Finite Group Databasebeta

← #37543644

Subgroups — #37543644

Order 23168.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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#26041790C211yesmaximal, characteristic
2#26041614C212yesmaximal, complemented
3#26041609C212yesmaximal, complemented
4#26041597C212yesmaximal, complemented
5#26041592C212yesmaximal, complemented
6#26041319C212yesmaximal, complemented
7#26041278C212yesmaximal, complemented
8#26041243C211yesmaximal, characteristic, complemented
9C22×C4⋊C4×C181C211yesmaximal, characteristic, complemented
10C2×#15668449C2211yescharacteristic
11C2×#15668433C2212yes—
12#19153799—21no—
13#19153795C2211yescharacteristic
14#19153795C2211yescharacteristic
15#19153790C2211yescharacteristic
16#19153790C2211yescharacteristic
17#19153785—21no—
18C4×C22⋊D181—21no—
19C4×C22⋊D181—21no—
20#19153775C2211yescharacteristic
21#19153749C2214yescomplemented
22#19153747C2214yescomplemented
23#19153739C2214yescomplemented
24#19153736C2214yescomplemented
25C22⋊#13089678C2212yes—
26C22⋊#13089678C2212yes—
27C23×C4×C181—21no—
28C23×C4×C181C2211yescharacteristic
29C2×C4⋊C4×C181—21no—
30C2×C4⋊C4×C181—21no—
31C2×C4⋊C4×C181—21no—
32C2×C4⋊C4×C181C2212yes—
33C2×C4⋊C4×C181C2212yes—
34C2×C4⋊C4×C181C2212yes—
35#15668449—24no—
36C2×Dic362C2311yescharacteristic
37C2×D724C2311yescharacteristic
38C2×C22⋊D181—21no—
39C2×C22⋊D181—21no—
40C2×C22⋊D181—21no—
41C2×C4×D181—21no—
42#15668433—24no—
43C2×#13089678C2314yes—
44C4⋊Dic181C2311yescharacteristic
45C4⋊Dic181C2311yescharacteristic
46#15668428—21no—
47#15668428—21no—
48C22⋊Dic181—21no—
49C22⋊Dic181—21no—
50C22⋊Dic181—21no—
51#15668426—21no—
52#15668426—21no—
53C4×Dic181—21no—
54C24×C181D411yescharacteristic
55C22×C4×C181—24no—
56C22×C4×C181—22no—
57C22×C4×C181—22no—
58C22×C4×C181—22no—
59C22×C4×C181—44no—
60C22×C4×C181D411yescharacteristic
61C22×C4×C181D411yescharacteristic
62C22×C4×C181D411yescharacteristic
63C22×C4×C181C2311yescharacteristic
64C22×C4×C181C2311yescharacteristic
65C22×C4×C181C2311yescharacteristic
66C4⋊C4×C181—22no—
67C4⋊C4×C181—22no—
68C4⋊C4×C181—22no—
69C4⋊C4×C181C2314yes—
70C22×D181—21no—
71Dic362—22no—
72D724—22no—
73C22⋊D181—42no—
74C22⋊D181—42no—
75C22⋊D181—42no—
76C2×Dic181—21no—
77C2×Dic181—21no—
78C2×Dic181—21no—
79C4×D181—42no—
80#13089678—24no—
81C23×C181—22no—
82C23×C181—22no—
83C23×C181—22no—
84C23×C181C2×D411yescharacteristic
85C23×C181C2×D411yescharacteristic
86C23×C181C2×D411yescharacteristic
87C2×C4×C181—22no—
88C2×C4×C181—22no—
89C2×C4×C181—22no—
90C2×C4×C181—22no—
91C2×C4×C181—22no—
92C2×C4×C181—24no—
93C2×C4×C181—44no—
94C2×C4×C181—44no—
95C2×C4×C181—44no—
96C2×C4×C181C2×D411yescharacteristic
97C2×C4×C181C2×D411yescharacteristic
98C2×C4×C181C2×D411yescharacteristic
99C2×C4×C181#4114yes—
100C2×C4×C181C2411yescharacteristic
101C22×C181—28no—
102C22×C181—21no—
103C22×C181—21no—
104C22×C181—21no—
105C22×C181—21no—
106C22×C181—21no—
107C22×C181—21no—
108C22×C181#12312yes—
109C22×C181AGL(1,ℤ/8)12yes—
110C22×C181#13712yes—
111C22×C181C22×D411yescharacteristic
112C2×D181—41no—
113C2×D181—41no—
114C2×D181—41no—
115C4×C181—21no—
116C4×C181—21no—
117C4×C181—44no—
118C4×C181#12312yes—
119C4×C181C2×#4112yes—
120Dic181—41no—
121Dic181—41no—
122Dic181—41no—
123C2×C181—22no—
124C2×C181—22no—
125C2×C181—22no—
126C2×C181C2×#12311yescharacteristic
127C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C181C2×#13711yescharacteristic
129D181—81no—
130C181#309211yescharacteristic, complemented, Sylow
131#3092—1811nomaximal, Sylow
132#525—1811no—
133C22×C4⋊C4D18111yescharacteristic, complemented
134#484—1812no—
135#483—1812no—
136#481—1812no—
137#480—1812no—
138#428—1812no—
139#417—1812no—
140#407—1811no—
141C2×#41—1811no—
142C23×C4—21no—
143C23×C4C2×D18111yescharacteristic
144C2×M16—1812no—
145#123—3621no—
146C22⋊Q8—1811no—
147C22⋊Q8—1811no—
148#121—1811no—
149#121—1811no—
150#120—3621no—
151C4×D4—3621no—
152C4×D4—3621no—
153#117—1811no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4C2×D18112yes—
158C2×C4⋊C4C2×D18112yes—
159C2×C4⋊C4C2×D18112yes—
160#107—1814no—
161#106—1814no—
162#103—1814no—
163#102—1814no—
164C22⋊C8—1812no—
165C22⋊C8—1812no—
166C24C22⋊D18111yescharacteristic
167#41—3624no—
168C2×Q8—1811no—
169C2×D4—3621no—
170C2×D4—3621no—
171C2×D4—3621no—
172C2×D4—1811no—
173C22×C4—24no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4—44no—
178C22×C4—3621no—
179C22×C4C22⋊D18111yescharacteristic
180C22×C4C22⋊D18111yescharacteristic
181C22×C4C22⋊D18111yescharacteristic
182C22×C4C22×D18111yescharacteristic
183C22×C4C22×D18111yescharacteristic
184C22×C4C22×D18111yescharacteristic
185M16—3624no—
186C2×C8—1814no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—3621no—
191C4⋊C4—3621no—
192C4⋊C4—1811no—
193C4⋊C4—1811no—
194C4⋊C4C22×D18114yes—
195C22⋊C4—3621no—
196C22⋊C4—3621no—
197C22⋊C4—3621no—
198C22⋊C4—3621no—
199C22⋊C4—3621no—
200C42—3621no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—3621no—
205C23C2×C22⋊D18111yescharacteristic
206C23C2×C22⋊D18111yescharacteristic
207C23C2×C22⋊D18111yescharacteristic
208Q8—3622no—
209D4—3622no—
210D4—7242no—
211D4—7242no—
212D4—7242no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—24no—
219C2×C4—44no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—3621no—
223C2×C4—3621no—
224C2×C4—3621no—
225C2×C4—7242no—
226C2×C4C2×C22⋊D18111yescharacteristic
227C2×C4C2×C22⋊D18111yescharacteristic
228C2×C4C2×C22⋊D18111yescharacteristic
229C2×C4#1566844914yes—
230C2×C4C23×D18111yescharacteristic
231C8—3624no—
232C22—28no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—21no—
239C22—7241no—
240C22—7241no—
241C22—7241no—
242C22#1915379912yes—
243C22#1915384212yes—
244C22#1915384712yes—
245C22C22×C22⋊D18111yescharacteristic
246C4—21no—
247C4—21no—
248C4—44no—
249C4—7241no—
250C4—7241no—
251C4—7241no—
252C4#1915379912yes—
253C4C2×#1566844912yes—
254C2—22no—
255C2—22no—
256C2—22no—
257C2—14481no—
258C2C2×#1915379911yescharacteristic
259C2C2×#1915384211yescharacteristic
260C2C2×#1915384711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC22×C4⋊C4×C181C2
socleC22×C181C22×D4
prime radical#26041790C2
hypercenterC22×C4⋊C4D181
hypocenterC181#3092
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #26041614C2semidirect
3. #26041609C2semidirect
4. #26041597C2semidirect
5. #26041592C2semidirect
6. #26041319C2semidirect
7. #26041278C2semidirect
8. #26041243C2semidirect
9. C22×C4⋊C4×C181C2semidirect
21. #19153749C22semidirect
22. #19153747C22semidirect
23. #19153739C22semidirect
24. #19153736C22semidirect
130. C181#3092semidirect
133. C22×C4⋊C4D181semidirect

Maximal subgroups

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

subgroupindex
#260417902
#260416142
#260416092
#260415972
#260415922
#260413192
#260412782
#260412432
C22×C4⋊C4×C1812
#3092181