Finite Group Databasebeta

← #21443718

Subgroups — #21443718

Order 7808.

144 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 61 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#16839819C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic
3C2×#97×C61C211yesmaximal, characteristic
4C4⋊#92418—21no—
5C4⋊#92418C412yes—
6C22⋊#92418—21no—
7C22⋊#92418C412yes—
8#14519688—21no—
9C4×#92418—21no—
10C22×C8×C61—21no—
11C2×C42×C61C2211yescharacteristic
12#97×C61—21no—
13#97×C61C412yes—
14C22×C4×C61C2×C411yescharacteristic
15C22×C4×C61D411yescharacteristic
16C22×C4×C61Q811yescharacteristic
17C2×C8×C61—24no—
18C2×C8×C61—22no—
19C42×C61C2×C411yescharacteristic
20C42×C61C2×C411yescharacteristic
21C42×C61D411yescharacteristic
22C42×C61D411yescharacteristic
23C2×#92418—22no—
24C2×#92418—22no—
25C23×C61C4⋊C411yescharacteristic
26C2×C4×C61—22no—
27C2×C4×C61—22no—
28C2×C4×C61—41no—
29C2×C4×C61C4211yescharacteristic
30C2×C4×C61C22⋊C411yescharacteristic
31C2×C4×C61C22⋊C411yescharacteristic
32C2×C4×C61C22⋊C411yescharacteristic
33C2×C4×C61C4⋊C411yescharacteristic
34C2×C4×C61C4⋊C411yescharacteristic
35C8×C61—24no—
36#92418—42no—
37#92418—42no—
38C22×C61—21no—
39C22×C61—21no—
40C22×C61#9511yescharacteristic
41C22×C61#10812yes—
42C4×C61—21no—
43C4×C61—21no—
44C4×C61—21no—
45C4×C61—21no—
46C4×C61—21no—
47C4×C61#10412yes—
48#1302—611nomaximal, Sylow
49C2×C61—22no—
50C2×C61#33911yescharacteristic
51C2×C61#34111yescharacteristic
52C2×C61#34411yescharacteristic
53#432—611no—
54#431—611no—
55C2×#97D6111yescharacteristic
56C61#130211yescharacteristic, complemented, Sylow
57C22×C8—21no—
58C2×C42C2×D6111yescharacteristic
59C4⋊C8—612no—
60C4⋊C8—1221no—
61C22⋊C8—612no—
62C22⋊C8—1221no—
63#97—21no—
64#97—1221no—
65#97Dic6112yes—
66C4×C8—1221no—
67C22×C4Dic12211yescharacteristic
68C22×C4C4×D6111yescharacteristic
69C22×C4C22⋊D6111yescharacteristic
70C2×C8—24no—
71C2×C8—22no—
72C2×C8—1222no—
73C2×C8—1222no—
74C42C4×D6111yescharacteristic
75C42D24411yescharacteristic
76C42C2×Dic6111yescharacteristic
77C42C22⋊D6111yescharacteristic
78C23#1175819611yescharacteristic
79C2×C4—22no—
80C2×C4—22no—
81C2×C4—41no—
82C2×C4C4×Dic6111yescharacteristic
83C2×C4#1175819611yescharacteristic
84C2×C4C4⋊Dic6111yescharacteristic
85C2×C4#1175819811yescharacteristic
86C2×C4#1175819811yescharacteristic
87C2×C4C22⋊Dic6111yescharacteristic
88C8—24no—
89C8—2442no—
90C8—2442no—
91C22—21no—
92C22—21no—
93C22#1451968411yescharacteristic
94C22#1451971212yes—
95C4—21no—
96C4—21no—
97C4—21no—
98C4—21no—
99C4—21no—
100C4#1451970512yes—
101C2—22no—
102C2#1683952211yescharacteristic
103C2#1683952611yescharacteristic
104C2#1683953411yescharacteristic
subgroupG/H
centerC2×C4#11758198
commutatorC2×C4×C61C42
FrattiniC2×C42C2×D61
FittingC2×#97×C61C2
socleC22×C61#95
hypercenterC2×#97D61
hypocenterC61#1302
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
56. C61#1302semidirect