Finite Group Databasebeta

← #23757476

Subgroups — #23757476

Order 10048.

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×#14578942C211yesmaximal, characteristic
2#19097769C211yesmaximal, characteristic, complemented
3D4×Dic157C211yesmaximal, characteristic
4#19097700C211yesmaximal, characteristic, complemented
5#19097696C211yesmaximal, characteristic, complemented
6#19097695C211yesmaximal, characteristic, complemented
7C2×SD16×C157C211yesmaximal, characteristic
8C2×Dic314C2211yescharacteristic
9C22×Dic157—21no—
10#14578942—22no—
11C2×#11929434C2211yescharacteristic
12C4⋊Dic157C2211yescharacteristic
13#14578933—21no—
14#14578933—21no—
15C22⋊Dic157—21no—
16C4×Dic157C2211yescharacteristic
17C2×Q8×C157C2211yescharacteristic
18C2×D4×C157C2211yescharacteristic
19SD16×C157—22no—
20C2×C8×C157C2211yescharacteristic
21Dic314—21no—
22Dic314—21no—
23C2×Dic157—21no—
24C2×Dic157—21no—
25C2×Dic157—42no—
26C2×Dic157D411yescharacteristic
27C2×Dic157D411yescharacteristic
28#11929434—21no—
29C23×C157—21no—
30Q8×C157—21no—
31Q8×C157—21no—
32D4×C157—21no—
33D4×C157D412yes—
34C2×C4×C157—21no—
35C2×C4×C157C2311yescharacteristic
36C8×C157—21no—
37C22×C157—22no—
38C22×C157—41no—
39C22×C157—41no—
40C22×C157C2×D411yescharacteristic
41C4×C157—41no—
42C4×C157C2×D411yescharacteristic
43C4×C157#4111yescharacteristic
44Dic157—21no—
45Dic157—41no—
46Dic157—41no—
47Dic157SD1612yescomplemented
48C2×C157—42no—
49C2×C157#12111yescharacteristic
50C2×C157C2×SD1611yescharacteristic
51C2×C157#13711yescharacteristic
52C157#46111yescharacteristic, complemented, Sylow
53#461—1571nomaximal, Sylow
54C2×SD16—1571no—
55C2×SD16D15711yescharacteristic
56C4⋊Q8—1571no—
57C4×D4—1571no—
58C4⋊C8—1571no—
59#103—1571no—
60#103—1571no—
61C2×Q8—1571no—
62C2×Q8C2×D15711yescharacteristic
63C2×D4C2×D15711yescharacteristic
64C22×C4—3141no—
65SD16—22no—
66SD16—3142no—
67C2×C8—1571no—
68C2×C8C2×D15711yescharacteristic
69C4⋊C4—3141no—
70C4⋊C4—3141no—
71C4⋊C4—1571no—
72C22⋊C4—3141no—
73C42—1571no—
74C23—21no—
75Q8—21no—
76Q8—21no—
77Q8—3141no—
78Q8—3141no—
79D4—21no—
80D4C22⋊D15712yes—
81C2×C4—21no—
82C2×C4—3141no—
83C2×C4—3141no—
84C2×C4—6282no—
85C2×C4—1571no—
86C2×C4—1571no—
87C2×C4C22×D15711yescharacteristic
88C8—21no—
89C8—3141no—
90C22—22no—
91C22—41no—
92C22—41no—
93C22D4×D15711yescharacteristic
94C4—41no—
95C4—3141no—
96C4—6281no—
97C4—6281no—
98C4—1572no—
99C4C2×C22⋊D15711yescharacteristic
100C4#1457895311yescharacteristic
101C2—42no—
102C2#1909774311yescharacteristic
103C2SD16×D15711yescharacteristic
104C2#1909780011yescharacteristic
subgroupG/H
centerC22D4×D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingC2×SD16×C157C2
socleC22×C157C2×D4
prime radicalC2×D4×C157C22
hypercenterC2×SD16D157
hypocenterC157#461
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
2. #19097769C2semidirect
4. #19097700C2semidirect
5. #19097696C2semidirect
6. #19097695C2semidirect
47. Dic157SD16semidirect
52. C157#461semidirect