Finite Group Databasebeta

← #23757452

Subgroups — #23757452

Order 10048.

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

normal subgroups only

This group has 152 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#19097817C211yesmaximal, characteristic
2#19097804C211yesmaximal, characteristic, complemented
3#19097801C211yesmaximal, characteristic, complemented
4#19097759C211yesmaximal, characteristic, complemented
5#19097699C211yesmaximal, characteristic, complemented
6#19097687C211yesmaximal, characteristic, complemented
7#104×C157C211yesmaximal, characteristic, complemented
8#14578955—21no—
9#14578954—21no—
10#14578954C2211yescharacteristic
11C2×Dic314C2211yescharacteristic, complemented
12C2×D628—21no—
13C2×D628C2211yescharacteristic
14D4×D157—22no—
15D4×D157—21no—
16Dic628—21no—
17#14578944—21no—
18#14578943—21no—
19#14578942—21no—
20#14578938C2211yescharacteristic, complemented
21#14578931—22no—
22#41×C157C2211yescharacteristic
23M16×C157C2211yescharacteristic, complemented
24C42×C157C2211yescharacteristic, complemented
25C22×D157—22no—
26C22×D157D412yes—
27Dic314—21no—
28Dic314—21no—
29Dic314D411yescharacteristic
30D628—22no—
31D628—21no—
32D628—21no—
33D628D411yescharacteristic
34C22⋊D157—22no—
35C22⋊D157—21no—
36C2×Dic157—21no—
37C4×D157—22no—
38C4×D157—21no—
39#11929434—21no—
40Q8×C157D411yescharacteristic
41D4×C157—21no—
42D4×C157D411yescharacteristic
43C2×C4×C157—21no—
44C2×C4×C157—21no—
45C2×C4×C157C2311yescharacteristic
46C8×C157—21no—
47C22×C157—21no—
48C22×C157C2×D411yescharacteristic
49C2×D157—22no—
50C2×D157—21no—
51C2×D157—42no—
52C2×D157—82no—
53C4×C157—21no—
54C4×C157—41no—
55C4×C157C2×D411yescharacteristic
56C4×C157C2×D411yescharacteristic
57Dic157—21no—
58Dic157—41no—
59C2×C157—21no—
60C2×C157—41no—
61C2×C157#12011yescharacteristic
62D157—42no—
63D157—41no—
64C157#45511yescharacteristic, complemented, Sylow
65#455—1571nomaximal, Sylow
66H(5,𝔽2)—1571no—
67#137—1571no—
68#137—1571no—
69#124—1571no—
70#104—1571no—
71#104D15711yescharacteristic, complemented
72#100—1571no—
73#41—3141no—
74#41—3141no—
75#41—1571no—
76#41C2×D15711yescharacteristic
77C2×Q8—1571no—
78C2×D4—3141no—
79C2×D4—3142no—
80C2×D4—3141no—
81C2×D4—1571no—
82Q16—3141no—
83Q16—3141no—
84SD16—3141no—
85SD16—3141no—
86M16—1571no—
87M16C2×D15711yescharacteristic, complemented
88C22⋊C4—3142no—
89C42C2×D15711yescharacteristic, complemented
90C23—3142no—
91C23—1572no—
92Q8—3141no—
93Q8—3141no—
94Q8—1571no—
95Q8D62811yescharacteristic
96D4—21no—
97D4—3142no—
98D4—3142no—
99D4—3141no—
100D4—3141no—
101D4—3141no—
102D4—1571no—
103D4D62811yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—3142no—
107C2×C4—3141no—
108C2×C4—3141no—
109C2×C4C22×D15711yescharacteristic
110C8—21no—
111C8—3141no—
112C22—21no—
113C22—3142no—
114C22—3141no—
115C22—6282no—
116C22—12562no—
117C22D4×D15711yescharacteristic
118C4—21no—
119C4—41no—
120C4—3141no—
121C4—6281no—
122C4D4×D15711yescharacteristic
123C4C2×D62811yescharacteristic
124C2—21no—
125C2—41no—
126C2—6282no—
127C2—6281no—
128C2#1909774111yescharacteristic
subgroupG/H
centerC2#19097741
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#104×C157C2
socleC2×C157#120
prime radical#19097817C2
hypercenter#104D157
hypocenterC157#455
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #19097804C2semidirect
3. #19097801C2semidirect
4. #19097759C2semidirect
5. #19097699C2semidirect
6. #19097687C2semidirect
7. #104×C157C2semidirect
11. C2×Dic314C22semidirect
20. #14578938C22semidirect
23. M16×C157C22semidirect
24. C42×C157C22semidirect
64. C157#455semidirect
71. #104D157semidirect
87. M16C2×D157semidirect
89. C42C2×D157semidirect