Finite Group Databasebeta

← #23749537

Subgroups — #23749537

Order 9536.

202 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C22×Dic298C211yesmaximal, characteristic, complemented
2C2×C22⋊Dic149C212yesmaximal
3#18011818C211yesmaximal, characteristic, complemented
4#18011818C212yesmaximal, complemented
5C2×C22⋊C4×C149C211yesmaximal, characteristic
6C2×Dic298—24no—
7C2×Dic298—22no—
8C22×Dic149C2212yes—
9C22×Dic149C2212yes—
10C22⋊Dic149—24no—
11C24×C149C2211yescharacteristic
12C22×C4×C149C2211yescharacteristic
13C22×C4×C149C2211yescharacteristic
14C22⋊C4×C149—22no—
15Dic298—28no—
16C2×Dic149—22no—
17C2×Dic149—22no—
18C2×Dic149—22no—
19C2×Dic149—22no—
20C2×Dic149—22no—
21C2×Dic149D414yes—
22C23×C149—21no—
23C23×C149—22no—
24C23×C149—22no—
25C23×C149—21no—
26C23×C149Q812yescomplemented
27C23×C149C2311yescharacteristic
28C2×C4×C149—22no—
29C2×C4×C149—21no—
30C2×C4×C149—22no—
31C2×C4×C149D412yes—
32C22×C149—24no—
33C22×C149—22no—
34C22×C149—41no—
35C22×C149—42no—
36C22×C149—41no—
37C22×C149C2×D412yes—
38C22×C149C2×D411yescharacteristic
39C22×C149C2×Q811yescharacteristic
40C22×C149#4112yes—
41C22×C149#4111yescharacteristic
42C4×C149—22no—
43C4×C149—41no—
44Dic149—24no—
45Dic149—42no—
46C2×C149—42no—
47C2×C149#12011yescharacteristic
48C2×C149C22⋊Q812yes—
49C2×C149C22⋊Q811yescharacteristic
50C2×C149#12412yes—
51C2×C149#12411yescharacteristic
52C149#39311yescharacteristic, complemented, Sylow
53#393—1491nomaximal, Sylow
54C22×Q8—1491no—
55C2×C22⋊C4—1492no—
56C2×C22⋊C4D14911yescharacteristic
57#95—1491no—
58#95—1492no—
59C24C2×D14911yescharacteristic
60C2×Q8—2984no—
61C2×Q8—2982no—
62C22×C4—1492no—
63C22×C4—1492no—
64C22×C4C2×D14911yescharacteristic
65C22×C4C2×D14911yescharacteristic
66C22⋊C4—22no—
67C22⋊C4—2984no—
68C23—22no—
69C23—21no—
70C23—22no—
71C23—21no—
72C23Dic29812yescomplemented
73C23C22×D14911yescharacteristic
74Q8—2988no—
75C2×C4—22no—
76C2×C4—21no—
77C2×C4—22no—
78C2×C4—2982no—
79C2×C4—2982no—
80C2×C4—2982no—
81C2×C4—2982no—
82C2×C4—2982no—
83C2×C4—1494no—
84C2×C4C22⋊D14912yes—
85C22—24no—
86C22—22no—
87C22—41no—
88C22—42no—
89C22—41no—
90C22D4×D14912yes—
91C22C2×C22⋊D14911yescharacteristic
92C22C2×Dic29811yescharacteristic
93C22#1455873512yes—
94C22#1455873611yescharacteristic
95C4—22no—
96C4—41no—
97C4—2984no—
98C4—5962no—
99C2—42no—
100C2#1801187911yescharacteristic
101C2#1801188812yes—
102C2#1801189011yescharacteristic
103C2#1801189712yes—
104C2#1801189811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D149
commutator, socle, cosocleC23×C149C23
FittingC2×C22⋊C4×C149C2
prime radicalC24×C149C22
hypercenterC2×C22⋊C4D149
hypocenterC149#393
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×Dic298C2semidirect
3. #18011818C2semidirect
4. #18011818C2semidirect
26. C23×C149Q8semidirect
52. C149#393semidirect
72. C23Dic298semidirect