Finite Group Databasebeta

← #11778545

Subgroups — #11778545

Order 1152.

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

normal subgroups only

This group has 762 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
2C32×#398C211yesmaximal, characteristic, complemented
3#10592666C212yesmaximal, complemented
4#10589394C211yesmaximal, characteristic, complemented
5#10589317C212yesmaximal, complemented
6#69712—34nomaximal
7C2×#3828—21no—
8C2×C32×C4⋊C4—21no—
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139—21no—
12#64139C2212yes—
13#64106—22no—
14#64104—22no—
15C32×#95—21no—
16C32×#95C2211yescharacteristic
17#63657C2212yes—
18#63636—22no—
19#63634—22no—
20#5510—34no—
21C3×#398D314yescomplemented
22#4967—38no—
23#4528—34no—
24#4451—38no—
25C22×C32×C4—21no—
26C22×C32×C4—21no—
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4C2311yescharacteristic
30C2×#638—22no—
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—
38C32×C4⋊C4—22no—
39C32×C4⋊C4—22no—
40C32×C4⋊C4—42no—
41#3752—22no—
42#3752—22no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)D412yes—
45C2×C3⋊(C3⋊C8)—22no—
46#1610—91noSylow
47C2×#235—64no—
48C2×C3×C4⋊C4—24no—
49C2×C3×C4⋊C4C2×D314yes—
50C2×C3×C4⋊C4C2×D314yes—
51#930—38no—
52#930—64no—
53#897—68no—
54#895—68no—
55C3×#95—24no—
56C3×#95C2×D314yes—
57#830—38no—
58#809—68no—
59#807—68no—
60C23×C32C2×D411yescharacteristic
61C22×C3⋊D3—22no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—22no—
65C2×C32×C4—21no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4—41no—
69C2×C32×C4—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4D812yes—
74C2×C32×C4C2×D412yes—
75#638—42no—
76#638—42no—
77C2×C3⋊Dic3—22no—
78C4⋊(C3⋊D3)—42no—
79C4⋊(C3⋊D3)—42no—
80C4⋊(C3⋊D3)—81no—
81C4×C3⋊D3—44no—
82#634—42no—
83C3⋊(C3⋊C8)—42no—
84#537—91no—
85#480—92no—
86#398C3⋊D311yescharacteristic, complemented
87#327—92no—
88#324—91no—
89C22×C3×C4—24no—
90C22×C3×C4—24no—
91C22×C3×C4#6714yes—
92C22×C3×C4#6714yes—
93C22×C3×C4C22×D314yes—
94C2×#67—68no—
95#235—128no—
96#235—128no—
97C2×D12—38no—
98C2×D12—64no—
99C2×D12—64no—
100C2×C4×D3—68no—
101C2×Dic6—64no—
102C3×C4⋊C4—28no—
103C3×C4⋊C4—28no—
104C3×C4⋊C4—48no—
105(C2×D3)⋊C4—68no—
106(C2×D3)⋊C4—68no—
107C4⋊Dic3—38no—
108C4⋊Dic3—64no—
109C2×C3⋊C8—68no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32#12011yescharacteristic
113C22×C32C2×D811yescharacteristic
114C22×C32AGL(1,ℤ/8)11yescharacteristic
115C2×C3⋊D3—42no—
116C2×C3⋊D3—42no—
117C2×C3⋊D3—42no—
118C32×C4—22no—
119C32×C4—22no—
120C32×C4—42no—
121C32×C4—41no—
122C32×C4—81no—
123C3⋊Dic3—42no—
124C2×#41—181no—
125C22⋊Q8—182no—
126#121—92no—
127#121—182no—
128#121—181no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4C2×C3⋊D311yescharacteristic
131C2×C4⋊C4C2×C3⋊D311yescharacteristic
132#107—182no—
133#102—182no—
134C22⋊C8—92no—
135#95—21no—
136#95C2×C3⋊D311yescharacteristic
137C23×C3C2×#6714yes—
138C22×D3—68no—
139C2×C3×C4—24no—
140C2×C3×C4—24no—
141C2×C3×C4—28no—
142C2×C3×C4—24no—
143C2×C3×C4—44no—
144C2×C3×C4—44no—
145C2×C3×C4—44no—
146C2×C3×C4—44no—
147C2×C3×C4—44no—
148C2×C3×C4—44no—
149C2×C3×C4—44no—
150C2×C3×C4#21318yes—
151C2×C3×C4D3×D418yes—
152#67—128no—
153#67—128no—
154C2×Dic3—68no—
155D12—128no—
156D12—128no—
157D12—244no—
158C4×D3—1216no—
159Dic6—128no—
160C3⋊C8—128no—
161C2×C32—21no—
162C2×C32—21no—
163C2×C32#44711yescharacteristic
164C2×C32#45611yescharacteristic
165C2×C32#45811yescharacteristic
166C3⋊D3—82no—
167#41—362no—
168#41—362no—
169C2×Q8—181no—
170C2×D4—92no—
171C2×D4—181no—
172C2×D4—181no—
173C2×D4—182no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—182no—
177C22×C4#63811yescharacteristic
178C22×C4#63811yescharacteristic
179C22×C4C22×C3⋊D311yescharacteristic
180C2×C8—182no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—42no—
184C4⋊C4—92no—
185C4⋊C4—181no—
186C22⋊C4—182no—
187C22⋊C4—182no—
188C22×C3—24no—
189C22×C3—24no—
190C22×C3C2×#21314yes—
191C22×C3#93714yes—
192C22×C3#94914yes—
193C2×D3—128no—
194C2×D3—128no—
195C2×D3—128no—
196C3×C4—28no—
197C3×C4—28no—
198C3×C4—48no—
199C3×C4—44no—
200C3×C4—84no—
201Dic3—128no—
202C32#161011yescharacteristic, complemented, Sylow
203C23—182no—
204C23C2×#63811yescharacteristic
205Q8—362no—
206D4—362no—
207D4—362no—
208D4—362no—
209D4—362no—
210D4—721no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—182no—
223C2×C4—364no—
224C2×C4#375312yes—
225C2×C4D4×C3⋊D312yes—
226C8—362no—
227C2×C3—24no—
228C2×C3—24no—
229C2×C3#503614yes—
230C2×C3#505314yes—
231C2×C3#509514yes—
232D3—248no—
233C22—21no—
234C22—21no—
235C22—362no—
236C22—362no—
237C22—362no—
238C22C2×#375311yescharacteristic
239C22#6414611yescharacteristic
240C22#6415811yescharacteristic
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—81no—
246C4—362no—
247C3#6971214yescomplemented
248C2—21no—
249C2—21no—
250C2—722no—
251C2#1059273511yescharacteristic
252C2#1059275211yescharacteristic
253C2#1059279411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#398C2
socleC22×C32#120
prime radical#10595981C2
hypercenter#398C3⋊D3
hypocenterC32#1610
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C32×#398C2semidirect
3. #10592666C2semidirect
4. #10589394C2semidirect
5. #10589317C2semidirect
21. C3×#398D3semidirect
86. #398C3⋊D3semidirect
202. C32#1610semidirect
247. C3#69712semidirect

Maximal subgroups

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

subgroupindex
#105959812
C32×#3982
#105926662
#105893942
#105893172
#697123