Finite Group Databasebeta

← #11778780

Subgroups — #11778780

Order 1152.

738 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 129 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#10595981C211yesmaximal, characteristic
2#10592685C211yesmaximal, characteristic, complemented
3#10592434C212yesmaximal, complemented
4C32×#324C211yesmaximal, characteristic, complemented
5#10589336C212yesmaximal, complemented
6#68137—34nomaximal
7C2×#3828—21no—
8C2×C32×C4⋊C4C2211yescharacteristic
9#64139—21no—
10#64139C2212yes—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12#64106—22no—
13#64104—22no—
14C32×C22⋊C8C2212yes—
15#63658—21no—
16#63658—21no—
17#63658C2211yescharacteristic
18#63648—22no—
19#63644—22no—
20#5510—34no—
21#4986—34no—
22#4735—38no—
23C3×#324D314yescomplemented
24#4470—38no—
25C22×C32×C4D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C2×#638—22no—
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31#3828—42no—
32#3828—42no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×C4⋊(C3⋊D3)—21no—
35C2×C4⋊(C3⋊D3)D412yes—
36C2×C4×C3⋊D3—22no—
37C2×#634—21no—
38C2×C32×C8—22no—
39C32×C4⋊C4—22no—
40#3752—22no—
41#3752—22no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—22no—
44C4⋊(C3⋊Dic3)D412yes—
45#1616—91noSylow
46C2×#235—64no—
47C2×C3×C4⋊C4C2×D314yes—
48#930—38no—
49#930—64no—
50C2×C4⋊Dic3—34no—
51#897—68no—
52#895—68no—
53C3×C22⋊C8C2×D318yes—
54C3⋊#95—34no—
55C3⋊#95—64no—
56C3⋊#95—64no—
57#821—68no—
58#817—68no—
59C23×C32C2×D411yescharacteristic
60C22×C3⋊D3—22no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4SD1612yes—
67C2×C32×C4C2×D412yes—
68#638—42no—
69#638—42no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—42no—
74C2×C3⋊Dic3—41no—
75C2×C3⋊Dic3—41no—
76C4⋊(C3⋊D3)—42no—
77C4⋊(C3⋊D3)—42no—
78C4⋊(C3⋊D3)—81no—
79C4×C3⋊D3—44no—
80#634—42no—
81C32×C8—42no—
82#537—91no—
83#481—92no—
84#400—91no—
85#327—92no—
86#324C3⋊D311yescharacteristic, complemented
87C22×C3×C4D1214yes—
88C22×C3×C4D1214yes—
89C22×C3×C4C22×D314yes—
90C2×#67—68no—
91C22×Dic3—64no—
92C22×Dic3—64no—
93#235—128no—
94#235—128no—
95C2×D12—38no—
96C2×D12—64no—
97C2×D12—64no—
98C2×C4×D3—68no—
99C2×Dic6—64no—
100C2×C3×C8—28no—
101C3×C4⋊C4—28no—
102(C2×D3)⋊C4—68no—
103(C2×D3)⋊C4—68no—
104C4⋊Dic3—38no—
105C4⋊Dic3—64no—
106C4⋊Dic3—68no—
107C22×C32—21no—
108C22×C32—21no—
109C22×C32#12011yescharacteristic
110C22×C32C2×SD1611yescharacteristic
111C22×C32AGL(1,ℤ/8)11yescharacteristic
112C2×C3⋊D3—42no—
113C2×C3⋊D3—42no—
114C2×C3⋊D3—42no—
115C32×C4—22no—
116C32×C4—22no—
117C32×C4—41no—
118C3⋊Dic3—42no—
119C3⋊Dic3—81no—
120C3⋊Dic3—81no—
121C2×#41—181no—
122C22⋊Q8—182no—
123#121—92no—
124#121—182no—
125#121—181no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4C2×C3⋊D311yescharacteristic
128#106—182no—
129#102—182no—
130C22⋊C8C2×C3⋊D312yes—
131#95—91no—
132#95—181no—
133#95—181no—
134C23×C3C2×D1214yes—
135C22×D3—68no—
136C2×C3×C4—24no—
137C2×C3×C4—24no—
138C2×C3×C4—24no—
139C2×C3×C4—44no—
140C2×C3×C4—44no—
141C2×C3×C4#20418yes—
142C2×C3×C4D3×D418yes—
143#67—128no—
144#67—128no—
145C2×Dic3—68no—
146C2×Dic3—124no—
147C2×Dic3—124no—
148C2×Dic3—128no—
149C2×Dic3—124no—
150C2×Dic3—124no—
151D12—128no—
152D12—128no—
153D12—244no—
154C4×D3—1216no—
155Dic6—128no—
156C3×C8—48no—
157C2×C32—21no—
158C2×C32—21no—
159C2×C32#45011yescharacteristic
160C2×C32#45411yescharacteristic
161C2×C32#45811yescharacteristic
162C3⋊D3—82no—
163#41—362no—
164#41—362no—
165C2×Q8—181no—
166C2×D4—92no—
167C2×D4—181no—
168C2×D4—181no—
169C2×D4—182no—
170C22×C4—182no—
171C22×C4—181no—
172C22×C4—181no—
173C22×C4C4⋊(C3⋊D3)11yescharacteristic
174C22×C4C4⋊(C3⋊D3)11yescharacteristic
175C22×C4C22×C3⋊D311yescharacteristic
176C2×C8—22no—
177C4⋊C4—22no—
178C4⋊C4—92no—
179C4⋊C4—181no—
180C4⋊C4—182no—
181C22⋊C4—182no—
182C22⋊C4—182no—
183C22×C3—24no—
184C22×C3—24no—
185C22×C3#88214yes—
186C22×C3C2×#20414yes—
187C22×C3#90814yes—
188C2×D3—128no—
189C2×D3—128no—
190C2×D3—128no—
191C3×C4—28no—
192C3×C4—28no—
193C3×C4—44no—
194Dic3—128no—
195Dic3—244no—
196Dic3—244no—
197C32#161611yescharacteristic, complemented, Sylow
198C23—182no—
199C23C2×C4⋊(C3⋊D3)11yescharacteristic
200Q8—362no—
201D4—362no—
202D4—362no—
203D4—362no—
204D4—362no—
205D4—721no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—182no—
212C2×C4—364no—
213C2×C4—361no—
214C2×C4—361no—
215C2×C4—362no—
216C2×C4—361no—
217C2×C4—361no—
218C2×C4#374412yes—
219C2×C4D4×C3⋊D312yes—
220C8—42no—
221C2×C3—24no—
222C2×C3—24no—
223C2×C3#473114yes—
224C2×C3#474214yes—
225C2×C3#475314yes—
226D3—248no—
227C22—21no—
228C22—21no—
229C22—362no—
230C22—362no—
231C22—362no—
232C22#6409111yescharacteristic
233C22C2×#374411yescharacteristic
234C22#6411711yescharacteristic
235C4—22no—
236C4—22no—
237C4—41no—
238C4—362no—
239C4—721no—
240C4—721no—
241C3#6813714yescomplemented
242C2—21no—
243C2—21no—
244C2—722no—
245C2#1059243011yescharacteristic
246C2#1059244111yescharacteristic
247C2#1059245211yescharacteristic
subgroupG/H
centerC22#64091
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#324C2
socleC22×C32#120
prime radical#10595981C2
hypercenter#324C3⋊D3
hypocenterC32#1616
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #10592685C2semidirect
3. #10592434C2semidirect
4. C32×#324C2semidirect
5. #10589336C2semidirect
23. C3×#324D3semidirect
86. #324C3⋊D3semidirect
197. C32#1616semidirect
241. C3#68137semidirect

Maximal subgroups

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

subgroupindex
#105959812
#105926852
#105924342
C32×#3242
#105893362
#681373