Finite Group Databasebeta

← C2×A4×#737 #14519347

Subgroups — C2×A4×#737 #14519347

Order 1944.

1092 conjugacy classes of subgroups; only the 490 normal subgroups are shown.

normal subgroups only

This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 490 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
1A4×#737C211yesmaximal, characteristic, direct product factor
2C23×#737C311yesmaximal, characteristic, complemented
3C2×#66440C3116yesmaximal, complemented
4C2×A4×3−1+2C318yesmaximal, complemented
5C2×A4×H(3,𝔽3)C311yesmaximal, characteristic
6C2×#66437C312yesmaximal, complemented
7C2×#66436C318yesmaximal, complemented
8C2×C3×C9×A4C314yesmaximal, complemented
9C2×C3×#737—41nomaximal
10C22×#737—31no—
11C22×#737—31no—
12C22×#737C2×C311yescharacteristic, complemented
13#66440C2×C3116yescomplemented
14A4×3−1+2C2×C318yescomplemented
15A4×H(3,𝔽3)C2×C311yescharacteristic
16#66437C2×C312yescomplemented
17#66436C2×C318yescomplemented
18C3×C9×A4C2×C314yescomplemented
19C3×#737—41noSylow
20C2×C32×A4C3214yes—
21C23×3−1+2C3218yescomplemented
22C23×H(3,𝔽3)C3211yescharacteristic
23C23×C3×C9C3214yescomplemented
24C2×C22⋊H(3,𝔽3)C3218yes—
25C2×#1094C32116yescomplemented
26C2×C3×C22⋊C9C3218yescomplemented
27C2×C9⋊A4C32148yescomplemented
28C2×C9×A4C3211yescharacteristic
29C2×C9×A4C3218yes—
30C2×C9×A4C3218yescomplemented
31C2×C9×A4C32116yescomplemented
32C2×#737—31no—
33C2×#737—31no—
34C2×#737—416no—
35C2×#737—42no—
36C2×#737—48no—
37C2×#737A411yescharacteristic, direct product factor
38C2×C3×3−1+2—48no—
39C2×C3×H(3,𝔽3)—41no—
40C2×C32×C9—44no—
41C32×A4C2×C3214yes—
42C22×3−1+2—38no—
43C22×3−1+2—38no—
44C22×3−1+2C2×C3218yescomplemented
45C22×H(3,𝔽3)—31no—
46C22×H(3,𝔽3)—31no—
47C22×H(3,𝔽3)C2×C3211yescharacteristic
48C22×C3×C9—34no—
49C22×C3×C9—34no—
50C22×C3×C9C2×C3214yescomplemented
51C22⋊H(3,𝔽3)C2×C3218yes—
52#1094C2×C32116yescomplemented
53C3×C22⋊C9C2×C3218yescomplemented
54C9⋊A4C2×C32148yescomplemented
55C9×A4C2×C3211yescharacteristic
56C9×A4C2×C3218yes—
57C9×A4C2×C3218yescomplemented
58C9×A4C2×C32116yescomplemented
59#737—416no—
60#737—42no—
61#737—48no—
62#737C2×A411yescharacteristic, direct product factor
63C3×3−1+2—48no—
64C3×H(3,𝔽3)—41no—
65C32×C9—44no—
66C23×C32C3314yes—
67C2×C3×A4—312no—
68C2×C3×A4C3318yes—
69C2×C3×A4C3311yescharacteristic
70C23×C9C3311yescharacteristic
71C23×C9C3318yes—
72C2×C22⋊C9C3312yes—
73C2×C22⋊C9C33116yes—
74C2×C33—44no—
75C2×3−1+2—38no—
76C2×3−1+2—38no—
77C2×3−1+2—416no—
78C2×3−1+2—448no—
79C2×3−1+2C3×A418yescomplemented
80C2×H(3,𝔽3)—31no—
81C2×H(3,𝔽3)—31no—
82C2×H(3,𝔽3)—48no—
83C2×H(3,𝔽3)C3×A411yescharacteristic
84C2×C3×C9—34no—
85C2×C3×C9—34no—
86C2×C3×C9—48no—
87C2×C3×C9—48no—
88C2×C3×C9—416no—
89C2×C3×C9—41no—
90C2×C3×C9—48no—
91C2×C3×C9C3×A414yescomplemented
92C22×C32—34no—
93C22×C32—34no—
94C22×C32C2×C3314yes—
95C3×A4—312no—
96C3×A4C2×C3318yes—
97C3×A4C2×C3311yescharacteristic
98C22×C9—31no—
99C22×C9—38no—
100C22×C9—38no—
101C22×C9—31no—
102C22×C9C2×C3311yescharacteristic
103C22×C9C2×C3318yes—
104C22⋊C9C2×C3312yes—
105C22⋊C9C2×C33116yes—
106C33—44no—
1073−1+2—416no—
1083−1+2—448no—
1093−1+2C2×C3×A418yescomplemented
110H(3,𝔽3)—48no—
111H(3,𝔽3)C2×C3×A411yescharacteristic
112C3×C9—48no—
113C3×C9—41no—
114C3×C9—48no—
115C3×C9—416no—
116C3×C9—48no—
117C3×C9C2×C3×A414yescomplemented
118C23×C3—34no—
119C23×C3C3411yescharacteristic
120C2×A4—38no—
121C2×A4#73713yesdirect product factor
122C2×C32—34no—
123C2×C32—34no—
124C2×C32—41no—
125C2×C32—48no—
126C2×C32—1212no—
127C2×C32C32×A414yes—
128C2×C9—31no—
129C2×C9—31no—
130C2×C9—38no—
131C2×C9—38no—
132C2×C9—42no—
133C2×C9—416no—
134C2×C9C32×A418yes—
135C2×C9C32×A411yescharacteristic
136C22×C3—31no—
137C22×C3—31no—
138C22×C3—34no—
139C22×C3—94no—
140C22×C3—94no—
141C22×C3C2×C3411yescharacteristic
142A4—38no—
143A4C2×#73713yesdirect product factor
144C32—41no—
145C32—48no—
146C32—1212no—
147C32C2×C32×A414yes—
148C9—42no—
149C9—416no—
150C9C2×C32×A418yes—
151C9C2×C32×A411yescharacteristic
152C23C3×#73711yescharacteristic, complemented, Sylow
153C2×C3—31no—
154C2×C3—31no—
155C2×C3—34no—
156C2×C3—43no—
157C2×C3—94no—
158C2×C3—94no—
159C2×C3—128no—
160C2×C3C33×A411yescharacteristic
161C22—31no—
162C22—31no—
163C22C2×C3×#73711yescharacteristic, complemented
164C3—34no—
165C3—43no—
166C3—128no—
167C3C2×C33×A411yescharacteristic
168C2—31no—
169C2—31no—
170C2A4×#73711yescharacteristic, direct product factor
subgroupG/H
centerC2×C9C32×A4
commutator, cosocleC22×C3C2×C34
FrattiniC3C2×C33×A4
FittingC23×#737C3
socleC23×C3C34
prime radicalC2×A4×H(3,𝔽3)C3
hypercenterC2×#737A4
hypocenterC22C2×C3×#737
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C9 ◁ C2×#737

Complements

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

NH ≅ G/Ntype
1. A4×#737C2direct (N × H)
2. C23×#737C3semidirect
3. C2×#66440C3semidirect
4. C2×A4×3−1+2C3semidirect
6. C2×#66437C3semidirect
7. C2×#66436C3semidirect
8. C2×C3×C9×A4C3semidirect
12. C22×#737C2×C3semidirect
13. #66440C2×C3semidirect
14. A4×3−1+2C2×C3semidirect
16. #66437C2×C3semidirect
17. #66436C2×C3semidirect
18. C3×C9×A4C2×C3semidirect
21. C23×3−1+2C32semidirect
23. C23×C3×C9C32semidirect
25. C2×#1094C32semidirect
26. C2×C3×C22⋊C9C32semidirect
27. C2×C9⋊A4C32semidirect
30. C2×C9×A4C32semidirect
31. C2×C9×A4C32semidirect
37. C2×#737A4direct (N × H)
44. C22×3−1+2C2×C32semidirect
50. C22×C3×C9C2×C32semidirect
52. #1094C2×C32semidirect
53. C3×C22⋊C9C2×C32semidirect
54. C9⋊A4C2×C32semidirect
57. C9×A4C2×C32semidirect
58. C9×A4C2×C32semidirect
62. #737C2×A4direct (N × H)
79. C2×3−1+2C3×A4semidirect
91. C2×C3×C9C3×A4semidirect
109. 3−1+2C2×C3×A4semidirect
117. C3×C9C2×C3×A4semidirect
121. C2×A4#737direct (N × H)
143. A4C2×#737direct (N × H)
152. C23C3×#737semidirect
163. C22C2×C3×#737semidirect
170. C2A4×#737direct (N × H)

Maximal subgroups

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

subgroupindex
A4×#7372
C23×#7373
C2×#664403
C2×A4×3−1+23
C2×A4×H(3,𝔽3)3
C2×#664373
C2×#664363
C2×C3×C9×A43
C2×C3×#7374