Finite Group Databasebeta

← #11797916

Subgroups — #11797916

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#10592883C211yesmaximal, characteristic, complemented
2#10592878C211yesmaximal, characteristic
3#10592593C211yesmaximal, characteristic
4C32×#362C211yesmaximal, characteristic, complemented
5#10589384C211yesmaximal, characteristic
6#10589378C211yesmaximal, characteristic, complemented
7#10589360C211yesmaximal, characteristic, complemented
8#69264—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10Q8×C3⋊Dic3—21no—
11#64116—21no—
12#64113C2211yescharacteristic
13C32×M32C2211yescharacteristic
14C32×#108C2211yescharacteristic
15#63662—21no—
16#63656C412yescomplemented
17#63655C412yescomplemented
18#63652—21no—
19#63644C2211yescharacteristic
20#63642C2211yescharacteristic
21#63639C2211yescharacteristic
22#5184—34no—
23#5179—34no—
24#4894—34no—
25C3×#362D314yescomplemented
26#4518—34no—
27#4512—34no—
28#4494—34no—
29C2×C32×Q8—21no—
30#3828—21no—
31C32×Q16—21no—
32C32×Q16C2×C412yes—
33C32×M16—21no—
34C2×C32×C8C2311yescharacteristic
35C4⋊(C3⋊Dic3)—21no—
36C4⋊(C3⋊Dic3)—41no—
37C4×C3⋊Dic3—41no—
38C4×C3⋊Dic3D411yescharacteristic
39C2×C3⋊(C3⋊C8)D411yescharacteristic
40#3746C2×C411yescharacteristic
41#3745C2×C411yescharacteristic
42#3744—21no—
43#3743—41no—
44C8×C3⋊D3—41no—
45C32×C16—21no—
46C3⋊(C3⋊C16)C2×C412yes—
47#2180—91noSylow
48C2×C3×Q16C2×D314yes—
49Q8×Dic3—64no—
50#907—64no—
51#904—34no—
52C3×M32C2×D314yes—
53C3×#108C2×D314yes—
54#835—64no—
55#829—38no—
56#828—38no—
57#825—64no—
58#817—34no—
59#815—34no—
60#812—34no—
61C32×Q8—22no—
62C32×Q8—41no—
63C2×C32×C4—41no—
64C2×C32×C4C2×D411yescharacteristic
65#638—41no—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—41no—
68C4⋊(C3⋊D3)—21no—
69C4×C3⋊D3—41no—
70#634—21no—
71C32×C8—41no—
72C32×C8C22×C411yescharacteristic
73C32×C8#4111yescharacteristic
74C3⋊(C3⋊C8)—21no—
75#510—91no—
76#444—91no—
77#441—91no—
78#365—91no—
79#362C3⋊D311yescharacteristic, complemented
80#360—91no—
81#347—91no—
82C2×C3×Q8—24no—
83#235—64no—
84C3×Q16—24no—
85C3×Q16C4×D318yes—
86C3×M16—24no—
87C2×C3×C8C22×D314yes—
88C4⋊Dic3—64no—
89C4⋊Dic3—124no—
90C4×Dic3—34no—
91C4×Dic3—124no—
92C2×C3⋊C8—34no—
93Dic12—34no—
94D24—34no—
95#204—64no—
96ΓL(1,𝔽25)—124no—
97D3×C8—124no—
98C3×C16—24no—
99C3⋊C16—38no—
100C22×C32AGL(1,ℤ/8)11yescharacteristic
101C2×C3⋊D3—41no—
102C32×C4—42no—
103C32×C4C4×D411yescharacteristic
104C32×C4AGL(1,ℤ/8)11yescharacteristic
105C3⋊Dic3—41no—
106C3⋊Dic3—41no—
107C3⋊Dic3—81no—
108#135—91no—
109C2×Q16C2×C3⋊D311yescharacteristic
110#131—181no—
111C4×Q8—181no—
112Q32—92no—
113SD32—92no—
114M32—91no—
115M32C2×C3⋊D311yescharacteristic
116#108C2×C3⋊D311yescharacteristic
117#106—91no—
118#104—181no—
119#103—181no—
120#97—91no—
121C3×Q8—28no—
122C3×Q8—44no—
123C2×C3×C4—44no—
124C2×C3×C4D3×D414yes—
125#67—124no—
126C2×Dic3—64no—
127C2×Dic3—124no—
128D12—64no—
129C4×D3—124no—
130Dic6—64no—
131C3×C8—44no—
132C3×C8C2×C4×D314yes—
133C3×C8#23714yes—
134C3⋊C8—64no—
135C2×C32—21no—
136C2×C32#44211yescharacteristic
137C3⋊D3—81no—
138#41—181no—
139C2×Q8—21no—
140Q16—21no—
141Q16—91no—
142Q16C4×C3⋊D312yes—
143SD16—181no—
144D8—91no—
145M16—21no—
146M16—361no—
147C2×C8—91no—
148C2×C8—361no—
149C2×C8C22×C3⋊D311yescharacteristic
150C4⋊C4—181no—
151C4⋊C4—361no—
152C42—91no—
153C42—361no—
154C16—21no—
155C16—92no—
156C22×C3#91414yes—
157C2×D3—124no—
158C3×C4—48no—
159C3×C4#67⋊C414yes—
160C3×C4#91114yes—
161Dic3—124no—
162Dic3—124no—
163Dic3—244no—
164C32#218011yescharacteristic, complemented, Sylow
165Q8—22no—
166Q8—41no—
167Q8—181no—
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#383011yescharacteristic
179C2×C3—24no—
180C2×C3#478514yes—
181D3—244no—
182C22—361no—
183C22#6412311yescharacteristic
184C4—42no—
185C4—361no—
186C4—361no—
187C4—721no—
188C4#6409011yescharacteristic
189C4#6412011yescharacteristic
190C3#6926414yescomplemented
191C2—21no—
192C2—721no—
193C2#1059248411yescharacteristic
subgroupG/H
centerC2#10592484
commutatorC32×C8C22×C4
FrattiniC2×C8C22×C3⋊D3
FittingC32×#362C2
socleC2×C32#442
prime radical#64113C22
cosocleC2×C32×C8C23
hypercenter#362C3⋊D3
hypocenterC32#2180
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. #10592883C2semidirect
4. C32×#362C2semidirect
6. #10589378C2semidirect
7. #10589360C2semidirect
16. #63656C4semidirect
17. #63655C4semidirect
25. C3×#362D3semidirect
79. #362C3⋊D3semidirect
164. C32#2180semidirect
190. C3#69264semidirect

Maximal subgroups

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

subgroupindex
#105928832
#105928782
#105925932
C32×#3622
#105893842
#105893782
#105893602
#692643