Finite Group Databasebeta

← #11797950

Subgroups — #11797950

Order 1152.

462 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 111 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#10592607C211yesmaximal, characteristic
2#10592593C211yesmaximal, characteristic, complemented
3#10592568C211yesmaximal, characteristic, complemented
4C32×#365C211yesmaximal, characteristic, complemented
5#10589378C211yesmaximal, characteristic, complemented
6#10589361C211yesmaximal, characteristic, complemented
7#10589354C211yesmaximal, characteristic, complemented
8#69310—34nomaximal
9#64116—21no—
10#64113C2211yescharacteristic
11C2×#3745C2211yescharacteristic
12#64102—21no—
13C32×M32C2211yescharacteristic
14C32×#108C2211yescharacteristic
15C32×#106C2211yescharacteristic
16#63652—21no—
17#63642C2211yescharacteristic
18#63639C2211yescharacteristic
19#63636—21no—
20#63627C412yescomplemented
21#63626C412yescomplemented
22#4908—34no—
23#4894—34no—
24#4869—34no—
25C3×#365D314yescomplemented
26#4512—34no—
27#4495—34no—
28#4488—34no—
29#3828—21no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×C4×C3⋊D3—41no—
32C32×M16—21no—
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35#3752—41no—
36C4×C3⋊Dic3D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3746C2×C411yescharacteristic, complemented
39#3745—21no—
40#3745C2×C412yes—
41#3745C2×C411yescharacteristic, complemented
42#3744—21no—
43#3743—41no—
44C8×C3⋊D3—41no—
45C32×C16C2×C412yescomplemented
46C3⋊(C3⋊C16)—21no—
47AGL(1,ℤ/16)—91noSylow
48#907—64no—
49#904—34no—
50C2×D24—34no—
51#893—64no—
52C3×M32C2×D314yes—
53C3×#108C2×D314yes—
54C3×#106C2×D314yes—
55#825—64no—
56#815—34no—
57#812—34no—
58#809—64no—
59#800—38no—
60D48—38no—
61C22×C3⋊D3—41no—
62C2×C32×C4—41no—
63C2×C32×C4C2×D411yescharacteristic
64#638—41no—
65C2×C3⋊Dic3—21no—
66C4⋊(C3⋊D3)—21no—
67C4⋊(C3⋊D3)—22no—
68C4⋊(C3⋊D3)—41no—
69C4×C3⋊D3—41no—
70C4×C3⋊D3—82no—
71#634—21no—
72C32×C8—41no—
73C32×C8C22×C411yescharacteristic
74C32×C8#4111yescharacteristic
75C3⋊(C3⋊C8)—21no—
76#509—91no—
77#444—91no—
78#442—91no—
79#365C3⋊D311yescharacteristic, complemented
80#361—91no—
81#360—91no—
82#347—91no—
83#235—64no—
84C2×D12—64no—
85C2×C4×D3—124no—
86C3×M16—24no—
87C2×C3×C8C22×D314yes—
88C3×C4⋊C4—24no—
89(C2×D3)⋊C4—124no—
90C4×Dic3—34no—
91C2×C3⋊C8—34no—
92Dic12—34no—
93D24—34no—
94D24—38no—
95D24—64no—
96#204—64no—
97ΓL(1,𝔽25)—124no—
98D3×C8—124no—
99C3×C16C4×D318yescomplemented
100C3⋊C16—64no—
101C22×C32AGL(1,ℤ/8)11yescharacteristic
102C2×C3⋊D3—41no—
103C2×C3⋊D3—42no—
104C2×C3⋊D3—81no—
105C2×C3⋊D3—81no—
106C32×C4—81no—
107C32×C4C4×D411yescharacteristic
108C32×C4AGL(1,ℤ/8)11yescharacteristic
109C3⋊Dic3—41no—
110C3⋊Dic3—41no—
111#135—91no—
112C2×D8—91no—
113#131—181no—
114C4×D4—181no—
115SD32—92no—
116D16—92no—
117M32—91no—
118M32C2×C3⋊D311yescharacteristic
119#108C2×C3⋊D311yescharacteristic
120#106C2×C3⋊D311yescharacteristic
121#104—181no—
122#102—181no—
123#97—91no—
124C22×D3—124no—
125C2×C3×C4—44no—
126C2×C3×C4D3×D414yes—
127#67—124no—
128C2×Dic3—64no—
129D12—64no—
130D12—68no—
131D12—124no—
132C4×D3—124no—
133C4×D3—248no—
134Dic6—64no—
135C3×C8—44no—
136C3×C8C2×C4×D314yes—
137C3×C8#23914yes—
138C3⋊C8—64no—
139C2×C32—21no—
140C2×C32#44211yescharacteristic
141C3⋊D3—81no—
142C3⋊D3—82no—
143#41—181no—
144C2×D4—181no—
145C22×C4—361no—
146Q16—91no—
147SD16—181no—
148D8—91no—
149D8—92no—
150D8—181no—
151M16—21no—
152M16—361no—
153C2×C8—91no—
154C2×C8—361no—
155C2×C8C22×C3⋊D311yescharacteristic
156C4⋊C4—21no—
157C22⋊C4—361no—
158C42—91no—
159C16—181no—
160C16C4×C3⋊D312yescomplemented
161C22×C3#91414yes—
162C2×D3—124no—
163C2×D3—128no—
164C2×D3—244no—
165C2×D3—244no—
166C3×C4—84no—
167C3×C4#89314yes—
168C3×C4#91414yes—
169Dic3—124no—
170Dic3—124no—
171C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
172C23—361no—
173Q8—181no—
174D4—182no—
175D4—181no—
176D4—361no—
177D4—361no—
178C2×C4—41no—
179C2×C4—181no—
180C2×C4—361no—
181C2×C4—722no—
182C2×C4D4×C3⋊D311yescharacteristic
183C8—41no—
184C8—181no—
185C8C2×C4×C3⋊D311yescharacteristic
186C8#383211yescharacteristic
187C2×C3—24no—
188C2×C3#486914yes—
189D3—248no—
190D3—244no—
191C22—361no—
192C22—362no—
193C22—721no—
194C22—721no—
195C22#6412311yescharacteristic
196C4—81no—
197C4—361no—
198C4—361no—
199C4#6410211yescharacteristic
200C4#6412311yescharacteristic
201C3#6931014yescomplemented
202C2—21no—
203C2—722no—
204C2—721no—
205C2#1059256811yescharacteristic
subgroupG/H
centerC2#10592568
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#365C2
socleC2×C32#442
prime radical#10592607C2
cosocleC2×C32×C8C23
hypercenter#365C3⋊D3
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
2. #10592593C2semidirect
3. #10592568C2semidirect
4. C32×#365C2semidirect
5. #10589378C2semidirect
6. #10589361C2semidirect
7. #10589354C2semidirect
20. #63627C4semidirect
21. #63626C4semidirect
25. C3×#365D3semidirect
38. #3746C2×C4semidirect
41. #3745C2×C4semidirect
45. C32×C16C2×C4semidirect
79. #365C3⋊D3semidirect
99. C3×C16C4×D3semidirect
160. C16C4×C3⋊D3semidirect
171. C32AGL(1,ℤ/16)semidirect
201. C3#69310semidirect

Maximal subgroups

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

subgroupindex
#105926072
#105925932
#105925682
C32×#3652
#105893782
#105893612
#105893542
#693103