Finite Group Databasebeta

← #11797962

Subgroups — #11797962

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#10592851C211yesmaximal, characteristic, complemented
2#10592846C211yesmaximal, characteristic
3#10592593C211yesmaximal, characteristic, complemented
4C32×#361C211yesmaximal, characteristic, complemented
5#10589384C211yesmaximal, characteristic, complemented
6#10589378C211yesmaximal, characteristic, complemented
7#10589360C211yesmaximal, characteristic, complemented
8#69254—34nomaximal
9C2×C32×D8C2211yescharacteristic
10D4×C3⋊Dic3—21no—
11#64116—21no—
12#64113C2211yescharacteristic
13C32×M32C2211yescharacteristic
14C32×#108C2211yescharacteristic
15#63659—21no—
16#63654C412yescomplemented
17#63653C412yescomplemented
18#63652—21no—
19#63644C2211yescharacteristic
20#63642C2211yescharacteristic
21#63639C2211yescharacteristic
22#5152—34no—
23#5147—34no—
24#4894—34no—
25C3×#361D314yescomplemented
26#4518—34no—
27#4512—34no—
28#4494—34no—
29C2×C32×D4—21no—
30C22×C3⋊Dic3—41no—
31#3828—21no—
32C32×D8—21no—
33C32×D8C2×C412yes—
34C32×M16—21no—
35C2×C32×C8C2311yescharacteristic
36#3757—41no—
37C4⋊(C3⋊Dic3)—21no—
38C4×C3⋊Dic3D411yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40#3746C2×C411yescharacteristic, complemented
41#3745C2×C411yescharacteristic, complemented
42#3744—21no—
43#3743—41no—
44C8×C3⋊D3—41no—
45C32×C16—21no—
46C3⋊(C3⋊C16)C2×C412yescomplemented
47AGL(1,ℤ/16)—91noSylow
48C2×C3×D8C2×D314yes—
49D4×Dic3—64no—
50#907—64no—
51#904—34no—
52C3×M32C2×D314yes—
53C3×#108C2×D314yes—
54#832—64no—
55#827—38no—
56#826—38no—
57#825—64no—
58#817—34no—
59#815—34no—
60#812—34no—
61C23×C32—41no—
62C32×D4—22no—
63C32×D4—41no—
64C2×C32×C4C2×D411yescharacteristic
65#638—41no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—41no—
68C2×C3⋊Dic3—82no—
69C4⋊(C3⋊D3)—21no—
70C4×C3⋊D3—41no—
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#365—91no—
80#361C3⋊D311yescharacteristic, complemented
81#360—91no—
82#347—91no—
83C2×C3×D4—24no—
84C22×Dic3—124no—
85#235—64no—
86C3×D8—24no—
87C3×D8C4×D318yes—
88C3×M16—24no—
89C2×C3×C8C22×D314yes—
90#217—124no—
91C4⋊Dic3—64no—
92C4×Dic3—34no—
93C2×C3⋊C8—34no—
94Dic12—34no—
95D24—34no—
96#204—64no—
97ΓL(1,𝔽25)—124no—
98D3×C8—124no—
99C3×C16—24no—
100C3⋊C16—38no—
101C22×C32—42no—
102C22×C32—81no—
103C22×C32—81no—
104C22×C32AGL(1,ℤ/8)11yescharacteristic
105C2×C3⋊D3—41no—
106C32×C4C4×D411yescharacteristic
107C32×C4AGL(1,ℤ/8)11yescharacteristic
108C3⋊Dic3—41no—
109C3⋊Dic3—41no—
110C3⋊Dic3—81no—
111#135—91no—
112C2×D8C2×C3⋊D311yescharacteristic
113#131—181no—
114C4×D4—181no—
115SD32—92no—
116D16—92no—
117M32—91no—
118M32C2×C3⋊D311yescharacteristic
119#108C2×C3⋊D311yescharacteristic
120#106—91no—
121#104—181no—
122#102—181no—
123#97—91no—
124C23×C3—44no—
125C3×D4—28no—
126C3×D4—44no—
127C2×C3×C4D3×D414yes—
128#67—124no—
129C2×Dic3—64no—
130C2×Dic3—124no—
131C2×Dic3—248no—
132D12—64no—
133C4×D3—124no—
134Dic6—64no—
135C3×C8—44no—
136C3×C8C2×C4×D314yes—
137C3×C8#23714yes—
138C3⋊C8—64no—
139C2×C32—21no—
140C2×C32—82no—
141C2×C32#44211yescharacteristic
142C3⋊D3—81no—
143#41—181no—
144C2×D4—21no—
145C22×C4—361no—
146Q16—91no—
147SD16—181no—
148D8—21no—
149D8—91no—
150D8C4×C3⋊D312yes—
151M16—21no—
152M16—361no—
153C2×C8—91no—
154C2×C8—361no—
155C2×C8C22×C3⋊D311yescharacteristic
156C4⋊C4—181no—
157C22⋊C4—361no—
158C42—91no—
159C16—21no—
160C16—92no—
161C22×C3—48no—
162C22×C3—84no—
163C22×C3—84no—
164C22×C3#91414yes—
165C2×D3—124no—
166C3×C4#67⋊C414yes—
167C3×C4#91114yes—
168Dic3—124no—
169Dic3—124no—
170Dic3—244no—
171C32AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
172C23—41no—
173Q8—181no—
174D4—22no—
175D4—41no—
176D4—181no—
177D4—361no—
178C2×C4—181no—
179C2×C4—361no—
180C2×C4—361no—
181C2×C4—722no—
182C2×C4D4×C3⋊D311yescharacteristic
183C8—41no—
184C8—181no—
185C8C2×C4×C3⋊D311yescharacteristic
186C8#383011yescharacteristic
187C2×C3—24no—
188C2×C3—88no—
189C2×C3#478514yes—
190D3—244no—
191C22—42no—
192C22—81no—
193C22—81no—
194C22—361no—
195C22#6412311yescharacteristic
196C4—361no—
197C4—361no—
198C4—721no—
199C4#6409011yescharacteristic
200C4#6412011yescharacteristic
201C3#6925414yescomplemented
202C2—21no—
203C2—82no—
204C2—721no—
205C2#1059248411yescharacteristic
subgroupG/H
centerC2#10592484
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#361C2
socleC2×C32#442
prime radical#10592846C2
cosocleC2×C32×C8C23
hypercenter#361C3⋊D3
hypocenterC32AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #10592851C2semidirect
3. #10592593C2semidirect
4. C32×#361C2semidirect
5. #10589384C2semidirect
6. #10589378C2semidirect
7. #10589360C2semidirect
16. #63654C4semidirect
17. #63653C4semidirect
25. C3×#361D3semidirect
40. #3746C2×C4semidirect
41. #3745C2×C4semidirect
46. C3⋊(C3⋊C16)C2×C4semidirect
80. #361C3⋊D3semidirect
171. C32AGL(1,ℤ/16)semidirect
201. C3#69254semidirect

Maximal subgroups

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

subgroupindex
#105928512
#105928462
#105925932
C32×#3612
#105893842
#105893782
#105893602
#692543