Finite Group Databasebeta

← #22624993

Subgroups — #22624993

Order 9344.

132 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D73⋊#108C211yesmaximal, characteristic
2#17989597C211yesmaximal, characteristic
3C2×C16×D73C211yesmaximal, characteristic
4D73⋊M16—21no—
5#14556670—21no—
6#14556662C412yescomplemented
7#14556661—21no—
8#14556660C412yes—
9#14556659—21no—
10C2×C8×D73C2211yescharacteristic
11C2×#11924003C411yescharacteristic, complemented
12C16×D73—21no—
13C16×D73—21no—
14C2×C16×C73C411yescharacteristic, complemented
15#11924038—22no—
16#11924037—41no—
17#11924036—41no—
18C4⋊#64408—22no—
19C22⋊#64408—41no—
20C4×#64408—41no—
21C2×C4×D73D411yescharacteristic
22C2×#10596831Q811yescharacteristic
23C8×D73C2×C411yescharacteristic
24C8×D73C2×C411yescharacteristic
25C8×D73D411yescharacteristic
26C8×D73D411yescharacteristic
27#11924003—21no—
28C2×C8×C73C2×C411yescharacteristic
29C16×C73—21no—
30C22×D73SD1611yescharacteristic
31C2×#64408—42no—
32C2×C4×C73C4⋊C411yescharacteristic
33C2×Dic73SD1611yescharacteristic
34C4×D73C22⋊C411yescharacteristic
35C4×D73C22⋊C411yescharacteristic
36C4×D73D811yescharacteristic
37C4×D73Q1611yescharacteristic
38#10596833—42no—
39C8×C73C4211yescharacteristic
40C8×C73C22⋊C411yescharacteristic
41#10596831C4⋊C411yescharacteristic
42#10596831C4⋊C411yescharacteristic
43C22×C73#10611yescharacteristic
44C2×D73—22no—
45C2×D73#10211yescharacteristic
46C2×D73#10311yescharacteristic
47#64408—82no—
48C4×C73#9511yescharacteristic
49C4×C73#10711yescharacteristic
50Dic73#10211yescharacteristic
51Dic73#10311yescharacteristic
52C2×C73—21no—
53C2×C73#34011yescharacteristic
54D73—21no—
55D73#35912yes—
56#1382—731nomaximal, Sylow
57C73#138211yescharacteristic, complemented, Sylow
58C22×C16—731no—
59C2×#108—731no—
60#427—731no—
61C2×M16—1461no—
62C22×C8—731no—
63#117—1461no—
64C2×C16—731no—
65C2×C16—1461no—
66C2×C16—1461no—
67C2×C16#6440811yescharacteristic, complemented
68#108—732no—
69#108—1461no—
70#107—732no—
71#106—1461no—
72C22×C4—731no—
73M16—2921no—
74M16—1462no—
75C2×C8—2921no—
76C2×C8—731no—
77C2×C8—731no—
78C2×C8—731no—
79C2×C8—731no—
80C2×C8—731no—
81C2×C8C2×#6440811yescharacteristic
82C4⋊C4—1462no—
83C22⋊C4—2921no—
84C42—2921no—
85C16—21no—
86C16—1461no—
87C23—731no—
88C2×C4—2922no—
89C2×C4—731no—
90C2×C4—731no—
91C2×C4—731no—
92C2×C4—731no—
93C2×C4—731no—
94C2×C4C4⋊#6440811yescharacteristic
95C8—2922no—
96C8—731no—
97C8—731no—
98C8C4×#6440811yescharacteristic
99C8C22⋊#6440811yescharacteristic
100C22—731no—
101C22—731no—
102C22—1462no—
103C22#1455665911yescharacteristic
104C4—5842no—
105C4—731no—
106C4—731no—
107C4(C2×#64408)⋊C411yescharacteristic
108C4#1455666011yescharacteristic
109C2—21no—
110C2—732no—
111C2—1461no—
112C2#1798946111yescharacteristic
subgroupG/H
centerC4#14556660
commutatorC8×C73C42
FrattiniC2×C8C2×#64408
FittingC2×C16×C73C4
socleC2×C73#340
hypercenterC2×C16#64408
hypocenterC73#1382
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
6. #14556662C4semidirect
11. C2×#11924003C4semidirect
14. C2×C16×C73C4semidirect
57. C73#1382semidirect
67. C2×C16#64408semidirect