Finite Group Databasebeta

← #10592562

Subgroups — #10592562

Order 576.

342 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 87 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#64104C211yesmaximal, characteristic
2C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×#106C211yesmaximal, characteristic, complemented
4#63648C211yesmaximal, characteristic, complemented
5#63647C211yesmaximal, characteristic, complemented
6#63636C211yesmaximal, characteristic, complemented
7#63635C211yesmaximal, characteristic, complemented
8#4863—34nomaximal
9C2×C4⋊(C3⋊D3)—21no—
10C2×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C4×C3⋊D3—21no—
12C2×C4×C3⋊D3C2211yescharacteristic
13C2×C32×C8C2211yescharacteristic
14C32×C4⋊C4C2211yescharacteristic
15C32×C4⋊C4C2211yescharacteristic
16#3752—21no—
17C4⋊(C3⋊Dic3)C2211yescharacteristic
18#3750—21no—
19C2×C3⋊(C3⋊C8)C2211yescharacteristic
20#895—34no—
21D3×C4⋊C4—34no—
22C3×#106D314yescomplemented
23#821—34no—
24(C2×D3)⋊C8—34no—
25#809—34no—
26#808—34no—
27C22×C3⋊D3—21no—
28C22×C3⋊D3D411yescharacteristic
29C2×C32×C4—21no—
30C2×C32×C4—21no—
31C2×C32×C4C2311yescharacteristic
32C2×C3⋊Dic3—21no—
33C2×C3⋊Dic3D411yescharacteristic
34C4⋊(C3⋊D3)—21no—
35C4⋊(C3⋊D3)—21no—
36C4⋊(C3⋊D3)—42no—
37C4×C3⋊D3—21no—
38C4×C3⋊D3—21no—
39C4×C3⋊D3—42no—
40C32×C8—21no—
41C3⋊(C3⋊C8)—21no—
42#481—91noSylow
43C2×D12—34no—
44C2×D12—64no—
45C2×C4×D3—34no—
46C2×C4×D3—64no—
47C2×C3×C8C2×D314yes—
48C3×C4⋊C4C2×D314yes—
49C3×C4⋊C4C2×D314yes—
50(C2×D3)⋊C4—64no—
51C4⋊Dic3—34no—
52Dic3⋊C4—64no—
53C2×C3⋊C8—34no—
54C22×C32C2×D411yescharacteristic
55C2×C3⋊D3—21no—
56C2×C3⋊D3—21no—
57C2×C3⋊D3—41no—
58C2×C3⋊D3—41no—
59C2×C3⋊D3—41no—
60C2×C3⋊D3SD1612yes—
61C32×C4—41no—
62C32×C4—41no—
63C32×C4#4111yescharacteristic
64C32×C4#4111yescharacteristic
65C3⋊Dic3—21no—
66C3⋊Dic3—41no—
67#121—91no—
68C2×C4⋊C4—91no—
69#106—91no—
70#106C3⋊D311yescharacteristic, complemented
71#102—91no—
72#102—91no—
73C22⋊C8—91no—
74C22×D3—34no—
75C22×D3—64no—
76C2×C3×C4—24no—
77C2×C3×C4—24no—
78C2×C3×C4C22×D314yes—
79C2×Dic3—34no—
80C2×Dic3—64no—
81D12—64no—
82D12—64no—
83D12—128no—
84C4×D3—64no—
85C4×D3—64no—
86C4×D3—128no—
87C3×C8—24no—
88C3⋊C8—64no—
89C2×C32#12311yescharacteristic
90C2×C32C2×SD1611yescharacteristic
91C2×C32AGL(1,ℤ/8)11yescharacteristic
92C3⋊D3—22no—
93C3⋊D3—81no—
94C2×D4—91no—
95C2×D4—181no—
96C22×C4—91no—
97C22×C4—181no—
98C2×C8—91no—
99C2×C8C2×C3⋊D311yescharacteristic
100C4⋊C4—91no—
101C4⋊C4—181no—
102C4⋊C4C2×C3⋊D311yescharacteristic
103C4⋊C4C2×C3⋊D311yescharacteristic
104C22⋊C4—181no—
105C22×C3D3×D414yes—
106C2×D3—38no—
107C2×D3—64no—
108C2×D3—64no—
109C2×D3—124no—
110C2×D3—124no—
111C2×D3—124no—
112C3×C4—44no—
113C3×C4—44no—
114C3×C4#23514yes—
115C3×C4#23914yes—
116Dic3—64no—
117Dic3—124no—
118C32#48111yescharacteristic, complemented, Sylow
119C23—91no—
120C23—181no—
121D4—181no—
122D4—181no—
123D4—362no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—91no—
127C2×C4—181no—
128C2×C4—181no—
129C2×C4—181no—
130C2×C4—362no—
131C2×C4C22×C3⋊D311yescharacteristic
132C8—21no—
133C8—181no—
134C2×C3#89414yes—
135C2×C3D3×SD1614yes—
136C2×C3#91414yes—
137D3—68no—
138D3—244no—
139C22—92no—
140C22—181no—
141C22—181no—
142C22—361no—
143C22—361no—
144C22—361no—
145C22D4×C3⋊D311yescharacteristic
146C4—41no—
147C4—41no—
148C4—181no—
149C4—361no—
150C4#382811yescharacteristic
151C4#383211yescharacteristic
152C3#486314yescomplemented
153C2—182no—
154C2—721no—
155C2#6410311yescharacteristic
156C2SD16×C3⋊D311yescharacteristic
157C2#6412311yescharacteristic
subgroupG/H
centerC22D4×C3⋊D3
commutator, cosocleC2×C32×C4C23
FrattiniC2×C4C22×C3⋊D3
FittingC32×#106C2
socleC22×C32C2×D4
prime radical#64104C2
hypercenter#106C3⋊D3
hypocenterC32#481
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C3⋊D3C2semidirect
3. C32×#106C2semidirect
4. #63648C2semidirect
5. #63647C2semidirect
6. #63636C2semidirect
7. #63635C2semidirect
22. C3×#106D3semidirect
70. #106C3⋊D3semidirect
118. C32#481semidirect
152. C3#4863semidirect

Maximal subgroups

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

subgroupindex
#641042
C4⋊C4×C3⋊D32
C32×#1062
#636482
#636472
#636362
#636352
#48633