Finite Group Databasebeta

← #23758086

Subgroups — #23758086

Order 10048.

248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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#19097819C212yesmaximal, complemented
2#19097803C214yesmaximal, complemented
3#19097802C212yesmaximal, complemented
4#19097794C212yesmaximal, complemented
5#19097793C211yesmaximal, characteristic, complemented
6Q16×D157C212yesmaximal, complemented
7#19097777C211yesmaximal, characteristic, complemented
8C2×Q16×C157C211yesmaximal, characteristic, complemented
9#14578955—22no—
10#14578955C2214yes—
11#14578954—24no—
12#14578954C2212yes—
13#14578954C2211yescharacteristic
14Q8×D157—22no—
15Q8×D157C2214yes—
16Dic628C2211yescharacteristic
17#14578944C2214yes—
18#14578943C2212yes—
19#14578941C2214yes—
20D1256C2211yescharacteristic
21#14578938C2211yescharacteristic
22#14578937C2212yes—
23C8×D157C2212yes—
24C2×Q8×C157C2212yes—
25Q16×C157C2212yes—
26Q16×C157C2212yes—
27C2×C8×C157C2211yescharacteristic
28Dic314—24no—
29Dic314D411yescharacteristic
30Dic314C2312yes—
31D628—24no—
32D628D411yescharacteristic
33D628C2312yes—
34C22⋊D157—22no—
35C22⋊D157D412yes—
36C4×D157—24no—
37C4×D157—22no—
38C4×D157—24no—
39C4×D157C2312yes—
40#11929434C2312yes—
41Q8×C157—22no—
42Q8×C157C2314yes—
43C2×C4×C157—22no—
44C2×C4×C157C2311yescharacteristic
45C8×C157C2311yescharacteristic
46C8×C157C2311yescharacteristic
47C22×C157C2×D411yescharacteristic
48C2×D157—22no—
49C2×D157C2×D412yes—
50C4×C157—24no—
51C4×C157C2×D411yescharacteristic
52C4×C157C2411yescharacteristic
53Dic157—22no—
54Dic157C2×D412yes—
55C2×C157—21no—
56C2×C157C22×D411yescharacteristic
57D157—22no—
58D157—42no—
59C157#57811yescharacteristic, complemented, Sylow
60#578—1571nomaximal, Sylow
612−1+4—1572no—
62#137—1572no—
63#137—1574no—
64#135—1572no—
65#135—1571no—
66C2×Q16—1572no—
67C2×Q16D15711yescharacteristic, complemented
68#131—1571no—
69#41—3144no—
70#41—3142no—
71#41—1574no—
72#41—1572no—
73#41—1571no—
74C2×Q8—3142no—
75C2×Q8—1574no—
76C2×Q8C2×D15712yes—
77Q16—1574no—
78Q16—1571no—
79Q16C2×D15712yes—
80Q16C2×D15712yes—
81SD16—1574no—
82SD16—1572no—
83D8—1571no—
84M16—1571no—
85M16—1572no—
86C2×C8—1572no—
87C2×C8C2×D15711yescharacteristic
88Q8—22no—
89Q8—3144no—
90Q8—1572no—
91Q8—1571no—
92Q8C22×D15714yes—
93D4—3144no—
94D4—3142no—
95D4—1572no—
96D4—1571no—
97D4—1572no—
98C2×C4—22no—
99C2×C4—3144no—
100C2×C4—3144no—
101C2×C4—3142no—
102C2×C4—1572no—
103C2×C4C22×D15711yescharacteristic
104C8—1572no—
105C8C22×D15711yescharacteristic
106C8C22×D15711yescharacteristic
107C22—3142no—
108C22—1572no—
109C22D4×D15711yescharacteristic
110C4—24no—
111C4—3142no—
112C4—1572no—
113C4D4×D15711yescharacteristic
114C4C23×D15711yescharacteristic
115C2—21no—
116C2—3142no—
117C2—6282no—
118C2C2×D4×D15711yescharacteristic
subgroupG/H
centerC2C2×D4×D157
commutator, cosocleC4×C157C24
FrattiniC4C23×D157
FittingC2×Q16×C157C2
socleC2×C157C22×D4
hypercenterC2×Q16D157
hypocenterC157#578
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #19097819C2semidirect
2. #19097803C2semidirect
3. #19097802C2semidirect
4. #19097794C2semidirect
5. #19097793C2semidirect
6. Q16×D157C2semidirect
7. #19097777C2semidirect
8. C2×Q16×C157C2semidirect
59. C157#578semidirect
67. C2×Q16D157semidirect