Finite Group Databasebeta

← #21460726

Subgroups — #21460726

Order 7808.

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

normal subgroups only

This group has 122 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#16840783C211yesmaximal, characteristic
2#16840782C211yesmaximal, characteristic
3#16839816C211yesmaximal, characteristic
4#14519844—21no—
5C4⋊#92420—21no—
6C22⋊#92420C412yes—
7C22⋊#92420C412yes—
8#14519832—21no—
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
18C2×#92420—22no—
19C2×#92420—22no—
20C2×C8×C61—21no—
21C4×Dic61D411yescharacteristic
22C4×Dic61D411yescharacteristic
23C4×Dic61D411yescharacteristic
24C4×Dic61Q811yescharacteristic
25C2×#92418—21no—
26C23×C61C4211yescharacteristic
27C2×C4×C61—41no—
28C2×C4×C61C22⋊C411yescharacteristic
29C2×C4×C61C4⋊C411yescharacteristic
30C2×Dic61—41no—
31C2×Dic61—41no—
32C2×Dic61C22⋊C411yescharacteristic
33C2×Dic61C22⋊C411yescharacteristic
34C2×Dic61C4⋊C411yescharacteristic
35C2×Dic61C4⋊C411yescharacteristic
36#92420—42no—
37#92420—42no—
38C8×C61—41no—
39#92418—41no—
40C22×C61—21no—
41C22×C61—21no—
42C22×C61—21no—
43C22×C61#9511yescharacteristic
44C4×C61—21no—
45C4×C61—21no—
46Dic61—21no—
47Dic61—21no—
48Dic61—21no—
49Dic61—21no—
50#1308—611nomaximal, Sylow
51C2×C61—41no—
52C2×C61#34411yescharacteristic
53C2×C61#34411yescharacteristic
54C2×C61#34411yescharacteristic
55#432—611no—
56#432—611no—
57#432—611no—
58C61#130811yescharacteristic, complemented, Sylow
59C2×C42—611no—
60C4⋊C8—1221no—
61C4⋊C8—1221no—
62C4⋊C8—1221no—
63C22⋊C8—612no—
64C22⋊C8—612no—
65C22⋊C8—611no—
66C22⋊C8#692311yescharacteristic
67#97—1221no—
68#97—1221no—
69#97—1221no—
70C22×C4—611no—
71C22×C4—611no—
72C22×C4C2×#692311yescharacteristic
73C2×C8—21no—
74C2×C8—1222no—
75C2×C8—1222no—
76C2×C8—1221no—
77C42—611no—
78C42—611no—
79C42—611no—
80C42—611no—
81C23C4×#692311yescharacteristic
82C2×C4—41no—
83C2×C4—611no—
84C2×C4—611no—
85C2×C4—611no—
86C2×C4—611no—
87C2×C4—2441no—
88C2×C4—2441no—
89C2×C4C4⋊#692311yescharacteristic
90C2×C4C22⋊#692311yescharacteristic
91C8—41no—
92C8—2441no—
93C8—2442no—
94C8—2442no—
95C22—21no—
96C22—21no—
97C22—21no—
98C22(C2×#6923)⋊C411yescharacteristic
99C4—21no—
100C4—21no—
101C4—1221no—
102C4—1221no—
103C4—1221no—
104C4—1221no—
105C2—41no—
106C2#1684064311yescharacteristic
107C2#1684064411yescharacteristic
108C2#1684064511yescharacteristic
subgroupG/H
centerC22(C2×#6923)⋊C4
commutatorC23×C61C42
FrattiniC22×C4C2×#6923
FittingC22⋊C8×C61C4
socleC22×C61#95
hypercenterC22⋊C8#6923
hypocenterC61#1308
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
58. C61#1308semidirect