Finite Group Databasebeta

← #11797904

Subgroups — #11797904

Order 1152.

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

normal subgroups only

This group has 426 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#10592608C211yesmaximal, characteristic
2#10592593C211yesmaximal, characteristic
3#10592552C211yesmaximal, characteristic, complemented
4C32×#365C211yesmaximal, characteristic, complemented
5#10589378C211yesmaximal, characteristic, complemented
6#10589362C211yesmaximal, characteristic, complemented
7#10589354C211yesmaximal, characteristic
8#69309—34nomaximal
9#64116—21no—
10C2×#3746C2211yescharacteristic
11#64113C2211yescharacteristic
12#64096—21no—
13C32×M32C2211yescharacteristic
14C32×#108C2211yescharacteristic
15C32×#106C2211yescharacteristic
16#63652—21no—
17#63642C2211yescharacteristic
18#63639C2211yescharacteristic
19#63637—21no—
20#63628C412yescomplemented
21#63627C412yescomplemented
22#4909—34no—
23#4894—34no—
24#4853—34no—
25C3×#365D314yescomplemented
26#4512—34no—
27#4496—34no—
28#4488—34no—
29#3828—21no—
30C2×#634—21no—
31C32×M16—21no—
32C2×C32×C8C2311yescharacteristic
33C32×C4⋊C4—21no—
34#3750—41no—
35C4×C3⋊Dic3—41no—
36C4×C3⋊Dic3D411yescharacteristic
37C2×C3⋊(C3⋊C8)D411yescharacteristic
38#3746—21no—
39#3746C2×C411yescharacteristic
40#3746C2×C412yes—
41#3745C2×C411yescharacteristic
42#3744—21no—
43#3743—41no—
44C8×C3⋊D3—41no—
45C32×C16C2×C412yes—
46C3⋊(C3⋊C16)—21no—
47#2180—91noSylow
48#907—64no—
49C2×Dic12—34no—
50#904—34no—
51#887—64no—
52C3×M32C2×D314yes—
53C3×#108C2×D314yes—
54C3×#106C2×D314yes—
55#825—64no—
56#815—34no—
57#812—34no—
58#810—64no—
59Dic24—38no—
60#800—38no—
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63#638—41no—
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—41no—
66C4⋊(C3⋊D3)—21no—
67C4×C3⋊D3—41no—
68#634—21no—
69#634—22no—
70#634—41no—
71C32×C8—41no—
72C32×C8C22×C411yescharacteristic
73C32×C8#4111yescharacteristic
74C3⋊(C3⋊C8)—21no—
75#510—91no—
76#444—91no—
77#441—91no—
78#365C3⋊D311yescharacteristic, complemented
79#362—91no—
80#360—91no—
81#347—91no—
82#235—64no—
83C2×Dic6—64no—
84C3×M16—24no—
85C2×C3×C8C22×D314yes—
86C3×C4⋊C4—24no—
87Dic3⋊C4—124no—
88C4×Dic3—34no—
89C4×Dic3—124no—
90C2×C3⋊C8—34no—
91Dic12—38no—
92Dic12—34no—
93Dic12—64no—
94D24—34no—
95#204—64no—
96ΓL(1,𝔽25)—124no—
97D3×C8—124no—
98C3×C16C4×D318yes—
99C3⋊C16—64no—
100C22×C32AGL(1,ℤ/8)11yescharacteristic
101C2×C3⋊D3—41no—
102C32×C4—81no—
103C32×C4C4×D411yescharacteristic
104C32×C4AGL(1,ℤ/8)11yescharacteristic
105C3⋊Dic3—41no—
106C3⋊Dic3—42no—
107C3⋊Dic3—41no—
108#135—91no—
109C2×Q16—91no—
110#131—181no—
111C4×Q8—181no—
112Q32—92no—
113SD32—92no—
114M32—91no—
115M32C2×C3⋊D311yescharacteristic
116#108C2×C3⋊D311yescharacteristic
117#106C2×C3⋊D311yescharacteristic
118#104—181no—
119#103—181no—
120#97—91no—
121C2×C3×C4—44no—
122C2×C3×C4D3×D414yes—
123#67—124no—
124C2×Dic3—64no—
125C2×Dic3—124no—
126D12—64no—
127C4×D3—124no—
128Dic6—64no—
129Dic6—68no—
130Dic6—124no—
131C3×C8—44no—
132C3×C8C2×C4×D314yes—
133C3×C8#23914yes—
134C3⋊C8—64no—
135C2×C32—21no—
136C2×C32#44211yescharacteristic
137C3⋊D3—81no—
138#41—181no—
139C2×Q8—181no—
140Q16—92no—
141Q16—91no—
142Q16—181no—
143SD16—181no—
144D8—91no—
145M16—21no—
146M16—361no—
147C2×C8—91no—
148C2×C8—361no—
149C2×C8C22×C3⋊D311yescharacteristic
150C4⋊C4—21no—
151C4⋊C4—361no—
152C42—91no—
153C42—361no—
154C16—181no—
155C16C4×C3⋊D312yes—
156C22×C3#91414yes—
157C2×D3—124no—
158C3×C4—84no—
159C3×C4#89314yes—
160C3×C4#91414yes—
161Dic3—124no—
162Dic3—128no—
163Dic3—124no—
164C32#218011yescharacteristic, complemented, Sylow
165Q8—181no—
166Q8—182no—
167Q8—361no—
168D4—181no—
169D4—361no—
170C2×C4—41no—
171C2×C4—181no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4D4×C3⋊D311yescharacteristic
175C8—41no—
176C8—181no—
177C8C2×C4×C3⋊D311yescharacteristic
178C8#383211yescharacteristic
179C2×C3—24no—
180C2×C3#486914yes—
181D3—244no—
182C22—361no—
183C22#6412311yescharacteristic
184C4—81no—
185C4—361no—
186C4—361no—
187C4—362no—
188C4#6410211yescharacteristic
189C4#6412311yescharacteristic
190C3#6930914yescomplemented
191C2—21no—
192C2—721no—
193C2#1059256811yescharacteristic
subgroupG/H
centerC2#10592568
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#365C2
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenter#365C3⋊D3
hypocenterC32#2180
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
3. #10592552C2semidirect
4. C32×#365C2semidirect
5. #10589378C2semidirect
6. #10589362C2semidirect
20. #63628C4semidirect
21. #63627C4semidirect
25. C3×#365D3semidirect
78. #365C3⋊D3semidirect
164. C32#2180semidirect
190. C3#69309semidirect

Maximal subgroups

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

subgroupindex
#105926082
#105925932
#105925522
C32×#3652
#105893782
#105893622
#105893542
#693093