Finite Group Databasebeta

← #22626960

Subgroups — #22626960

Order 9344.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 25 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#17989685C212yesmaximal, complemented
2#17989557C211yesmaximal, characteristic
3#14556687—22no—
4C2×#11924037C411yescharacteristic
5C2×#11924037C2211yescharacteristic
6C22⋊#10596833—22no—
7C23×Dic73C411yescharacteristic
8#11924040—42no—
9#11924037—41no—
10#11924037—41no—
11C2×#10596833—21no—
12C2×#10596833D412yes—
13C22×Dic73—21no—
14C22×Dic73—21no—
15C22×Dic73—41no—
16C22×Dic73—41no—
17C22×Dic73C811yescharacteristic
18C22×Dic73C2×C411yescharacteristic
19C24×C73C811yescharacteristic
20C23×C73—21no—
21C23×C73—42no—
22C23×C73—41no—
23C23×C73C2×C811yescharacteristic
24C2×Dic73—21no—
25C2×Dic73—21no—
26C2×Dic73—21no—
27C2×Dic73—42no—
28C2×Dic73—41no—
29C2×Dic73—41no—
30C2×Dic73—41no—
31C2×Dic73C22⋊C411yescharacteristic
32C2×Dic73M1611yescharacteristic
33#10596833—22no—
34#10596833—41no—
35C22×C73—22no—
36C22×C73—21no—
37C22×C73—41no—
38C22×C73—41no—
39C22×C73—42no—
40C22×C73—42no—
41C22×C73—41no—
42C22×C73C22⋊C811yescharacteristic
43Dic73—21no—
44Dic73—41no—
45Dic73#9911yescharacteristic
46Dic73#10011yescharacteristic
47C2×C73—21no—
48C2×C73—42no—
49C2×C73—41no—
50C2×C73#32311yescharacteristic
51#1320—731nomaximal, Sylow
52C73#132011yescharacteristic, complemented, Sylow
53#407—731no—
54#349—732no—
55C23×C4—731no—
56C2×M16—731no—
57C2×M16—731no—
58M32—1462no—
59C22⋊C8—1462no—
60C24#1059684211yescharacteristic
61C22×C4—2921no—
62C22×C4—2921no—
63C22×C4—731no—
64C22×C4—731no—
65C22×C4—1461no—
66C22×C4—1461no—
67M16—2921no—
68M16—2921no—
69C2×C8—732no—
70C2×C8—1461no—
71C16—2922no—
72C23—21no—
73C23—41no—
74C23—42no—
75C23C2×#1059684211yescharacteristic
76C2×C4—2921no—
77C2×C4—2921no—
78C2×C4—2922no—
79C2×C4—2921no—
80C2×C4—731no—
81C2×C4—731no—
82C2×C4—1461no—
83C2×C4—1461no—
84C2×C4—1461no—
85C8—2921no—
86C8—1462no—
87C22—22no—
88C22—21no—
89C22—41no—
90C22—41no—
91C22—42no—
92C22—42no—
93C22—41no—
94C22C22⋊#1059684211yescharacteristic
95C4—2921no—
96C4—731no—
97C4—731no—
98C4—1461no—
99C2—21no—
100C2—42no—
101C2—41no—
102C2#1798967211yescharacteristic
subgroupG/H
centerC2#17989672
commutatorC23×C73C2×C8
FrattiniC23C2×#10596842
FittingC24×C73C8
socleC2×C73#323
hypercenterC24#10596842
hypocenterC73#1320
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. #17989685C2semidirect
52. C73#1320semidirect