Finite Group Databasebeta

← #37545963

Subgroups — #37545963

Order 23168.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#26041994C211yesmaximal, characteristic, complemented
2#26041625C211yesmaximal, characteristic, complemented
3#26041600C212yesmaximal, complemented
4#26041569C211yesmaximal, characteristic, complemented
5#26041530C212yesmaximal, complemented
6#26041471C211yesmaximal, characteristic, complemented
7#26041413C212yesmaximal, complemented
8C4×#15668434C211yesmaximal, characteristic, complemented
9#26041357C211yesmaximal, characteristic, complemented
10#26041284C212yesmaximal, complemented
11D42×C181C211yesmaximal, characteristic, complemented
12C2×#15668434C2211yescharacteristic
13C2×#15668434C2212yescomplemented
14C2×#15668433C2212yescomplemented
15#19153816C2211yescharacteristic, complemented
16#19153802—22no—
17#19153790C2212yescomplemented
18#19153787—21no—
19C4×D724C2211yescharacteristic, complemented
20#19153775C2212yescomplemented
21#19153774—21no—
22#19153749C2211yescharacteristic, complemented
23#19153747C2212yescomplemented
24C4⋊#13089678C2211yescharacteristic, complemented
25#19153737C2211yescharacteristic
26#19153737C2212yes—
27#19153737C2212yescomplemented
28#19153737C2212yescomplemented
29#19153737C2212yescomplemented
30#19153736C2211yescharacteristic, complemented
31C22⋊#13089678C2212yescomplemented
32C4×#13089678C2211yescharacteristic, complemented
33C22×D4×C181—21no—
34C22×D4×C181C2212yes—
35#127×C181C2211yescharacteristic
36#121×C181—21no—
37#121×C181C2212yes—
38#120×C181—22no—
39C4×D4×C181C2211yescharacteristic
40C4×D4×C181C2211yescharacteristic
41C2×Dic362—21no—
42C2×D724C2311yescharacteristic
43C2×C22⋊D181—22no—
44C2×C4×D181—21no—
45#15668434—22no—
46#15668434—42no—
47#15668433—42no—
48C2×#13089678C2311yescharacteristic
49C2×#13089678C2311yescharacteristic
50C2×#13089678C2312yes—
51C4⋊Dic181—21no—
52C4⋊Dic181C2312yes—
53C4⋊Dic181C2311yescharacteristic
54C22⋊Dic181—22no—
55#15668426—22no—
56#15668426—21no—
57C4×Dic181—22no—
58C24×C181—22no—
59C2×D4×C181—24no—
60C2×D4×C181—22no—
61C2×D4×C181—22no—
62C2×D4×C181—21no—
63C2×D4×C181—21no—
64C2×D4×C181—42no—
65C2×D4×C181—44no—
66C2×D4×C181D411yescharacteristic
67C2×D4×C181C2312yes—
68C2×D4×C181C2311yescharacteristic
69C22×C4×C181—21no—
70C22×C4×C181C2312yes—
71C4⋊C4×C181D411yescharacteristic
72C4⋊C4×C181C2311yescharacteristic
73C22⋊C4×C181—21no—
74C22⋊C4×C181—22no—
75C22⋊C4×C181D412yes—
76C42×C181C2311yescharacteristic
77C22×D181—21no—
78Dic362—81no—
79D724—21no—
80D724—21no—
81C22⋊D181—82no—
82C2×Dic181—21no—
83C2×Dic181—22no—
84C4×D181—42no—
85#13089678—21no—
86#13089678—21no—
87#13089678—22no—
88C23×C181—21no—
89C23×C181—22no—
90C23×C181—44no—
91C23×C181—44no—
92C23×C181—82no—
93C23×C181C2×D412yes—
94D4×C181—22no—
95D4×C181—22no—
96D4×C181—21no—
97D4×C181—22no—
98D4×C181—44no—
99D4×C181—44no—
100D4×C181—42no—
101D4×C181—81no—
102D4×C181#4112yes—
103C2×C4×C181—22no—
104C2×C4×C181—22no—
105C2×C4×C181—21no—
106C2×C4×C181—42no—
107C2×C4×C181C2×D411yescharacteristic
108C2×C4×C181C2×D412yes—
109C2×C4×C181C2×D411yescharacteristic
110C2×C4×C181C2411yescharacteristic
111C22×C181—22no—
112C22×C181—22no—
113C22×C181—22no—
114C22×C181—22no—
115C22×C181—41no—
116C22×C181—41no—
117C22×C181—42no—
118C22×C181—42no—
119C22×C181—42no—
120C22×C181—88no—
121C22×C181C22×D411yescharacteristic
122C2×D181—41no—
123C2×D181—41no—
124C2×D181—41no—
125C4×C181—22no—
126C4×C181—21no—
127C4×C181—41no—
128C4×C181AGL(1,ℤ/8)12yes—
129C4×C181C2×#4111yescharacteristic
130C4×C181H(5,𝔽2)11yescharacteristic
131Dic181—41no—
132Dic181—42no—
133C2×C181—42no—
134C2×C181—42no—
135C2×C181—82no—
136C2×C181#54611yescharacteristic
137C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C181#57611yescharacteristic
139D181—81no—
140C181#332511yescharacteristic, complemented, Sylow
141#3325—1811nomaximal, Sylow
142#555—1811no—
143D42D18111yescharacteristic, complemented
144#486—1811no—
145#482—1812no—
146#476—1811no—
147#469—1812no—
148#459—1811no—
149#447—1812no—
150C4×D8—1811no—
151#436—1811no—
152#418—1812no—
153C22×D4—21no—
154C22×D4C2×D18112yes—
155C2×D8—1811no—
156C2×D8—1812no—
157C2×M16—1812no—
158C4⋊Q8—1811no—
159#127C2×D18111yescharacteristic
160#124—3622no—
161#121—21no—
162#121—3621no—
163#121—1812no—
164#121C2×D18112yes—
165#120—22no—
166C4×D4—1811no—
167C4×D4C2×D18111yescharacteristic
168C4×D4C2×D18111yescharacteristic
169#117—3621no—
170#117—1812no—
171#107—1811no—
172#106—1812no—
173C4⋊C8—1811no—
174#102—1811no—
175#102—1812no—
176#102—1812no—
177#102—1812no—
178#102—1812no—
179#102—1811no—
180C22⋊C8—1812no—
181C4×C8—1811no—
182C24—22no—
183C2×Q8—3621no—
184C2×D4—24no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—42no—
190C2×D4—44no—
191C2×D4—3622no—
192C2×D4—1811no—
193C2×D4C22⋊D18111yescharacteristic
194C2×D4C22×D18112yes—
195C2×D4C22×D18111yescharacteristic
196C22×C4—21no—
197C22×C4—3621no—
198C22×C4C22×D18112yes—
199D8—3622no—
200D8—7242no—
201M16—7242no—
202C2×C8—1811no—
203C2×C8—1811no—
204C2×C8—1812no—
205C4⋊C4—3621no—
206C4⋊C4—1812no—
207C4⋊C4—1811no—
208C4⋊C4C22⋊D18111yescharacteristic
209C4⋊C4C22×D18111yescharacteristic
210C22⋊C4—21no—
211C22⋊C4—22no—
212C22⋊C4—3622no—
213C22⋊C4—3622no—
214C22⋊C4—3621no—
215C22⋊C4C22⋊D18112yes—
216C42—3622no—
217C42C22×D18111yescharacteristic
218C23—21no—
219C23—22no—
220C23—44no—
221C23—44no—
222C23—82no—
223C23—3621no—
224C23C2×C22⋊D18112yes—
225Q8—14481no—
226D4—22no—
227D4—22no—
228D4—21no—
229D4—22no—
230D4—44no—
231D4—44no—
232D4—42no—
233D4—81no—
234D4—3621no—
235D4—3621no—
236D4—14482no—
237D4#1566844812yes—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—3621no—
243C2×C4—3622no—
244C2×C4—7242no—
245C2×C4C2×C22⋊D18112yes—
246C2×C4C2×C22⋊D18111yescharacteristic
247C2×C4C2×C22⋊D18111yescharacteristic
248C2×C4C23×D18111yescharacteristic
249C8—3621no—
250C8—3621no—
251C8—3622no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—88no—
262C22—7241no—
263C22—7241no—
264C22—7241no—
265C22C22×C22⋊D18111yescharacteristic
266C4—22no—
267C4—21no—
268C4—41no—
269C4—7241no—
270C4—7242no—
271C4#1915384212yes—
272C4C2×#1566844811yescharacteristic
273C4#1915386111yescharacteristic
274C2—42no—
275C2—42no—
276C2—82no—
277C2—14481no—
278C2#2604192311yescharacteristic
279C2C2×#1915384211yescharacteristic
280C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingD42×C181C2
socleC22×C181C22×D4
hypercenterD42D181
hypocenterC181#3325
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #26041994C2semidirect
2. #26041625C2semidirect
3. #26041600C2semidirect
4. #26041569C2semidirect
5. #26041530C2semidirect
6. #26041471C2semidirect
7. #26041413C2semidirect
8. C4×#15668434C2semidirect
9. #26041357C2semidirect
10. #26041284C2semidirect
11. D42×C181C2semidirect
13. C2×#15668434C22semidirect
14. C2×#15668433C22semidirect
15. #19153816C22semidirect
17. #19153790C22semidirect
19. C4×D724C22semidirect
20. #19153775C22semidirect
22. #19153749C22semidirect
23. #19153747C22semidirect
24. C4⋊#13089678C22semidirect
27. #19153737C22semidirect
28. #19153737C22semidirect
29. #19153737C22semidirect
30. #19153736C22semidirect
31. C22⋊#13089678C22semidirect
32. C4×#13089678C22semidirect
140. C181#3325semidirect
143. D42D181semidirect

Maximal subgroups

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

subgroupindex
#260419942
#260416252
#260416002
#260415692
#260415302
#260414712
#260414132
C4×#156684342
#260413572
#260412842
D42×C1812
#3325181