Finite Group Databasebeta

← #23750598

Subgroups — #23750598

Order 9536.

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

normal subgroups only

This group has 158 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×#14558745C211yesmaximal, characteristic, complemented
2C22×#11924753C211yesmaximal, characteristic, complemented
3#18011968C212yesmaximal, complemented
4C22⋊#11924753C212yesmaximal, complemented
5C2×#14558735C211yesmaximal, characteristic
6#14558745—22no—
7C2×#11924753—22no—
8C2×#11924753C2212yes—
9C2×#11924753C2212yes—
10#14558735—22no—
11#14558735—22no—
12C2×Dic298C411yescharacteristic
13C2×C22⋊D149C411yescharacteristic
14C2×C22⋊D149C411yescharacteristic
15C22×Dic149C2211yescharacteristic
16C22×Dic149C2211yescharacteristic
17C2×C4×D149C2211yescharacteristic
18C2×D4×C149C411yescharacteristic
19#11924753—22no—
20#11924753—22no—
21C22×D149C2×C411yescharacteristic
22Dic298—22no—
23C22⋊D149—22no—
24C22⋊D149—22no—
25C2×Dic149—21no—
26C2×Dic149—21no—
27C2×Dic149C2×C411yescharacteristic
28C2×Dic149C2×C411yescharacteristic
29C2×Dic149D412yes—
30C2×Dic149D412yes—
31C2×Dic149C2311yescharacteristic
32C4×D149—21no—
33C4×D149—21no—
34C23×C149C2×C411yescharacteristic
35C23×C149C2×C411yescharacteristic
36D4×C149—22no—
37C2×C4×C149C2×C411yescharacteristic
38C22×C149—22no—
39C22×C149—21no—
40C22×C149—22no—
41C22×C149C22⋊C412yes—
42C22×C149C22×C411yescharacteristic
43C2×D149—21no—
44C2×D149—22no—
45C4×C149—21no—
46Dic149—21no—
47Dic149C22⋊C412yes—
48Dic149C2×D411yescharacteristic
49Dic149C2×D411yescharacteristic
50C2×C149—22no—
51C2×C149—41no—
52C2×C149C2×C22⋊C411yescharacteristic
53C2×C149#13112yes—
54D149—41no—
55C149#40811yescharacteristic, complemented, Sylow
56#408—1491nomaximal, Sylow
57C2×#41—1491no—
58C2×M16—1491no—
59C22×C8—1491no—
60C22⋊C8—1492no—
61C22⋊C8—1492no—
62#41—2982no—
63#41—2982no—
64C2×Q8—1491no—
65C2×D4—1491no—
66C2×D4—1491no—
67C2×D4#1059701011yescharacteristic
68C22×C4—1491no—
69C22×C4—1491no—
70C22×C4—1491no—
71M16—2982no—
72C2×C8—2982no—
73C2×C8—1492no—
74C2×C8—1492no—
75C23—1491no—
76C23C2×#1059701011yescharacteristic
77C23C2×#1059701011yescharacteristic
78Q8—2982no—
79D4—22no—
80D4—2982no—
81D4—2982no—
82C2×C4—2981no—
83C2×C4—2981no—
84C2×C4—2981no—
85C2×C4—2981no—
86C2×C4—1491no—
87C2×C4—1492no—
88C2×C4—1492no—
89C2×C4—1491no—
90C2×C4—1491no—
91C2×C4C2×#1059701011yescharacteristic
92C8—2982no—
93C8—2982no—
94C22—22no—
95C22—21no—
96C22—22no—
97C22—2981no—
98C22—2982no—
99C22C22⋊#1059701012yes—
100C22C22×#1059701011yescharacteristic
101C4—21no—
102C4—2981no—
103C4—1491no—
104C4—1491no—
105C4—1492no—
106C2—22no—
107C2—41no—
108C2—5961no—
109C2C2×C22⋊#1059701011yescharacteristic
110C2#1801199812yes—
subgroupG/H
center, FrattiniC22C22×#10597010
commutator, socleC22×C149C22×C4
FittingC2×D4×C149C4
prime radicalC2×#14558735C2
cosocleC2×Dic149C23
hypercenterC2×D4#10597010
hypocenterC149#408
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14558745C2semidirect
2. C22×#11924753C2semidirect
3. #18011968C2semidirect
4. C22⋊#11924753C2semidirect
55. C149#408semidirect