Finite Group Databasebeta

← #11799995

Subgroups — #11799995

Order 1152.

333 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 333 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592564C211yesmaximal, characteristic
2#10590914C211yesmaximal, characteristic, complemented
3C3×#4487C212yesmaximal, complemented
4#10589128C212yesmaximal, complemented
5#10589110C211yesmaximal, characteristic, complemented
6#69313—32nomaximal
7C2×#3745C2211yescharacteristic
8C2×#3743C2211yescharacteristic
9#64104—21no—
10#63818—21no—
11C32×#106C2211yescharacteristic
12#63636—21no—
13C3×#819C2212yes—
14C3×#812C2212yes—
15#63578—21no—
16#4893—32no—
17#4865—32no—
18#4865—61no—
19C3×#365—32no—
20#4516—32no—
21#4514—32no—
22#4495—32no—
23#4487D312yescomplemented
24C2×C4⋊(C3⋊D3)—21no—
25C2×C4⋊(C3⋊D3)—41no—
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C32×C8C2311yescharacteristic
28C32×C4⋊C4—21no—
29#3752—41no—
30C2×C3⋊(C3⋊C8)D411yescharacteristic
31#3745—22no—
32#3743—22no—
33C3×#208—22no—
34#3712—41no—
35#3710—41no—
36C3×C3⋊C16—22no—
37#2238—91noSylow
38D3×M16—62no—
39C2×D24—32no—
40C2×D24—61no—
41C2×ΓL(1,𝔽25)—32no—
42C2×ΓL(1,𝔽25)—61no—
43#895—62no—
44#895—62no—
45C3×M32—32no—
46C3×#108—32no—
47C3×#106—21no—
48C3×#106C2×D312yes—
49#822—62no—
50#819C2×D312yes—
51#812C2×D312yes—
52#809—62no—
53#809—62no—
54C22×C3⋊D3—41no—
55C22×C3⋊D3SD1611yescharacteristic
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3SD1611yescharacteristic
59C4⋊(C3⋊D3)—41no—
60C4⋊(C3⋊D3)—41no—
61C4⋊(C3⋊D3)—82no—
62C4×C3⋊D3—21no—
63C4×C3⋊D3—21no—
64C32×C8#4112yes—
65C3⋊(C3⋊C8)—21no—
66C3×C3⋊C8—42no—
67#469—91no—
68#430—91no—
69#365—32no—
70#361—92no—
71#349—91no—
72C2×D12—62no—
73C2×D12—62no—
74C2×D12—122no—
75C2×D12—122no—
76C2×C4×D3—32no—
77C2×C4×D3—61no—
78C3×M16—62no—
79C2×C3×C8—21no—
80C2×C3×C8C22×D312yes—
81C3×C4⋊C4—22no—
82C3×C4⋊C4—22no—
83(C2×D3)⋊C4—122no—
84(C2×D3)⋊C4—122no—
85#208—22no—
86C2×C3⋊C8—32no—
87C2×C3⋊C8—61no—
88D24—62no—
89D24—62no—
90D24—122no—
91ΓL(1,𝔽25)—62no—
92ΓL(1,𝔽25)—62no—
93ΓL(1,𝔽25)—122no—
94ΓL(1,𝔽25)—122no—
95D3×C8—122no—
96C3×C16—62no—
97C3⋊C16—22no—
98C22×C32C2×SD1611yescharacteristic
99C2×C3⋊D3—21no—
100C2×C3⋊D3—41no—
101C2×C3⋊D3—81no—
102C2×C3⋊D3—81no—
103C2×C3⋊D3—81no—
104C32×C4—81no—
105C32×C4#12311yescharacteristic
106C32×C4AGL(1,ℤ/8)11yescharacteristic
107C3⋊Dic3—21no—
108C2×D8—91no—
109C2×M16—91no—
110C2×M16—181no—
111#121—181no—
112M32—32no—
113#108—32no—
114#108—181no—
115#106D3211yescharacteristic
116#102—181no—
117C22×D3—32no—
118C22×D3—61no—
119C22×D3—122no—
120C22×D3—122no—
121C2×C3×C4—21no—
122C2×C3×C4—42no—
123C2×C3×C4—42no—
124C2×C3×C4D3×D412yes—
125C2×Dic3—32no—
126C2×Dic3—61no—
127D12—122no—
128D12—122no—
129D12—122no—
130D12—122no—
131D12—244no—
132D12—244no—
133C4×D3—62no—
134C4×D3—62no—
135C4×D3—121no—
136C4×D3—121no—
137C3×C8—22no—
138C3×C8—122no—
139C3×C8#23512yes—
140C3×C8#23912yes—
141C3⋊C8—42no—
142C3⋊C8—62no—
143C3⋊C8—121no—
144C2×C32—21no—
145C2×C32#48111yescharacteristic
146C3⋊D3—41no—
147C3⋊D3—161no—
148C2×D4—181no—
149C2×D4—361no—
150C22×C4—91no—
151D8—182no—
152M16—62no—
153M16—182no—
154M16—361no—
155C2×C8—91no—
156C2×C8—361no—
157C2×C8C2×D3211yescharacteristic
158C4⋊C4—21no—
159C22⋊C4—361no—
160C16—62no—
161C22×C3—21no—
162C22×C3D3×SD1612yes—
163C2×D3—62no—
164C2×D3—121no—
165C2×D3—122no—
166C2×D3—122no—
167C2×D3—242no—
168C2×D3—242no—
169C2×D3—242no—
170C2×D3—242no—
171C2×D3—242no—
172C2×D3—242no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—82no—
176C3×C4—82no—
177C3×C4#89412yes—
178C3×C4#91412yes—
179Dic3—62no—
180Dic3—121no—
181C32#223811yescharacteristic, complemented, Sylow
182C23—91no—
183C23—361no—
184D4—361no—
185D4—361no—
186D4—722no—
187C2×C4—41no—
188C2×C4—91no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4#381111yescharacteristic
192C8—122no—
193C8—181no—
194C8#379912yes—
195C2×C3—22no—
196C2×C3—22no—
197C2×C3—21no—
198C2×C3#486312yes—
199D3—122no—
200D3—241no—
201D3—482no—
202D3—482no—
203C22—181no—
204C22—361no—
205C22—721no—
206C22—721no—
207C22—721no—
208C22#6393011yescharacteristic
209C4—81no—
210C4—181no—
211C4#6389711yescharacteristic
212C4#6394111yescharacteristic
213C3—21no—
214C3#6931312yescomplemented
215C2—21no—
216C2—361no—
217C2—1441no—
218C2#1059044511yescharacteristic
subgroupG/H
centerC2#10590445
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32#481
prime radical#10592564C2
hypercenter#106D32
hypocenterC32#2238
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10590914C2semidirect
3. C3×#4487C2semidirect
4. #10589128C2semidirect
5. #10589110C2semidirect
23. #4487D3semidirect
181. C32#2238semidirect
214. C3#69313semidirect

Maximal subgroups

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

subgroupindex
#105925642
#105909142
C3×#44872
#105891282
#105891102
#693133