Finite Group Databasebeta

← #23757417

Subgroups — #23757417

Order 10048.

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

normal subgroups only

This group has 162 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×#14578955C211yesmaximal, characteristic, complemented
2C2×#14578939C211yesmaximal, characteristic, complemented
3#19097742C211yesmaximal, characteristic, complemented
4#19097695C211yesmaximal, characteristic, complemented
5#19097693C211yesmaximal, characteristic, complemented
6#19097683C211yesmaximal, characteristic, complemented
7C2×SD16×C157C211yesmaximal, characteristic, complemented
8#14578955—22no—
9#14578955—22no—
10C2×D628—21no—
11C2×D628C2211yescharacteristic
12C2×C22⋊D157—21no—
13C2×C4×D157—21no—
14C2×C4×D157C2211yescharacteristic
15#14578939—22no—
16C2×#11929434C2211yescharacteristic
17C4⋊Dic157C2211yescharacteristic
18C22⋊Dic157—21no—
19C2×Q8×C157C2211yescharacteristic
20C2×D4×C157C2211yescharacteristic
21SD16×C157—22no—
22C2×C8×C157C2211yescharacteristic
23C22×D157—21no—
24C22×D157D411yescharacteristic
25D628—24no—
26D628—21no—
27D628D412yescomplemented
28C22⋊D157—42no—
29C2×Dic157—21no—
30C2×Dic157D411yescharacteristic
31C4×D157—24no—
32C4×D157—21no—
33C4×D157—21no—
34#11929434—21no—
35C23×C157—21no—
36Q8×C157—21no—
37Q8×C157D412yescomplemented
38D4×C157—21no—
39D4×C157—21no—
40C2×C4×C157—21no—
41C2×C4×C157C2311yescharacteristic
42C8×C157—21no—
43C22×C157—41no—
44C22×C157—41no—
45C22×C157—41no—
46C22×C157C2×D411yescharacteristic
47C2×D157—21no—
48C2×D157—22no—
49C2×D157—21no—
50C2×D157—21no—
51C2×D157—41no—
52C2×D157—41no—
53C4×C157—22no—
54C4×C157C2×D411yescharacteristic
55C4×C157C2×D411yescharacteristic
56Dic157—21no—
57Dic157—41no—
58C2×C157—81no—
59C2×C157#12011yescharacteristic
60C2×C157#13511yescharacteristic
61C2×C157AGL(1,ℤ/8)11yescharacteristic
62D157—41no—
63D157—42no—
64C157#44911yescharacteristic, complemented, Sylow
65#449—1571nomaximal, Sylow
66C2×#41—1571no—
67C2×SD16D15711yescharacteristic, complemented
68C2×D8—1571no—
69#121—1571no—
70#103—1571no—
71#102—1571no—
72C22⋊C8—1571no—
73#41—3142no—
74#41—3142no—
75C2×Q8C2×D15711yescharacteristic
76C2×D4—3141no—
77C2×D4—3141no—
78C2×D4—1571no—
79C2×D4C2×D15711yescharacteristic
80C22×C4—3141no—
81C22×C4—1571no—
82SD16—22no—
83D8—3142no—
84C2×C8—1571no—
85C2×C8C2×D15711yescharacteristic
86C4⋊C4—1571no—
87C22⋊C4—3141no—
88C23—21no—
89C23—3141no—
90C23—1571no—
91Q8—21no—
92Q8C22⋊D15712yescomplemented
93D4—21no—
94D4—21no—
95D4—3144no—
96D4—3141no—
97D4—6282no—
98D4—1572no—
99C2×C4—21no—
100C2×C4—3144no—
101C2×C4—3141no—
102C2×C4—3141no—
103C2×C4—3141no—
104C2×C4—1571no—
105C2×C4C22×D15711yescharacteristic
106C8—21no—
107C8—3141no—
108C22—41no—
109C22—41no—
110C22—41no—
111C22—3141no—
112C22—3142no—
113C22—3141no—
114C22—3141no—
115C22—6281no—
116C22—6281no—
117C22D4×D15711yescharacteristic
118C4—22no—
119C4—3141no—
120C4—6281no—
121C4D4×D15711yescharacteristic
122C4C2×C22⋊D15711yescharacteristic
123C2—81no—
124C2—6281no—
125C2—6282no—
126C2#1909773911yescharacteristic
127C2#1909779211yescharacteristic
128C2#1909779811yescharacteristic
subgroupG/H
centerC22D4×D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingC2×SD16×C157C2
socleC22×C157C2×D4
hypercenterC2×SD16D157
hypocenterC157#449
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
1. C2×#14578955C2semidirect
2. C2×#14578939C2semidirect
3. #19097742C2semidirect
4. #19097695C2semidirect
5. #19097693C2semidirect
6. #19097683C2semidirect
7. C2×SD16×C157C2semidirect
27. D628D4semidirect
37. Q8×C157D4semidirect
64. C157#449semidirect
67. C2×SD16D157semidirect
92. Q8C22⋊D157semidirect