Finite Group Databasebeta

← #10593635

Subgroups — #10593635

Order 576.

184 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C4⋊(C3⋊S4)C211yesmaximal, characteristic
2#64259C211yesmaximal, characteristic, complemented
3C3×C8×A4C211yesmaximal, characteristic, complemented
4#5401—33nomaximal
5#5114—31nomaximal
6C2×C3⋊S4—21no—
7C3×C4×A4C2211yescharacteristic
8C3⋊SL(2,ℤ/4)—21no—
9#3744—41nomaximal
10C4⋊S4—33no—
11A4⋊Q8—33no—
12C22×C3×C8D311yescharacteristic, complemented
13#930—31no—
14#924—31no—
15C2×#204—31no—
16C8×A4D313yescomplemented
17#821—31no—
18#817—31no—
19#816—31no—
20C2×C3×A4D411yescharacteristic
21C3⋊S4—41no—
22C4⋊(C3⋊D3)—41no—
23#634—41no—
24C32×C8—41no—
25#465—91noSylow
26C2×S4—63no—
27C22×C3×C4C2×D311yescharacteristic
28C2×#67—61no—
29C2×D12—31no—
30C2×Dic6—31no—
31C4×A4C2×D313yes—
32SL(2,ℤ/4)—63no—
33C2×C3×C8—31no—
34C2×C3×C8—31no—
35#217—61no—
36(C2×D3)⋊C4—61no—
37C4⋊Dic3—31no—
38C4⋊Dic3—31no—
39Dic3⋊C4—61no—
40#204—61no—
41#204—61no—
42#204—123no—
43C2×C3⋊D3—81no—
44C3×A4SD1611yescharacteristic, complemented
45C32×C4—41no—
46C3⋊Dic3—81no—
47C2×SD16—91no—
48C22×C8C3⋊D311yescharacteristic, complemented
49C22⋊Q8—91no—
50#121—91no—
51#106—91no—
52#103—91no—
53#102—91no—
54C23×C3D1211yescharacteristic
55C22×D3—61no—
56C2×A4D1213yes—
57S4—123no—
58C2×C3×C4—31no—
59C2×C3×C4—31no—
60#67—121no—
61#67—121no—
62C2×Dic3—61no—
63C2×Dic3—61no—
64C2×Dic3—61no—
65D12—61no—
66D12—61no—
67D12—123no—
68Dic6—61no—
69Dic6—61no—
70Dic6—123no—
71C3×C8—31no—
72C3×C8—43no—
73C3×C8S411yescharacteristic, complemented
74C2×C32—41no—
75C3⋊D3—161no—
76C2×Q8—91no—
77C2×D4—91no—
78C2×D4—181no—
79C22×C4C2×C3⋊D311yescharacteristic
80SD16—181no—
81SD16—181no—
82C2×C8—31no—
83C2×C8—31no—
84C4⋊C4—91no—
85C4⋊C4—91no—
86C4⋊C4—181no—
87C22⋊C4—181no—
88C22⋊C4—181no—
89C22×C3—31no—
90C22×C3—31no—
91C22×C3#20411yescharacteristic, complemented
92C2×D3—121no—
93C2×D3—121no—
94C2×D3—121no—
95C2×D3—243no—
96A4#20413yescomplemented
97C3×C4—31no—
98C3×C4—43no—
99C3×C4C2×S411yescharacteristic
100Dic3—121no—
101Dic3—121no—
102Dic3—121no—
103Dic3—243no—
104C32—41noSylow
105C23—181no—
106C23C4⋊(C3⋊D3)11yescharacteristic
107Q8—181no—
108Q8—181no—
109D4—181no—
110D4—181no—
111D4—361no—
112D4—361no—
113C2×C4—31no—
114C2×C4—31no—
115C2×C4—181no—
116C2×C4—181no—
117C2×C4—181no—
118C8—31no—
119C8C3⋊S411yescharacteristic, complemented
120C2×C3—31no—
121C2×C3—31no—
122C2×C3—43no—
123C2×C3C4⋊S411yescharacteristic
124D3—241no—
125D3—483no—
126C22—31no—
127C22—31no—
128C22—361no—
129C22—361no—
130C22—361no—
131C22#374411yescharacteristic, complemented
132C4—31no—
133C4—361no—
134C4—361no—
135C4—361no—
136C4C2×C3⋊S411yescharacteristic
137C3—43no—
138C3#540111yescharacteristic, complemented
139C2—31no—
140C2—31no—
141C2—721no—
142C2C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC2C4⋊(C3⋊S4)
commutator, cosocleC3×C4×A4C22
FrattiniC4C2×C3⋊S4
FittingC22×C3×C8D3
socleC23×C3D12
prime radicalC4⋊(C3⋊S4)C2
hypercenterC8C3⋊S4
hypocenterC3×A4SD16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #64259C2semidirect
3. C3×C8×A4C2semidirect
12. C22×C3×C8D3semidirect
16. C8×A4D3semidirect
44. C3×A4SD16semidirect
48. C22×C8C3⋊D3semidirect
73. C3×C8S4semidirect
91. C22×C3#204semidirect
96. A4#204semidirect
119. C8C3⋊S4semidirect
131. C22#3744semidirect
138. C3#5401semidirect

Maximal subgroups

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

subgroupindex
C4⋊(C3⋊S4)2
#642592
C3×C8×A42
#54013
#51143
#37444