Finite Group Databasebeta

← C24×C22⋊C4×C37 #22683892

Subgroups — C24×C22⋊C4×C37 #22683892

Order 9472.

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×C37C211yesmaximal, characteristic
2C25×C4×C37C212yesmaximal, complemented
3C23×C22⋊C4×C37C2160yesmaximal, direct product factor
4C26×C37—232no—
5C26×C37C4132yescomplemented
6C26×C37C22130yes—
7C26×C37C2211yescharacteristic
8C24×C4×C37—232no—
9C24×C4×C37C22160yescomplemented
10C22×C22⋊C4×C37C221560yesdirect product factor
11C25×C37—2512no—
12C25×C37—2480no—
13C25×C37C2×C4116yes—
14C25×C37C2×C41480yescomplemented
15C25×C37D4132yes—
16C25×C37C231140yes—
17C25×C37C23115yes—
18C23×C4×C37—2480no—
19C23×C4×C37C231280yescomplemented
20C2×C22⋊C4×C37C231960yesdirect product factor
21C24×C37—23840no—
22C24×C37—21120no—
23C24×C37C22⋊C41256yesdirect product factor
24C24×C37C22×C41120yes—
25C24×C37C22×C411120yescomplemented
26C24×C37C2×D41240yes—
27C24×C37C241120yes—
28C24×C37C24135yes—
29C22×C4×C37—21120no—
30C22×C4×C37C241240yescomplemented
31C22⋊C4×C37C241256yesdirect product factor
32C23×C37—24480no—
33C23×C37—2480no—
34C23×C37C2×C22⋊C41960yesdirect product factor
35C23×C37C23×C41140yes—
36C23×C37C23×C41480yescomplemented
37C23×C37C22×D41280yes—
38C23×C37C25116yes—
39C23×C37C25115yes—
40C2×C4×C37—2480no—
41C2×C4×C37C25132yescomplemented
42C24×C22⋊C4C3711yesmaximal, characteristic, direct product factor, Sylow
43C22×C37—232no—
44C22×C37—2960no—
45C22×C37C22×C22⋊C41560yesdirect product factor
46C22×C37C24×C4130yes—
47C22×C37C24×C4132yescomplemented
48C22×C37C23×D4160yes—
49C22×C37C2611yescharacteristic
50C4×C37—232no—
51C27C2×C3711yescharacteristic
52C25×C4C2×C3712yescomplemented
53C23×C22⋊C4C2×C37160yesdirect product factor
54C2×C37—232no—
55C2×C37C23×C22⋊C4160yesdirect product factor
56C2×C37C25×C411yescharacteristic
57C2×C37C24×D412yes—
58C26—232no—
59C26C4×C37132yescomplemented
60C26C22×C37130yes—
61C26C22×C3711yescharacteristic
62C24×C4—232no—
63C24×C4C22×C37160yescomplemented
64C22×C22⋊C4C22×C371560yesdirect product factor
65C37C24×C22⋊C411yescharacteristic, direct product factor, Sylow
66C25—2512no—
67C25—2480no—
68C25C2×C4×C37116yes—
69C25C2×C4×C371480yescomplemented
70C25D4×C37132yes—
71C25C23×C371140yes—
72C25C23×C37115yes—
73C23×C4—2480no—
74C23×C4C23×C371280yescomplemented
75C2×C22⋊C4C23×C371960yesdirect product factor
76C24—23840no—
77C24—21120no—
78C24C22⋊C4×C371256yesdirect product factor
79C24C22×C4×C371120yes—
80C24C22×C4×C3711120yescomplemented
81C24C2×D4×C371240yes—
82C24C24×C371120yes—
83C24C24×C37135yes—
84C22×C4—21120no—
85C22×C4C24×C371240yescomplemented
86C22⋊C4C24×C371256yesdirect product factor
87C23—2480no—
88C23—24480no—
89C23C2×C22⋊C4×C371960yesdirect product factor
90C23C23×C4×C371140yes—
91C23C23×C4×C371480yescomplemented
92C23C22×D4×C371280yes—
93C23C25×C37116yes—
94C23C25×C37115yes—
95C2×C4—2480no—
96C2×C4C25×C37132yescomplemented
97C22—2960no—
98C22—232no—
99C22C22×C22⋊C4×C371560yesdirect product factor
100C22C24×C4×C37130yes—
101C22C24×C4×C37132yescomplemented
102C22C23×D4×C37160yes—
103C22C26×C3711yescharacteristic
104C4—232no—
105C2—232no—
106C2C23×C22⋊C4×C37160yesdirect product factor
107C2C25×C4×C3711yescharacteristic
108C2C24×D4×C3712yes—
subgroupG/H
center, socleC26×C37C22
commutatorC2C25×C4×C37
Frattini, cosocleC22C26×C37
prime radicalC27×C37C2
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C26×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C25×C4×C37C2semidirect
3. C23×C22⋊C4×C37C2direct (N × H)
5. C26×C37C4semidirect
9. C24×C4×C37C22semidirect
10. C22×C22⋊C4×C37C22direct (N × H)
14. C25×C37C2×C4semidirect
19. C23×C4×C37C23semidirect
20. C2×C22⋊C4×C37C23direct (N × H)
23. C24×C37C22⋊C4direct (N × H)
25. C24×C37C22×C4semidirect
30. C22×C4×C37C24semidirect
31. C22⋊C4×C37C24direct (N × H)
34. C23×C37C2×C22⋊C4direct (N × H)
36. C23×C37C23×C4semidirect
41. C2×C4×C37C25semidirect
42. C24×C22⋊C4C37direct (N × H)
45. C22×C37C22×C22⋊C4direct (N × H)
47. C22×C37C24×C4semidirect
52. C25×C4C2×C37semidirect
53. C23×C22⋊C4C2×C37direct (N × H)
55. C2×C37C23×C22⋊C4direct (N × H)
59. C26C4×C37semidirect
63. C24×C4C22×C37semidirect
64. C22×C22⋊C4C22×C37direct (N × H)
65. C37C24×C22⋊C4direct (N × H)
69. C25C2×C4×C37semidirect
74. C23×C4C23×C37semidirect
75. C2×C22⋊C4C23×C37direct (N × H)
78. C24C22⋊C4×C37direct (N × H)
80. C24C22×C4×C37semidirect
85. C22×C4C24×C37semidirect
86. C22⋊C4C24×C37direct (N × H)
89. C23C2×C22⋊C4×C37direct (N × H)
91. C23C23×C4×C37semidirect
96. C2×C4C25×C37semidirect
99. C22C22×C22⋊C4×C37direct (N × H)
101. C22C24×C4×C37semidirect
106. C2C23×C22⋊C4×C37direct (N × H)

Maximal subgroups

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

subgroupindex
C27×C372
C25×C4×C372
C23×C22⋊C4×C372
C24×C22⋊C437