Finite Group Databasebeta

← #23757477

Subgroups — #23757477

Order 10048.

120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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×#14578943C211yesmaximal, characteristic
2C2×#14578941C211yesmaximal, characteristic
3#19097769C211yesmaximal, characteristic, complemented
4#19097733C211yesmaximal, characteristic
5#19097700C211yesmaximal, characteristic, complemented
6#19097694C211yesmaximal, characteristic, complemented
7#103×C157C211yesmaximal, characteristic, complemented
8C2×Dic314C2211yescharacteristic
9C2×D628C2211yescharacteristic
10C2×C4×D157—21no—
11#14578943—22no—
12#14578941—22no—
13C2×#11929434C2211yescharacteristic
14#14578933—21no—
15#14578933—21no—
16#14578931—21no—
17C4×Dic157C2211yescharacteristic
18C2×Q8×C157C2211yescharacteristic
19C2×C8×C157C2211yescharacteristic
20C4⋊C4×C157C2211yescharacteristic
21C22×D157—21no—
22Dic314—21no—
23Dic314—21no—
24D628—21no—
25D628D412yes—
26C2×Dic157—21no—
27C2×Dic157D411yescharacteristic
28C2×Dic157D411yescharacteristic
29C4×D157—42no—
30#11929434—21no—
31Q8×C157—21no—
32Q8×C157—21no—
33C2×C4×C157—21no—
34C2×C4×C157—21no—
35C2×C4×C157C2311yescharacteristic
36C8×C157—21no—
37C22×C157C2×D411yescharacteristic
38C2×D157—22no—
39C2×D157—41no—
40C2×D157—41no—
41C4×C157—41no—
42C4×C157—41no—
43C4×C157C2×D411yescharacteristic
44C4×C157#4111yescharacteristic
45Dic157—21no—
46Dic157—41no—
47Dic157SD1612yescomplemented
48C2×C157#12111yescharacteristic
49C2×C157C2×SD1611yescharacteristic
50C2×C157#13711yescharacteristic
51D157—42no—
52C157#46111yescharacteristic, complemented, Sylow
53#461—1571nomaximal, Sylow
54C2×SD16—1571no—
55C2×SD16—1571no—
56C4⋊Q8—1571no—
57C4×D4—1571no—
58C4⋊C8—1571no—
59#103—1571no—
60#103D15711yescharacteristic, complemented
61C2×Q8—1571no—
62C2×Q8C2×D15711yescharacteristic
63C2×D4—1571no—
64C22×C4—3141no—
65SD16—3142no—
66SD16—3142no—
67C2×C8—1571no—
68C2×C8C2×D15711yescharacteristic
69C4⋊C4—3141no—
70C4⋊C4—3141no—
71C4⋊C4C2×D15711yescharacteristic
72C22⋊C4—3141no—
73C42—1571no—
74C23—3141no—
75Q8—21no—
76Q8—21no—
77Q8—3141no—
78Q8—3141no—
79D4—3141no—
80D4—1572no—
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—3141no—
84C2×C4—6282no—
85C2×C4—1571no—
86C2×C4—1571no—
87C2×C4C22×D15711yescharacteristic
88C8—21no—
89C8—3141no—
90C22—3142no—
91C22—6281no—
92C22—6281no—
93C22D4×D15711yescharacteristic
94C4—41no—
95C4—41no—
96C4—3141no—
97C4—6281no—
98C4—1572no—
99C4D4×D15711yescharacteristic
100C4#1457895411yescharacteristic
101C2—6282no—
102C2#1909774411yescharacteristic
103C2SD16×D15711yescharacteristic
104C2#1909780311yescharacteristic
subgroupG/H
centerC22D4×D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#103×C157C2
socleC22×C157C2×D4
prime radicalC2×D628C22
hypercenter#103D157
hypocenterC157#461
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #19097769C2semidirect
5. #19097700C2semidirect
6. #19097694C2semidirect
7. #103×C157C2semidirect
47. Dic157SD16semidirect
52. C157#461semidirect
60. #103D157semidirect