Finite Group Databasebeta

← #23757547

Subgroups — #23757547

Order 10048.

100 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 100 conjugacy classes of subgroups — too many to draw. Only its 35 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#19097804C211yesmaximal, characteristic
2#19097802C211yesmaximal, characteristic
3C2×#14578944C211yesmaximal, characteristic, complemented
4#19097779C211yesmaximal, characteristic
5#19097706C211yesmaximal, characteristic, complemented
6#19097689C211yesmaximal, characteristic, complemented
7#101×C157C211yesmaximal, characteristic, complemented
8#14578954C2211yescharacteristic
9C2×Dic314C2211yescharacteristic
10Dic628—21no—
11#14578944—21no—
12#14578944—21no—
13#14578944—21no—
14#14578943—21no—
15#14578941—21no—
16#14578938C2211yescharacteristic
17#14578937—21no—
18C2×#11929434C2211yescharacteristic
19C8×D157—21no—
20C2×Q8×C157C2211yescharacteristic
21M16×C157C2211yescharacteristic
22M16×C157C2211yescharacteristic
23Dic314—21no—
24Dic314—21no—
25Dic314D411yescharacteristic
26D628D411yescharacteristic
27C22⋊D157—21no—
28C2×Dic157—21no—
29C4×D157—21no—
30#11929434—21no—
31#11929434D411yescharacteristic
32#11929434D411yescharacteristic
33Q8×C157—21no—
34Q8×C157—21no—
35C2×C4×C157—21no—
36C2×C4×C157C2311yescharacteristic
37C8×C157—21no—
38C8×C157—21no—
39C22×C157#4111yescharacteristic
40C2×D157—21no—
41C4×C157—41no—
42C4×C157C2×D411yescharacteristic
43C4×C157C2×D411yescharacteristic
44Dic157—21no—
45Dic157—41no—
46C2×C157—21no—
47C2×C157#12111yescharacteristic
48D157—41no—
49C157#47311yescharacteristic, complemented, Sylow
50#473—1571nomaximal, Sylow
51#137—1571no—
52#137—1571no—
53C2×Q16—1571no—
54#131—1571no—
55#108—1571no—
56#101—1571no—
57#101D15711yescharacteristic, complemented
58#41—1571no—
59C2×Q8—1571no—
60C2×Q8C2×D15711yescharacteristic
61Q16—3141no—
62Q16—3141no—
63Q16—3141no—
64Q16—3141no—
65SD16—3141no—
66SD16—3141no—
67M16—3141no—
68M16—1571no—
69M16C2×D15711yescharacteristic
70M16C2×D15711yescharacteristic
71C2×C8—3141no—
72C2×C8—1571no—
73Q8—21no—
74Q8—21no—
75Q8—3141no—
76Q8—3141no—
77Q8—1571no—
78D4—3141no—
79D4—1571no—
80C2×C4—21no—
81C2×C4—3141no—
82C2×C4—3141no—
83C2×C4C22×D15711yescharacteristic
84C8—21no—
85C8—21no—
86C8—3141no—
87C8—1571no—
88C8—1571no—
89C22—3141no—
90C22#1457895411yescharacteristic
91C4—41no—
92C4—3141no—
93C4—6281no—
94C4D4×D15711yescharacteristic
95C4D4×D15711yescharacteristic
96C2—21no—
97C2—6281no—
98C2#1909774411yescharacteristic
subgroupG/H
centerC2#19097744
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#101×C157C2
socleC2×C157#121
prime radical#14578954C22
hypercenter#101D157
hypocenterC157#473
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
3. C2×#14578944C2semidirect
5. #19097706C2semidirect
6. #19097689C2semidirect
7. #101×C157C2semidirect
49. C157#473semidirect
57. #101D157semidirect