Finite Group Databasebeta

← #11799737

Subgroups — #11799737

Order 1152.

360 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592594C211yesmaximal, characteristic
2#10592557C211yesmaximal, characteristic, complemented
3C32×#365C211yesmaximal, characteristic, complemented
4#10589384C211yesmaximal, characteristic
5#10589377C211yesmaximal, characteristic, complemented
6#10589360C211yesmaximal, characteristic, complemented
7#10589354C211yesmaximal, characteristic
8#69316—34nomaximal
9#64116—21no—
10#64113C2211yescharacteristic
11#64099—21no—
12C32×M32C2211yescharacteristic
13C32×#108C2211yescharacteristic
14C32×#106C2211yescharacteristic
15#63652—21no—
16#63644C2211yescharacteristic
17C8×C3⋊Dic3C2211yescharacteristic
18#63639C2211yescharacteristic
19#63634—21no—
20#4895—34no—
21#4858—34no—
22C3×#365D314yescomplemented
23#4518—34no—
24#4511—34no—
25#4494—34no—
26#4488—34no—
27#3828—21no—
28C32×M16—21no—
29C2×C32×C8C2311yescharacteristic
30C32×C4⋊C4—21no—
31C4⋊(C3⋊Dic3)—21no—
32C4⋊(C3⋊Dic3)—41no—
33#3750—41no—
34C4×C3⋊Dic3D411yescharacteristic
35C2×C3⋊(C3⋊C8)D411yescharacteristic
36#3746Q811yescharacteristic
37#3745Q811yescharacteristic
38#3744—21no—
39#3743—41no—
40C8×C3⋊D3—41no—
41C32×C16—21no—
42C3⋊(C3⋊C16)—21no—
43#2231—91noSylow
44#907—64no—
45#904—34no—
46#890—64no—
47C3×M32C2×D314yes—
48C3×#108C2×D314yes—
49C3×#106C2×D314yes—
50#825—64no—
51#817—34no—
52C8×Dic3—34no—
53#812—34no—
54#807—64no—
55C2×C32×C4—41no—
56C2×C32×C4C2×D411yescharacteristic
57#638—41no—
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—41no—
60C4⋊(C3⋊D3)—21no—
61C4×C3⋊D3—41no—
62#634—21no—
63C32×C8—41no—
64C32×C8C2×Q811yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)SD1611yescharacteristic
67C3⋊(C3⋊C8)SD1611yescharacteristic
68#499—91no—
69#443—91no—
70#365—91no—
71#365C3⋊D311yescharacteristic, complemented
72#364—91no—
73#360—91no—
74#360—91no—
75#235—64no—
76C3×M16—24no—
77C2×C3×C8C22×D314yes—
78C3×C4⋊C4—24no—
79C4⋊Dic3—64no—
80C4⋊Dic3—124no—
81Dic3⋊C4—124no—
82C4×Dic3—34no—
83C2×C3⋊C8—34no—
84Dic12—34no—
85D24—34no—
86#204—64no—
87ΓL(1,𝔽25)—124no—
88D3×C8—124no—
89C3×C16—24no—
90C3⋊C16—64no—
91C22×C32AGL(1,ℤ/8)11yescharacteristic
92C2×C3⋊D3—41no—
93C32×C4—81no—
94C32×C4C22⋊Q811yescharacteristic
95C32×C4C2×SD1611yescharacteristic
96C3⋊Dic3—41no—
97C3⋊Dic3—41no—
98C3⋊Dic3—81no—
99#135—91no—
100#131—181no—
101#125—181no—
102M32—91no—
103M32C2×C3⋊D311yescharacteristic
104#108C2×C3⋊D311yescharacteristic
105#107—181no—
106#106—91no—
107#106C2×C3⋊D311yescharacteristic
108#104—181no—
109C4×C8—91no—
110C2×C3×C4—44no—
111C2×C3×C4D3×D414yes—
112#67—124no—
113C2×Dic3—64no—
114C2×Dic3—124no—
115D12—64no—
116C4×D3—124no—
117Dic6—64no—
118C3×C8—44no—
119C3×C8#23514yes—
120C3×C8D3×Q814yes—
121C3⋊C8—34no—
122C3⋊C8—34no—
123C2×C32—21no—
124C2×C32#47611yescharacteristic
125C3⋊D3—81no—
126#41—181no—
127Q16—91no—
128SD16—181no—
129D8—91no—
130M16—21no—
131M16—361no—
132C2×C8—91no—
133C2×C8—361no—
134C2×C8C22×C3⋊D311yescharacteristic
135C4⋊C4—21no—
136C4⋊C4—181no—
137C4⋊C4—361no—
138C4⋊C4—361no—
139C42—91no—
140C16—21no—
141C16—181no—
142C22×C3#91414yes—
143C2×D3—124no—
144C3×C4—84no—
145C3×C4#89614yes—
146C3×C4D3×SD1614yes—
147Dic3—124no—
148Dic3—124no—
149Dic3—244no—
150C32#223111yescharacteristic, complemented, Sylow
151Q8—181no—
152D4—181no—
153D4—361no—
154C2×C4—41no—
155C2×C4—181no—
156C2×C4—361no—
157C2×C4—361no—
158C2×C4D4×C3⋊D311yescharacteristic
159C8—41no—
160C8—91no—
161C8—91no—
162C8#382811yescharacteristic
163C8Q8×C3⋊D311yescharacteristic
164C2×C3—24no—
165C2×C3#487014yes—
166D3—244no—
167C22—361no—
168C22#6412311yescharacteristic
169C4—81no—
170C4—361no—
171C4—361no—
172C4—721no—
173C4#6410511yescharacteristic
174C4SD16×C3⋊D311yescharacteristic
175C3#6931614yescomplemented
176C2—21no—
177C2—721no—
178C2#1059256911yescharacteristic
subgroupG/H
centerC2#10592569
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#365C2
socleC2×C32#476
prime radical#64113C22
hypercenter#365C3⋊D3
hypocenterC32#2231
LCSG ▷ C2×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. #10592557C2semidirect
3. C32×#365C2semidirect
5. #10589377C2semidirect
6. #10589360C2semidirect
22. C3×#365D3semidirect
71. #365C3⋊D3semidirect
150. C32#2231semidirect
175. C3#69316semidirect

Maximal subgroups

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

subgroupindex
#105925942
#105925572
C32×#3652
#105893842
#105893772
#105893602
#105893542
#693163