Finite Group Databasebeta

← #23757439

Subgroups — #23757439

Order 10048.

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

normal subgroups only

This group has 168 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, complemented
2#19097797C211yesmaximal, characteristic, complemented
3#19097767C211yesmaximal, characteristic, complemented
4#19097698C211yesmaximal, characteristic, complemented
5#19097697C211yesmaximal, characteristic, complemented
6#19097687C211yesmaximal, characteristic, complemented
7AGL(1,ℤ/8)×C157C211yesmaximal, characteristic, complemented
8#14578955—21no—
9#14578954—21no—
10#14578954C2211yescharacteristic
11C2×D628—21no—
12C2×D628C2211yescharacteristic
13C2×C22⋊D157—22no—
14D4×D157—22no—
15D4×D157—21no—
16#14578942—21no—
17#14578939—21no—
18#14578938C2211yescharacteristic, complemented
19C4×Dic157C2211yescharacteristic, complemented
20#41×C157C2211yescharacteristic
21C2×D4×C157C2211yescharacteristic, complemented
22SD16×C157—21no—
23D8×C157—21no—
24M16×C157C2211yescharacteristic, complemented
25C22×D157—22no—
26C22×D157D412yes—
27Dic314D411yescharacteristic, complemented
28D628—22no—
29D628—21no—
30D628—21no—
31D628D411yescharacteristic, complemented
32C22⋊D157—22no—
33C22⋊D157—21no—
34C22⋊D157—44no—
35C2×Dic157—21no—
36C4×D157—22no—
37C4×D157—21no—
38#11929434—21no—
39C23×C157—21no—
40Q8×C157D411yescharacteristic, complemented
41D4×C157—21no—
42D4×C157—21no—
43D4×C157—21no—
44D4×C157D411yescharacteristic, complemented
45C2×C4×C157—21no—
46C2×C4×C157C2311yescharacteristic
47C8×C157—21no—
48C22×C157—21no—
49C22×C157—42no—
50C22×C157—41no—
51C22×C157C2×D411yescharacteristic
52C2×D157—22no—
53C2×D157—21no—
54C2×D157—42no—
55C2×D157—82no—
56C4×C157—21no—
57C4×C157C2×D411yescharacteristic
58C4×C157C2×D411yescharacteristic
59Dic157—22no—
60Dic157—21no—
61C2×C157—21no—
62C2×C157—41no—
63C2×C157—81no—
64C2×C157#12011yescharacteristic
65D157—42no—
66D157—41no—
67C157#45311yescharacteristic, complemented, Sylow
68#453—1571nomaximal, Sylow
69H(5,𝔽2)—1571no—
70AGL(1,ℤ/8)—1571no—
71AGL(1,ℤ/8)D15711yescharacteristic, complemented
72#127—1571no—
73#104—1571no—
74#104—1571no—
75#100—1571no—
76#41—3141no—
77#41—3141no—
78#41—1571no—
79#41C2×D15711yescharacteristic
80C2×D4—3141no—
81C2×D4—3142no—
82C2×D4—3141no—
83C2×D4—3142no—
84C2×D4—1571no—
85C2×D4C2×D15711yescharacteristic, complemented
86SD16—21no—
87SD16—3141no—
88D8—21no—
89D8—3141no—
90M16—1571no—
91M16C2×D15711yescharacteristic, complemented
92C42—1571no—
93C23—21no—
94C23—3142no—
95C23—1572no—
96Q8—1571no—
97Q8C22⋊D15711yescharacteristic, complemented
98D4—21no—
99D4—21no—
100D4—21no—
101D4—3142no—
102D4—3142no—
103D4—3141no—
104D4—3141no—
105D4—3141no—
106D4—6284no—
107D4—1571no—
108D4C22⋊D15711yescharacteristic, complemented
109C2×C4—21no—
110C2×C4—3142no—
111C2×C4—3141no—
112C2×C4—3141no—
113C2×C4C22×D15711yescharacteristic
114C8—21no—
115C8—3141no—
116C22—21no—
117C22—42no—
118C22—41no—
119C22—3142no—
120C22—3141no—
121C22—6282no—
122C22—12562no—
123C22D4×D15711yescharacteristic
124C4—21no—
125C4—3142no—
126C4—3141no—
127C4D4×D15711yescharacteristic
128C4C2×C22⋊D15711yescharacteristic
129C2—21no—
130C2—41no—
131C2—81no—
132C2—6282no—
133C2—6281no—
134C2#1909773911yescharacteristic
subgroupG/H
centerC2#19097739
commutator, cosocleC2×C4×C157C23
FrattiniC2×C4C22×D157
FittingAGL(1,ℤ/8)×C157C2
socleC2×C157#120
hypercenterAGL(1,ℤ/8)D157
hypocenterC157#453
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #19097817C2semidirect
2. #19097797C2semidirect
3. #19097767C2semidirect
4. #19097698C2semidirect
5. #19097697C2semidirect
6. #19097687C2semidirect
7. AGL(1,ℤ/8)×C157C2semidirect
18. #14578938C22semidirect
19. C4×Dic157C22semidirect
21. C2×D4×C157C22semidirect
24. M16×C157C22semidirect
27. Dic314D4semidirect
31. D628D4semidirect
40. Q8×C157D4semidirect
44. D4×C157D4semidirect
67. C157#453semidirect
71. AGL(1,ℤ/8)D157semidirect
85. C2×D4C2×D157semidirect
91. M16C2×D157semidirect
97. Q8C22⋊D157semidirect
108. D4C22⋊D157semidirect