Finite Group Databasebeta

← #22626957

Subgroups — #22626957

Order 9344.

150 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 27 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#17989672C212yesmaximal
2#17989530C211yesmaximal, characteristic
3C22⋊#10596842—22no—
4C2×C22⋊#64408C411yescharacteristic
5C2×C22⋊#64408C2211yescharacteristic
6(C2×#64408)⋊C4—22no—
7C22×C4×D73C411yescharacteristic
8C2×#10596842—42no—
9C22×#64408—21no—
10C22×#64408D412yes—
11C22⋊#64408—41no—
12C22⋊#64408—41no—
13C23×D73C2×C411yescharacteristic
14C22×Dic73C811yescharacteristic, complemented
15C2×C4×D73—21no—
16C2×C4×D73—21no—
17C2×C4×D73—41no—
18C2×C4×D73—41no—
19C22×C4×C73C811yescharacteristic, complemented
20C23×C73C2×C811yescharacteristic
21C22×D73—21no—
22C22×D73—21no—
23C22×D73—42no—
24C22×D73C22⋊C411yescharacteristic
25C22×D73M1611yescharacteristic
26C2×#64408—22no—
27C2×#64408—42no—
28C2×#64408—42no—
29C2×#64408—41no—
30#10596842—82no—
31C2×C4×C73—21no—
32C2×C4×C73—41no—
33C2×Dic73—21no—
34C2×Dic73—41no—
35C4×D73—42no—
36C4×D73—41no—
37C4×D73—41no—
38C22×C73—21no—
39C22×C73—41no—
40C22×C73C22⋊C811yescharacteristic
41C2×D73—22no—
42C2×D73—21no—
43C2×D73—42no—
44C2×D73—42no—
45C2×D73—41no—
46C2×D73#9911yescharacteristic
47C2×D73#10011yescharacteristic
48#64408—42no—
49#64408—81no—
50C4×C73—41no—
51Dic73—41no—
52C2×C73—21no—
53C2×C73—41no—
54C2×C73#32311yescharacteristic
55D73—21no—
56D73—41no—
57D73#35212yes—
58#1317—731nomaximal, Sylow
59C73#131711yescharacteristic, complemented, Sylow
60#381—731no—
61#323—732no—
62C23×C4—731no—
63C2×C22⋊C4—731no—
64C2×C22⋊C4—731no—
65C22⋊C8—1462no—
66#95—1462no—
67C24—731no—
68C22×C4—2921no—
69C22×C4—2921no—
70C22×C4—732no—
71C22×C4—731no—
72C22×C4—1461no—
73C22×C4—1461no—
74C22×C4—1461no—
75C22×C4#1059684211yescharacteristic, complemented
76C2×C8—2922no—
77C22⋊C4—2921no—
78C22⋊C4—2921no—
79C23—2922no—
80C23—731no—
81C23—731no—
82C23—1461no—
83C23—1461no—
84C23C2×#1059684211yescharacteristic
85C2×C4—21no—
86C2×C4—41no—
87C2×C4—2921no—
88C2×C4—2921no—
89C2×C4—2922no—
90C2×C4—2921no—
91C2×C4—2922no—
92C2×C4—2921no—
93C2×C4—2922no—
94C2×C4—1462no—
95C2×C4—1461no—
96C8—5842no—
97C22—21no—
98C22—41no—
99C22—2921no—
100C22—2922no—
101C22—2922no—
102C22—731no—
103C22—731no—
104C22—1462no—
105C22—1461no—
106C22C22⋊#1059684211yescharacteristic
107C4—41no—
108C4—2922no—
109C4—2921no—
110C4—5841no—
111C2—21no—
112C2—41no—
113C2—2921no—
114C2—732no—
115C2—1461no—
116C2#1798967211yescharacteristic
subgroupG/H
centerC2#17989672
commutatorC23×C73C2×C8
FrattiniC23C2×#10596842
FittingC22×C4×C73C8
socleC2×C73#323
hypercenterC22×C4#10596842
hypocenterC73#1317
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
14. C22×Dic73C8semidirect
19. C22×C4×C73C8semidirect
59. C73#1317semidirect
75. C22×C4#10596842semidirect