Finite Group Databasebeta

← #11785343

Subgroups — #11785343

Order 1152.

1008 conjugacy classes of subgroups; only the 241 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 241 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
1C22×C8×C3⋊D3C211yesmaximal, characteristic
2#10592686C212yesmaximal
3C2×#63635C212yesmaximal, complemented
4C32×#340C211yesmaximal, characteristic, complemented
5#10589417C211yesmaximal, characteristic, complemented
6#68868—34nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C32×C8C2211yescharacteristic
9C2×C32×C4⋊C4C2212yes—
10C2×#3752—22no—
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C8×C3⋊D3—24no—
14C2×C8×C3⋊D3C414yescomplemented
15#63658—22no—
16#63635—24no—
17C22×D3×C8—34no—
18#4987—38no—
19C2×#808—38no—
20C3×#340D314yescomplemented
21#4551—34no—
22C23×C3⋊D3D411yescharacteristic
23C22×C32×C4—22no—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3—22no—
26C22×C3⋊Dic3D411yescharacteristic
27C2×C4×C3⋊D3—22no—
28C2×C4×C3⋊D3—22no—
29C2×C4×C3⋊D3C2×C412yes—
30C2×C4×C3⋊D3Q812yes—
31C2×C32×C8—22no—
32C2×C32×C8C2×C412yes—
33C32×C4⋊C4—22no—
34C32×C4⋊C4—22no—
35#3752—44no—
36C4⋊(C3⋊Dic3)—22no—
37C4⋊(C3⋊Dic3)—22no—
38C2×C3⋊(C3⋊C8)C2×C412yes—
39C2×C3⋊(C3⋊C8)D414yes—
40C8×C3⋊D3—28no—
41#1807—91noSylow
42C22×C4×D3—34no—
43C22×C3×C8C2×D314yes—
44C2×C3×C4⋊C4C2×D318yes—
45C2×(C2×D3)⋊C4—68no—
46C2×C4⋊Dic3—38no—
47C22×C3⋊C8—34no—
48C2×D3×C8—316no—
49C2×D3×C8—616no—
50C3⋊#95—68no—
51#808—616no—
52C23×C32C2×D411yescharacteristic
53C22×C3⋊D3—22no—
54C22×C3⋊D3—21no—
55C22×C3⋊D3—21no—
56C22×C3⋊D3C4⋊C412yes—
57C22×C3⋊D3SD1614yes—
58C2×C32×C4—42no—
59C2×C32×C4—42no—
60C2×C32×C4—42no—
61C2×C32×C4C22×C411yescharacteristic
62C2×C32×C4C2×D412yes—
63C2×C32×C4C2×Q811yescharacteristic
64C2×C32×C4#4112yes—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—42no—
67C2×C3⋊Dic3—42no—
68C2×C3⋊Dic3—42no—
69C2×C3⋊Dic3C4⋊C412yes—
70C4×C3⋊D3—22no—
71C4×C3⋊D3—22no—
72C4×C3⋊D3—24no—
73C32×C8—22no—
74C3⋊(C3⋊C8)C22⋊C414yescomplemented
75C23×C8—91no—
76C2×#106—92no—
77#380—92no—
78#340—91no—
79#340C3⋊D311yescharacteristic, complemented
80C23×D3—34no—
81C22×C3×C4—28no—
82C22×C3×C4C22×D314yes—
83C22×Dic3—34no—
84C22×Dic3—68no—
85C2×C4×D3—38no—
86C2×C4×D3—38no—
87C2×C4×D3—68no—
88C2×C4×D3—68no—
89C2×C3×C8—28no—
90C2×C3×C8C4×D318yes—
91C3×C4⋊C4—28no—
92C3×C4⋊C4—28no—
93(C2×D3)⋊C4—1216no—
94C4⋊Dic3—68no—
95C4⋊Dic3—68no—
96C2×C3⋊C8—38no—
97C2×C3⋊C8—316no—
98D3×C8—632no—
99C22×C32C2×C4⋊C411yescharacteristic
100C22×C32#12112yes—
101C22×C32C2×SD1612yes—
102C22×C32#13511yescharacteristic
103C22×C32#13511yescharacteristic
104C2×C3⋊D3—22no—
105C2×C3⋊D3—22no—
106C2×C3⋊D3—24no—
107C2×C3⋊D3—24no—
108C2×C3⋊D3#10614yescomplemented
109C32×C4—82no—
110C32×C4C2×C22⋊C411yescharacteristic
111C32×C4#11711yescharacteristic
112C32×C4C22⋊Q812yes—
113C3⋊Dic3—22no—
114C3⋊Dic3—82no—
115C23×C4—91no—
116C22×C8—91no—
117C22×C8—94no—
118C22×C8—184no—
119C22×C8C2×C3⋊D311yescharacteristic
120C2×C4⋊C4—92no—
121C2×C4⋊C4C2×C3⋊D312yes—
122C2×C22⋊C4—182no—
123#106—184no—
124#95—182no—
125C23×C3D3×D414yes—
126C22×D3—38no—
127C22×D3—316no—
128C22×D3—68no—
129C22×D3—64no—
130C22×D3—64no—
131C2×C3×C4—48no—
132C2×C3×C4—48no—
133C2×C3×C4—48no—
134C2×C3×C4C2×C4×D314yes—
135C2×C3×C4#23518yes—
136C2×C3×C4D3×D418yes—
137C2×C3×C4D3×Q814yes—
138C2×Dic3—38no—
139C2×Dic3—68no—
140C2×Dic3—128no—
141C2×Dic3—128no—
142C2×Dic3—128no—
143C4×D3—68no—
144C4×D3—68no—
145C4×D3—616no—
146C3×C8—28no—
147C3⋊C8—316no—
148C2×C32#38011yescharacteristic
149C2×C32C2×#10611yescharacteristic
150C2×C32#42711yescharacteristic
151C2×C32#46512yes—
152C2×C32#46512yes—
153C3⋊D3—24no—
154C24—91no—
155C22×C4—22no—
156C22×C4—91no—
157C22×C4—92no—
158C22×C4—92no—
159C22×C4—182no—
160C22×C4—182no—
161C22×C4—182no—
162C22×C4C22×C3⋊D311yescharacteristic
163C2×C8—22no—
164C2×C8—92no—
165C2×C8—94no—
166C2×C8—188no—
167C2×C8C4×C3⋊D312yes—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—182no—
171C4⋊C4—182no—
172C22⋊C4—364no—
173C22×C3#88418yes—
174C22×C3D3×C4⋊C414yes—
175C22×C3#91214yes—
176C22×C3D3×SD1618yes—
177C22×C3#91914yes—
178C2×D3—316no—
179C2×D3—68no—
180C2×D3—68no—
181C2×D3—616no—
182C2×D3—616no—
183C3×C4—88no—
184C3×C4#87214yes—
185C3×C4D3×C22⋊C414yes—
186C3×C4#89618yes—
187Dic3—68no—
188Dic3—248no—
189C32#180711yescharacteristic, complemented, Sylow
190C23—92no—
191C23—94no—
192C23—182no—
193C23—181no—
194C23—181no—
195C23D4×C3⋊D311yescharacteristic
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—92no—
200C2×C4—182no—
201C2×C4—182no—
202C2×C4—182no—
203C2×C4—184no—
204C2×C4—362no—
205C2×C4—362no—
206C2×C4—362no—
207C2×C4C2×C4×C3⋊D311yescharacteristic
208C2×C4#382812yes—
209C2×C4D4×C3⋊D312yes—
210C2×C4Q8×C3⋊D311yescharacteristic
211C8—22no—
212C8—94no—
213C2×C3#466714yes—
214C2×C3#477818yes—
215C2×C3#480718yes—
216C2×C3D3×#10614yes—
217C2×C3#488014yes—
218D3—616no—
219C22—94no—
220C22—182no—
221C22—182no—
222C22—184no—
223C22—184no—
224C22#6409312yes—
225C22C4⋊C4×C3⋊D311yescharacteristic
226C22#6412111yescharacteristic
227C22SD16×C3⋊D312yes—
228C22#6412811yescharacteristic
229C4—82no—
230C4—182no—
231C4—722no—
232C4#6408111yescharacteristic
233C4C22⋊C4×C3⋊D311yescharacteristic
234C4#6410512yes—
235C3#6886814yescomplemented
236C2—184no—
237C2#1059236611yescharacteristic
238C2#1059247712yes—
239C2#1059250612yes—
240C2C3⋊D3×#10611yescharacteristic
241C2#1059257911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1807
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. C2×#63635C2semidirect
4. C32×#340C2semidirect
5. #10589417C2semidirect
14. C2×C8×C3⋊D3C4semidirect
20. C3×#340D3semidirect
74. C3⋊(C3⋊C8)C22⋊C4semidirect
79. #340C3⋊D3semidirect
108. C2×C3⋊D3#106semidirect
189. C32#1807semidirect
235. C3#68868semidirect

Maximal subgroups

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

subgroupindex
C22×C8×C3⋊D32
#105926862
C2×#636352
C32×#3402
#105894172
#688683