Finite Group Databasebeta

← C22×#16813591 #28403790

Subgroups — C22×#16813591 #28403790

Order 14464.

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⋊D113C213yesmaximal, complemented
2C2×#16813591C2124yesmaximal, direct product factor
3C22×C22⋊Dic113C213yesmaximal, complemented
4C26×C113C211yesmaximal, characteristic, complemented
5C24×D113C2211yescharacteristic, complemented
6C22×C22⋊D113—224no—
7C22×C22⋊D113C22136yescomplemented
8C23×Dic113C2213yescomplemented
9#16813591C22164yesdirect product factor
10C2×C22⋊Dic113C22136yescomplemented
11C25×C113—224no—
12C25×C113C2213yes—
13C25×C113C22112yescomplemented
14C23×D113—212no—
15C23×D113C2316yescomplemented
16C2×C22⋊D113—2144no—
17C2×C22⋊D113C23148yescomplemented
18C22×Dic113—212no—
19C22×Dic113C23118yescomplemented
20C22⋊Dic113C23148yescomplemented
21C24×C113—2128no—
22C24×C113—224no—
23C24×C113—2144no—
24C24×C113D4124yescomplemented
25C24×C113C23118yes—
26C24×C113C2311yescharacteristic
27C24×C113C23116yescomplemented
28C23×C113—2384no—
29C23×C113—296no—
30C23×C113—272no—
31C23×C113—296no—
32C23×C113C2×D4112yes—
33C23×C113C2×D4172yescomplemented
34C23×C113C24112yes—
35C23×C113C2413yes—
36C22×D113—236no—
37C22×D113—416no—
38C22×D113C2414yescomplemented
39C22⋊D113—296no—
40C2×Dic113—236no—
41C2×Dic113C24112yescomplemented
42C22×C113—2128no—
43C22×C113—2144no—
44C22×C113—224no—
45C22×C113#120116yescomplemented
46C22×C113C22×D4118yes—
47C22×C113C22×D4124yescomplemented
48C22×C113C2511yescharacteristic
49C2×D113—212no—
50C2×D113—424no—
51Dic113—212no—
52C2×C113—224no—
53C2×C113C2×#120112yescomplemented
54C2×C113C23×D413yes—
55D113—44no—
56C22×#120—1131nomaximal, Sylow
57C113C22×#12011yescharacteristic, complemented, Sylow
58C26D11311yescharacteristic, complemented
59C23×D4—1133no—
60C2×#120—11324no—
61C22×C22⋊C4—1133no—
62C25—224no—
63C25—1131no—
64C25C2×D11313yes—
65C25C2×D113112yescomplemented
66C22×D4—11336no—
67C22×D4—22624no—
68C23×C4—1133no—
69#120—11364no—
70C2×C22⋊C4—11336no—
71C24—2128no—
72C24—224no—
73C24—2144no—
74C24—1136no—
75C24—22612no—
76C24C22⋊D113124yescomplemented
77C24C22×D113118yes—
78C24C22×D11311yescharacteristic
79C24C22×D113116yescomplemented
80C2×D4—11348no—
81C2×D4—226144no—
82C22×C4—11318no—
83C22×C4—22612no—
84C22⋊C4—11348no—
85C23—2384no—
86C23—296no—
87C23—272no—
88C23—296no—
89C23—1134no—
90C23—45216no—
91C23—22636no—
92C23C2×C22⋊D113112yes—
93C23C2×C22⋊D113172yescomplemented
94C23C23×D113112yes—
95C23C23×D11313yes—
96D4—22696no—
97C2×C4—11312no—
98C2×C4—22636no—
99C22—2128no—
100C22—2144no—
101C22—224no—
102C22—45224no—
103C22—22612no—
104C22#16813591116yesdirect product factor
105C22C22×C22⋊D113118yes—
106C22C22×C22⋊D113124yescomplemented
107C22C24×D11311yescharacteristic
108C4—22612no—
109C2—224no—
110C2—4524no—
111C2C2×#16813591112yesdirect product factor
112C2C23×C22⋊D11313yes—
subgroupG/H
centerC24C22×D113
commutator, cosocleC22×C113C25
FrattiniC22C24×D113
FittingC26×C113C2
socleC24×C113C23
hypercenterC26D113
hypocenterC113C22×#120
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D113C2semidirect
2. C2×#16813591C2direct (N × H)
3. C22×C22⋊Dic113C2semidirect
4. C26×C113C2semidirect
5. C24×D113C22semidirect
7. C22×C22⋊D113C22semidirect
8. C23×Dic113C22semidirect
9. #16813591C22direct (N × H)
10. C2×C22⋊Dic113C22semidirect
13. C25×C113C22semidirect
15. C23×D113C23semidirect
17. C2×C22⋊D113C23semidirect
19. C22×Dic113C23semidirect
20. C22⋊Dic113C23semidirect
24. C24×C113D4semidirect
27. C24×C113C23semidirect
33. C23×C113C2×D4semidirect
38. C22×D113C24semidirect
41. C2×Dic113C24semidirect
45. C22×C113#120semidirect
47. C22×C113C22×D4semidirect
53. C2×C113C2×#120semidirect
57. C113C22×#120semidirect
58. C26D113semidirect
65. C25C2×D113semidirect
76. C24C22⋊D113semidirect
79. C24C22×D113semidirect
93. C23C2×C22⋊D113semidirect
104. C22#16813591direct (N × H)
106. C22C22×C22⋊D113semidirect
111. C2C2×#16813591direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1132
C2×#168135912
C22×C22⋊Dic1132
C26×C1132
C22×#120113