Finite Group Databasebeta

← C23×D4×D109 #28377823

Subgroups — C23×D4×D109 #28377823

Order 13952.

10552 conjugacy classes of subgroups; only the 3557 normal subgroups are shown.

normal subgroups only

This group has 10552 conjugacy classes of subgroups — too many to draw. Only its 3557 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
1C25×D109C212yesmaximal, complemented
2C23×D436C211yesmaximal, characteristic, complemented
3C23×C22⋊D109C212yesmaximal, complemented
4C22×D4×D109C2156yesmaximal, direct product factor
5C23×C4×D109C211yesmaximal, characteristic, complemented
6C23×D4×C109C211yesmaximal, characteristic, complemented
7C24×D109—232no—
8C24×D109C2211yescharacteristic
9C24×D109C2212yescomplemented
10C24×D109C22156yescomplemented
11C22×D436C22128yescomplemented
12C22×C22⋊D109C22156yescomplemented
13C2×D4×D109C221448yesdirect product factor
14C23×Dic109C2211yescharacteristic, complemented
15C22×C4×D109C22128yescomplemented
16C25×C109C2212yescomplemented
17C22×D4×C109C22128yescomplemented
18C23×C4×C109C2211yescharacteristic, complemented
19C23×D109—216no—
20C23×D109—2448no—
21C23×D109D4116yesdirect product factor
22C23×D109C23114yes—
23C23×D109C231224yescomplemented
24C23×D109C23128yescomplemented
25C2×D436C231112yescomplemented
26C2×C22⋊D109C231224yescomplemented
27D4×D109C231512yesdirect product factor
28C22×Dic109C23114yescomplemented
29C2×C4×D109C231112yescomplemented
30C24×C109—216no—
31C24×C109C2311yescharacteristic
32C24×C109C23128yescomplemented
33C2×D4×C109C231112yescomplemented
34C22×C4×C109C23114yescomplemented
35C23×C109—2112no—
36C23×C109C2×D418yescomplemented
37C23×C109C2417yes—
38C23×C109C24156yescomplemented
39C22×D109—2112no—
40C22×D109—2896no—
41C22×D109C2×D41112yesdirect product factor
42C22×D109C24128yes—
43C22×D109C241128yescomplemented
44C22×D109C24156yescomplemented
45D4×C109C24164yescomplemented
46C2×C4×C109C24128yescomplemented
47C22⋊D109C241128yescomplemented
48C2×Dic109C24128yescomplemented
49D436C24164yescomplemented
50C4×D109C24164yescomplemented
51C22×C109—2112no—
52C22×C109C22×D4128yescomplemented
53C22×C109C2517yes—
54C22×C109C25116yescomplemented
55C2×D109—2112no—
56C2×D109—2256no—
57C2×D109C22×D41112yesdirect product factor
58C2×D109C2518yes—
59C2×D109C25116yescomplemented
60C4×C109C2518yescomplemented
61Dic109C2518yescomplemented
62C2×C109—216no—
63C2×C109C23×D4114yescomplemented
64C2×C109C2611yescharacteristic
65D109—216no—
66D109C23×D4116yesdirect product factor
67C24×D4—1091nomaximal, Sylow
68C109C24×D411yescharacteristic, complemented, Sylow
69C26—1092no—
70C23×D4—1092no—
71C23×D4—10956no—
72C23×D4—1091no—
73C23×D4D10911yescharacteristic, direct product factor
74C24×C4—1091no—
75C25—1091no—
76C25—1092no—
77C25—10956no—
78C25—21832no—
79C25C2×D10912yescomplemented
80C22×D4—10956no—
81C22×D4—109448no—
82C22×D4—10928no—
83C22×D4C2×D109128yesdirect product factor
84C23×C4—1091no—
85C23×C4—10928no—
86C23×C4C2×D10911yescharacteristic, complemented
87C24—216no—
88C24—10916no—
89C24—10914no—
90C24—10928no—
91C24—109224no—
92C24—218448no—
93C24—21816no—
94C24C22×D10911yescharacteristic
95C24C22×D109128yescomplemented
96C2×D4—109224no—
97C2×D4—109512no—
98C2×D4—109112no—
99C2×D4C22×D1091112yesdirect product factor
100C22×C4—10914no—
101C22×C4—109112no—
102C22×C4C22×D109114yescomplemented
103C23—2112no—
104C23—109112no—
105C23—10928no—
106C23—10956no—
107C23—109128no—
108C23—218896no—
109C23—218112no—
110C23D4×D10918yesdirect product factor
111C23C23×D10917yes—
112C23C23×D109156yescomplemented
113D4—109128no—
114D4—10964no—
115D4C23×D109164yesdirect product factor
116C2×C4—10928no—
117C2×C4—10964no—
118C2×C4C23×D109128yescomplemented
119C22—2112no—
120C22—109112no—
121C22—1098no—
122C22—10916no—
123C22—218256no—
124C22—218112no—
125C22C2×D4×D109128yesdirect product factor
126C22C24×D10917yes—
127C22C24×D109116yescomplemented
128C4—1098no—
129C4C24×D10918yescomplemented
130C2—216no—
131C2—10916no—
132C2—21816no—
133C2C22×D4×D109114yesdirect product factor
134C2C25×D10911yescharacteristic
subgroupG/H
centerC24C22×D109
commutator, cosocleC2×C109C26
FrattiniC2C25×D109
FittingC23×D4×C109C2
socleC24×C109C23
hypercenterC23×D4D109
hypocenterC109C24×D4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C24 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C25×D109C2semidirect
2. C23×D436C2semidirect
3. C23×C22⋊D109C2semidirect
4. C22×D4×D109C2direct (N × H)
5. C23×C4×D109C2semidirect
6. C23×D4×C109C2semidirect
9. C24×D109C22semidirect
10. C24×D109C22semidirect
11. C22×D436C22semidirect
12. C22×C22⋊D109C22semidirect
13. C2×D4×D109C22direct (N × H)
14. C23×Dic109C22semidirect
15. C22×C4×D109C22semidirect
16. C25×C109C22semidirect
17. C22×D4×C109C22semidirect
18. C23×C4×C109C22semidirect
21. C23×D109D4direct (N × H)
23. C23×D109C23semidirect
24. C23×D109C23semidirect
25. C2×D436C23semidirect
26. C2×C22⋊D109C23semidirect
27. D4×D109C23direct (N × H)
28. C22×Dic109C23semidirect
29. C2×C4×D109C23semidirect
32. C24×C109C23semidirect
33. C2×D4×C109C23semidirect
34. C22×C4×C109C23semidirect
36. C23×C109C2×D4semidirect
38. C23×C109C24semidirect
41. C22×D109C2×D4direct (N × H)
43. C22×D109C24semidirect
44. C22×D109C24semidirect
45. D4×C109C24semidirect
46. C2×C4×C109C24semidirect
47. C22⋊D109C24semidirect
48. C2×Dic109C24semidirect
49. D436C24semidirect
50. C4×D109C24semidirect
52. C22×C109C22×D4semidirect
54. C22×C109C25semidirect
57. C2×D109C22×D4direct (N × H)
59. C2×D109C25semidirect
60. C4×C109C25semidirect
61. Dic109C25semidirect
63. C2×C109C23×D4semidirect
66. D109C23×D4direct (N × H)
68. C109C24×D4semidirect
73. C23×D4D109direct (N × H)
79. C25C2×D109semidirect
83. C22×D4C2×D109direct (N × H)
86. C23×C4C2×D109semidirect
95. C24C22×D109semidirect
99. C2×D4C22×D109direct (N × H)
102. C22×C4C22×D109semidirect
110. C23D4×D109direct (N × H)
112. C23C23×D109semidirect
115. D4C23×D109direct (N × H)
118. C2×C4C23×D109semidirect
125. C22C2×D4×D109direct (N × H)
127. C22C24×D109semidirect
129. C4C24×D109semidirect
133. C2C22×D4×D109direct (N × H)

Maximal subgroups

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

subgroupindex
C25×D1092
C23×D4362
C23×C22⋊D1092
C22×D4×D1092
C23×C4×D1092
C23×D4×C1092
C24×D4109