Finite Group Databasebeta

← #23757546

Subgroups — #23757546

Order 10048.

100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 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
1#19097801C211yesmaximal, characteristic
2C2×#14578944C211yesmaximal, characteristic, complemented
3#19097778C211yesmaximal, characteristic
4#19097706C211yesmaximal, characteristic, complemented
5#19097690C211yesmaximal, characteristic, complemented
6#19097689C211yesmaximal, characteristic, complemented
7#137×C157C211yesmaximal, characteristic
8C2×Dic314C2211yescharacteristic
9#14578944—21no—
10#14578944—21no—
11#14578944—21no—
12#14578942—21no—
13#14578938—21no—
14#14578938C2211yescharacteristic
15#14578938C2211yescharacteristic
16C2×#11929434—21no—
17C2×#11929434C2211yescharacteristic
18#41×C157C2211yescharacteristic
19C2×Q8×C157C2211yescharacteristic
20Q16×C157—21no—
21SD16×C157—21no—
22M16×C157C2211yescharacteristic
23Dic314—21no—
24Dic314—21no—
25C2×Dic157—21no—
26#11929434—21no—
27#11929434—21no—
28#11929434D411yescharacteristic
29#11929434D411yescharacteristic
30Q8×C157—21no—
31Q8×C157—21no—
32Q8×C157D411yescharacteristic
33D4×C157—21no—
34D4×C157D411yescharacteristic
35C2×C4×C157—21no—
36C2×C4×C157—21no—
37C2×C4×C157C2311yescharacteristic
38C8×C157—21no—
39C22×C157—21no—
40C22×C157#4111yescharacteristic
41C4×C157—21no—
42C4×C157—41no—
43C4×C157C2×D411yescharacteristic
44C4×C157C2×D411yescharacteristic
45Dic157—41no—
46C2×C157—21no—
47C2×C157—41no—
48C2×C157#12111yescharacteristic
49C157#47311yescharacteristic, complemented, Sylow
50#473—1571nomaximal, Sylow
51#137—1571no—
52#137D15711yescharacteristic
53C2×Q16—1571no—
54#131—1571no—
55#108—1571no—
56#101—1571no—
57#101—1571no—
58#41C2×D15711yescharacteristic
59C2×Q8—1571no—
60C2×Q8C2×D15711yescharacteristic
61Q16—21no—
62Q16—3141no—
63Q16—3141no—
64Q16—3141no—
65SD16—21no—
66SD16—3141no—
67M16—3141no—
68M16—1571no—
69M16—1571no—
70M16C2×D15711yescharacteristic
71C2×C8—3141no—
72C2×C8—1571no—
73Q8—21no—
74Q8—21no—
75Q8—3141no—
76Q8—3141no—
77Q8C22⋊D15711yescharacteristic
78D4—21no—
79D4C22⋊D15711yescharacteristic
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3141no—
83C2×C4C22×D15711yescharacteristic
84C8—21no—
85C8—3141no—
86C8—3141no—
87C8—1571no—
88C8—1571no—
89C22—21no—
90C22#1457895311yescharacteristic
91C4—21no—
92C4—41no—
93C4—6281no—
94C4D4×D15711yescharacteristic
95C4C2×C22⋊D15711yescharacteristic
96C2—21no—
97C2—41no—
98C2#1909774311yescharacteristic
subgroupG/H
centerC2#19097743
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#137×C157C2
socleC2×C157#121
prime radical#41×C157C22
hypercenter#137D157
hypocenterC157#473
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
2. C2×#14578944C2semidirect
4. #19097706C2semidirect
5. #19097690C2semidirect
6. #19097689C2semidirect
49. C157#473semidirect