Finite Group Databasebeta

← #19143444

Subgroups — #19143444

Order 5504.

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×D43C211yesmaximal, characteristic
2#14583371C212yesmaximal, complemented
3#14583012C211yesmaximal, characteristic, complemented
4#14583011C211yesmaximal, characteristic, complemented
5#14583010C211yesmaximal, characteristic, complemented
6C4×#10621882C212yesmaximal, complemented
7#14582979C212yesmaximal, complemented
8#14582934C211yesmaximal, characteristic, complemented
9#14582902C212yesmaximal, complemented
10#14582856C211yesmaximal, characteristic, complemented
11C43×#442C211yesmaximal, characteristic, complemented
12C2×D4×D43C2212yes—
13C2×D344C2211yescharacteristic
14C2×#10621882C2212yes—
15D8×D43C418yescomplemented
16C2×#10621872C2211yescharacteristic
17C2×C8×D43C2211yescharacteristic
18C4×D172C2212yescomplemented
19D4×Dic43C2212yescomplemented
20#13063287C2212yescomplemented
21C4×C22⋊D43—22no—
22(C22⋊D43)⋊C4—22no—
23#13063283C2212yes—
24#13063282C2211yescharacteristic
25C2×(C2×D43)⋊C4—22no—
26C22⋊C4×D43—22no—
27#13063258C2212yescomplemented
28#13063257C2211yescharacteristic, complemented
29#13063247C2212yescomplemented
30#13063246C2212yescomplemented
31#13063245C2212yescomplemented
32#13063235C2211yescharacteristic, complemented
33C4×C43⋊C8C2211yescharacteristic, complemented
34C8×Dic43C2211yescharacteristic, complemented
35C2×D8×C43C2211yescharacteristic
36C4×D4×C43C2212yescomplemented
37#106×C43C2211yescharacteristic, complemented
38#102×C43C2212yescomplemented
39#97×C43C2211yescharacteristic, complemented
40C23×D43—22no—
41C2×D4×C43C2312yes—
42C22×C4×C43—22no—
43C2×C22⋊D43—22no—
44C22×Dic43—22no—
45D4×D43—24no—
46D4×D43C2×C418yescomplemented
47C2×D172C2312yes—
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×C4×D43C2311yescharacteristic
51D8×C43C2×C414yescomplemented
52C2×C8×C43C2311yescharacteristic
53C2×C8×C43C2311yescharacteristic
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—22no—
56C42×C43C2311yescharacteristic
57C22⋊Dic43—22no—
58#10621882C2×C418yescomplemented
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4D412yes—
63C4⋊Dic43C2312yes—
64Dic43⋊C4D412yes—
65C4×Dic43—22no—
66C4×Dic43C2311yescharacteristic
67C2×C43⋊C8C2311yescharacteristic
68C2×C43⋊C8C2311yescharacteristic
69D344C2×C414yescomplemented
70#10621872—22no—
71C8×D43C2×C414yescomplemented
72C23×C43—22no—
73C22×D43—22no—
74C22×D43—28no—
75C22×D43—82no—
76C22×D43—82no—
77C22×D43C2×D411yescharacteristic
78D4×C43—22no—
79D4×C43C22×C414yes—
80C2×C4×C43—22no—
81C2×C4×C43—82no—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2411yescharacteristic
84C22⋊D43—28no—
85C2×Dic43—22no—
86C2×Dic43—82no—
87C2×Dic43C2×D412yes—
88C2×Dic43C2×D411yescharacteristic
89D172—22no—
90D172C22×C414yes—
91C4×D43—82no—
92C4×D43—82no—
93C4×D43C22×C412yes—
94C4×D43#4112yes—
95C8×C43—21no—
96C8×C43C22×C412yes—
97C43⋊C8—21no—
98C43⋊C8C22×C412yes—
99C22×C43—24no—
100C22×C43—42no—
101C22×C43—42no—
102C22×C43C22×D411yescharacteristic
103C2×D43—22no—
104C2×D43—24no—
105C2×D43—42no—
106C2×D43—42no—
107C2×D43—88no—
108C2×D43C4×D412yes—
109C4×C43—22no—
110C4×C43—42no—
111C4×C43C23×C411yescharacteristic
112C4×C43C2×#4111yescharacteristic
113Dic43—22no—
114Dic43—42no—
115Dic43C4×D412yes—
116#2948—431nomaximal, Sylow
117C2×C43—44no—
118C2×C43C2×C4×D411yescharacteristic
119C2×C43#57612yes—
120D43—22no—
121D43—44no—
122C22×D8—431no—
123#518—432no—
124#442—431no—
125#442—431no—
126#442—431no—
127#442D4311yescharacteristic, complemented
128C4×D8—432no—
129C4×D8—432no—
130#427—431no—
131#418—432no—
132#405—431no—
133C43#294811yescharacteristic, complemented, Sylow
134C22×D4—432no—
135C2×D8—432no—
136C2×D8—438no—
137C2×D8—431no—
138C2×D8C2×D4311yescharacteristic
139C2×M16—431no—
140C22×C8—431no—
141C4×D4—432no—
142C4×D4—432no—
143C4×D4—432no—
144C4×D4—862no—
145C4×D4—862no—
146C4×D4C2×D4312yescomplemented
147#117—431no—
148#117—432no—
149C2×C22⋊C4—862no—
150C2×C22⋊C4—862no—
151#107—432no—
152#106—431no—
153#106C2×D4311yescharacteristic, complemented
154#102—432no—
155#102—432no—
156#102—432no—
157#102C2×D4312yescomplemented
158#97—431no—
159#97C2×D4311yescharacteristic, complemented
160C4×C8—431no—
161C4×C8—431no—
162C24—862no—
163C2×D4—438no—
164C2×D4—432no—
165C2×D4—864no—
166C2×D4—862no—
167C2×D4C22×D4312yes—
168C22×C4—22no—
169C22×C4—431no—
170C22×C4—862no—
171C22×C4—862no—
172C22×C4—862no—
173D8—438no—
174D8—434no—
175D8C4×D4314yescomplemented
176M16—862no—
177C2×C8—431no—
178C2×C8—434no—
179C2×C8—431no—
180C2×C8C22×D4311yescharacteristic
181C2×C8C22×D4311yescharacteristic
182C4⋊C4—432no—
183C4⋊C4—432no—
184C4⋊C4C22×D4312yes—
185C22⋊C4—22no—
186C22⋊C4—432no—
187C22⋊C4—862no—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C42—431no—
192C42—862no—
193C42C22×D4311yescharacteristic
194C23—22no—
195C23—431no—
196C23—868no—
197C23—862no—
198C23—3442no—
199C23—3442no—
200D4—22no—
201D4—434no—
202D4—868no—
203D4—862no—
204D4C2×C4×D4314yes—
205C2×C4—22no—
206C2×C4—82no—
207C2×C4—431no—
208C2×C4—432no—
209C2×C4—432no—
210C2×C4—432no—
211C2×C4—862no—
212C2×C4—3442no—
213C2×C4—3442no—
214C2×C4—3442no—
215C2×C4D4×D4312yes—
216C2×C4C23×D4311yescharacteristic
217C8—21no—
218C8—432no—
219C8—861no—
220C8C2×C4×D4312yes—
221C22—24no—
222C22—42no—
223C22—42no—
224C22—432no—
225C22—862no—
226C22—864no—
227C22—3448no—
228C22—1722no—
229C22—1722no—
230C22C2×D4×D4311yescharacteristic
231C4—22no—
232C4—42no—
233C4—432no—
234C4—862no—
235C4—1722no—
236C4C22×C4×D4311yescharacteristic
237C4#41×D4311yescharacteristic
238C2—44no—
239C2—862no—
240C2—1724no—
241C2C4×D4×D4311yescharacteristic
242C2#1458370312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC4×C43C23×C4
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#2948
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #14583371C2semidirect
3. #14583012C2semidirect
4. #14583011C2semidirect
5. #14583010C2semidirect
6. C4×#10621882C2semidirect
7. #14582979C2semidirect
8. #14582934C2semidirect
9. #14582902C2semidirect
10. #14582856C2semidirect
11. C43×#442C2semidirect
15. D8×D43C4semidirect
18. C4×D172C22semidirect
19. D4×Dic43C22semidirect
20. #13063287C22semidirect
27. #13063258C22semidirect
28. #13063257C22semidirect
29. #13063247C22semidirect
30. #13063246C22semidirect
31. #13063245C22semidirect
32. #13063235C22semidirect
33. C4×C43⋊C8C22semidirect
34. C8×Dic43C22semidirect
36. C4×D4×C43C22semidirect
37. #106×C43C22semidirect
38. #102×C43C22semidirect
39. #97×C43C22semidirect
46. D4×D43C2×C4semidirect
51. D8×C43C2×C4semidirect
58. #10621882C2×C4semidirect
69. D344C2×C4semidirect
71. C8×D43C2×C4semidirect
127. #442D43semidirect
133. C43#2948semidirect
146. C4×D4C2×D43semidirect
153. #106C2×D43semidirect
157. #102C2×D43semidirect
159. #97C2×D43semidirect
175. D8C4×D43semidirect