Finite Group Databasebeta

← #103×D157 #23757262

Subgroups — #103×D157 #23757262

Order 10048.

162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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×Q8×D157C211yesmaximal, characteristic
2C2×C8×D157C211yesmaximal, characteristic
3C4⋊C4×D157C211yesmaximal, characteristic
4#19097696C211yesmaximal, characteristic, complemented
5#19097695C211yesmaximal, characteristic, complemented
6#19097694C211yesmaximal, characteristic, complemented
7#103×C157C211yesmaximal, characteristic, complemented
8C2×Dic314—21no—
9C2×Dic314C2211yescharacteristic
10Q8×D157—22no—
11Q8×D157C414yescomplemented
12C2×C4×D157—21no—
13C2×C4×D157—21no—
14C2×C4×D157C2211yescharacteristic
15C2×#11929434C2211yescharacteristic
16C8×D157—22no—
17C4⋊Dic157C2211yescharacteristic
18#14578933—21no—
19C2×Q8×C157C2211yescharacteristic
20C2×C8×C157C2211yescharacteristic
21C4⋊C4×C157C2211yescharacteristic
22C22×D157D411yescharacteristic
23Dic314—21no—
24Dic314—24no—
25Dic314C2×C412yescomplemented
26C2×Dic157—21no—
27C2×Dic157—21no—
28C2×Dic157D411yescharacteristic
29C4×D157—24no—
30C4×D157—42no—
31C4×D157C2×C412yes—
32C4×D157D412yes—
33#11929434—21no—
34Q8×C157—21no—
35Q8×C157C2×C412yescomplemented
36C2×C4×C157—21no—
37C2×C4×C157—21no—
38C2×C4×C157C2311yescharacteristic
39C8×C157—21no—
40C22×C157C2×D411yescharacteristic
41C2×D157C22⋊C412yes—
42C2×D157SD1612yes—
43C2×D157Q1612yes—
44C4×C157—22no—
45C4×C157—41no—
46C4×C157C22×C411yescharacteristic
47C4×C157C2×D411yescharacteristic
48Dic157—22no—
49Dic157—41no—
50Dic157C22⋊C412yes—
51C2×C157C2×C22⋊C411yescharacteristic
52C2×C157C2×SD1611yescharacteristic
53C2×C157C2×Q1611yescharacteristic
54D157#10314yesdirect product factor
55C157C2×#10311yescharacteristic, complemented, Sylow
56C2×#103—1571nomaximal, Sylow
57C22×Q8—1571no—
58C22×C8—1571no—
59C2×C4⋊C4—1571no—
60#103—1571no—
61#103—1571no—
62#103—1571no—
63#103D15711yescharacteristic, direct product factor
64C2×Q8—3141no—
65C2×Q8—3142no—
66C2×Q8—1574no—
67C2×Q8—1571no—
68C2×Q8C2×D15711yescharacteristic
69C22×C4—3141no—
70C22×C4—3141no—
71C22×C4—1571no—
72C2×C8—3142no—
73C2×C8—1571no—
74C2×C8C2×D15711yescharacteristic
75C4⋊C4—3141no—
76C4⋊C4—1571no—
77C4⋊C4C2×D15711yescharacteristic
78C23—1571no—
79Q8—21no—
80Q8—3144no—
81Q8—3141no—
82Q8—1572no—
83Q8C4×D15712yescomplemented
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—3144no—
87C2×C4—3141no—
88C2×C4—3141no—
89C2×C4—6282no—
90C2×C4—1571no—
91C2×C4—1572no—
92C2×C4—1572no—
93C2×C4C22×D15711yescharacteristic
94C8—21no—
95C8—3141no—
96C22—1572no—
97C22—1572no—
98C22—1572no—
99C22D4×D15711yescharacteristic
100C4—22no—
101C4—41no—
102C4—3142no—
103C4—6281no—
104C4—1572no—
105C4C2×C4×D15711yescharacteristic
106C4D4×D15711yescharacteristic
107C2—1574no—
108C2C22⋊C4×D15711yescharacteristic
109C2SD16×D15711yescharacteristic
110C2Q16×D15711yescharacteristic
subgroupG/H
centerC22D4×D157
commutatorC4×C157C22×C4
FrattiniC2×C4C22×D157
Fitting#103×C157C2
socleC22×C157C2×D4
prime radicalC22×D157D4
cosocleC2×C4×C157C23
hypercenter#103D157
hypocenterC157C2×#103
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
4. #19097696C2semidirect
5. #19097695C2semidirect
6. #19097694C2semidirect
7. #103×C157C2semidirect
11. Q8×D157C4semidirect
25. Dic314C2×C4semidirect
35. Q8×C157C2×C4semidirect
54. D157#103direct (N × H)
55. C157C2×#103semidirect
63. #103D157direct (N × H)
83. Q8C4×D157semidirect