Finite Group Databasebeta

← #23757462

Subgroups — #23757462

Order 10048.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#19097816C211yesmaximal, characteristic
2#19097754C212yesmaximal, complemented
3#19097686C211yesmaximal, characteristic, complemented
4#19097685C212yesmaximal, complemented
5#123×C157C211yesmaximal, characteristic, complemented
6#14578954—21no—
7#14578953—22no—
8C2×C22⋊D157—21no—
9C2×C22⋊D157C2212yes—
10D4×D157—22no—
11#14578933—22no—
12C22⋊Dic157C2212yescomplemented
13#14578931—22no—
14C2×D4×C157C2211yescharacteristic
15C22×C4×C157C2211yescharacteristic, complemented
16C4⋊C4×C157—21no—
17C22⋊C4×C157—21no—
18C22⋊C4×C157C2211yescharacteristic, complemented
19C22×D157—21no—
20C22×D157D412yes—
21Dic314—21no—
22D628—21no—
23C22⋊D157—22no—
24C22⋊D157—22no—
25C22⋊D157—22no—
26C2×Dic157—21no—
27C2×Dic157—22no—
28C2×Dic157D412yes—
29C4×D157—22no—
30C23×C157D411yescharacteristic
31C23×C157C2311yescharacteristic
32D4×C157—22no—
33C2×C4×C157—21no—
34C2×C4×C157—21no—
35C2×C4×C157—22no—
36C2×C4×C157D411yescharacteristic
37C22×C157—21no—
38C22×C157—41no—
39C22×C157—41no—
40C22×C157C2×D412yes—
41C22×C157C2×D411yescharacteristic
42C2×D157—22no—
43C2×D157—42no—
44C2×D157—81no—
45C4×C157—21no—
46C4×C157—41no—
47C4×C157—41no—
48Dic157—22no—
49Dic157—42no—
50C2×C157—22no—
51C2×C157—21no—
52C2×C157—41no—
53C2×C157#12011yescharacteristic
54D157—42no—
55C157#45811yescharacteristic, complemented, Sylow
56#458—1571nomaximal, Sylow
57H(5,𝔽2)—1571no—
58#123—1572no—
59#123D15711yescharacteristic, complemented
60#99—1571no—
61#99—1572no—
62#41—3142no—
63#41—3141no—
64C2×D4—3142no—
65C2×D4—3141no—
66C2×D4—1572no—
67C2×D4C2×D15711yescharacteristic
68C22×C4C2×D15711yescharacteristic, complemented
69C4⋊C4—21no—
70C4⋊C4—3142no—
71C22⋊C4—21no—
72C22⋊C4—3142no—
73C22⋊C4—1572no—
74C22⋊C4C2×D15711yescharacteristic, complemented
75C23—3141no—
76C23—1572no—
77C23C22⋊D15711yescharacteristic
78C23C22×D15711yescharacteristic
79Q8—3141no—
80D4—22no—
81D4—3141no—
82D4—3142no—
83D4—3142no—
84D4—3142no—
85C2×C4—22no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—3142no—
89C2×C4—3141no—
90C2×C4—3142no—
91C2×C4—1572no—
92C2×C4C22⋊D15711yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—3142no—
97C22—6282no—
98C22—12561no—
99C22D4×D15712yes—
100C22C2×C22⋊D15711yescharacteristic
101C4—21no—
102C4—41no—
103C4—41no—
104C4—3142no—
105C4—6282no—
106C2—21no—
107C2—22no—
108C2—41no—
109C2—6282no—
110C2#1909773911yescharacteristic
subgroupG/H
centerC2#19097739
commutator, cosocleC23×C157C23
FrattiniC23C22×D157
Fitting#123×C157C2
socleC2×C157#120
prime radical#19097816C2
hypercenter#123D157
hypocenterC157#458
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #19097754C2semidirect
3. #19097686C2semidirect
4. #19097685C2semidirect
5. #123×C157C2semidirect
12. C22⋊Dic157C22semidirect
15. C22×C4×C157C22semidirect
18. C22⋊C4×C157C22semidirect
55. C157#458semidirect
59. #123D157semidirect
68. C22×C4C2×D157semidirect
74. C22⋊C4C2×D157semidirect