Finite Group Databasebeta

← #23750618

Subgroups — #23750618

Order 9536.

150 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D149⋊M16C211yesmaximal, characteristic
2#18011990C211yesmaximal, characteristic
3#18011974C214yesmaximal, complemented
4C2×Q8×D149C211yesmaximal, characteristic
5#14558746—21no—
6#14558745—21no—
7D149⋊C8C2212yes—
8C4⋊#10597010C2212yes—
9C22⋊#10597010—21no—
10C4×#10597010—21no—
11C2×Dic298—21no—
12C2×Dic298C411yescharacteristic, complemented
13Q8×D149—21no—
14Q8×D149—21no—
15Q8×D149C412yescomplemented
16Q8×D149C2212yes—
17C2×C4×D149—21no—
18C2×C4×D149C2211yescharacteristic
19C2×Q8×C149C411yescharacteristic, complemented
20C2×#10597010—22no—
21#11924753—22no—
22C22×D149D411yescharacteristic
23Dic298—21no—
24Dic298—22no—
25Dic298—22no—
26Dic298C2×C412yes—
27C2×Dic149—21no—
28C2×Dic149D411yescharacteristic
29C4×D149—22no—
30C4×D149—22no—
31C4×D149C2×C411yescharacteristic
32C4×D149D411yescharacteristic
33C4×D149D411yescharacteristic
34C4×D149C2311yescharacteristic
35Q8×C149—21no—
36Q8×C149C2×C412yes—
37C2×C4×C149—21no—
38C2×C4×C149C2×C411yescharacteristic
39C22×C149C22⋊C411yescharacteristic
40C2×D149—22no—
41C2×D149C22⋊C411yescharacteristic
42C2×D149C2×D411yescharacteristic
43#10597010—42no—
44C4×C149—22no—
45C4×C149C22⋊C411yescharacteristic
46C4×C149C22×C411yescharacteristic
47Dic149—22no—
48Dic149C22⋊C411yescharacteristic
49Dic149C2×D411yescharacteristic
50C2×C149—21no—
51C2×C149C2×C22⋊C411yescharacteristic
52D149—21no—
53D149#13712yes—
54C149#41911yescharacteristic, complemented, Sylow
55#419—1491nomaximal, Sylow
56C22×Q8—1491no—
57C2×M16—1491no—
58#117—1491no—
59#103—1494no—
60C2×Q8—2981no—
61C2×Q8—2981no—
62C2×Q8—2981no—
63C2×Q8—1492no—
64C2×Q8—1492no—
65C2×Q8—1491no—
66C2×Q8#1059701011yescharacteristic, complemented
67C22×C4—2981no—
68C22×C4—1491no—
69M16—2981no—
70M16—2981no—
71C2×C8—1492no—
72C4⋊C4—1492no—
73C22⋊C4—2981no—
74C42—2981no—
75C23—1491no—
76Q8—21no—
77Q8—2982no—
78Q8—2982no—
79Q8—2981no—
80Q8—1492no—
81Q8C2×#1059701012yes—
82C2×C4—21no—
83C2×C4—2982no—
84C2×C4—2982no—
85C2×C4—2981no—
86C2×C4—2982no—
87C2×C4—1491no—
88C2×C4—1491no—
89C2×C4—1491no—
90C2×C4—1491no—
91C2×C4—1491no—
92C2×C4C2×#1059701011yescharacteristic
93C8—2982no—
94C22—2982no—
95C22—1491no—
96C22—1491no—
97C22C22⋊#1059701011yescharacteristic
98C4—22no—
99C4—2982no—
100C4—5962no—
101C4—1491no—
102C4—1491no—
103C4C22⋊#1059701011yescharacteristic
104C4C22×#1059701011yescharacteristic
105C2—21no—
106C2—2981no—
107C2—1492no—
108C2C2×C22⋊#1059701011yescharacteristic
subgroupG/H
centerC2C2×C22⋊#10597010
commutatorC4×C149C22×C4
FrattiniC4C22×#10597010
FittingC2×Q8×C149C4
socleC2×C149C2×C22⋊C4
prime radicalC22×D149D4
cosocleC4×D149C23
hypercenterC2×Q8#10597010
hypocenterC149#419
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
3. #18011974C2semidirect
12. C2×Dic298C4semidirect
15. Q8×D149C4semidirect
19. C2×Q8×C149C4semidirect
54. C149#419semidirect
66. C2×Q8#10597010semidirect