Finite Group Databasebeta

← C24×C22⋊C4×C43 #24982656

Subgroups — C24×C22⋊C4×C43 #24982656

Order 11008.

43678 conjugacy classes of subgroups; only the 15454 normal subgroups are shown.

normal subgroups only

This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 15454 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
1C27×C43C211yesmaximal, characteristic
2C25×C4×C43C212yesmaximal, complemented
3C23×C22⋊C4×C43C2160yesmaximal, direct product factor
4C26×C43—232no—
5C26×C43C4132yescomplemented
6C26×C43C22130yes—
7C26×C43C2211yescharacteristic
8C24×C4×C43—232no—
9C24×C4×C43C22160yescomplemented
10C22×C22⋊C4×C43C221560yesdirect product factor
11C25×C43—2512no—
12C25×C43—2480no—
13C25×C43C2×C4116yes—
14C25×C43C2×C41480yescomplemented
15C25×C43D4132yes—
16C25×C43C231140yes—
17C25×C43C23115yes—
18C23×C4×C43—2480no—
19C23×C4×C43C231280yescomplemented
20C2×C22⋊C4×C43C231960yesdirect product factor
21C24×C43—23840no—
22C24×C43—21120no—
23C24×C43C22⋊C41256yesdirect product factor
24C24×C43C22×C41120yes—
25C24×C43C22×C411120yescomplemented
26C24×C43C2×D41240yes—
27C24×C43C241120yes—
28C24×C43C24135yes—
29C22×C4×C43—21120no—
30C22×C4×C43C241240yescomplemented
31C22⋊C4×C43C241256yesdirect product factor
32C23×C43—24480no—
33C23×C43—2480no—
34C23×C43C2×C22⋊C41960yesdirect product factor
35C23×C43C23×C41140yes—
36C23×C43C23×C41480yescomplemented
37C23×C43C22×D41280yes—
38C23×C43C25116yes—
39C23×C43C25115yes—
40C2×C4×C43—2480no—
41C2×C4×C43C25132yescomplemented
42C24×C22⋊C4C4311yesmaximal, characteristic, direct product factor, Sylow
43C22×C43—232no—
44C22×C43—2960no—
45C22×C43C22×C22⋊C41560yesdirect product factor
46C22×C43C24×C4130yes—
47C22×C43C24×C4132yescomplemented
48C22×C43C23×D4160yes—
49C22×C43C2611yescharacteristic
50C4×C43—232no—
51C27C2×C4311yescharacteristic
52C25×C4C2×C4312yescomplemented
53C23×C22⋊C4C2×C43160yesdirect product factor
54C2×C43—232no—
55C2×C43C23×C22⋊C4160yesdirect product factor
56C2×C43C25×C411yescharacteristic
57C2×C43C24×D412yes—
58C26—232no—
59C26C4×C43132yescomplemented
60C26C22×C43130yes—
61C26C22×C4311yescharacteristic
62C24×C4—232no—
63C24×C4C22×C43160yescomplemented
64C22×C22⋊C4C22×C431560yesdirect product factor
65C43C24×C22⋊C411yescharacteristic, direct product factor, Sylow
66C25—2512no—
67C25—2480no—
68C25C2×C4×C43116yes—
69C25C2×C4×C431480yescomplemented
70C25D4×C43132yes—
71C25C23×C431140yes—
72C25C23×C43115yes—
73C23×C4—2480no—
74C23×C4C23×C431280yescomplemented
75C2×C22⋊C4C23×C431960yesdirect product factor
76C24—23840no—
77C24—21120no—
78C24C22⋊C4×C431256yesdirect product factor
79C24C22×C4×C431120yes—
80C24C22×C4×C4311120yescomplemented
81C24C2×D4×C431240yes—
82C24C24×C431120yes—
83C24C24×C43135yes—
84C22×C4—21120no—
85C22×C4C24×C431240yescomplemented
86C22⋊C4C24×C431256yesdirect product factor
87C23—24480no—
88C23—2480no—
89C23C2×C22⋊C4×C431960yesdirect product factor
90C23C23×C4×C431140yes—
91C23C23×C4×C431480yescomplemented
92C23C22×D4×C431280yes—
93C23C25×C43116yes—
94C23C25×C43115yes—
95C2×C4—2480no—
96C2×C4C25×C43132yescomplemented
97C22—2960no—
98C22—232no—
99C22C22×C22⋊C4×C431560yesdirect product factor
100C22C24×C4×C43130yes—
101C22C24×C4×C43132yescomplemented
102C22C23×D4×C43160yes—
103C22C26×C4311yescharacteristic
104C4—232no—
105C2—232no—
106C2C23×C22⋊C4×C43160yesdirect product factor
107C2C25×C4×C4311yescharacteristic
108C2C24×D4×C4312yes—
subgroupG/H
center, socleC26×C43C22
commutatorC2C25×C4×C43
Frattini, cosocleC22C26×C43
prime radicalC27×C43C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C26×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C43C2semidirect
3. C23×C22⋊C4×C43C2direct (N × H)
5. C26×C43C4semidirect
9. C24×C4×C43C22semidirect
10. C22×C22⋊C4×C43C22direct (N × H)
14. C25×C43C2×C4semidirect
19. C23×C4×C43C23semidirect
20. C2×C22⋊C4×C43C23direct (N × H)
23. C24×C43C22⋊C4direct (N × H)
25. C24×C43C22×C4semidirect
30. C22×C4×C43C24semidirect
31. C22⋊C4×C43C24direct (N × H)
34. C23×C43C2×C22⋊C4direct (N × H)
36. C23×C43C23×C4semidirect
41. C2×C4×C43C25semidirect
42. C24×C22⋊C4C43direct (N × H)
45. C22×C43C22×C22⋊C4direct (N × H)
47. C22×C43C24×C4semidirect
52. C25×C4C2×C43semidirect
53. C23×C22⋊C4C2×C43direct (N × H)
55. C2×C43C23×C22⋊C4direct (N × H)
59. C26C4×C43semidirect
63. C24×C4C22×C43semidirect
64. C22×C22⋊C4C22×C43direct (N × H)
65. C43C24×C22⋊C4direct (N × H)
69. C25C2×C4×C43semidirect
74. C23×C4C23×C43semidirect
75. C2×C22⋊C4C23×C43direct (N × H)
78. C24C22⋊C4×C43direct (N × H)
80. C24C22×C4×C43semidirect
85. C22×C4C24×C43semidirect
86. C22⋊C4C24×C43direct (N × H)
89. C23C2×C22⋊C4×C43direct (N × H)
91. C23C23×C4×C43semidirect
96. C2×C4C25×C43semidirect
99. C22C22×C22⋊C4×C43direct (N × H)
101. C22C24×C4×C43semidirect
106. C2C23×C22⋊C4×C43direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C432
C25×C4×C432
C23×C22⋊C4×C432
C24×C22⋊C443