Finite Group Databasebeta

← C2×#11758106 #14519348

Subgroups — C2×#11758106 #14519348

Order 1944.

1052 conjugacy classes of subgroups; only the 484 normal subgroups are shown.

normal subgroups only

This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 484 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
1#11758106C211yesmaximal, 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
9C2×3−1+4—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
193−1+4—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⋊A4C3211yescharacteristic
28C2×C9⋊A4C3218yes—
29C2×C9⋊A4C3218yescomplemented
30C2×C9⋊A4C32116yescomplemented
31C2×C9⋊A4C32124yescomplemented
32C2×C9×A4C32124yescomplemented
33C2×#737—31no—
34C2×#737—31no—
35C2×#737—416no—
36C2×#737—42no—
37C2×#737—48no—
38C2×#737A411yescharacteristic, complemented
39C2×C3×3−1+2—48no—
40C2×C3×3−1+2—44no—
41C2×C3×H(3,𝔽3)—41no—
42C32×A4C2×C3214yes—
43C22×3−1+2—38no—
44C22×3−1+2—38no—
45C22×3−1+2C2×C3218yescomplemented
46C22×H(3,𝔽3)—31no—
47C22×H(3,𝔽3)—31no—
48C22×H(3,𝔽3)C2×C3211yescharacteristic
49C22×C3×C9—34no—
50C22×C3×C9—34no—
51C22×C3×C9C2×C3214yescomplemented
52C22⋊H(3,𝔽3)C2×C3218yes—
53#1094C2×C32116yescomplemented
54C3×C22⋊C9C2×C3218yescomplemented
55C9⋊A4C2×C3211yescharacteristic
56C9⋊A4C2×C3218yes—
57C9⋊A4C2×C3218yescomplemented
58C9⋊A4C2×C32116yescomplemented
59C9⋊A4C2×C32124yescomplemented
60C9×A4C2×C32124yescomplemented
61#737—416no—
62#737—42no—
63#737—48no—
64#737C2×A411yescharacteristic, complemented
65C3×3−1+2—48no—
66C3×3−1+2—44no—
67C3×H(3,𝔽3)—41no—
68C23×C32C3314yes—
69C2×C3×A4—94no—
70C2×C3×A4C3318yes—
71C2×C3×A4C3311yescharacteristic
72C23×C9C3318yes—
73C23×C9C3311yescharacteristic
74C2×C22⋊C9C33116yes—
75C2×C22⋊C9C3312yes—
76C2×C33—44no—
77C2×3−1+2—38no—
78C2×3−1+2—38no—
79C2×3−1+2—416no—
80C2×3−1+2—48no—
81C2×3−1+2—41no—
82C2×3−1+2—424no—
83C2×3−1+2—416no—
84C2×3−1+2—48no—
85C2×3−1+2C3×A418yescomplemented
86C2×H(3,𝔽3)—31no—
87C2×H(3,𝔽3)—31no—
88C2×H(3,𝔽3)—48no—
89C2×H(3,𝔽3)C3×A411yescharacteristic
90C2×C3×C9—34no—
91C2×C3×C9—34no—
92C2×C3×C9—48no—
93C2×C3×C9—424no—
94C2×C3×C9C3×A414yescomplemented
95C22×C32—34no—
96C22×C32—34no—
97C22×C32C2×C3314yes—
98C3×A4—94no—
99C3×A4C2×C3318yes—
100C3×A4C2×C3311yescharacteristic
101C22×C9—31no—
102C22×C9—38no—
103C22×C9—31no—
104C22×C9—38no—
105C22×C9C2×C3318yes—
106C22×C9C2×C3311yescharacteristic
107C22⋊C9C2×C33116yes—
108C22⋊C9C2×C3312yes—
109C33—44no—
1103−1+2—416no—
1113−1+2—48no—
1123−1+2—41no—
1133−1+2—416no—
1143−1+2—424no—
1153−1+2—48no—
1163−1+2C2×C3×A418yescomplemented
117H(3,𝔽3)—48no—
118H(3,𝔽3)C2×C3×A411yescharacteristic
119C3×C9—48no—
120C3×C9—424no—
121C3×C9C2×C3×A414yescomplemented
122C23×C3—34no—
123C23×C3C3411yescharacteristic
124C2×A4—31no—
125C2×A4—38no—
126C2×C32—34no—
127C2×C32—34no—
128C2×C32—48no—
129C2×C32—41no—
130C2×C32—364no—
131C2×C32C32×A414yes—
132C2×C9—31no—
133C2×C9—31no—
134C2×C9—38no—
135C2×C9—38no—
136C2×C9—42no—
137C2×C9—416no—
138C2×C9C32×A418yes—
139C2×C9C32×A411yescharacteristic
140C22×C3—31no—
141C22×C3—31no—
142C22×C3—34no—
143C22×C3—94no—
144C22×C3—94no—
145C22×C3C2×C3411yescharacteristic
146A4—31no—
147A4—38no—
148C32—48no—
149C32—41no—
150C32—364no—
151C32C2×C32×A414yes—
152C9—42no—
153C9—416no—
154C9C2×C32×A418yes—
155C9C2×C32×A411yescharacteristic
156C233−1+411yescharacteristic, complemented, Sylow
157C2×C3—31no—
158C2×C3—31no—
159C2×C3—34no—
160C2×C3—94no—
161C2×C3—94no—
162C2×C3—121no—
163C2×C3—128no—
164C2×C3C33×A411yescharacteristic
165C22—31no—
166C22—31no—
167C22C2×3−1+411yescharacteristic, complemented
168C3—34no—
169C3—121no—
170C3—128no—
171C3C2×C33×A411yescharacteristic
172C2—31no—
173C2—31no—
174C2#1175810611yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C33×A4
commutator, cosocleC22×C3C2×C34
FrattiniC3C2×C33×A4
FittingC23×#737C3
socleC23×C3C34
prime radicalC2×A4×H(3,𝔽3)C3
hypercenterC2×#737A4
hypocenterC22C2×3−1+4
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C3 ◁ C2×#737

Complements

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

NH ≅ G/Ntype
1. #11758106C2direct (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
29. C2×C9⋊A4C32semidirect
30. C2×C9⋊A4C32semidirect
31. C2×C9⋊A4C32semidirect
32. C2×C9×A4C32semidirect
38. C2×#737A4semidirect
45. C22×3−1+2C2×C32semidirect
51. C22×C3×C9C2×C32semidirect
53. #1094C2×C32semidirect
54. C3×C22⋊C9C2×C32semidirect
57. C9⋊A4C2×C32semidirect
58. C9⋊A4C2×C32semidirect
59. C9⋊A4C2×C32semidirect
60. C9×A4C2×C32semidirect
64. #737C2×A4semidirect
85. C2×3−1+2C3×A4semidirect
94. C2×C3×C9C3×A4semidirect
116. 3−1+2C2×C3×A4semidirect
121. C3×C9C2×C3×A4semidirect
156. C233−1+4semidirect
167. C22C2×3−1+4semidirect
174. C2#11758106direct (N × H)

Maximal subgroups

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

subgroupindex
#117581062
C23×#7373
C2×#664403
C2×A4×3−1+23
C2×A4×H(3,𝔽3)3
C2×#664373
C2×#664363
C2×C3×C9⋊A43
C2×3−1+44