Finite Group Databasebeta

← #21460724

Subgroups — #21460724

Order 7808.

130 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 42 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#16840782C211yesmaximal, characteristic
2#16840765C211yesmaximal, characteristic
3#16839816C211yesmaximal, characteristic
4C2×#11758217C412yes—
5#14519844—21no—
6#14519844—21no—
7C4⋊#92420—21no—
8C22⋊#92420C412yes—
9#14519832—21no—
10C2×C4×Dic61C2211yescharacteristic
11#14519706—21no—
12C22⋊#92418C411yescharacteristic
13#14519687—21no—
14C22⋊C8×C61C411yescharacteristic
15C22×C4×C61C2×C411yescharacteristic
16C22×Dic61C2×C411yescharacteristic
17C22×Dic61C2×C411yescharacteristic
18#11758217—42no—
19C2×#92420—22no—
20C2×#92420—22no—
21C2×C8×C61—21no—
22C4×Dic61D411yescharacteristic
23C4×Dic61D411yescharacteristic
24C4×Dic61D411yescharacteristic
25C4×Dic61Q811yescharacteristic
26C2×#92418—21no—
27C23×C61C4211yescharacteristic
28C2×C4×C61—41no—
29C2×C4×C61C22⋊C411yescharacteristic
30C2×C4×C61C4⋊C411yescharacteristic
31C2×Dic61—21no—
32C2×Dic61—21no—
33C2×Dic61—41no—
34C2×Dic61C22⋊C411yescharacteristic
35C2×Dic61C22⋊C411yescharacteristic
36C2×Dic61C4⋊C411yescharacteristic
37C2×Dic61C4⋊C411yescharacteristic
38#92420—42no—
39#92420—42no—
40C8×C61—41no—
41#92418—41no—
42C22×C61—21no—
43C22×C61—21no—
44C22×C61—21no—
45C22×C61#9511yescharacteristic
46C4×C61—21no—
47C4×C61—21no—
48Dic61—21no—
49Dic61—21no—
50Dic61—21no—
51Dic61#10011yescharacteristic
52Dic61#10111yescharacteristic
53#1307—611nomaximal, Sylow
54C2×C61—41no—
55C2×C61#34311yescharacteristic
56C2×C61#34411yescharacteristic
57C2×C61#34411yescharacteristic
58#432—611no—
59#432—611no—
60#423—611no—
61C61#130711yescharacteristic, complemented, Sylow
62C2×M16—612no—
63C2×C42—611no—
64C4⋊C8—1221no—
65C4⋊C8—1221no—
66C4⋊C8—1221no—
67C4⋊C8—1221no—
68C22⋊C8—612no—
69C22⋊C8—611no—
70C22⋊C8#692311yescharacteristic
71#97—1221no—
72#97—1221no—
73C22×C4—611no—
74C22×C4—611no—
75C22×C4C2×#692311yescharacteristic
76M16—2442no—
77C2×C8—21no—
78C2×C8—1222no—
79C2×C8—1222no—
80C2×C8—1221no—
81C42—611no—
82C42—611no—
83C42—611no—
84C42—611no—
85C23C4×#692311yescharacteristic
86C2×C4—41no—
87C2×C4—611no—
88C2×C4—611no—
89C2×C4—611no—
90C2×C4—611no—
91C2×C4—1221no—
92C2×C4—1221no—
93C2×C4—2441no—
94C2×C4C4⋊#692311yescharacteristic
95C2×C4C22⋊#692311yescharacteristic
96C8—41no—
97C8—2441no—
98C8—2442no—
99C8—2442no—
100C22—21no—
101C22—21no—
102C22—21no—
103C22(C2×#6923)⋊C411yescharacteristic
104C4—21no—
105C4—21no—
106C4—611no—
107C4—611no—
108C4—1221no—
109C4—1221no—
110C4—1221no—
111C2—41no—
112C2#1684064111yescharacteristic
113C2#1684064311yescharacteristic
114C2#1684064411yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC23×C61C42
FrattiniC22×C4C2×#6923
FittingC22⋊C8×C61C4
socleC22×C61#95
hypercenterC22⋊C8#6923
hypocenterC61#1307
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
61. C61#1307semidirect