Finite Group Databasebeta

← #11797913

Subgroups — #11797913

Order 1152.

426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 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#10592416C211yesmaximal, characteristic
3#10592415C211yesmaximal, characteristic, complemented
4C32×#347C211yesmaximal, characteristic, complemented
5#10589384C211yesmaximal, characteristic
6#10589383C211yesmaximal, characteristic, complemented
7#10589379C211yesmaximal, characteristic, complemented
8#69090—34nomaximal
9C2×#3746C2211yescharacteristic
10#64113C2211yescharacteristic
11#64110—21no—
12C4×#634—21no—
13C32×M32C2211yescharacteristic
14C32×M32C2211yescharacteristic
15C32×#97C2211yescharacteristic
16#63646C2211yescharacteristic
17#63644C2211yescharacteristic
18#63643—21no—
19#63632—21no—
20#63628C412yescomplemented
21#63627C412yescomplemented
22#4909—34no—
23#4717—34no—
24#4716—34no—
25C3×#347D314yescomplemented
26#4518—34no—
27#4517—34no—
28#4513—34no—
29#3828—21no—
30C2×#634—21no—
31C2×C32×C8D411yescharacteristic
32C2×C32×C8C2311yescharacteristic
33C32×C42D411yescharacteristic
34C4⋊(C3⋊Dic3)—21no—
35#3750—41no—
36C4×C3⋊Dic3—41no—
37#3748—21no—
38#3746—21no—
39#3746C2×C411yescharacteristic
40#3746C2×C412yes—
41#3745C2×C411yescharacteristic
42#3744—21no—
43#3743—41no—
44C8×C3⋊D3—41no—
45C32×C16—21no—
46C32×C16C2×C412yes—
47#2180—91noSylow
48C2×Dic12—34no—
49#904—34no—
50#901—64no—
51C4×Dic6—64no—
52C3×M32C2×D314yes—
53C3×M32C2×D314yes—
54C3×#97C2×D314yes—
55#819—34no—
56#817—34no—
57#816—64no—
58#805—64no—
59Dic24—38no—
60#800—38no—
61C2×C32×C4—21no—
62C2×C32×C4C2×D411yescharacteristic
63#638—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66C4⋊(C3⋊D3)—21no—
67C4×C3⋊D3—41no—
68#634—21no—
69#634—22no—
70#634—41no—
71C32×C8—21no—
72C32×C8C22×C411yescharacteristic
73C32×C8#4111yescharacteristic
74C3⋊(C3⋊C8)—41no—
75#510—91no—
76#444—91no—
77#441—91no—
78#365—91no—
79#362—91no—
80#360—91no—
81#347C3⋊D311yescharacteristic, complemented
82#235—64no—
83C2×Dic6—64no—
84C2×C3×C8D1214yes—
85C2×C3×C8C22×D314yes—
86C3×C42D1214yes—
87C4⋊Dic3—64no—
88Dic3⋊C4—124no—
89C4×Dic3—124no—
90#208—64no—
91Dic12—38no—
92Dic12—34no—
93Dic12—64no—
94D24—34no—
95#204—64no—
96ΓL(1,𝔽25)—124no—
97D3×C8—124no—
98C3×C16—24no—
99C3×C16C4×D318yes—
100C22×C32AGL(1,ℤ/8)11yescharacteristic
101C2×C3⋊D3—41no—
102C32×C4—41no—
103C32×C4C4×D411yescharacteristic
104C32×C4AGL(1,ℤ/8)11yescharacteristic
105C3⋊Dic3—42no—
106C3⋊Dic3—41no—
107C3⋊Dic3—81no—
108#135—91no—
109C2×Q16—91no—
110#131—181no—
111C4×Q8—181no—
112Q32—92no—
113SD32—92no—
114M32C2×C3⋊D311yescharacteristic
115M32C2×C3⋊D311yescharacteristic
116#108—91no—
117#106—91no—
118#104—181no—
119#103—181no—
120#97C2×C3⋊D311yescharacteristic
121C2×C3×C4—24no—
122C2×C3×C4C2×D1214yes—
123#67—124no—
124C2×Dic3—124no—
125C2×Dic3—124no—
126D12—64no—
127C4×D3—124no—
128Dic6—64no—
129Dic6—68no—
130Dic6—124no—
131C3×C8—24no—
132C3×C8C2×C4×D314yes—
133C3×C8#23514yes—
134C3⋊C8—124no—
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—181no—
146M16—361no—
147C2×C8—361no—
148C2×C8C4⋊(C3⋊D3)11yescharacteristic
149C2×C8C22×C3⋊D311yescharacteristic
150C4⋊C4—181no—
151C4⋊C4—361no—
152C42—361no—
153C42C4⋊(C3⋊D3)11yescharacteristic
154C16—21no—
155C16C4×C3⋊D312yes—
156C22×C3#90814yes—
157C2×D3—124no—
158C3×C4—44no—
159C3×C4C4×D1214yes—
160C3×C4#90814yes—
161Dic3—128no—
162Dic3—124no—
163Dic3—244no—
164C32#218011yescharacteristic, complemented, Sylow
165Q8—181no—
166Q8—182no—
167Q8—361no—
168D4—181no—
169D4—361no—
170C2×C4—21no—
171C2×C4—361no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
175C8—21no—
176C8—361no—
177C8C2×C4×C3⋊D311yescharacteristic
178C8#382811yescharacteristic
179C2×C3—24no—
180C2×C3#471114yes—
181D3—244no—
182C22—361no—
183C22#6411711yescharacteristic
184C4—41no—
185C4—361no—
186C4—362no—
187C4—721no—
188C4C4×C4⋊(C3⋊D3)11yescharacteristic
189C4#6411711yescharacteristic
190C3#6909014yescomplemented
191C2—21no—
192C2—721no—
193C2#1059241011yescharacteristic
subgroupG/H
centerC2#10592410
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#347C2
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenter#347C3⋊D3
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #347

Complements

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

NH ≅ G/Ntype
3. #10592415C2semidirect
4. C32×#347C2semidirect
6. #10589383C2semidirect
7. #10589379C2semidirect
20. #63628C4semidirect
21. #63627C4semidirect
25. C3×#347D3semidirect
81. #347C3⋊D3semidirect
164. C32#2180semidirect
190. C3#69090semidirect

Maximal subgroups

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

subgroupindex
#105926082
#105924162
#105924152
C32×#3472
#105893842
#105893832
#105893792
#690903