Finite Group Databasebeta

← #37542570

Subgroups — #37542570

Order 23168.

528 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 175 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×D8×D181C211yesmaximal, characteristic
2#26041751C212yesmaximal, complemented
3#26041392C211yesmaximal, characteristic, complemented
4#26041391C211yesmaximal, characteristic, complemented
5#26041390C211yesmaximal, characteristic, complemented
6C4×#15668434C212yesmaximal, complemented
7#26041359C212yesmaximal, complemented
8#26041314C211yesmaximal, characteristic, complemented
9#26041282C212yesmaximal, complemented
10#26041236C211yesmaximal, characteristic, complemented
11#442×C181C211yesmaximal, characteristic, complemented
12C2×D4×D181C2212yes—
13C2×D1448C2211yescharacteristic
14C2×#15668434C2212yes—
15D8×D181C418yescomplemented
16C2×#15668432C2211yescharacteristic
17C2×C8×D181C2211yescharacteristic
18C4×D724C2212yescomplemented
19D4×Dic181C2212yescomplemented
20#19153778C2212yescomplemented
21C4×C22⋊D181—22no—
22#19153776—22no—
23#19153774C2212yes—
24#19153773C2211yescharacteristic
25C2×#15668426—22no—
26C22⋊C4×D181—22no—
27#19153749C2212yescomplemented
28#19153748C2211yescharacteristic, complemented
29#19153738C2212yescomplemented
30#19153737C2212yescomplemented
31#19153736C2212yescomplemented
32#19153726C2211yescharacteristic, complemented
33C4×#13089678C2211yescharacteristic, complemented
34C8×Dic181C2211yescharacteristic, complemented
35C2×D8×C181C2211yescharacteristic
36C4×D4×C181C2212yescomplemented
37#106×C181C2211yescharacteristic, complemented
38#102×C181C2212yescomplemented
39#97×C181C2211yescharacteristic, complemented
40C23×D181—22no—
41C2×D724C2312yes—
42C2×C22⋊D181—22no—
43D4×D181—24no—
44D4×D181C2×C418yescomplemented
45C22×Dic181—22no—
46C2×C4×D181—22no—
47C2×C4×D181—22no—
48C2×C4×D181C2311yescharacteristic
49D1448C2×C414yescomplemented
50#15668434C2×C418yescomplemented
51#15668432—22no—
52C2×#13089678C2311yescharacteristic
53C2×#13089678C2311yescharacteristic
54C8×D181C2×C414yescomplemented
55C4⋊Dic181C2312yes—
56#15668428D412yes—
57C22⋊Dic181—22no—
58#15668426—22no—
59#15668426—22no—
60#15668426—22no—
61#15668426D412yes—
62C4×Dic181—22no—
63C4×Dic181C2311yescharacteristic
64C2×D4×C181C2312yes—
65C22×C4×C181—22no—
66D8×C181C2×C414yescomplemented
67C2×C8×C181C2311yescharacteristic
68C2×C8×C181C2311yescharacteristic
69C4⋊C4×C181C2312yes—
70C22⋊C4×C181—22no—
71C42×C181C2311yescharacteristic
72C22×D181—22no—
73C22×D181—28no—
74C22×D181—82no—
75C22×D181—82no—
76C22×D181C2×D411yescharacteristic
77D724—22no—
78D724C22×C414yes—
79C22⋊D181—28no—
80C2×Dic181—22no—
81C2×Dic181—82no—
82C2×Dic181C2×D412yes—
83C2×Dic181C2×D411yescharacteristic
84C4×D181—82no—
85C4×D181—82no—
86C4×D181C22×C412yes—
87C4×D181#4112yes—
88#13089678—21no—
89#13089678C22×C412yes—
90C23×C181—22no—
91D4×C181—22no—
92D4×C181C22×C414yes—
93C2×C4×C181—22no—
94C2×C4×C181—82no—
95C2×C4×C181C2×D412yes—
96C2×C4×C181C2411yescharacteristic
97C8×C181—21no—
98C8×C181C22×C412yes—
99C22×C181—24no—
100C22×C181—42no—
101C22×C181—42no—
102C22×C181C22×D411yescharacteristic
103C2×D181—22no—
104C2×D181—24no—
105C2×D181—42no—
106C2×D181—42no—
107C2×D181—88no—
108C2×D181C4×D412yes—
109C4×C181—22no—
110C4×C181—42no—
111C4×C181C23×C411yescharacteristic
112C4×C181C2×#4111yescharacteristic
113Dic181—22no—
114Dic181—42no—
115Dic181C4×D412yes—
116C2×C181—44no—
117C2×C181C2×C4×D411yescharacteristic
118C2×C181#57612yes—
119D181—22no—
120D181—44no—
121C181#294811yescharacteristic, complemented, Sylow
122#2948—1811nomaximal, Sylow
123C22×D8—1811no—
124#518—1812no—
125#442—1811no—
126#442—1811no—
127#442—1811no—
128#442D18111yescharacteristic, complemented
129C4×D8—1812no—
130C4×D8—1812no—
131#427—1811no—
132#418—1812no—
133#405—1811no—
134C22×D4—1812no—
135C2×D8—1812no—
136C2×D8—1818no—
137C2×D8—1811no—
138C2×D8C2×D18111yescharacteristic
139C2×M16—1811no—
140C22×C8—1811no—
141C4×D4—3622no—
142C4×D4—3622no—
143C4×D4—1812no—
144C4×D4—1812no—
145C4×D4—1812no—
146C4×D4C2×D18112yescomplemented
147#117—1812no—
148#117—1811no—
149C2×C22⋊C4—3622no—
150C2×C22⋊C4—3622no—
151#107—1812no—
152#106—1811no—
153#106C2×D18111yescharacteristic, complemented
154#102—1812no—
155#102—1812no—
156#102—1812no—
157#102C2×D18112yescomplemented
158#97—1811no—
159#97C2×D18111yescharacteristic, complemented
160C4×C8—1811no—
161C4×C8—1811no—
162C24—3622no—
163C2×D4—3624no—
164C2×D4—3622no—
165C2×D4—1818no—
166C2×D4—1812no—
167C2×D4C22×D18112yes—
168C22×C4—22no—
169C22×C4—3622no—
170C22×C4—3622no—
171C22×C4—3622no—
172C22×C4—1811no—
173D8—1818no—
174D8—1814no—
175D8C4×D18114yescomplemented
176M16—3622no—
177C2×C8—1811no—
178C2×C8—1811no—
179C2×C8—1814no—
180C2×C8C22×D18111yescharacteristic
181C2×C8C22×D18111yescharacteristic
182C4⋊C4—1812no—
183C4⋊C4—1812no—
184C4⋊C4C22×D18112yes—
185C22⋊C4—22no—
186C22⋊C4—3622no—
187C22⋊C4—3622no—
188C22⋊C4—3622no—
189C22⋊C4—3622no—
190C22⋊C4—1812no—
191C42—3622no—
192C42—1811no—
193C42C22×D18111yescharacteristic
194C23—22no—
195C23—3628no—
196C23—3622no—
197C23—14482no—
198C23—14482no—
199C23—1811no—
200D4—22no—
201D4—3628no—
202D4—3622no—
203D4—1814no—
204D4C2×C4×D18114yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—3622no—
208C2×C4—14482no—
209C2×C4—14482no—
210C2×C4—14482no—
211C2×C4—1812no—
212C2×C4—1811no—
213C2×C4—1812no—
214C2×C4—1812no—
215C2×C4D4×D18112yes—
216C2×C4C23×D18111yescharacteristic
217C8—21no—
218C8—3621no—
219C8—1812no—
220C8C2×C4×D18112yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—3622no—
225C22—3624no—
226C22—14488no—
227C22—1812no—
228C22—7242no—
229C22—7242no—
230C22C2×D4×D18111yescharacteristic
231C4—22no—
232C4—42no—
233C4—3622no—
234C4—1812no—
235C4—7242no—
236C4C22×C4×D18111yescharacteristic
237C4#41×D18111yescharacteristic
238C2—44no—
239C2—3622no—
240C2—7244no—
241C2C4×D4×D18111yescharacteristic
242C2#2604208312yes—
subgroupG/H
centerC22C2×D4×D181
commutatorC4×C181C23×C4
FrattiniC2×C4C23×D181
Fitting#442×C181C2
socleC22×C181C22×D4
prime radicalC2×D8×D181C2
cosocleC2×C4×C181C24
hypercenter#442D181
hypocenterC181#2948
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #26041751C2semidirect
3. #26041392C2semidirect
4. #26041391C2semidirect
5. #26041390C2semidirect
6. C4×#15668434C2semidirect
7. #26041359C2semidirect
8. #26041314C2semidirect
9. #26041282C2semidirect
10. #26041236C2semidirect
11. #442×C181C2semidirect
15. D8×D181C4semidirect
18. C4×D724C22semidirect
19. D4×Dic181C22semidirect
20. #19153778C22semidirect
27. #19153749C22semidirect
28. #19153748C22semidirect
29. #19153738C22semidirect
30. #19153737C22semidirect
31. #19153736C22semidirect
32. #19153726C22semidirect
33. C4×#13089678C22semidirect
34. C8×Dic181C22semidirect
36. C4×D4×C181C22semidirect
37. #106×C181C22semidirect
38. #102×C181C22semidirect
39. #97×C181C22semidirect
44. D4×D181C2×C4semidirect
49. D1448C2×C4semidirect
50. #15668434C2×C4semidirect
54. C8×D181C2×C4semidirect
66. D8×C181C2×C4semidirect
121. C181#2948semidirect
128. #442D181semidirect
146. C4×D4C2×D181semidirect
153. #106C2×D181semidirect
157. #102C2×D181semidirect
159. #97C2×D181semidirect
175. D8C4×D181semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1812
#260417512
#260413922
#260413912
#260413902
C4×#156684342
#260413592
#260413142
#260412822
#260412362
#442×C1812
#2948181