Finite Group Databasebeta

← #21445968

Subgroups — #21445968

Order 7808.

162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839533C212yesmaximal
2#16839522C212yesmaximal
3#16839520C211yesmaximal, characteristic
4#16839519C211yesmaximal, characteristic
5C4×M16×C61C211yesmaximal, characteristic
6C2×#11758194C2212yes—
7#14519736C2212yes—
8C2×M16×C61C2211yescharacteristic
9C2×M16×C61C2211yescharacteristic
10C2×C42×C61C2211yescharacteristic
11#97×C61C412yescomplemented
12C4×C8×C61C412yescomplemented
13C22×C4×C61—21no—
14C22×C4×C61C2311yescharacteristic
15M16×C61—22no—
16M16×C61—22no—
17C2×C8×C61C2×C412yes—
18C2×C8×C61C2×C412yes—
19C42×C61—21no—
20C42×C61C2×C411yescharacteristic
21C42×C61C2×C411yescharacteristic
22C22⋊Dic61—22no—
23C4⋊Dic61—22no—
24C4×Dic61—22no—
25#11758194—22no—
26#11758194—22no—
27C2×#92418—22no—
28C23×C61#4111yescharacteristic
29C2×C4×C61—21no—
30C2×C4×C61—21no—
31C2×C4×C61—42no—
32C2×C4×C61C22×C411yescharacteristic
33C2×C4×C61#4112yes—
34C2×C4×C61#4112yes—
35C2×C4×C61#4111yescharacteristic
36C2×Dic61—42no—
37C8×C61—22no—
38C8×C61—22no—
39#92418—42no—
40C22×C61—41no—
41C22×C61#11711yescharacteristic
42C22×C61#12612yes—
43C4×C61—22no—
44C4×C61—41no—
45C4×C61#11711yescharacteristic
46C4×C61#11711yescharacteristic
47C4×C61#12612yes—
48Dic61—82no—
49#1841—611nomaximal, Sylow
50C2×C61—22no—
51C2×C61—21no—
52C2×C61#38311yescharacteristic
53C4×M16D6111yescharacteristic
54#344—612no—
55#339—612no—
56#338—611no—
57H(3,ℤ/4)—611no—
58C61#184111yescharacteristic, complemented, Sylow
59C2×M16—612no—
60C2×M16C2×D6111yescharacteristic
61C2×M16C2×D6111yescharacteristic
62#117—612no—
63C2×C42C2×D6111yescharacteristic
64#97Dic6112yescomplemented
65C4×C8Dic6112yescomplemented
66C22×C4—21no—
67C22×C4C22×D6111yescharacteristic
68M16—22no—
69M16—22no—
70M16—1222no—
71M16—1222no—
72C2×C8—1222no—
73C2×C8C2×Dic6112yes—
74C2×C8C2×Dic6112yes—
75C4⋊C4—1222no—
76C22⋊C4—1222no—
77C42—21no—
78C42—1222no—
79C42C2×Dic6111yescharacteristic
80C42C2×Dic6111yescharacteristic
81C23#1175822211yescharacteristic
82C2×C4—21no—
83C2×C4—21no—
84C2×C4—42no—
85C2×C4—2442no—
86C2×C4#1175822212yes—
87C2×C4#1175822212yes—
88C2×C4#1175822211yescharacteristic
89C2×C4C22×Dic6111yescharacteristic
90C8—22no—
91C8—22no—
92C8—2442no—
93C22—41no—
94C22#1451973611yescharacteristic
95C22#1451977112yes—
96C4—22no—
97C4—41no—
98C4—4882no—
99C4#1451973611yescharacteristic
100C4#1451973611yescharacteristic
101C4#1451977112yes—
102C2—21no—
103C2—22no—
104C2#1683963011yescharacteristic
subgroupG/H
centerC4#14519736
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×M16×C61C2
socleC2×C61#383
hypercenterC4×M16D61
hypocenterC61#1841
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×M16 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
11. #97×C61C4semidirect
12. C4×C8×C61C4semidirect
58. C61#1841semidirect
64. #97Dic61semidirect
65. C4×C8Dic61semidirect