Finite Group Databasebeta

← #23752485

Subgroups — #23752485

Order 9664.

100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#18012769C211yesmaximal, characteristic
2C2×#14558994C211yesmaximal, characteristic, complemented
3#18012746C211yesmaximal, characteristic
4#18012674C211yesmaximal, characteristic, complemented
5#18012658C211yesmaximal, characteristic, complemented
6#18012657C211yesmaximal, characteristic, complemented
7#137×C151C211yesmaximal, characteristic
8C2×Dic302C2211yescharacteristic
9#14558994—21no—
10#14558994—21no—
11#14558994—21no—
12#14558992—21no—
13#14558988—21no—
14#14558988C2211yescharacteristic
15#14558988C2211yescharacteristic
16C2×C151⋊C8—21no—
17C2×C151⋊C8C2211yescharacteristic
18#41×C151C2211yescharacteristic
19C2×Q8×C151C2211yescharacteristic
20Q16×C151—21no—
21SD16×C151—21no—
22M16×C151C2211yescharacteristic
23Dic302—21no—
24Dic302—21no—
25C2×Dic151—21no—
26C151⋊C8—21no—
27C151⋊C8—21no—
28C151⋊C8D411yescharacteristic
29C151⋊C8D411yescharacteristic
30Q8×C151—21no—
31Q8×C151—21no—
32Q8×C151D411yescharacteristic
33D4×C151—21no—
34D4×C151D411yescharacteristic
35C2×C4×C151—21no—
36C2×C4×C151—21no—
37C2×C4×C151C2311yescharacteristic
38C8×C151—21no—
39C22×C151—21no—
40C22×C151#4111yescharacteristic
41C4×C151—21no—
42C4×C151—41no—
43C4×C151C2×D411yescharacteristic
44C4×C151C2×D411yescharacteristic
45Dic151—41no—
46C2×C151—21no—
47C2×C151—41no—
48C2×C151#12111yescharacteristic
49C151#47311yescharacteristic, complemented, Sylow
50#473—1511nomaximal, Sylow
51#137—1511no—
52#137D15111yescharacteristic
53C2×Q16—1511no—
54#131—1511no—
55#108—1511no—
56#101—1511no—
57#101—1511no—
58#41C2×D15111yescharacteristic
59C2×Q8—1511no—
60C2×Q8C2×D15111yescharacteristic
61Q16—21no—
62Q16—3021no—
63Q16—3021no—
64Q16—3021no—
65SD16—21no—
66SD16—3021no—
67M16—3021no—
68M16—1511no—
69M16—1511no—
70M16C2×D15111yescharacteristic
71C2×C8—3021no—
72C2×C8—1511no—
73Q8—21no—
74Q8—21no—
75Q8—3021no—
76Q8—3021no—
77Q8C22⋊D15111yescharacteristic
78D4—21no—
79D4C22⋊D15111yescharacteristic
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3021no—
83C2×C4C22×D15111yescharacteristic
84C8—21no—
85C8—3021no—
86C8—3021no—
87C8—1511no—
88C8—1511no—
89C22—21no—
90C22#1455900311yescharacteristic
91C4—21no—
92C4—41no—
93C4—6041no—
94C4D4×D15111yescharacteristic
95C4C2×C22⋊D15111yescharacteristic
96C2—21no—
97C2—41no—
98C2#1801271111yescharacteristic
subgroupG/H
centerC2#18012711
commutator, cosocleC2×C4×C151C23
FrattiniC2×C4C22×D151
Fitting#137×C151C2
socleC2×C151#121
prime radical#41×C151C22
hypercenter#137D151
hypocenterC151#473
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×#14558994C2semidirect
4. #18012674C2semidirect
5. #18012658C2semidirect
6. #18012657C2semidirect
49. C151#473semidirect