Finite Group Databasebeta

← #23757497

Subgroups — #23757497

Order 10048.

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

normal subgroups only

This group has 112 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×#14578941C211yesmaximal, characteristic
2#19097760C211yesmaximal, characteristic
3Q8×Dic157C211yesmaximal, characteristic, complemented
4#19097700C211yesmaximal, characteristic, complemented
5#19097695C211yesmaximal, characteristic, complemented
6#19097693C211yesmaximal, characteristic
7C2×Q16×C157C211yesmaximal, characteristic, complemented
8C2×D628C2211yescharacteristic
9#14578941—22no—
10C2×#11929434C2211yescharacteristic
11C4⋊Dic157—21no—
12C4⋊Dic157C2211yescharacteristic
13#14578931—21no—
14#14578931—21no—
15C4×Dic157—21no—
16C4×Dic157C2211yescharacteristic
17C2×Q8×C157C2211yescharacteristic
18C2×Q8×C157C2211yescharacteristic
19Q16×C157—22no—
20C2×C8×C157C2211yescharacteristic
21C22×D157—21no—
22D628—21no—
23D628—21no—
24C2×Dic157—21no—
25C2×Dic157D411yescharacteristic
26C2×Dic157D411yescharacteristic
27#11929434—21no—
28Q8×C157—21no—
29Q8×C157—21no—
30Q8×C157—21no—
31Q8×C157D412yes—
32C2×C4×C157—21no—
33C2×C4×C157—21no—
34C2×C4×C157C2311yescharacteristic
35C8×C157—21no—
36C22×C157C2×D411yescharacteristic
37C2×D157—41no—
38C2×D157—41no—
39C2×D157—41no—
40C4×C157—22no—
41C4×C157—41no—
42C4×C157C2×D411yescharacteristic
43C4×C157#4111yescharacteristic
44Dic157—21no—
45Dic157—21no—
46Dic157—41no—
47C2×C157#12111yescharacteristic
48C2×C157#13511yescharacteristic
49C2×C157#13711yescharacteristic
50D157—81no—
51C157#46411yescharacteristic, complemented, Sylow
52#464—1571nomaximal, Sylow
53C2×Q16D15711yescharacteristic, complemented
54C2×SD16—1571no—
55#124—1571no—
56C4×Q8—1571no—
57C4⋊C8—1571no—
58#103—1571no—
59#102—1571no—
60C2×Q8C2×D15711yescharacteristic
61C2×Q8C2×D15711yescharacteristic
62C2×D4—1571no—
63Q16—22no—
64SD16—3142no—
65C2×C8—1571no—
66C2×C8C2×D15711yescharacteristic
67C4⋊C4—3141no—
68C4⋊C4—1571no—
69C22⋊C4—3141no—
70C22⋊C4—3141no—
71C42—3141no—
72C42—1571no—
73C23—3141no—
74Q8—21no—
75Q8—21no—
76Q8—21no—
77Q8C22⋊D15712yes—
78D4—3141no—
79D4—3141no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3141no—
83C2×C4—1571no—
84C2×C4—1571no—
85C2×C4C22×D15711yescharacteristic
86C8—21no—
87C8—3141no—
88C22—6281no—
89C22—6281no—
90C22—6281no—
91C22D4×D15711yescharacteristic
92C4—22no—
93C4—41no—
94C4—3141no—
95C4—3141no—
96C4—6281no—
97C4C2×C22⋊D15711yescharacteristic
98C4#1457895311yescharacteristic
99C2—12561no—
100C2#1909774311yescharacteristic
101C2#1909779411yescharacteristic
102C2#1909780311yescharacteristic
subgroupG/H
centerC22D4×D157
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingC2×Q16×C157C2
socleC22×C157C2×D4
prime radicalC2×D628C22
hypercenterC2×Q16D157
hypocenterC157#464
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. Q8×Dic157C2semidirect
4. #19097700C2semidirect
5. #19097695C2semidirect
7. C2×Q16×C157C2semidirect
51. C157#464semidirect
53. C2×Q16D157semidirect