Finite Group Databasebeta

← #23758264

Subgroups — #23758264

Order 10048.

162 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D157⋊M16C211yesmaximal, characteristic, complemented
2C2×C4⋊#10597845C211yesmaximal, characteristic, complemented
3#19097834C212yesmaximal, complemented
4#19097833C212yesmaximal, complemented
5#41×D157C211yesmaximal, characteristic
6C22×#10597845—21no—
7#14578964—21no—
8#14578963—21no—
9D157⋊C8C2212yes—
10C4⋊#10597845—21no—
11C4⋊#10597845C2212yes—
12#14578955C411yescharacteristic, complemented
13#14578954—21no—
14#14578954C411yescharacteristic, complemented
15#14578953—21no—
16#14578953C411yescharacteristic, complemented
17Q8×D157C2211yescharacteristic
18D4×D157—21no—
19D4×D157C2211yescharacteristic
20C2×C4×D157—21no—
21C2×C4×D157C2211yescharacteristic
22#41×C157C411yescharacteristic, complemented
23C2×#10597845—22no—
24C2×#10597845—42no—
25#11929441—22no—
26C22×D157—21no—
27C22×D157D411yescharacteristic
28Dic314—21no—
29Dic314C2×C411yescharacteristic, complemented
30D628—21no—
31D628C2×C411yescharacteristic, complemented
32C22⋊D157—21no—
33C22⋊D157—21no—
34C22⋊D157—21no—
35C2×Dic157—21no—
36C2×Dic157D411yescharacteristic
37C4×D157—21no—
38C4×D157—21no—
39C4×D157—21no—
40C4×D157C2×C411yescharacteristic
41C4×D157D411yescharacteristic
42C4×D157D411yescharacteristic
43C4×D157C2311yescharacteristic
44Q8×C157C2×C411yescharacteristic, complemented
45D4×C157—21no—
46D4×C157C2×C411yescharacteristic, complemented
47C2×C4×C157—21no—
48C2×C4×C157C2×C411yescharacteristic
49C22×C157—21no—
50C22×C157C22⋊C411yescharacteristic
51C2×D157—21no—
52C2×D157—21no—
53C2×D157—21no—
54C2×D157—41no—
55C2×D157—41no—
56C2×D157C22⋊C411yescharacteristic
57C2×D157C2×D411yescharacteristic
58#10597845—42no—
59C4×C157—21no—
60C4×C157C22⋊C411yescharacteristic
61C4×C157C22×C411yescharacteristic
62Dic157—21no—
63Dic157C22⋊C411yescharacteristic
64Dic157C2×D411yescharacteristic
65C2×C157—21no—
66C2×C157—41no—
67C2×C157C2×C22⋊C411yescharacteristic
68D157—21no—
69D157—41no—
70D157AGL(1,ℤ/8)11yescharacteristic
71D157#13711yescharacteristic
72C157#41711yescharacteristic, complemented, Sylow
73#417—1571nomaximal, Sylow
74C2×#41—1571no—
75C2×M16—1571no—
76C2×C4⋊C4—1571no—
77#103—1572no—
78#102—1572no—
79#41—3141no—
80#41—3141no—
81#41—1571no—
82#41—1571no—
83#41—1571no—
84#41#1059784511yescharacteristic, complemented
85C2×Q8—1571no—
86C2×D4—3141no—
87C2×D4—1571no—
88C22×C4—3141no—
89C22×C4—3141no—
90C22×C4—1571no—
91M16—3141no—
92M16—3141no—
93C2×C8—1572no—
94C4⋊C4—3141no—
95C4⋊C4—1572no—
96C23—3141no—
97C23—1571no—
98Q8—3141no—
99Q8—1571no—
100Q8C2×#1059784511yescharacteristic, complemented
101D4—21no—
102D4—3141no—
103D4—3141no—
104D4—3141no—
105D4—3141no—
106D4—1571no—
107D4C2×#1059784511yescharacteristic, complemented
108C2×C4—21no—
109C2×C4—3141no—
110C2×C4—3141no—
111C2×C4—3141no—
112C2×C4—3141no—
113C2×C4—3142no—
114C2×C4—6282no—
115C2×C4—1571no—
116C2×C4—1571no—
117C2×C4—1571no—
118C2×C4—1571no—
119C2×C4—1571no—
120C2×C4C2×#1059784511yescharacteristic
121C8—3142no—
122C22—21no—
123C22—3141no—
124C22—3141no—
125C22—3141no—
126C22—6281no—
127C22—6281no—
128C22—1571no—
129C22—1571no—
130C22C22⋊#1059784511yescharacteristic
131C4—21no—
132C4—3141no—
133C4—6282no—
134C4—1571no—
135C4—1571no—
136C4C22⋊#1059784511yescharacteristic
137C4C22×#1059784511yescharacteristic
138C2—21no—
139C2—41no—
140C2—3141no—
141C2—6281no—
142C2—1571no—
143C2—1571no—
144C2C2×C22⋊#1059784511yescharacteristic
subgroupG/H
centerC2C2×C22⋊#10597845
commutatorC4×C157C22×C4
FrattiniC4C22×#10597845
Fitting#41×C157C4
socleC2×C157C2×C22⋊C4
prime radical#41×D157C2
cosocleC4×D157C23
hypercenter#41#10597845
hypocenterC157#417
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. D157⋊M16C2semidirect
2. C2×C4⋊#10597845C2semidirect
3. #19097834C2semidirect
4. #19097833C2semidirect
12. #14578955C4semidirect
14. #14578954C4semidirect
16. #14578953C4semidirect
22. #41×C157C4semidirect
29. Dic314C2×C4semidirect
31. D628C2×C4semidirect
44. Q8×C157C2×C4semidirect
46. D4×C157C2×C4semidirect
72. C157#417semidirect
84. #41#10597845semidirect
100. Q8C2×#10597845semidirect
107. D4C2×#10597845semidirect