Finite Group Databasebeta

← #23752415

Subgroups — #23752415

Order 9664.

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

normal subgroups only

This group has 120 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×#14558992C211yesmaximal, characteristic
2#18012737C211yesmaximal, characteristic, complemented
3D4×Dic151C211yesmaximal, characteristic
4Dic151⋊C8C211yesmaximal, characteristic, complemented
5#18012664C211yesmaximal, characteristic, complemented
6#18012663C211yesmaximal, characteristic, complemented
7C2×SD16×C151C211yesmaximal, characteristic
8C2×Dic302C2211yescharacteristic
9C22×Dic151—21no—
10#14558992—22no—
11C2×C151⋊C8C2211yescharacteristic
12C4⋊Dic151C2211yescharacteristic
13Dic151⋊C4—21no—
14Dic151⋊C4—21no—
15C22⋊Dic151—21no—
16C4×Dic151C2211yescharacteristic
17C2×Q8×C151C2211yescharacteristic
18C2×D4×C151C2211yescharacteristic
19SD16×C151—22no—
20C2×C8×C151C2211yescharacteristic
21Dic302—21no—
22Dic302—21no—
23C2×Dic151—21no—
24C2×Dic151—21no—
25C2×Dic151—42no—
26C2×Dic151D411yescharacteristic
27C2×Dic151D411yescharacteristic
28C151⋊C8—21no—
29C23×C151—21no—
30Q8×C151—21no—
31Q8×C151—21no—
32D4×C151—21no—
33D4×C151D412yes—
34C2×C4×C151—21no—
35C2×C4×C151C2311yescharacteristic
36C8×C151—21no—
37C22×C151—22no—
38C22×C151—41no—
39C22×C151—41no—
40C22×C151C2×D411yescharacteristic
41C4×C151—41no—
42C4×C151C2×D411yescharacteristic
43C4×C151#4111yescharacteristic
44Dic151—21no—
45Dic151—41no—
46Dic151—41no—
47Dic151SD1612yescomplemented
48C2×C151—42no—
49C2×C151#12111yescharacteristic
50C2×C151C2×SD1611yescharacteristic
51C2×C151#13711yescharacteristic
52C151#46111yescharacteristic, complemented, Sylow
53#461—1511nomaximal, Sylow
54C2×SD16—1511no—
55C2×SD16D15111yescharacteristic
56C4⋊Q8—1511no—
57C4×D4—1511no—
58C4⋊C8—1511no—
59#103—1511no—
60#103—1511no—
61C2×Q8—1511no—
62C2×Q8C2×D15111yescharacteristic
63C2×D4C2×D15111yescharacteristic
64C22×C4—3021no—
65SD16—22no—
66SD16—3022no—
67C2×C8—1511no—
68C2×C8C2×D15111yescharacteristic
69C4⋊C4—3021no—
70C4⋊C4—3021no—
71C4⋊C4—1511no—
72C22⋊C4—3021no—
73C42—1511no—
74C23—21no—
75Q8—21no—
76Q8—21no—
77Q8—3021no—
78Q8—3021no—
79D4—21no—
80D4C22⋊D15112yes—
81C2×C4—21no—
82C2×C4—3021no—
83C2×C4—3021no—
84C2×C4—6042no—
85C2×C4—1511no—
86C2×C4—1511no—
87C2×C4C22×D15111yescharacteristic
88C8—21no—
89C8—3021no—
90C22—22no—
91C22—41no—
92C22—41no—
93C22D4×D15111yescharacteristic
94C4—41no—
95C4—3021no—
96C4—6041no—
97C4—6041no—
98C4—1512no—
99C4C2×C22⋊D15111yescharacteristic
100C4#1455900311yescharacteristic
101C2—42no—
102C2#1801271111yescharacteristic
103C2SD16×D15111yescharacteristic
104C2#1801276811yescharacteristic
subgroupG/H
centerC22D4×D151
commutator, cosocleC2×C4×C151C23
FrattiniC2×C4C22×D151
FittingC2×SD16×C151C2
socleC22×C151C2×D4
prime radicalC2×D4×C151C22
hypercenterC2×SD16D151
hypocenterC151#461
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
2. #18012737C2semidirect
4. Dic151⋊C8C2semidirect
5. #18012664C2semidirect
6. #18012663C2semidirect
47. Dic151SD16semidirect
52. C151#461semidirect