Finite Group Databasebeta

← #22626952

Subgroups — #22626952

Order 9344.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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
1C22⋊#11924040C212yesmaximal, complemented
2C2×C22⋊#10596833C211yesmaximal, characteristic
3C2×#11924040—22no—
4C22×#10596833C411yescharacteristic
5C22×#10596833C2211yescharacteristic
6C22⋊#10596833—22no—
7C23×Dic73C411yescharacteristic
8#11924040—42no—
9C2×#10596833—21no—
10C2×#10596833—41no—
11C2×#10596833—41no—
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—21no—
22C23×C73—41no—
23C23×C73—41no—
24C23×C73C1612yescomplemented
25C23×C73C2×C811yescharacteristic
26C2×Dic73—21no—
27C2×Dic73—21no—
28C2×Dic73—21no—
29C2×Dic73—42no—
30C2×Dic73—41no—
31C2×Dic73—41no—
32C2×Dic73—41no—
33C2×Dic73C22⋊C411yescharacteristic
34C2×Dic73M1611yescharacteristic
35#10596833—22no—
36#10596833—41no—
37C22×C73—21no—
38C22×C73—21no—
39C22×C73—22no—
40C22×C73—42no—
41C22×C73—42no—
42C22×C73—41no—
43C22×C73—41no—
44C22×C73C22⋊C811yescharacteristic
45C22×C73C2×C1611yescharacteristic
46C22×C73M3211yescharacteristic
47Dic73—21no—
48Dic73—41no—
49Dic73#9911yescharacteristic
50Dic73#10011yescharacteristic
51C2×C73—21no—
52C2×C73—21no—
53C2×C73—42no—
54C2×C73#32311yescharacteristic
55C2×C73C22⋊C1611yescharacteristic
56C2×C73#34911yescharacteristic
57#1314—731nomaximal, Sylow
58C73#131411yescharacteristic, complemented, Sylow
59C2×C22⋊C8—731no—
60C22⋊C16—732no—
61C23×C4—731no—
62C22×C8—731no—
63C22×C8—731no—
64C2×C16—1462no—
65C22⋊C8—1462no—
66C24#1059684211yescharacteristic
67C22×C4—2921no—
68C22×C4—2921no—
69C22×C4—731no—
70C22×C4—731no—
71C22×C4—1461no—
72C22×C4—1461no—
73C2×C8—2921no—
74C2×C8—2921no—
75C2×C8—732no—
76C2×C8—1461no—
77C16—2922no—
78C23—21no—
79C23—21no—
80C23—41no—
81C23—41no—
82C23#1192404012yescomplemented
83C23C2×#1059684211yescharacteristic
84C2×C4—2921no—
85C2×C4—2921no—
86C2×C4—2922no—
87C2×C4—2921no—
88C2×C4—731no—
89C2×C4—731no—
90C2×C4—1461no—
91C2×C4—1461no—
92C2×C4—1461no—
93C8—2921no—
94C8—1462no—
95C22—21no—
96C22—21no—
97C22—22no—
98C22—42no—
99C22—42no—
100C22—41no—
101C22—41no—
102C22C22⋊#1059684211yescharacteristic
103C22C2×#1192404011yescharacteristic
104C22#1455668711yescharacteristic
105C4—2921no—
106C4—731no—
107C4—731no—
108C4—1461no—
109C2—21no—
110C2—21no—
111C2—42no—
112C2#1798967211yescharacteristic
113C2C22⋊#1192404011yescharacteristic
114C2#1798968511yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC22×C73C2×C16
FrattiniC23C2×#10596842
FittingC24×C73C8
socleC22×C73C22⋊C8
hypercenterC24#10596842
hypocenterC73#1314
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22⋊#11924040C2semidirect
24. C23×C73C16semidirect
58. C73#1314semidirect
82. C23#11924040semidirect