Finite Group Databasebeta

← C22×#19097740 #34113352

Subgroups — C22×#19097740 #34113352

Order 20096.

4544 conjugacy classes of subgroups; only the 805 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 805 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
1C23×C22⋊D157C213yesmaximal, complemented
2C2×#19097740C2124yesmaximal, direct product factor
3C22×C22⋊Dic157C213yesmaximal, complemented
4C26×C157C211yesmaximal, characteristic, complemented
5C24×D157C2211yescharacteristic, complemented
6C22×C22⋊D157—224no—
7C22×C22⋊D157C22136yescomplemented
8C23×Dic157C2213yescomplemented
9#19097740C22164yesdirect product factor
10C2×C22⋊Dic157C22136yescomplemented
11C25×C157—224no—
12C25×C157C2213yes—
13C25×C157C22112yescomplemented
14C23×D157—212no—
15C23×D157C2316yescomplemented
16C2×C22⋊D157—2144no—
17C2×C22⋊D157C23148yescomplemented
18C22×Dic157—212no—
19C22×Dic157C23118yescomplemented
20C22⋊Dic157C23148yescomplemented
21C24×C157—2128no—
22C24×C157—224no—
23C24×C157—2144no—
24C24×C157D4124yescomplemented
25C24×C157C23118yes—
26C24×C157C2311yescharacteristic
27C24×C157C23116yescomplemented
28C22×D157—236no—
29C22×D157—416no—
30C22×D157C2414yescomplemented
31C22⋊D157—296no—
32C2×Dic157—236no—
33C2×Dic157C24112yescomplemented
34C23×C157—2384no—
35C23×C157—296no—
36C23×C157—272no—
37C23×C157—296no—
38C23×C157C2×D4112yes—
39C23×C157C2×D4172yescomplemented
40C23×C157C24112yes—
41C23×C157C2413yes—
42C22×C157—2128no—
43C22×C157—2144no—
44C22×C157—224no—
45C22×C157#120116yescomplemented
46C22×C157C22×D4118yes—
47C22×C157C22×D4124yescomplemented
48C22×C157C2511yescharacteristic
49C2×D157—212no—
50C2×D157—424no—
51Dic157—212no—
52C2×C157—224no—
53C2×C157C2×#120112yescomplemented
54C2×C157C23×D413yes—
55D157—44no—
56C157C22×#12011yescharacteristic, complemented, Sylow
57C22×#120—1571nomaximal, Sylow
58C26D15711yescharacteristic, complemented
59C23×D4—1573no—
60C2×#120—15724no—
61C22×C22⋊C4—1573no—
62C25—224no—
63C25—1571no—
64C25C2×D15713yes—
65C25C2×D157112yescomplemented
66C22×D4—31424no—
67C22×D4—15736no—
68C23×C4—1573no—
69#120—15764no—
70C2×C22⋊C4—15736no—
71C24—2128no—
72C24—224no—
73C24—2144no—
74C24—31412no—
75C24—1576no—
76C24C22⋊D157124yescomplemented
77C24C22×D157118yes—
78C24C22×D15711yescharacteristic
79C24C22×D157116yescomplemented
80C2×D4—314144no—
81C2×D4—15748no—
82C22×C4—31412no—
83C22×C4—15718no—
84C22⋊C4—15748no—
85C23—2384no—
86C23—296no—
87C23—272no—
88C23—296no—
89C23—31436no—
90C23—62816no—
91C23—1574no—
92C23C2×C22⋊D157112yes—
93C23C2×C22⋊D157172yescomplemented
94C23C23×D157112yes—
95C23C23×D15713yes—
96D4—31496no—
97C2×C4—31436no—
98C2×C4—15712no—
99C22—2128no—
100C22—224no—
101C22—2144no—
102C22—31412no—
103C22—62824no—
104C22#19097740116yesdirect product factor
105C22C22×C22⋊D157118yes—
106C22C22×C22⋊D157124yescomplemented
107C22C24×D15711yescharacteristic
108C4—31412no—
109C2—224no—
110C2—6284no—
111C2C2×#19097740112yesdirect product factor
112C2C23×C22⋊D15713yes—
subgroupG/H
centerC24C22×D157
commutator, cosocleC22×C157C25
FrattiniC22C24×D157
FittingC26×C157C2
socleC24×C157C23
hypercenterC26D157
hypocenterC157C22×#120
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D157C2semidirect
2. C2×#19097740C2direct (N × H)
3. C22×C22⋊Dic157C2semidirect
4. C26×C157C2semidirect
5. C24×D157C22semidirect
7. C22×C22⋊D157C22semidirect
8. C23×Dic157C22semidirect
9. #19097740C22direct (N × H)
10. C2×C22⋊Dic157C22semidirect
13. C25×C157C22semidirect
15. C23×D157C23semidirect
17. C2×C22⋊D157C23semidirect
19. C22×Dic157C23semidirect
20. C22⋊Dic157C23semidirect
24. C24×C157D4semidirect
27. C24×C157C23semidirect
30. C22×D157C24semidirect
33. C2×Dic157C24semidirect
39. C23×C157C2×D4semidirect
45. C22×C157#120semidirect
47. C22×C157C22×D4semidirect
53. C2×C157C2×#120semidirect
56. C157C22×#120semidirect
58. C26D157semidirect
65. C25C2×D157semidirect
76. C24C22⋊D157semidirect
79. C24C22×D157semidirect
93. C23C2×C22⋊D157semidirect
104. C22#19097740direct (N × H)
106. C22C22×C22⋊D157semidirect
111. C2C2×#19097740direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1572
C2×#190977402
C22×C22⋊Dic1572
C26×C1572
C22×#120157