Finite Group Databasebeta

← #23750596

Subgroups — #23750596

Order 9536.

190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 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×#14558746C212yesmaximal, complemented
2#18011968C212yesmaximal, complemented
3C22⋊#11924753C212yesmaximal, complemented
4C22×C4×D149C211yesmaximal, characteristic
5#14558746—24no—
6C2×#11924753C2214yescomplemented
7C23×D149C411yescharacteristic
8C22×Dic149C2211yescharacteristic
9C2×C4×D149—24no—
10C2×C4×D149C411yescharacteristic
11C2×C4×D149C411yescharacteristic
12C2×C4×D149C2211yescharacteristic
13C2×C4×D149C2211yescharacteristic
14C22×C4×C149C411yescharacteristic
15#11924753—24no—
16C22×D149—22no—
17C22×D149—22no—
18C22×D149—22no—
19C22×D149C2×C411yescharacteristic
20C22×D149C2×C411yescharacteristic
21C2×Dic149—22no—
22C2×Dic149C2×C411yescharacteristic
23C2×Dic149C2311yescharacteristic
24C4×D149—22no—
25C4×D149—22no—
26C4×D149—22no—
27C4×D149D414yes—
28C23×C149C2×C411yescharacteristic
29C2×C4×C149—22no—
30C2×C4×C149C2×C411yescharacteristic
31C2×C4×C149C2×C411yescharacteristic
32C22×C149—21no—
33C22×C149—21no—
34C22×C149M1612yescomplemented
35C22×C149C22×C411yescharacteristic
36C2×D149—28no—
37C2×D149—21no—
38C2×D149—21no—
39C2×D149—21no—
40C2×D149—21no—
41C2×D149C22⋊C412yes—
42C2×D149M1612yescomplemented
43C4×C149—21no—
44C4×C149C22⋊C412yes—
45Dic149—21no—
46Dic149C2×D412yes—
47C2×C149—22no—
48C2×C149C2×C22⋊C411yescharacteristic
49C2×C149C2×M1611yescharacteristic
50C2×C149C2×M1611yescharacteristic
51D149—22no—
52D149—22no—
53C149#40711yescharacteristic, complemented, Sylow
54#407—1491nomaximal, Sylow
55C23×C4—1491no—
56C2×M16—1492no—
57C22⋊C8—1492no—
58C22⋊C8—1492no—
59C24—1491no—
60C22×C4—2984no—
61C22×C4—1491no—
62C22×C4—1491no—
63C22×C4—1491no—
64C22×C4—1491no—
65C22×C4—1491no—
66C22×C4#1059701011yescharacteristic
67M16—2984no—
68C2×C8—1494no—
69C23—2982no—
70C23—2982no—
71C23—2982no—
72C23—1491no—
73C23—1491no—
74C23C2×#1059701011yescharacteristic
75C2×C4—22no—
76C2×C4—2982no—
77C2×C4—2982no—
78C2×C4—2982no—
79C2×C4—2982no—
80C2×C4—1491no—
81C2×C4—1491no—
82C2×C4—1494no—
83C2×C4C2×#1059701011yescharacteristic
84C2×C4C2×#1059701011yescharacteristic
85C8—2984no—
86C22—21no—
87C22—21no—
88C22—2988no—
89C22—2981no—
90C22—2981no—
91C22—2981no—
92C22—2981no—
93C22—1492no—
94C22—1492no—
95C22#1455874612yescomplemented
96C22C22×#1059701011yescharacteristic
97C4—21no—
98C4—2981no—
99C4—1492no—
100C4C22⋊#1059701012yes—
101C2—22no—
102C2—2982no—
103C2—2982no—
104C2C2×C22⋊#1059701011yescharacteristic
105C2D149⋊M1611yescharacteristic
106C2C2×#1455874611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#10597010
commutator, socleC22×C149C22×C4
FittingC22×C4×C149C4
prime radicalC23×D149C4
cosocleC2×Dic149C23
hypercenterC22×C4#10597010
hypocenterC149#407
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#14558746C2semidirect
2. #18011968C2semidirect
3. C22⋊#11924753C2semidirect
6. C2×#11924753C22semidirect
34. C22×C149M16semidirect
42. C2×D149M16semidirect
53. C149#407semidirect
95. C22#14558746semidirect