Finite Group Databasebeta

← C2×#18011971 #23750607

Subgroups — C2×#18011971 #23750607

Order 9536.

186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 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#18011971C214yesmaximal, direct product factor
3C22×C22⋊D149C211yesmaximal, characteristic
4#14558745—22no—
5#14558745C2214yescomplemented
6C2×#11924753—22no—
7C23×D149C411yescharacteristic
8C2×C22⋊D149—22no—
9C2×C22⋊D149—22no—
10C2×C22⋊D149C412yes—
11C2×C22⋊D149C2212yes—
12C22×Dic149C2211yescharacteristic
13C24×C149C411yescharacteristic
14#11924753—24no—
15C22×D149—21no—
16C22×D149—21no—
17C22×D149—42no—
18C22×D149C2×C412yes—
19C22⋊D149—24no—
20C22⋊D149—24no—
21C2×Dic149C2×C411yescharacteristic
22C2×Dic149D412yes—
23C2×Dic149D412yes—
24C2×Dic149C2311yescharacteristic
25C23×C149—21no—
26C23×C149—21no—
27C23×C149—42no—
28C23×C149C2×C412yes—
29C23×C149C2×C411yescharacteristic
30C22×C149—22no—
31C22×C149—22no—
32C22×C149—42no—
33C22×C149—42no—
34C22×C149—42no—
35C22×C149C22⋊C411yescharacteristic
36C22×C149C22⋊C411yescharacteristic
37C22×C149C22×C411yescharacteristic
38C2×D149—22no—
39C2×D149—42no—
40C2×D149—42no—
41C2×D149—42no—
42Dic149C22⋊C412yes—
43Dic149C2×D412yes—
44C2×C149—21no—
45C2×C149—21no—
46C2×C149—42no—
47C2×C149#10012yescomplemented
48C2×C149C2×C22⋊C411yescharacteristic
49D149—42no—
50C149C2×#10011yescharacteristic, complemented, Sylow
51C2×#100—1491nomaximal, Sylow
52C22×D4—1491no—
53C2×M16—1492no—
54#100—1494no—
55C24—1491no—
56C24#1059701011yescharacteristic
57C2×D4—2982no—
58C2×D4—2982no—
59C2×D4—1492no—
60C2×D4—1492no—
61C22×C4—1491no—
62M16—2982no—
63M16—1494no—
64C2×C8—2982no—
65C23—21no—
66C23—21no—
67C23—42no—
68C23—2981no—
69C23—2981no—
70C23—5962no—
71C23—1492no—
72C23C2×#1059701012yes—
73C23C2×#1059701011yescharacteristic
74D4—2984no—
75D4—2984no—
76C2×C4—1492no—
77C2×C4—1492no—
78C2×C4—1491no—
79C2×C4—1491no—
80C8—2984no—
81C22—22no—
82C22—22no—
83C22—42no—
84C22—42no—
85C22—42no—
86C22—2982no—
87C22—5962no—
88C22—5962no—
89C22—5962no—
90C22C22⋊#1059701011yescharacteristic
91C22C22⋊#1059701011yescharacteristic
92C22C22×#1059701011yescharacteristic
93C4—1492no—
94C4—1492no—
95C2—21no—
96C2—21no—
97C2—42no—
98C2—5962no—
99C2#1801197112yesdirect product factor
100C2C2×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC22C22⋊#10597010
commutatorC22×C149C22×C4
FrattiniC22C22×#10597010
FittingC24×C149C4
socleC22×C149C22⋊C4
prime radicalC22×C22⋊D149C2
cosocleC2×Dic149C23
hypercenterC24#10597010
hypocenterC149C2×#100
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C2×#14558745C2semidirect
2. #18011971C2direct (N × H)
5. #14558745C22semidirect
47. C2×C149#100semidirect
50. C149C2×#100semidirect
99. C2#18011971direct (N × H)