Finite Group Databasebeta

← C24×C3×C4×D3 #11919147

Subgroups — C24×C3×C4×D3 #11919147

Order 1152.

21785 conjugacy classes of subgroups.

The subgroup lattice has 155 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C25×C3×D3C211yesmaximal, characteristic
2C24×C32×C4C211yesmaximal, characteristic, complemented
3C24×C3×Dic3C211yesmaximal, characteristic, complemented
4C23×C3×C4×D3C2160yesmaximal, direct product factor
5C25×C3×C4—31nomaximal
6C24×C4×D3C311yesmaximal, characteristic, direct product factor
7C25×C32C2211yescharacteristic
8C24×C3×D3C4132yesdirect product factor
9C24×C3×D3C22130yes—
10C23×C32×C4C22130yescomplemented
11C23×C3×Dic3C22130yescomplemented
12C22×C3×C4×D3C221560yesdirect product factor
13C26×C3—31no—
14C25×D3C2×C311yescharacteristic
15C24×C3×C4—21no—
16C24×C3×C4—360no—
17C24×C3×C4—31no—
18C24×C3×C4D311yescharacteristic, direct product factor
19C24×C3×C4C2×C311yescharacteristic, complemented
20C24×Dic3C2×C311yescharacteristic, complemented
21C23×C4×D3C2×C3160yesdirect product factor
22C24×C32C2×C4116yescomplemented
23C24×C32C23115yes—
24C23×C3×D3C2×C41480yesdirect product factor
25C23×C3×D3C231140yes—
26C22×C32×C4C231140yescomplemented
27C22×C3×Dic3C231140yescomplemented
28C2×C3×C4×D3C231960yesdirect product factor
29C25×C4—31noSylow
30C25×C3—21no—
31C25×C3—332no—
32C25×C3—330no—
33C25×C3C2×D311yescharacteristic
34C25×C3C22×C311yescharacteristic
35C24×D3C3×C4132yesdirect product factor
36C24×D3C22×C3130yes—
37C23×C3×C4—230no—
38C23×C3×C4—330no—
39C23×C3×C4—3560no—
40C23×C3×C4C2×D3130yesdirect product factor
41C23×C3×C4C22×C3130yescomplemented
42C23×Dic3C22×C3130yescomplemented
43C22×C4×D3C22×C31560yesdirect product factor
44C23×C32C22×C41120yescomplemented
45C23×C32C24135yes—
46C22×C3×D3C22×C411120yesdirect product factor
47C22×C3×D3C241120yes—
48C2×C32×C4C241120yescomplemented
49C2×C3×Dic3C241120yescomplemented
50C3×C4×D3C241256yesdirect product factor
51C26—31no—
52C24×C4—31no—
53C24×C4—360no—
54C24×C4C3×D311yescharacteristic, direct product factor
55C24×C3—216no—
56C24×C3—215no—
57C24×C3—3480no—
58C24×C3—3140no—
59C24×C3C4×D3116yesdirect product factor
60C24×C3C2×C3×C4116yescomplemented
61C24×C3C22×D3115yes—
62C24×C3C23×C3115yes—
63C23×D3C2×C3×C41480yesdirect product factor
64C23×D3C23×C31140yes—
65C22×C3×C4—2140no—
66C22×C3×C4—3140no—
67C22×C3×C4—3960no—
68C22×C3×C4C22×D31140yesdirect product factor
69C22×C3×C4C23×C31140yescomplemented
70C22×Dic3C23×C31140yescomplemented
71C2×C4×D3C23×C31960yesdirect product factor
72C22×C32C23×C41140yescomplemented
73C22×C32C25115yes—
74C2×C3×D3C23×C41480yesdirect product factor
75C2×C3×D3C25116yes—
76C32×C4C25116yescomplemented
77C3×Dic3C25116yescomplemented
78C25—332no—
79C25—330no—
80C25C2×C3×D311yescharacteristic
81C23×C4—330no—
82C23×C4—3560no—
83C23×C4C2×C3×D3130yesdirect product factor
84C23×C3—235no—
85C23×C3—2120no—
86C23×C3—31120no—
87C23×C3—3120no—
88C23×C3C2×C4×D31120yesdirect product factor
89C23×C3C22×C3×C41120yescomplemented
90C23×C3C23×D3135yes—
91C23×C3C24×C3135yes—
92C22×D3C22×C3×C411120yesdirect product factor
93C22×D3C24×C31120yes—
94C2×C3×C4—2120no—
95C2×C3×C4—3120no—
96C2×C3×C4—3256no—
97C2×C3×C4C23×D31120yesdirect product factor
98C2×C3×C4C24×C31120yescomplemented
99C2×Dic3C24×C31120yescomplemented
100C4×D3C24×C31256yesdirect product factor
101C2×C32C24×C4130yescomplemented
102C2×C32C2611yescharacteristic
103C3×D3C24×C4132yesdirect product factor
104C24—3140no—
105C24—3480no—
106C24C3×C4×D3116yesdirect product factor
107C24C22×C3×D3115yes—
108C22×C4—3140no—
109C22×C4—3960no—
110C22×C4C22×C3×D31140yesdirect product factor
111C22×C3—2140no—
112C22×C3—215no—
113C22×C3—3480no—
114C22×C3—316no—
115C22×C3C22×C4×D31140yesdirect product factor
116C22×C3C23×C3×C41140yescomplemented
117C22×C3C24×D3115yes—
118C22×C3C25×C3115yes—
119C2×D3C23×C3×C41480yesdirect product factor
120C2×D3C25×C3116yes—
121C3×C4—216no—
122C3×C4—316no—
123C3×C4C24×D3116yesdirect product factor
124C3×C4C25×C3116yescomplemented
125Dic3C25×C3116yescomplemented
126C32C25×C411yescharacteristic, complemented, Sylow
127C23—31120no—
128C23—3120no—
129C23C2×C3×C4×D31120yesdirect product factor
130C23C23×C3×D3135yes—
131C2×C4—3120no—
132C2×C4—3256no—
133C2×C4C23×C3×D31120yesdirect product factor
134C2×C3—230no—
135C2×C3—21no—
136C2×C3—332no—
137C2×C3C23×C4×D3130yesdirect product factor
138C2×C3C24×C3×C4130yescomplemented
139C2×C3C25×D311yescharacteristic
140C2×C3C26×C311yescharacteristic
141D3C24×C3×C4132yesdirect product factor
142C22—3480no—
143C22—316no—
144C22C22×C3×C4×D31140yesdirect product factor
145C22C24×C3×D3115yes—
146C4—316no—
147C4C24×C3×D3116yesdirect product factor
148C3—21no—
149C3C24×C4×D311yescharacteristic, direct product factor
150C3C25×C3×C411yescharacteristic, complemented
151C2—332no—
152C2C23×C3×C4×D3130yesdirect product factor
153C2C25×C3×D311yescharacteristic
subgroupG/H
center, hypercenterC24×C3×C4D3
commutator, hypocenterC3C25×C3×C4
FrattiniC2C25×C3×D3
FittingC24×C32×C4C2
socleC25×C32C22
prime radicalC25×C3×D3C2
cosocleC2×C3C26×C3
LCSG ▷ C3
UCSC1 ◁ C24×C3×C4

Complements

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

NH ≅ G/Ntype
2. C24×C32×C4C2semidirect
3. C24×C3×Dic3C2semidirect
4. C23×C3×C4×D3C2direct (N × H)
6. C24×C4×D3C3direct (N × H)
8. C24×C3×D3C4direct (N × H)
10. C23×C32×C4C22semidirect
11. C23×C3×Dic3C22semidirect
12. C22×C3×C4×D3C22direct (N × H)
18. C24×C3×C4D3direct (N × H)
19. C24×C3×C4C2×C3semidirect
20. C24×Dic3C2×C3semidirect
21. C23×C4×D3C2×C3direct (N × H)
22. C24×C32C2×C4semidirect
24. C23×C3×D3C2×C4direct (N × H)
26. C22×C32×C4C23semidirect
27. C22×C3×Dic3C23semidirect
28. C2×C3×C4×D3C23direct (N × H)
35. C24×D3C3×C4direct (N × H)
40. C23×C3×C4C2×D3direct (N × H)
41. C23×C3×C4C22×C3semidirect
42. C23×Dic3C22×C3semidirect
43. C22×C4×D3C22×C3direct (N × H)
44. C23×C32C22×C4semidirect
46. C22×C3×D3C22×C4direct (N × H)
48. C2×C32×C4C24semidirect
49. C2×C3×Dic3C24semidirect
50. C3×C4×D3C24direct (N × H)
54. C24×C4C3×D3direct (N × H)
59. C24×C3C4×D3direct (N × H)
60. C24×C3C2×C3×C4semidirect
63. C23×D3C2×C3×C4direct (N × H)
68. C22×C3×C4C22×D3direct (N × H)
69. C22×C3×C4C23×C3semidirect
70. C22×Dic3C23×C3semidirect
71. C2×C4×D3C23×C3direct (N × H)
72. C22×C32C23×C4semidirect
74. C2×C3×D3C23×C4direct (N × H)
76. C32×C4C25semidirect
77. C3×Dic3C25semidirect
83. C23×C4C2×C3×D3direct (N × H)
88. C23×C3C2×C4×D3direct (N × H)
89. C23×C3C22×C3×C4semidirect
92. C22×D3C22×C3×C4direct (N × H)
97. C2×C3×C4C23×D3direct (N × H)
98. C2×C3×C4C24×C3semidirect
99. C2×Dic3C24×C3semidirect
100. C4×D3C24×C3direct (N × H)
101. C2×C32C24×C4semidirect
103. C3×D3C24×C4direct (N × H)
106. C24C3×C4×D3direct (N × H)
110. C22×C4C22×C3×D3direct (N × H)
115. C22×C3C22×C4×D3direct (N × H)
116. C22×C3C23×C3×C4semidirect
119. C2×D3C23×C3×C4direct (N × H)
123. C3×C4C24×D3direct (N × H)
124. C3×C4C25×C3semidirect
125. Dic3C25×C3semidirect
126. C32C25×C4semidirect
129. C23C2×C3×C4×D3direct (N × H)
133. C2×C4C23×C3×D3direct (N × H)
137. C2×C3C23×C4×D3direct (N × H)
138. C2×C3C24×C3×C4semidirect
141. D3C24×C3×C4direct (N × H)
144. C22C22×C3×C4×D3direct (N × H)
147. C4C24×C3×D3direct (N × H)
149. C3C24×C4×D3direct (N × H)
150. C3C25×C3×C4semidirect
152. C2C23×C3×C4×D3direct (N × H)

Maximal subgroups

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

subgroupindex
C25×C3×D32
C24×C32×C42
C24×C3×Dic32
C23×C3×C4×D32
C25×C3×C43
C24×C4×D33