Dic61—21no—
37D244—41no—
38#92420—42no—
39#92418—41no—
40C22×C61—41no—
41C22×C61#9911yescharacteristic
42C2×D61—41no—
43C2×D61—81no—
44#6923—161no—
45C4×C61—21no—
46C4×C61—41no—
47C4×C61—41no—
48Dic61—41no—
49#1404—611nomaximal, Sylow
50C2×C61—21no—
51C2×C61—81no—
52C2×C61AΣL(1,𝔽16)11yescharacteristic
53D61—81no—
54#454—611no—
55#354—611no—
56#329—611no—
57C61#140411yescharacteristic, complemented, Sylow
582−1+4#692311yescharacteristic, complemented
59AGL(1,ℤ/8)—1221no—
60#124—611no—
61#104—1221no—
62#101—611no—
63#99—1221no—
64#97—1221no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×#692311yescharacteristic
70C2×D4—611no—
71SD16—2441no—
72D8—2441no—
73M16—1221no—
74C2×C8—2441no—
75C22⋊C4—2441no—
76C22⋊C4—2441no—
77C42—611no—
78C23—1221no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—2441no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—1221no—
90C2×C4—4881no—
91C2×C4C22⋊#692311yescharacteristic
92C8—2441no—
93C8—2442no—
94C22—41no—
95C22—4881no—
96C22—2441no—
97C22#1451983511yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—9761no—
102C4—2441no—
103C2—21no—
104C2—81no—
105C2—4881no—
106C2#1684066211yescharacteristic
subgroupG/H
centerC2#16840662
commutatorC2×Q8×C61C2×C4
FrattiniC2×Q8C2×#6923
Fitting2−1+4×C61C4
socleC2×C61AΣL(1,𝔽16)
hypercenter2−1+4#6923
hypocenterC61#1404
LCSG ▷ C2×Q8×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #16840668C2semidirect
2. #16840618C2semidirect
9. #14519696C4semidirect
10. 2−1+4×C61C4semidirect
57. C61#1404semidirect
58. 2−1+4#6923semidirect