Finite Group Databasebeta

← C2×#127×D157 #34113406

Subgroups — C2×#127×D157 #34113406

Order 20096.

3000 conjugacy classes of subgroups; only the 661 normal subgroups are shown.

normal subgroups only

This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 661 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
1C22×D4×D157C216yesmaximal, complemented
2C2×#19097768C211yesmaximal, characteristic, complemented
3C2×#19097767C216yesmaximal, complemented
4#127×D157C2116yesmaximal, direct product factor
5C2×C42×D157C211yesmaximal, characteristic, complemented
6C2×#127×C157C211yesmaximal, characteristic, complemented
7C24×D157C2214yes—
8C22×D628C2216yescomplemented
9C22×C22⋊D157C22112yescomplemented
10C2×D4×D157—248no—
11C2×D4×D157C22148yescomplemented
12C22×C4×D157C2213yes—
13#19097768C2218yescomplemented
14#19097767C22148yescomplemented
15C2×C4×Dic157C2213yescomplemented
16C42×D157C2218yescomplemented
17C22×D4×C157C2216yescomplemented
18#127×C157C2218yescomplemented
19C2×C42×C157C2211yescharacteristic, complemented
20C23×D157—248no—
21C23×D157C23116yes—
22C23×D157C2314yes—
23C23×D157C2311yescharacteristic
24C2×D628—224no—
25C2×D628C23124yescomplemented
26C2×C22⋊D157—248no—
27C2×C22⋊D157C23148yescomplemented
28D4×D157—2192no—
29C22×Dic157C2313yes—
30C2×C4×D157D4124yescomplemented
31C2×C4×D157C23112yes—
32C4×Dic157C23112yescomplemented
33C24×C157C2314yes—
34C2×D4×C157—224no—
35C2×D4×C157C23124yescomplemented
36C22×C4×C157C2313yes—
37C42×C157C2314yescomplemented
38C22×D157—224no—
39C22×D157—296no—
40C22×D157—464no—
41C22×D157C2×D4112yes—
42C22×D157C2418yes—
43C22×D157C2412yes—
44D628—248no—
45C22⋊D157—296no—
46C2×Dic157C2×D4112yescomplemented
47C2×Dic157C2416yes—
48C4×D157C2×D4148yescomplemented
49C23×C157—224no—
50C23×C157C2418yes—
51C23×C157C2411yescharacteristic
52D4×C157—248no—
53C2×C4×C157C2×D4112yescomplemented
54C2×C4×C157C2416yes—
55C22×C157—224no—
56C22×C157—416no—
57C22×C157C22×D416yes—
58C22×C157C2511yescharacteristic
59C2×D157—224no—
60C2×D157—416no—
61C2×D157—464no—
62C2×D157#127116yesdirect product factor
63C2×D157C22×D4112yes—
64C4×C157C22×D4112yescomplemented
65Dic157C22×D4112yescomplemented
66C2×C157—48no—
67C2×C157C2×#12714yescomplemented
68C2×C157C23×D413yes—
69D157—48no—
70D157C2×#12718yesdirect product factor
71C157C22×#12711yescharacteristic, complemented, Sylow
72C22×#127—1571nomaximal, Sylow
73C23×D4—1576no—
74C2×#127—1576no—
75C2×#127—15716no—
76C2×#127—1571no—
77C2×#127D15711yescharacteristic, direct product factor
78C22×C42—1571no—
79C25—1574no—
80C22×D4—31448no—
81C22×D4—15712no—
82C22×D4—15748no—
83C22×D4—1576no—
84C22×D4C2×D15716yescomplemented
85C23×C4—1573no—
86#127—15748no—
87#127—1578no—
88#127C2×D15718yesdirect product factor
89C2×C42—1573no—
90C2×C42—1578no—
91C2×C42C2×D15711yescharacteristic, complemented
92C24—31448no—
93C24—15716no—
94C24—1574no—
95C24—1571no—
96C24C22×D15714yes—
97C2×D4—224no—
98C2×D4—314192no—
99C2×D4—31448no—
100C2×D4—31424no—
101C2×D4—15748no—
102C2×D4—15724no—
103C2×D4C22×D157124yescomplemented
104C22×C4—1573no—
105C22×C4—15724no—
106C22×C4—15712no—
107C22×C4C22×D15713yes—
108C42—15712no—
109C42C22×D15714yescomplemented
110C23—224no—
111C23—31496no—
112C23—31424no—
113C23—62864no—
114C23—1578no—
115C23—15712no—
116C23—1572no—
117C23C23×D15718yes—
118C23C23×D15711yescharacteristic
119D4—248no—
120D4—31496no—
121D4—31448no—
122C2×C4—15712no—
123C2×C4—1576no—
124C2×C4—15748no—
125C2×C4D4×D157112yescomplemented
126C2×C4C23×D15716yes—
127C22—224no—
128C22—416no—
129C22—31424no—
130C22—62864no—
131C22—62816no—
132C22—15712no—
133C22—15716no—
134C22C2×D4×D15716yes—
135C22C24×D15711yescharacteristic
136C4—15712no—
137C4C2×D4×D157112yescomplemented
138C2—48no—
139C2—6288no—
140C2—1578no—
141C2#127×D15714yesdirect product factor
142C2C22×D4×D15713yes—
subgroupG/H
centerC23C23×D157
commutator, cosocleC22×C157C25
FrattiniC22C24×D157
FittingC2×#127×C157C2
socleC23×C157C24
hypercenterC2×#127D157
hypocenterC157C22×#127
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C22×D4×D157C2semidirect
2. C2×#19097768C2semidirect
3. C2×#19097767C2semidirect
4. #127×D157C2direct (N × H)
5. C2×C42×D157C2semidirect
6. C2×#127×C157C2semidirect
8. C22×D628C22semidirect
9. C22×C22⋊D157C22semidirect
11. C2×D4×D157C22semidirect
13. #19097768C22semidirect
14. #19097767C22semidirect
15. C2×C4×Dic157C22semidirect
16. C42×D157C22semidirect
17. C22×D4×C157C22semidirect
18. #127×C157C22semidirect
19. C2×C42×C157C22semidirect
25. C2×D628C23semidirect
27. C2×C22⋊D157C23semidirect
30. C2×C4×D157D4semidirect
32. C4×Dic157C23semidirect
35. C2×D4×C157C23semidirect
37. C42×C157C23semidirect
46. C2×Dic157C2×D4semidirect
48. C4×D157C2×D4semidirect
53. C2×C4×C157C2×D4semidirect
62. C2×D157#127direct (N × H)
64. C4×C157C22×D4semidirect
65. Dic157C22×D4semidirect
67. C2×C157C2×#127semidirect
70. D157C2×#127direct (N × H)
71. C157C22×#127semidirect
77. C2×#127D157direct (N × H)
84. C22×D4C2×D157semidirect
88. #127C2×D157direct (N × H)
91. C2×C42C2×D157semidirect
103. C2×D4C22×D157semidirect
109. C42C22×D157semidirect
125. C2×C4D4×D157semidirect
137. C4C2×D4×D157semidirect
141. C2#127×D157direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D4×D1572
C2×#190977682
C2×#190977672
#127×D1572
C2×C42×D1572
C2×#127×C1572
C22×#127157