Finite Group Databasebeta

← C22×#18012708 #34082326

Subgroups — C22×#18012708 #34082326

Order 19328.

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⋊D151C213yesmaximal, complemented
2C2×#18012708C2124yesmaximal, direct product factor
3C22×C22⋊Dic151C213yesmaximal, complemented
4C26×C151C211yesmaximal, characteristic, complemented
5C24×D151C2211yescharacteristic, complemented
6C22×C22⋊D151—224no—
7C22×C22⋊D151C22136yescomplemented
8C23×Dic151C2213yescomplemented
9#18012708C22164yesdirect product factor
10C2×C22⋊Dic151C22136yescomplemented
11C25×C151—224no—
12C25×C151C2213yes—
13C25×C151C22112yescomplemented
14C23×D151—212no—
15C23×D151C2316yescomplemented
16C2×C22⋊D151—2144no—
17C2×C22⋊D151C23148yescomplemented
18C22×Dic151—212no—
19C22×Dic151C23118yescomplemented
20C22⋊Dic151C23148yescomplemented
21C24×C151—2128no—
22C24×C151—224no—
23C24×C151—2144no—
24C24×C151D4124yescomplemented
25C24×C151C23118yes—
26C24×C151C2311yescharacteristic
27C24×C151C23116yescomplemented
28C22×D151—236no—
29C22×D151—416no—
30C22×D151C2414yescomplemented
31C22⋊D151—296no—
32C2×Dic151—236no—
33C2×Dic151C24112yescomplemented
34C23×C151—2384no—
35C23×C151—296no—
36C23×C151—272no—
37C23×C151—296no—
38C23×C151C2×D4112yes—
39C23×C151C2×D4172yescomplemented
40C23×C151C24112yes—
41C23×C151C2413yes—
42C22×C151—2128no—
43C22×C151—2144no—
44C22×C151—224no—
45C22×C151#120116yescomplemented
46C22×C151C22×D4118yes—
47C22×C151C22×D4124yescomplemented
48C22×C151C2511yescharacteristic
49C2×D151—212no—
50C2×D151—424no—
51Dic151—212no—
52C2×C151—224no—
53C2×C151C2×#120112yescomplemented
54C2×C151C23×D413yes—
55D151—44no—
56C151C22×#12011yescharacteristic, complemented, Sylow
57C22×#120—1511nomaximal, Sylow
58C26D15111yescharacteristic, complemented
59C23×D4—1513no—
60C2×#120—15124no—
61C22×C22⋊C4—1513no—
62C25—224no—
63C25—1511no—
64C25C2×D15113yes—
65C25C2×D151112yescomplemented
66C22×D4—30224no—
67C22×D4—15136no—
68C23×C4—1513no—
69#120—15164no—
70C2×C22⋊C4—15136no—
71C24—2128no—
72C24—224no—
73C24—2144no—
74C24—30212no—
75C24—1516no—
76C24C22⋊D151124yescomplemented
77C24C22×D151118yes—
78C24C22×D15111yescharacteristic
79C24C22×D151116yescomplemented
80C2×D4—302144no—
81C2×D4—15148no—
82C22×C4—30212no—
83C22×C4—15118no—
84C22⋊C4—15148no—
85C23—2384no—
86C23—296no—
87C23—272no—
88C23—296no—
89C23—30236no—
90C23—60416no—
91C23—1514no—
92C23C2×C22⋊D151112yes—
93C23C2×C22⋊D151172yescomplemented
94C23C23×D151112yes—
95C23C23×D15113yes—
96D4—30296no—
97C2×C4—30236no—
98C2×C4—15112no—
99C22—2128no—
100C22—224no—
101C22—2144no—
102C22—30212no—
103C22—60424no—
104C22#18012708116yesdirect product factor
105C22C22×C22⋊D151118yes—
106C22C22×C22⋊D151124yescomplemented
107C22C24×D15111yescharacteristic
108C4—30212no—
109C2—224no—
110C2—6044no—
111C2C2×#18012708112yesdirect product factor
112C2C23×C22⋊D15113yes—
subgroupG/H
centerC24C22×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC26×C151C2
socleC24×C151C23
hypercenterC26D151
hypocenterC151C22×#120
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C24 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C23×C22⋊D151C2semidirect
2. C2×#18012708C2direct (N × H)
3. C22×C22⋊Dic151C2semidirect
4. C26×C151C2semidirect
5. C24×D151C22semidirect
7. C22×C22⋊D151C22semidirect
8. C23×Dic151C22semidirect
9. #18012708C22direct (N × H)
10. C2×C22⋊Dic151C22semidirect
13. C25×C151C22semidirect
15. C23×D151C23semidirect
17. C2×C22⋊D151C23semidirect
19. C22×Dic151C23semidirect
20. C22⋊Dic151C23semidirect
24. C24×C151D4semidirect
27. C24×C151C23semidirect
30. C22×D151C24semidirect
33. C2×Dic151C24semidirect
39. C23×C151C2×D4semidirect
45. C22×C151#120semidirect
47. C22×C151C22×D4semidirect
53. C2×C151C2×#120semidirect
56. C151C22×#120semidirect
58. C26D151semidirect
65. C25C2×D151semidirect
76. C24C22⋊D151semidirect
79. C24C22×D151semidirect
93. C23C2×C22⋊D151semidirect
104. C22#18012708direct (N × H)
106. C22C22×C22⋊D151semidirect
111. C2C2×#18012708direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C22⋊D1512
C2×#180127082
C22×C22⋊Dic1512
C26×C1512
C22×#120151