Finite Group Databasebeta

← #23750612

Subgroups — #23750612

Order 9536.

150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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×#14558745C212yesmaximal, complemented
2#18011972C212yesmaximal, complemented
3#18011971C212yesmaximal, complemented
4C2×#14558735C211yesmaximal, characteristic
5#14558745—22no—
6#14558745C2214yes—
7C2×#11924753—22no—
8#14558735—22no—
9#14558735—22no—
10C2×Dic298C2211yescharacteristic
11C2×C22⋊D149C411yescharacteristic
12C2×C22⋊D149C2211yescharacteristic
13C22×Dic149C411yescharacteristic
14C22×Dic149C2211yescharacteristic
15C2×C4×D149C411yescharacteristic
16C2×D4×C149C411yescharacteristic
17#11924753—24no—
18C22×D149C2×C411yescharacteristic
19Dic298—22no—
20C22⋊D149—22no—
21C22⋊D149—22no—
22C2×Dic149—21no—
23C2×Dic149—21no—
24C2×Dic149C2×C411yescharacteristic
25C2×Dic149C2×C411yescharacteristic
26C2×Dic149D412yes—
27C2×Dic149D412yes—
28C2×Dic149C2311yescharacteristic
29C4×D149—21no—
30C4×D149—21no—
31C23×C149C2×C411yescharacteristic
32C23×C149C2×C411yescharacteristic
33D4×C149—22no—
34C2×C4×C149C2×C411yescharacteristic
35C22×C149—21no—
36C22×C149—41no—
37C22×C149—41no—
38C22×C149C22⋊C412yes—
39C22×C149C22×C411yescharacteristic
40C2×D149—21no—
41C2×D149—41no—
42C4×C149—21no—
43Dic149—21no—
44Dic149C22⋊C411yescharacteristic
45Dic149C22⋊C411yescharacteristic
46Dic149C2×D412yes—
47C2×C149—21no—
48C2×C149—22no—
49C2×C149—41no—
50C2×C149C2×C22⋊C411yescharacteristic
51D149—41no—
52C149#41311yescharacteristic, complemented, Sylow
53#413—1491nomaximal, Sylow
54C2×#41—1491no—
55C2×M16—1492no—
56#101—1492no—
57#100—1492no—
58#41—2982no—
59#41—2982no—
60C2×Q8—1491no—
61C2×D4—1491no—
62C2×D4—1491no—
63C2×D4#1059701011yescharacteristic
64C22×C4—1491no—
65C22×C4—1491no—
66C22×C4—1491no—
67M16—2982no—
68M16—1494no—
69C2×C8—2982no—
70C23—1491no—
71C23C2×#1059701011yescharacteristic
72C23C2×#1059701011yescharacteristic
73Q8—2982no—
74D4—22no—
75D4—2982no—
76D4—2982no—
77C2×C4—2981no—
78C2×C4—2981no—
79C2×C4—2981no—
80C2×C4—2981no—
81C2×C4—1491no—
82C2×C4—1492no—
83C2×C4—1492no—
84C2×C4—1491no—
85C2×C4—1491no—
86C2×C4C2×#1059701011yescharacteristic
87C8—2984no—
88C22—21no—
89C22—41no—
90C22—41no—
91C22—2981no—
92C22—5961no—
93C22C22⋊#1059701012yes—
94C22C22×#1059701011yescharacteristic
95C4—21no—
96C4—2981no—
97C4—1492no—
98C4—1491no—
99C4—1491no—
100C2—21no—
101C2—22no—
102C2—41no—
103C2—5961no—
104C2C2×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC2C2×C22⋊#10597010
commutatorC22×C149C22×C4
FrattiniC22C22×#10597010
FittingC2×D4×C149C4
socleC2×C149C2×C22⋊C4
prime radicalC2×#14558735C2
cosocleC2×Dic149C23
hypercenterC2×D4#10597010
hypocenterC149#413
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14558745C2semidirect
2. #18011972C2semidirect
3. #18011971C2semidirect
52. C149#413semidirect