Finite Group Databasebeta

← #23757449

Subgroups — #23757449

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#19097802C211yesmaximal, characteristic, complemented
3#19097760C211yesmaximal, characteristic, complemented
4#19097698C211yesmaximal, characteristic, complemented
5#19097697C211yesmaximal, characteristic, complemented
6#19097687C211yesmaximal, characteristic, complemented
7#137×C157C211yesmaximal, characteristic, complemented
8#14578955—21no—
9#14578954—21no—
10#14578954C2211yescharacteristic
11C2×D628—21no—
12C2×D628C2211yescharacteristic
13D4×D157—22no—
14D4×D157—21no—
15#14578944—21no—
16#14578941—21no—
17#14578938C2211yescharacteristic, complemented
18#14578931—22no—
19C4×Dic157C2211yescharacteristic, complemented
20#41×C157C2211yescharacteristic
21C2×Q8×C157C2211yescharacteristic, complemented
22Q16×C157—21no—
23SD16×C157—21no—
24M16×C157C2211yescharacteristic, complemented
25C22×D157—22no—
26C22×D157D412yes—
27Dic314D411yescharacteristic
28D628—22no—
29D628—21no—
30D628—21no—
31D628D411yescharacteristic
32C22⋊D157—22no—
33C22⋊D157—21no—
34C2×Dic157—21no—
35C4×D157—22no—
36C4×D157—21no—
37#11929434—21no—
38Q8×C157—21no—
39Q8×C157—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#137D15711yescharacteristic, complemented
69#124—1571no—
70#104—1571no—
71#104—1571no—
72#100—1571no—
73#41—3141no—
74#41—3141no—
75#41—1571no—
76#41C2×D15711yescharacteristic
77C2×Q8C2×D15711yescharacteristic, complemented
78C2×D4—3141no—
79C2×D4—3142no—
80C2×D4—3141no—
81C2×D4—1571no—
82Q16—21no—
83Q16—3141no—
84SD16—21no—
85SD16—3141no—
86M16—1571no—
87M16C2×D15711yescharacteristic, complemented
88C22⋊C4—3142no—
89C42—1571no—
90C23—3142no—
91C23—1572no—
92Q8—21no—
93Q8—21no—
94Q8—1571no—
95Q8C22⋊D15711yescharacteristic
96D4—21no—
97D4—3142no—
98D4—3142no—
99D4—3141no—
100D4—3141no—
101D4—3141no—
102D4—1571no—
103D4C22⋊D15711yescharacteristic
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×C22⋊D15711yescharacteristic
124C2—21no—
125C2—41no—
126C2—6282no—
127C2—6281no—
128C2#1909773911yescharacteristic
subgroupG/H
centerC2#19097739
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
Fitting#137×C157C2
socleC2×C157#120
prime radical#19097817C2
hypercenter#137D157
hypocenterC157#455
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. #19097802C2semidirect
3. #19097760C2semidirect
4. #19097698C2semidirect
5. #19097697C2semidirect
6. #19097687C2semidirect
7. #137×C157C2semidirect
17. #14578938C22semidirect
19. C4×Dic157C22semidirect
21. C2×Q8×C157C22semidirect
24. M16×C157C22semidirect
64. C157#455semidirect
68. #137D157semidirect
77. C2×Q8C2×D157semidirect
87. M16C2×D157semidirect