Finite Group Databasebeta

← #37543221

Subgroups — #37543221

Order 23168.

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

normal subgroups only

This group has 526 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
1C2×#19153842C211yesmaximal, characteristic, complemented
2#26041846C211yesmaximal, characteristic, complemented
3#26041754C211yesmaximal, characteristic, complemented
4#26041492C214yesmaximal, complemented
5#26041472C214yesmaximal, complemented
6#26041305C211yesmaximal, characteristic, complemented
7#26041284C211yesmaximal, characteristic, complemented
8#26041276C211yesmaximal, characteristic, complemented
9C22×D8×C181C211yesmaximal, characteristic, complemented
10C2×#15668449C2211yescharacteristic
11#19153842—24no—
12C2×#15668437C2212yescomplemented
13C2×#15668434C2212yescomplemented
14C2×#15668433C2211yescharacteristic
15#19153812C2212yescomplemented
16#19153803C2212yescomplemented
17#19153787—22no—
18#19153785—22no—
19D4×Dic181—22no—
20D4×Dic181C2214yescomplemented
21#19153775C2211yescharacteristic
22#19153775C2211yescharacteristic
23C2×C22⋊Dic181—22no—
24#19153745C2214yescomplemented
25#19153741C2212yescomplemented
26#19153738C2212yescomplemented
27#19153737C2214yescomplemented
28C22×D4×C181C2211yescharacteristic
29C22×D4×C181C2211yescharacteristic
30C2×D8×C181—24no—
31C2×D8×C181C2214yes—
32C22×C8×C181C2211yescharacteristic
33#15668449—22no—
34#15668449—22no—
35C2×Dic362C2311yescharacteristic
36C2×D724C2311yescharacteristic
37C2×C22⋊D181—24no—
38C2×C22⋊D181—21no—
39C22×Dic181—24no—
40C2×C4×D181—21no—
41#15668437—24no—
42#15668434—24no—
43#15668433—22no—
44C2×#13089678C2312yes—
45C4⋊Dic181D412yes—
46C4⋊Dic181C2312yes—
47C22⋊Dic181—24no—
48C22⋊Dic181—24no—
49C22⋊Dic181—21no—
50C22⋊Dic181D412yes—
51C4×Dic181—21no—
52C4×Dic181C2312yes—
53C24×C181—21no—
54C24×C181—21no—
55C2×D4×C181—21no—
56C2×D4×C181—22no—
57C2×D4×C181—21no—
58C2×D4×C181—22no—
59C2×D4×C181—22no—
60C2×D4×C181D414yescomplemented
61C2×D4×C181C2312yes—
62C2×D4×C181C2312yes—
63C22×C4×C181C2311yescharacteristic
64D8×C181—28no—
65C2×C8×C181—22no—
66C2×C8×C181C2312yes—
67C22×D181—21no—
68Dic362—21no—
69Dic362—21no—
70D724—21no—
71D724—21no—
72C22⋊D181—42no—
73C22⋊D181—84no—
74C2×Dic181—22no—
75C2×Dic181—21no—
76C2×Dic181—84no—
77C2×Dic181C2×D414yes—
78C4×D181—42no—
79#13089678—22no—
80C23×C181—22no—
81C23×C181—24no—
82C23×C181—22no—
83C23×C181—42no—
84C23×C181—82no—
85C23×C181—82no—
86C23×C181C2×D411yescharacteristic
87D4×C181—24no—
88D4×C181—22no—
89D4×C181—22no—
90D4×C181—22no—
91D4×C181—42no—
92D4×C181C2×D414yes—
93C2×C4×C181C2×D411yescharacteristic
94C2×C4×C181C2×D412yes—
95C2×C4×C181#4112yes—
96C2×C4×C181C2411yescharacteristic
97C8×C181—22no—
98C22×C181—22no—
99C22×C181—24no—
100C22×C181—44no—
101C22×C181—42no—
102C22×C181—44no—
103C22×C181—84no—
104C22×C181—84no—
105C22×C181#12112yes—
106C22×C181C22×D411yescharacteristic
107C2×D181—41no—
108C2×D181—42no—
109C4×C181#12112yes—
110C4×C181C22×D411yescharacteristic
111C4×C181C2×#4111yescharacteristic
112Dic181—24no—
113Dic181—41no—
114Dic181—42no—
115C2×C181—22no—
116C2×C181—44no—
117C2×C181—82no—
118C2×C181C2×#12111yescharacteristic
119C2×C181#57612yes—
120D181—81no—
121C181#304111yescharacteristic, complemented, Sylow
122#3041—1811nomaximal, Sylow
123C2×AGL(1,ℤ/8)—1811no—
124C22×D8D18111yescharacteristic, complemented
125#535—1811no—
126#518—1811no—
127#463—1814no—
128#459—1814no—
129#424—1811no—
130#418—1811no—
131#416—1811no—
132C2×#41—1811no—
133C22×D4C2×D18111yescharacteristic
134C22×D4C2×D18111yescharacteristic
135AGL(1,ℤ/8)—3624no—
136C2×SD16—1812no—
137C2×D8—24no—
138C2×D8—1812no—
139C2×D8C2×D18114yes—
140C2×M16—1811no—
141C22×C8C2×D18111yescharacteristic
142#127—1812no—
143#124—1812no—
144#121—3622no—
145#120—3622no—
146C4×D4—3622no—
147C4×D4—1814no—
148#117—1811no—
149#117—1811no—
150C2×C22⋊C4—3622no—
151C4⋊C8—1814no—
152#103—1812no—
153#102—1814no—
154#102—1812no—
155C24—21no—
156C24—21no—
157#41—3622no—
158#41—3622no—
159C2×Q8—1811no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—22no—
165C2×D4—3621no—
166C2×D4—3624no—
167C2×D4—1811no—
168C2×D4C22⋊D18114yescomplemented
169C2×D4C22×D18112yes—
170C2×D4C22×D18112yes—
171C22×C4—3624no—
172C22×C4—3621no—
173C22×C4C22×D18111yescharacteristic
174SD16—3624no—
175D8—28no—
176D8—3624no—
177M16—3622no—
178C2×C8—22no—
179C2×C8—1812no—
180C2×C8C22×D18112yes—
181C4⋊C4—1812no—
182C4⋊C4—1812no—
183C22⋊C4—3621no—
184C22⋊C4—3624no—
185C22⋊C4—3624no—
186C22⋊C4—1812no—
187C42—3621no—
188C42—1812no—
189C23—22no—
190C23—24no—
191C23—22no—
192C23—42no—
193C23—82no—
194C23—82no—
195C23—3621no—
196C23D4×D18111yescharacteristic
197Q8—3621no—
198Q8—3621no—
199D4—24no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—3621no—
205D4—3621no—
206D4—14484no—
207D4—7242no—
208D4C2×C22⋊D18114yes—
209C2×C4—3622no—
210C2×C4—3621no—
211C2×C4—14484no—
212C2×C4—1814no—
213C2×C4—7242no—
214C2×C4D4×D18111yescharacteristic
215C2×C4C2×C22⋊D18112yes—
216C2×C4#1566844812yes—
217C2×C4C23×D18111yescharacteristic
218C8—22no—
219C8—3622no—
220C22—22no—
221C22—24no—
222C22—44no—
223C22—42no—
224C22—44no—
225C22—84no—
226C22—84no—
227C22—7241no—
228C22—7242no—
229C22#1915378812yes—
230C22C2×D4×D18111yescharacteristic
231C4—3624no—
232C4—7241no—
233C4—7242no—
234C4#1915378812yes—
235C4C22×C22⋊D18111yescharacteristic
236C4C2×#1566844811yescharacteristic
237C2—22no—
238C2—44no—
239C2—82no—
240C2—14481no—
241C2C2×#1915378811yescharacteristic
242C2#2604208012yes—
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC22×D8×C181C2
socleC22×C181C22×D4
hypercenterC22×D8D181
hypocenterC181#3041
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#19153842C2semidirect
2. #26041846C2semidirect
3. #26041754C2semidirect
4. #26041492C2semidirect
5. #26041472C2semidirect
6. #26041305C2semidirect
7. #26041284C2semidirect
8. #26041276C2semidirect
9. C22×D8×C181C2semidirect
12. C2×#15668437C22semidirect
13. C2×#15668434C22semidirect
15. #19153812C22semidirect
16. #19153803C22semidirect
20. D4×Dic181C22semidirect
24. #19153745C22semidirect
25. #19153741C22semidirect
26. #19153738C22semidirect
27. #19153737C22semidirect
60. C2×D4×C181D4semidirect
121. C181#3041semidirect
124. C22×D8D181semidirect
168. C2×D4C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538422
#260418462
#260417542
#260414922
#260414722
#260413052
#260412842
#260412762
C22×D8×C1812
#3041181