Finite Group Databasebeta

← #23752603

Subgroups — #23752603

Order 9664.

124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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×Dic604C211yesmaximal, characteristic, complemented
2C2×#14558994C211yesmaximal, characteristic, complemented
3C2×#14558992C211yesmaximal, characteristic
4#18012737C211yesmaximal, characteristic, complemented
5#18012726C211yesmaximal, characteristic
6#18012649C211yesmaximal, characteristic, complemented
7C2×SD16×C151C211yesmaximal, characteristic
8C2×Dic302C2211yescharacteristic
9C2×Dic302C2211yescharacteristic
10Dic604—22no—
11#14558994—22no—
12#14558992—22no—
13C2×C151⋊C8C2211yescharacteristic
14Dic151⋊C4—22no—
15C22⋊Dic151—22no—
16C4×Dic151C2211yescharacteristic
17C2×Q8×C151C2211yescharacteristic
18C2×D4×C151C2211yescharacteristic
19SD16×C151—22no—
20C2×C8×C151C2211yescharacteristic
21Dic302—21no—
22Dic302—21no—
23Dic302—21no—
24Dic302—21no—
25C2×Dic151—21no—
26C2×Dic151—21no—
27C2×Dic151D412yes—
28C151⋊C8D412yes—
29C23×C151—21no—
30Q8×C151—21no—
31Q8×C151—21no—
32D4×C151—21no—
33D4×C151—21no—
34C2×C4×C151—21no—
35C2×C4×C151C2311yescharacteristic
36C8×C151D412yes—
37C22×C151—41no—
38C22×C151—42no—
39C22×C151C2×D411yescharacteristic
40C4×C151—41no—
41C4×C151C2×D411yescharacteristic
42C4×C151C2×D411yescharacteristic
43Dic151—22no—
44Dic151—41no—
45Dic151—41no—
46C2×C151—81no—
47C2×C151#12711yescharacteristic
48C2×C151#13712yes—
49C151#49711yescharacteristic, complemented, Sylow
50#497—1511nomaximal, Sylow
51C2×Q16—1511no—
52C2×Q16—1511no—
53C2×SD16—1511no—
54C2×SD16D15111yescharacteristic
55C4⋊Q8—1511no—
56#124—1511no—
57#97—1511no—
58C2×Q8—1511no—
59C2×Q8—1511no—
60C2×Q8C2×D15111yescharacteristic
61C2×D4C2×D15111yescharacteristic
62Q16—3022no—
63Q16—3022no—
64SD16—22no—
65SD16—3022no—
66C2×C8—1511no—
67C2×C8C2×D15111yescharacteristic
68C4⋊C4—3022no—
69C22⋊C4—3022no—
70C42—1511no—
71C23—21no—
72Q8—21no—
73Q8—21no—
74Q8—3021no—
75Q8—3021no—
76Q8—3021no—
77Q8—3021no—
78D4—21no—
79D4—21no—
80C2×C4—21no—
81C2×C4—3021no—
82C2×C4—3021no—
83C2×C4—1512no—
84C2×C4C22×D15111yescharacteristic
85C8—1512no—
86C8C22⋊D15112yes—
87C22—41no—
88C22—42no—
89C22D4×D15111yescharacteristic
90C4—41no—
91C4—3022no—
92C4—6041no—
93C4—6041no—
94C4D4×D15111yescharacteristic
95C4C2×C22⋊D15111yescharacteristic
96C2—81no—
97C2#1801273511yescharacteristic
98C2#1801276812yes—
subgroupG/H
centerC22D4×D151
commutator, cosocleC2×C4×C151C23
FrattiniC2×C4C22×D151
FittingC2×SD16×C151C2
socleC22×C151C2×D4
prime radicalC2×D4×C151C22
hypercenterC2×SD16D151
hypocenterC151#497
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Dic604C2semidirect
2. C2×#14558994C2semidirect
4. #18012737C2semidirect
6. #18012649C2semidirect
49. C151#497semidirect