Finite Group Databasebeta

← #11799757

Subgroups — #11799757

Order 1152.

293 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 293 conjugacy classes of subgroups — too many to draw. Only its 66 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#10590874C211yesmaximal, characteristic, complemented
3C3×#4494C212yesmaximal, complemented
4#10589135C211yesmaximal, characteristic, complemented
5#10589125C212yesmaximal
6#69316—32nomaximal
7#64116—21no—
8#64113C2211yescharacteristic
9#63872—21no—
10C32×#108C2211yescharacteristic
11#63652—21no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#817C2212yes—
14C3×#812C2212yes—
15#63576—21no—
16#4895—32no—
17#4895—61no—
18#4858—32no—
19C3×#365—32no—
20#4518—32no—
21#4511—32no—
22#4494D312yescomplemented
23#4488—32no—
24#3828—21no—
25C32×M16—21no—
26C2×C32×C8C2311yescharacteristic
27C4×C3⋊Dic3D411yescharacteristic
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29#3746Q811yescharacteristic
30#3745Q811yescharacteristic
31#3744—21no—
32#3743—41no—
33C8×C3⋊D3—41no—
34C3×C4⋊Dic3—22no—
35Dic3⋊Dic3—42no—
36C3×C3⋊C16—22no—
37#2231—91noSylow
38#907—62no—
39#907—62no—
40#904—32no—
41#904—61no—
42#890—62no—
43C3×M32—32no—
44C3×#108—21no—
45C3×#108C2×D312yes—
46C3×#106—32no—
47#825—62no—
48#825—62no—
49#817C2×D312yes—
50C8×Dic3—32no—
51C8×Dic3—61no—
52#812C2×D312yes—
53#807—62no—
54C2×C32×C4C2×D411yescharacteristic
55#638—41no—
56C2×C3⋊Dic3—21no—
57C4⋊(C3⋊D3)—21no—
58C4×C3⋊D3—41no—
59#634—21no—
60C2×C3×Dic3—42no—
61C32×C8—41no—
62C32×C8C2×Q811yescharacteristic
63C32×C8#4111yescharacteristic
64C3⋊(C3⋊C8)SD1611yescharacteristic
65C3⋊(C3⋊C8)SD1611yescharacteristic
66#499—91no—
67#443—91no—
68#365—32no—
69#364—91no—
70#360—92no—
71#235—62no—
72#235—62no—
73C3×M16—22no—
74C3×M16—22no—
75C2×C3×C8—21no—
76C2×C3×C8C22×D312yes—
77C3×C4⋊C4—62no—
78C4⋊Dic3—22no—
79C4⋊Dic3—122no—
80Dic3⋊C4—122no—
81C4×Dic3—32no—
82C4×Dic3—61no—
83C2×C3⋊C8—32no—
84C2×C3⋊C8—61no—
85Dic12—32no—
86Dic12—61no—
87D24—32no—
88D24—61no—
89#204—62no—
90#204—62no—
91ΓL(1,𝔽25)—122no—
92ΓL(1,𝔽25)—122no—
93D3×C8—122no—
94D3×C8—122no—
95C3×C16—62no—
96C3⋊C16—22no—
97C22×C32AGL(1,ℤ/8)11yescharacteristic
98C2×C3⋊D3—41no—
99C32×C4C22⋊Q811yescharacteristic
100C32×C4C2×SD1611yescharacteristic
101C3⋊Dic3—41no—
102C3⋊Dic3—41no—
103C3×Dic3—82no—
104#135—91no—
105#131—181no—
106#125—181no—
107M32—32no—
108#108D3211yescharacteristic
109#107—181no—
110#106—32no—
111#104—181no—
112C4×C8—91no—
113C2×C3×C4—21no—
114C2×C3×C4—122no—
115C2×C3×C4D3×D412yes—
116#67—122no—
117#67—122no—
118C2×Dic3—42no—
119C2×Dic3—62no—
120C2×Dic3—121no—
121D12—62no—
122D12—62no—
123C4×D3—122no—
124C4×D3—122no—
125Dic6—62no—
126Dic6—62no—
127C3×C8—21no—
128C3×C8—21no—
129C3×C8—42no—
130C3×C8—42no—
131C3×C8#23512yes—
132C3×C8D3×Q812yes—
133C3⋊C8—32no—
134C3⋊C8—32no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C2×C32—21no—
138C2×C32#47611yescharacteristic
139C3⋊D3—81no—
140#41—181no—
141Q16—91no—
142SD16—181no—
143D8—91no—
144M16—21no—
145M16—361no—
146C2×C8—91no—
147C2×C8—361no—
148C2×C8C2×D3211yescharacteristic
149C4⋊C4—62no—
150C4⋊C4—362no—
151C42—91no—
152C16—62no—
153C22×C3—21no—
154C22×C3#91412yes—
155C2×D3—122no—
156C2×D3—122no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—242no—
160C3×C4#89612yes—
161C3×C4D3×SD1612yes—
162Dic3—82no—
163Dic3—122no—
164Dic3—122no—
165Dic3—122no—
166Dic3—122no—
167C32#223111yescharacteristic, complemented, Sylow
168Q8—181no—
169D4—181no—
170D4—361no—
171C2×C4—122no—
172C2×C4—181no—
173C2×C4—361no—
174C2×C4#381111yescharacteristic
175C8—41no—
176C8—91no—
177C8—91no—
178C8#379711yescharacteristic
179C8#379811yescharacteristic
180C2×C3—22no—
181C2×C3—21no—
182C2×C3—41no—
183C2×C3#487012yes—
184D3—242no—
185D3—242no—
186C22—361no—
187C22#6394111yescharacteristic
188C4—242no—
189C4—361no—
190C4—361no—
191C4#6386511yescharacteristic
192C4#6393011yescharacteristic
193C3—21no—
194C3#6931612yescomplemented
195C2—21no—
196C2—721no—
197C2#1059043311yescharacteristic
subgroupG/H
centerC2#10590433
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#476
prime radical#64113C22
hypercenter#108D32
hypocenterC32#2231
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #108

Complements

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

NH ≅ G/Ntype
2. #10590874C2semidirect
3. C3×#4494C2semidirect
4. #10589135C2semidirect
22. #4494D3semidirect
167. C32#2231semidirect
194. C3#69316semidirect

Maximal subgroups

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

subgroupindex
#105925942
#105908742
C3×#44942
#105891352
#105891252
#693163