Finite Group Databasebeta

← #11778319

Subgroups — #11778319

Order 1152.

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

normal subgroups only

This group has 846 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×#395C211yesmaximal, characteristic, complemented
3#10592926C212yesmaximal, complemented
4#10589394C211yesmaximal, characteristic, complemented
5#10589317C212yesmaximal, complemented
6#69706—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×#3828—21no—
9C2×C32×C4⋊C4—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×#3755—22no—
12#64139—21no—
13#64139C2212yes—
14#64106—22no—
15#64104—22no—
16C32×#95—21no—
17C32×#95C2211yescharacteristic
18#63662—22no—
19#63657C2212yes—
20#5510—34no—
21C3×#395D314yescomplemented
22#5227—38no—
23#4528—34no—
24#4451—38no—
25C2×C32×Q8—22no—
26C2×C32×Q8—42no—
27C22×C32×C4—21no—
28C22×C32×C4—21no—
29C22×C32×C4D411yescharacteristic
30C22×C32×C4D411yescharacteristic
31C22×C32×C4C2311yescharacteristic
32C2×#638—22no—
33#3828—42no—
34#3828—42no—
35C2×C4⋊(C3⋊D3)—21no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)D412yes—
38C2×C4×C3⋊D3—22no—
39C2×#634—21no—
40C32×C4⋊C4—22no—
41C32×C4⋊C4—42no—
42#3755—44no—
43#3752—22no—
44#3752—22no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)D412yes—
47C2×C3⋊(C3⋊C8)—22no—
48#1604—91noSylow
49C22×C3×Q8C2×D314yes—
50C2×#235—64no—
51C2×C3×C4⋊C4—24no—
52C2×C3×C4⋊C4C2×D314yes—
53C2×#215—68no—
54#930—38no—
55#930—64no—
56#897—68no—
57#895—68no—
58C3×#95—24no—
59C3×#95C2×D314yes—
60#835—68no—
61#830—38no—
62C23×C32C2×D411yescharacteristic
63C22×C3⋊D3—22no—
64C32×Q8—24no—
65C32×Q8—42no—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4—22no—
69C2×C32×C4—22no—
70C2×C32×C4—21no—
71C2×C32×C4—41no—
72C2×C32×C4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4SD1612yescomplemented
78C2×C32×C4C2×D412yes—
79#638—42no—
80#638—42no—
81C2×C3⋊Dic3—22no—
82C4⋊(C3⋊D3)—42no—
83C4⋊(C3⋊D3)—42no—
84C4⋊(C3⋊D3)—81no—
85C4×C3⋊D3—44no—
86#634—42no—
87C3⋊(C3⋊C8)—42no—
88#537—91no—
89#448—92no—
90#395C3⋊D311yescharacteristic, complemented
91#327—92no—
92#324—91no—
93C2×C3×Q8—28no—
94C2×C3×Q8—48no—
95C22×C3×C4—24no—
96C22×C3×C4—24no—
97C22×C3×C4#6714yes—
98C22×C3×C4#6714yes—
99C22×C3×C4C22×D314yes—
100C2×#67—68no—
101#235—128no—
102#235—128no—
103C2×D12—38no—
104C2×D12—64no—
105C2×D12—64no—
106C2×C4×D3—68no—
107C2×Dic6—64no—
108C3×C4⋊C4—28no—
109C3×C4⋊C4—48no—
110#215—1216no—
111(C2×D3)⋊C4—68no—
112(C2×D3)⋊C4—68no—
113C4⋊Dic3—38no—
114C4⋊Dic3—64no—
115C2×C3⋊C8—68no—
116C22×C32—21no—
117C22×C32—21no—
118C22×C32#12011yescharacteristic
119C22×C32C2×SD1611yescharacteristic
120C22×C32AGL(1,ℤ/8)11yescharacteristic
121C2×C3⋊D3—42no—
122C2×C3⋊D3—42no—
123C2×C3⋊D3—42no—
124C32×C4—22no—
125C32×C4—22no—
126C32×C4—42no—
127C32×C4—41no—
128C32×C4—42no—
129C3⋊Dic3—42no—
130C2×#41—181no—
131C22×Q8C2×C3⋊D311yescharacteristic
132C2×SD16—182no—
133C22⋊Q8—182no—
134#121—92no—
135#121—182no—
136#121—181no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4C2×C3⋊D311yescharacteristic
139#103—182no—
140C22⋊C8—92no—
141#95—21no—
142#95C2×C3⋊D311yescharacteristic
143C23×C3C2×#6714yes—
144C22×D3—68no—
145C3×Q8—216no—
146C3×Q8—48no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—28no—
150C2×C3×C4—28no—
151C2×C3×C4—24no—
152C2×C3×C4—44no—
153C2×C3×C4—44no—
154C2×C3×C4—44no—
155C2×C3×C4—44no—
156C2×C3×C4—44no—
157C2×C3×C4—44no—
158C2×C3×C4#21518yescomplemented
159C2×C3×C4D3×D418yes—
160#67—128no—
161#67—128no—
162C2×Dic3—68no—
163D12—128no—
164D12—128no—
165D12—244no—
166C4×D3—1216no—
167Dic6—128no—
168C3⋊C8—128no—
169C2×C32—21no—
170C2×C32—21no—
171C2×C32#45011yescharacteristic
172C2×C32#45611yescharacteristic
173C2×C32B(4,𝔽2)11yescharacteristic
174C3⋊D3—82no—
175#41—362no—
176#41—362no—
177C2×Q8—22no—
178C2×Q8—42no—
179C2×Q8—181no—
180C2×D4—92no—
181C2×D4—181no—
182C2×D4—181no—
183C2×D4—182no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—182no—
187C22×C4#63811yescharacteristic
188C22×C4#63811yescharacteristic
189C22×C4C22×C3⋊D311yescharacteristic
190SD16—364no—
191C2×C8—182no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—92no—
195C4⋊C4—181no—
196C22⋊C4—182no—
197C22⋊C4—182no—
198C22×C3—24no—
199C22×C3—24no—
200C22×C3#93714yes—
201C22×C3C2×#21514yes—
202C22×C3#94914yes—
203C2×D3—128no—
204C2×D3—128no—
205C2×D3—128no—
206C3×C4—28no—
207C3×C4—28no—
208C3×C4—48no—
209C3×C4—44no—
210C3×C4—48no—
211Dic3—128no—
212C32#160411yescharacteristic, complemented, Sylow
213C23—182no—
214C23C2×#63811yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—362no—
218D4—362no—
219D4—362no—
220D4—362no—
221D4—362no—
222D4—721no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—182no—
235C2×C4—364no—
236C2×C4#375512yescomplemented
237C2×C4D4×C3⋊D312yes—
238C8—362no—
239C2×C3—24no—
240C2×C3—24no—
241C2×C3#503214yes—
242C2×C3#504614yes—
243C2×C3#509514yes—
244D3—248no—
245C22—21no—
246C22—21no—
247C22—362no—
248C22—362no—
249C22—362no—
250C22#6414611yescharacteristic
251C22C2×#375511yescharacteristic
252C22#6415811yescharacteristic
253C4—22no—
254C4—22no—
255C4—42no—
256C4—42no—
257C4—41no—
258C4—362no—
259C3#6970614yescomplemented
260C2—21no—
261C2—21no—
262C2—722no—
263C2#1059273111yescharacteristic
264C2#1059274511yescharacteristic
265C2#1059279411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#395C2
socleC22×C32#120
prime radical#10595981C2
hypercenter#395C3⋊D3
hypocenterC32#1604
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C32×#395C2semidirect
3. #10592926C2semidirect
4. #10589394C2semidirect
5. #10589317C2semidirect
21. C3×#395D3semidirect
77. C2×C32×C4SD16semidirect
90. #395C3⋊D3semidirect
158. C2×C3×C4#215semidirect
212. C32#1604semidirect
236. C2×C4#3755semidirect
259. C3#69706semidirect

Maximal subgroups

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

subgroupindex
#105959812
C32×#3952
#105929262
#105893942
#105893172
#697063