Finite Group Databasebeta

← #22627007

Subgroups — #22627007

Order 9344.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14556687C212yesmaximal
2C2×#14556646C211yesmaximal, characteristic
3#14556687—22no—
4#14556687C414yescomplemented
5C2×#11924040—22no—
6C22×#10596833C411yescharacteristic
7C22×#10596833C2211yescharacteristic
8#14556646—22no—
9C2×C4×Dic73C411yescharacteristic
10#11924040—24no—
11C2×#10596833—21no—
12C2×#10596833—21no—
13C2×#10596833C812yes—
14C2×#10596833C2×C412yes—
15C2×#10596833D411yescharacteristic
16C2×#10596833D412yes—
17C2×#10596833Q811yescharacteristic
18C22×Dic73C811yescharacteristic
19C22×Dic73C2×C411yescharacteristic
20C4×Dic73—21no—
21C4×Dic73—21no—
22C22×C4×C73C811yescharacteristic
23C23×C73C2×C811yescharacteristic
24C2×C4×C73—21no—
25C2×C4×C73—41no—
26C2×Dic73—21no—
27C2×Dic73—41no—
28C2×Dic73C4211yescharacteristic
29C2×Dic73C22⋊C411yescharacteristic
30C2×Dic73C4⋊C411yescharacteristic
31C2×Dic73C2×C811yescharacteristic
32C2×Dic73M1611yescharacteristic
33C2×Dic73M1611yescharacteristic
34#10596833—22no—
35#10596833C22⋊C412yes—
36#10596833C4⋊C412yes—
37C22×C73—21no—
38C22×C73—21no—
39C22×C73C4×C811yescharacteristic
40C22×C73C22⋊C811yescharacteristic
41C22×C73C4⋊C811yescharacteristic
42C4×C73—41no—
43Dic73—41no—
44Dic73#9511yescharacteristic
45Dic73#9711yescharacteristic
46Dic73C22⋊C811yescharacteristic
47Dic73C4⋊C811yescharacteristic
48C2×C73—21no—
49C2×C73—21no—
50C2×C73#33611yescharacteristic
51C2×C73#34911yescharacteristic
52C2×C73#34911yescharacteristic
53#1377—731nomaximal, Sylow
54C73#137711yescharacteristic, complemented, Sylow
55C2×M32—732no—
56C2×#97—731no—
57C22×C8—731no—
58C22×C8—731no—
59C2×C42—731no—
60M32—734no—
61M32—1462no—
62C2×C16—1462no—
63#97—1462no—
64C22×C4—731no—
65C22×C4—731no—
66C22×C4#1059684211yescharacteristic
67C2×C8—732no—
68C2×C8—732no—
69C2×C8—731no—
70C2×C8—731no—
71C2×C8—732no—
72C2×C8—1461no—
73C2×C8—1461no—
74C42—1461no—
75C42—1461no—
76C16—1464no—
77C23C2×#1059684211yescharacteristic
78C2×C4—21no—
79C2×C4—41no—
80C2×C4—2921no—
81C2×C4—731no—
82C2×C4—731no—
83C2×C4—731no—
84C2×C4—731no—
85C2×C4—731no—
86C2×C4—731no—
87C2×C4—1461no—
88C8—732no—
89C8—732no—
90C8—1462no—
91C22—21no—
92C22—21no—
93C22C4×#1059684211yescharacteristic
94C22C22⋊#1059684211yescharacteristic
95C22C4⋊#1059684211yescharacteristic
96C4—41no—
97C4—2921no—
98C4—731no—
99C4—731no—
100C4—731no—
101C4—731no—
102C2—21no—
103C2—21no—
104C2(C2×#10596842)⋊C411yescharacteristic
105C2#1798968511yescharacteristic
106C2#1798968611yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC22×C73C4×C8
FrattiniC23C2×#10596842
FittingC22×C4×C73C8
socleC22×C73C22⋊C8
hypercenterC22×C4#10596842
hypocenterC73#1377
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #14556687C4semidirect
54. C73#1377semidirect