Finite Group Databasebeta

← C24×D4×D43 #26010473

Subgroups — C24×D4×D43 #26010473

Order 11008.

111198 conjugacy classes of subgroups; only the 34795 normal subgroups are shown.

normal subgroups only

This group has 111198 conjugacy classes of subgroups — too many to draw. Only its 34795 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
1C26×D43C212yesmaximal, complemented
2C24×D172C211yesmaximal, characteristic, complemented
3C24×C22⋊D43C212yesmaximal, complemented
4C23×D4×D43C21120yesmaximal, direct product factor
5C24×C4×D43C211yesmaximal, characteristic, complemented
6C24×D4×C43C211yesmaximal, characteristic, complemented
7C25×D43—264no—
8C25×D43C2211yescharacteristic
9C25×D43C2212yescomplemented
10C25×D43C221120yescomplemented
11C23×D172C22160yescomplemented
12C23×C22⋊D43C221120yescomplemented
13C22×D4×D43C2212240yesdirect product factor
14C24×Dic43C2211yescharacteristic, complemented
15C23×C4×D43C22160yescomplemented
16C26×C43C2212yescomplemented
17C23×D4×C43C22160yescomplemented
18C24×C4×C43C2211yescharacteristic, complemented
19C24×D43—232no—
20C24×D43—21920no—
21C24×D43D4132yesdirect product factor
22C24×D43C23130yes—
23C24×D43C2311120yescomplemented
24C24×D43C23160yescomplemented
25C22×D172C231560yescomplemented
26C22×C22⋊D43C2311120yescomplemented
27C2×D4×D43C2317680yesdirect product factor
28C23×Dic43C23130yescomplemented
29C22×C4×D43C231560yescomplemented
30C25×C43—232no—
31C25×C43C2311yescharacteristic
32C25×C43C23160yescomplemented
33C22×D4×C43C231560yescomplemented
34C23×C4×C43C23130yescomplemented
35C24×C43—2480no—
36C24×C43C2×D4116yescomplemented
37C24×C43C24115yes—
38C24×C43C241280yescomplemented
39C23×D43—2480no—
40C23×D43—28960no—
41C23×D43C2×D41480yesdirect product factor
42C23×D43C241140yes—
43C23×D43C2411920yescomplemented
44C23×D43C241280yescomplemented
45C2×D4×C43C241960yescomplemented
46C22×C4×C43C241140yescomplemented
47C2×C22⋊D43C2411920yescomplemented
48C22×Dic43C241140yescomplemented
49D4×D43C2414096yesdirect product factor
50C2×D172C241960yescomplemented
51C2×C4×D43C241960yescomplemented
52C23×C43—21120no—
53C23×C43C22×D41120yescomplemented
54C23×C43C25135yes—
55C23×C43C251240yescomplemented
56C22×D43—21120no—
57C22×D43—27680no—
58C22×D43C22×D411120yesdirect product factor
59C22×D43C251120yes—
60C22×D43C251512yescomplemented
61C22×D43C251240yescomplemented
62D4×C43C251256yescomplemented
63C2×C4×C43C251120yescomplemented
64C22⋊D43C251512yescomplemented
65C2×Dic43C251120yescomplemented
66D172C251256yescomplemented
67C4×D43C251256yescomplemented
68C25×D4—431nomaximal, Sylow
69C22×C43—2480no—
70C22×C43C23×D41140yescomplemented
71C22×C43C26115yes—
72C22×C43C26132yescomplemented
73C2×D43—2480no—
74C2×D43—21024no—
75C2×D43C23×D41480yesdirect product factor
76C2×D43C26116yes—
77C2×D43C26132yescomplemented
78C4×C43C26116yescomplemented
79Dic43C26116yescomplemented
80C27—432no—
81C24×D4—432no—
82C24×D4—43120no—
83C24×D4—431no—
84C24×D4D4311yescharacteristic, direct product factor
85C25×C4—431no—
86C2×C43—232no—
87C2×C43C24×D4130yescomplemented
88C2×C43C2711yescharacteristic
89D43—232no—
90D43C24×D4132yesdirect product factor
91C26—431no—
92C26—432no—
93C26—43120no—
94C26—8664no—
95C26C2×D4312yescomplemented
96C23×D4—43120no—
97C23×D4—432240no—
98C23×D4—4360no—
99C23×D4C2×D43160yesdirect product factor
100C24×C4—431no—
101C24×C4—4360no—
102C24×C4C2×D4311yescharacteristic, complemented
103C43C25×D411yescharacteristic, complemented, Sylow
104C25—232no—
105C25—4332no—
106C25—4330no—
107C25—4360no—
108C25—431120no—
109C25—861920no—
110C25—8632no—
111C25C22×D4311yescharacteristic
112C25C22×D43160yescomplemented
113C22×D4—431120no—
114C22×D4—437680no—
115C22×D4—43560no—
116C22×D4C22×D431560yesdirect product factor
117C23×C4—4330no—
118C23×C4—43560no—
119C23×C4C22×D43130yescomplemented
120C24—2480no—
121C24—43480no—
122C24—43140no—
123C24—43280no—
124C24—431920no—
125C24—868960no—
126C24—86480no—
127C24D4×D43116yesdirect product factor
128C24C23×D43115yes—
129C24C23×D431280yescomplemented
130C2×D4—431920no—
131C2×D4—434096no—
132C2×D4—43960no—
133C2×D4C23×D431960yesdirect product factor
134C22×C4—43140no—
135C22×C4—43960no—
136C22×C4C23×D431140yescomplemented
137C23—21120no—
138C23—431120no—
139C23—43120no—
140C23—43240no—
141C23—43512no—
142C23—867680no—
143C23—861120no—
144C23C2×D4×D431120yesdirect product factor
145C23C24×D43135yes—
146C23C24×D431240yescomplemented
147D4—43512no—
148D4—43256no—
149D4C24×D431256yesdirect product factor
150C2×C4—43120no—
151C2×C4—43256no—
152C2×C4C24×D431120yescomplemented
153C22—2480no—
154C22—43480no—
155C22—4316no—
156C22—4332no—
157C22—861024no—
158C22—86480no—
159C22C22×D4×D431140yesdirect product factor
160C22C25×D43115yes—
161C22C25×D43132yescomplemented
162C4—4316no—
163C4C25×D43116yescomplemented
164C2—232no—
165C2—4332no—
166C2—8632no—
167C2C23×D4×D43130yesdirect product factor
168C2C26×D4311yescharacteristic
subgroupG/H
centerC25C22×D43
commutator, cosocleC2×C43C27
FrattiniC2C26×D43
FittingC24×D4×C43C2
socleC25×C43C23
hypercenterC24×D4D43
hypocenterC43C25×D4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C26×D43C2semidirect
2. C24×D172C2semidirect
3. C24×C22⋊D43C2semidirect
4. C23×D4×D43C2direct (N × H)
5. C24×C4×D43C2semidirect
6. C24×D4×C43C2semidirect
9. C25×D43C22semidirect
10. C25×D43C22semidirect
11. C23×D172C22semidirect
12. C23×C22⋊D43C22semidirect
13. C22×D4×D43C22direct (N × H)
14. C24×Dic43C22semidirect
15. C23×C4×D43C22semidirect
16. C26×C43C22semidirect
17. C23×D4×C43C22semidirect
18. C24×C4×C43C22semidirect
21. C24×D43D4direct (N × H)
23. C24×D43C23semidirect
24. C24×D43C23semidirect
25. C22×D172C23semidirect
26. C22×C22⋊D43C23semidirect
27. C2×D4×D43C23direct (N × H)
28. C23×Dic43C23semidirect
29. C22×C4×D43C23semidirect
32. C25×C43C23semidirect
33. C22×D4×C43C23semidirect
34. C23×C4×C43C23semidirect
36. C24×C43C2×D4semidirect
38. C24×C43C24semidirect
41. C23×D43C2×D4direct (N × H)
43. C23×D43C24semidirect
44. C23×D43C24semidirect
45. C2×D4×C43C24semidirect
46. C22×C4×C43C24semidirect
47. C2×C22⋊D43C24semidirect
48. C22×Dic43C24semidirect
49. D4×D43C24direct (N × H)
50. C2×D172C24semidirect
51. C2×C4×D43C24semidirect
53. C23×C43C22×D4semidirect
55. C23×C43C25semidirect
58. C22×D43C22×D4direct (N × H)
60. C22×D43C25semidirect
61. C22×D43C25semidirect
62. D4×C43C25semidirect
63. C2×C4×C43C25semidirect
64. C22⋊D43C25semidirect
65. C2×Dic43C25semidirect
66. D172C25semidirect
67. C4×D43C25semidirect
70. C22×C43C23×D4semidirect
72. C22×C43C26semidirect
75. C2×D43C23×D4direct (N × H)
77. C2×D43C26semidirect
78. C4×C43C26semidirect
79. Dic43C26semidirect
84. C24×D4D43direct (N × H)
87. C2×C43C24×D4semidirect
90. D43C24×D4direct (N × H)
95. C26C2×D43semidirect
99. C23×D4C2×D43direct (N × H)
102. C24×C4C2×D43semidirect
103. C43C25×D4semidirect
112. C25C22×D43semidirect
116. C22×D4C22×D43direct (N × H)
119. C23×C4C22×D43semidirect
127. C24D4×D43direct (N × H)
129. C24C23×D43semidirect
133. C2×D4C23×D43direct (N × H)
136. C22×C4C23×D43semidirect
144. C23C2×D4×D43direct (N × H)
146. C23C24×D43semidirect
149. D4C24×D43direct (N × H)
152. C2×C4C24×D43semidirect
159. C22C22×D4×D43direct (N × H)
161. C22C25×D43semidirect
163. C4C25×D43semidirect
167. C2C23×D4×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C26×D432
C24×D1722
C24×C22⋊D432
C23×D4×D432
C24×C4×D432
C24×D4×C432
C25×D443