Finite Group Databasebeta

← #11799723

Subgroups — #11799723

Order 1152.

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

normal subgroups only

This group has 305 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#10590900C211yesmaximal, characteristic, complemented
3C3×#4494C212yesmaximal, complemented
4#10589135C211yesmaximal, characteristic, complemented
5#10589125C212yesmaximal
6#69315—32nomaximal
7#64116—21no—
8#64113C2211yescharacteristic
9#63919—21no—
10C32×#108C2211yescharacteristic
11#63652—21no—
12C8×C3⋊Dic3C2211yescharacteristic
13C3×#817C2212yes—
14C3×#812C2212yes—
15#63574—21no—
16#4895—32no—
17#4895—61no—
18#4855—32no—
19C3×#365—32no—
20#4518—32no—
21#4511—32no—
22#4494D312yescomplemented
23#4488—32no—
24#3828—21no—
25C2×#627—41no—
26C32×M16—21no—
27C2×C32×C8C2311yescharacteristic
28C4×C3⋊Dic3D411yescharacteristic
29C2×C3⋊(C3⋊C8)D411yescharacteristic
30#3746Q811yescharacteristic, complemented
31#3745Q811yescharacteristic, complemented
32#3744—21no—
33#3743—41no—
34C8×C3⋊D3—41no—
35C3×C4⋊Dic3—22no—
36#3724—41no—
37C3×C3⋊C16—22no—
38#2230—91noSylow
39#907—62no—
40#907—62no—
41#904—32no—
42#904—61no—
43#888—62no—
44C3×M32—32no—
45C3×#108—21no—
46C3×#108C2×D312yes—
47C3×#106—32no—
48#825—62no—
49#825—62no—
50#817C2×D312yes—
51C8×Dic3—32no—
52C8×Dic3—61no—
53#812C2×D312yes—
54#808—62no—
55C2×C32×C4C2×D411yescharacteristic
56#638—41no—
57C2×C3⋊Dic3—21no—
58C4⋊(C3⋊D3)—21no—
59C4×C3⋊D3—41no—
60#634—21no—
61C2×C3×Dic3—42no—
62#627—82no—
63C32×C8—41no—
64C32×C8C2×Q811yescharacteristic
65C32×C8#4111yescharacteristic
66C3⋊(C3⋊C8)SD1611yescharacteristic
67C3⋊(C3⋊C8)SD1611yescharacteristic
68#498—91no—
69#443—91no—
70#365—32no—
71#364—91no—
72#360—92no—
73#235—62no—
74#235—62no—
75C2×Dic6—122no—
76C3×M16—22no—
77C3×M16—22no—
78C2×C3×C8—21no—
79C2×C3×C8C22×D312yes—
80C3×C4⋊C4—62no—
81C4⋊Dic3—22no—
82Dic3⋊C4—122no—
83C4×Dic3—32no—
84C4×Dic3—61no—
85C2×C3⋊C8—32no—
86C2×C3⋊C8—61no—
87Dic12—32no—
88Dic12—61no—
89D24—32no—
90D24—61no—
91#204—62no—
92#204—62no—
93ΓL(1,𝔽25)—122no—
94ΓL(1,𝔽25)—122no—
95D3×C8—122no—
96D3×C8—122no—
97C3×C16—62no—
98C3⋊C16—22no—
99C22×C32AGL(1,ℤ/8)11yescharacteristic
100C2×C3⋊D3—41no—
101C32×C4C22⋊Q811yescharacteristic
102C32×C4C2×SD1611yescharacteristic
103C3⋊Dic3—22no—
104C3⋊Dic3—41no—
105C3×Dic3—82no—
106#135—91no—
107#131—181no—
108C4⋊Q8—181no—
109M32—32no—
110#108D3211yescharacteristic
111#106—32no—
112#106—181no—
113#104—181no—
114C4×C8—91no—
115C2×C3×C4—21no—
116C2×C3×C4—122no—
117C2×C3×C4D3×D412yes—
118#67—122no—
119#67—122no—
120C2×Dic3—42no—
121C2×Dic3—62no—
122C2×Dic3—121no—
123D12—62no—
124D12—62no—
125C4×D3—122no—
126C4×D3—122no—
127Dic6—62no—
128Dic6—62no—
129Dic6—244no—
130C3×C8—21no—
131C3×C8—21no—
132C3×C8—42no—
133C3×C8—42no—
134C3×C8#23512yes—
135C3×C8D3×Q812yes—
136C3⋊C8—32no—
137C3⋊C8—32no—
138C3⋊C8—61no—
139C3⋊C8—61no—
140C2×C32—21no—
141C2×C32#47611yescharacteristic
142C3⋊D3—81no—
143#41—181no—
144C2×Q8—361no—
145Q16—91no—
146SD16—181no—
147D8—91no—
148M16—21no—
149M16—361no—
150C2×C8—91no—
151C2×C8—361no—
152C2×C8C2×D3211yescharacteristic
153C4⋊C4—62no—
154C4⋊C4—361no—
155C42—91no—
156C16—62no—
157C22×C3—21no—
158C22×C3#91412yes—
159C2×D3—122no—
160C2×D3—122no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—242no—
164C3×C4#89612yes—
165C3×C4D3×SD1612yes—
166Dic3—64no—
167Dic3—82no—
168Dic3—122no—
169Dic3—122no—
170Dic3—122no—
171C32#223011yescharacteristic, complemented, Sylow
172Q8—181no—
173Q8—722no—
174D4—181no—
175D4—361no—
176C2×C4—122no—
177C2×C4—181no—
178C2×C4—361no—
179C2×C4#381111yescharacteristic
180C8—41no—
181C8—91no—
182C8—91no—
183C8#379711yescharacteristic
184C8#379811yescharacteristic
185C2×C3—22no—
186C2×C3—21no—
187C2×C3—41no—
188C2×C3#487012yes—
189D3—242no—
190D3—242no—
191C22—361no—
192C22#6394111yescharacteristic
193C4—182no—
194C4—242no—
195C4—361no—
196C4#6386511yescharacteristic
197C4#6393011yescharacteristic
198C3—21no—
199C3#6931512yescomplemented
200C2—21no—
201C2—721no—
202C2#1059043311yescharacteristic
subgroupG/H
centerC2#10590433
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#108C22
socleC2×C32#476
prime radical#64113C22
hypercenter#108D32
hypocenterC32#2230
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. #10590900C2semidirect
3. C3×#4494C2semidirect
4. #10589135C2semidirect
22. #4494D3semidirect
30. #3746Q8semidirect
31. #3745Q8semidirect
171. C32#2230semidirect
199. C3#69315semidirect

Maximal subgroups

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

subgroupindex
#105925942
#105909002
C3×#44942
#105891352
#105891252
#693153