Finite Group Databasebeta

← #21443920

Subgroups — #21443920

Order 7808.

132 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#14519717C211yesmaximal, characteristic
2#16839800C211yesmaximal, characteristic
3C61×#427C211yesmaximal, characteristic
4#14519736—21no—
5#14519717—21no—
6#14519717—21no—
7C2×#11758185C412yescomplemented
8#14519711—21no—
9#14519709C412yescomplemented
10C22×C8×C61C2211yescharacteristic
11#117×C61—21no—
12#107×C61—21no—
13#106×C61C412yescomplemented
14C22×C4×C61D411yescharacteristic
15C2×C8×C61C2×C411yescharacteristic
16C2×C8×C61C2×C411yescharacteristic
17C2×C8×C61C2×C411yescharacteristic
18C2×C8×C61D411yescharacteristic
19C2×C8×C61D411yescharacteristic
20C2×C8×C61Q811yescharacteristic
21C4⋊C4×C61—22no—
22C22⋊C4×C61—41no—
23C42×C61—41no—
24C22⋊Dic61—41no—
25C4⋊Dic61—22no—
26C4×Dic61—41no—
27#11758185—22no—
28C23×C61D811yescharacteristic
29C2×C4×C61—42no—
30C2×C4×C61C22⋊C411yescharacteristic
31C2×C4×C61C22⋊C411yescharacteristic
32C2×C4×C61C4⋊C411yescharacteristic
33C2×C4×C61SD1611yescharacteristic
34C2×C4×C61SD1611yescharacteristic
35C2×C4×C61Q1611yescharacteristic
36C2×Dic61—42no—
37C8×C61C4211yescharacteristic
38C8×C61C22⋊C411yescharacteristic
39C8×C61C4⋊C411yescharacteristic
40C8×C61C4⋊C411yescharacteristic
41C22×C61—41no—
42C22×C61#10211yescharacteristic
43C22×C61#10211yescharacteristic
44C22×C61#10711yescharacteristic
45C4×C61—82no—
46C4×C61#9511yescharacteristic
47C4×C61#10311yescharacteristic
48C4×C61#10311yescharacteristic
49C4×C61#10611yescharacteristic
50Dic61—82no—
51#1384—611nomaximal, Sylow
52C2×C61—21no—
53C2×C61—21no—
54C2×C61—21no—
55C2×C61#34011yescharacteristic
56C2×M32—611no—
57#427—611no—
58#427D6111yescharacteristic
59C61#138411yescharacteristic, complemented, Sylow
60C22×C8C2×D6111yescharacteristic
61#117—21no—
62#117—1221no—
63M32—1221no—
64M32—1221no—
65C2×C16—612no—
66#107—21no—
67#107—1221no—
68#106—612no—
69#106Dic6112yescomplemented
70C22×C4C22⋊D6111yescharacteristic
71C2×C8Dic12211yescharacteristic
72C2×C8C4×D6111yescharacteristic
73C2×C8C4×D6111yescharacteristic
74C2×C8D24411yescharacteristic
75C2×C8C2×Dic6111yescharacteristic
76C2×C8C22⋊D6111yescharacteristic
77C4⋊C4—22no—
78C4⋊C4—1222no—
79C22⋊C4—41no—
80C22⋊C4—2441no—
81C42—41no—
82C42—2441no—
83C16—1222no—
84C23#1175819911yescharacteristic
85C2×C4—42no—
86C2×C4—2442no—
87C2×C4#1175819611yescharacteristic
88C2×C4#1175819811yescharacteristic
89C2×C4#1175820011yescharacteristic
90C2×C4#1175820111yescharacteristic
91C2×C4#1175820211yescharacteristic
92C2×C4C22⋊Dic6111yescharacteristic
93C8C4×Dic6111yescharacteristic
94C8#1175819611yescharacteristic
95C8C4⋊Dic6111yescharacteristic
96C8#1175819811yescharacteristic
97C22—41no—
98C22#1451969711yescharacteristic
99C22#1451969811yescharacteristic
100C22#1451971011yescharacteristic
101C4—82no—
102C4—4882no—
103C4#1451968411yescharacteristic
104C4#1451970011yescharacteristic
105C4#1451970111yescharacteristic
106C4#1451970811yescharacteristic
107C2—21no—
108C2—21no—
109C2—21no—
110C2#1683952411yescharacteristic
subgroupG/H
centerC4#14519708
commutatorC8×C61C42
FrattiniC22×C8C2×D61
FittingC61×#427C2
socleC2×C61#340
hypercenter#427D61
hypocenterC61#1384
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
7. C2×#11758185C4semidirect
9. #14519709C4semidirect
13. #106×C61C4semidirect
59. C61#1384semidirect
69. #106Dic61semidirect