Finite Group Databasebeta

← #19146207

Subgroups — #19146207

Order 5504.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13063353C212yesmaximal, complemented
2#14583545C212yesmaximal, complemented
3#14583283C211yesmaximal, characteristic, complemented
4#14583145C212yesmaximal, complemented
5#14583115C212yesmaximal, complemented
6#14583063C212yesmaximal, complemented
7#14583035C212yesmaximal, complemented
8C4×D344C211yesmaximal, characteristic, complemented
9C43×#436C211yesmaximal, characteristic, complemented
10C2×#10621898C2212yes—
11C22×D172C2212yescomplemented
12#13063353—28no—
13C2×Dic172C2211yescharacteristic, complemented
14C2×#10621873C2212yescomplemented
15C2×#10621873C2212yescomplemented
16C2×D344C2212yes—
17C2×D344C2211yescharacteristic
18C2×D344C2211yescharacteristic
19#13063313C2212yescomplemented
20#13063310—22no—
21#13063304C2212yescomplemented
22#13063299C2212yes—
23#13063298—22no—
24#13063293—22no—
25C4×D172C2212yescomplemented
26C22⋊C4×D43—22no—
27#13063259C2211yescharacteristic, complemented
28#13063250C2212yescomplemented
29#13063247C2212yescomplemented
30#13063247C2212yescomplemented
31C2×M16×C43C2212yescomplemented
32C4×D4×C43C2211yescharacteristic
33C4⋊C8×C43C2211yescharacteristic, complemented
34C22⋊C8×C43C2212yescomplemented
35C4×C8×C43C2211yescharacteristic, complemented
36C23×D43—22no—
37C2×D4×C43D411yescharacteristic
38C22×C4×C43C2312yes—
39C2×C22⋊D43—22no—
40C2×C22⋊D43—22no—
41#10621898—24no—
42#10621898—42no—
43C2×D172—22no—
44C2×D172—24no—
45C2×D172—42no—
46C2×D172C2312yes—
47C2×D172C2312yes—
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×Dic86C2312yes—
51M16×C43—24no—
52C2×C8×C43C2311yescharacteristic
53C2×C8×C43C2312yes—
54C2×C8×C43C2311yescharacteristic
55C4⋊C4×C43D411yescharacteristic
56C22⋊C4×C43D412yes—
57C42×C43C2311yescharacteristic
58C22⋊Dic43—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4—22no—
63C4⋊Dic43C2312yes—
64Dic43⋊C4—22no—
65Dic172—41no—
66D344—24no—
67D344—41no—
68D344D414yescomplemented
69#10621873—24no—
70#10621873—24no—
71C23×C43C2×D412yes—
72C22×D43—22no—
73C22×D43—22no—
74C22×D43—44no—
75C22×D43—44no—
76C22×D43—82no—
77D4×C43—41no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43C2×D412yes—
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2411yescharacteristic
84C22⋊D43—44no—
85C22⋊D43—82no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88D172—22no—
89D172—22no—
90D172—22no—
91D172—44no—
92D172C2×D414yes—
93C4×D43—44no—
94C4×D43—82no—
95Dic86—22no—
96Dic86—22no—
97C8×C43—22no—
98C8×C43—21no—
99C8×C43C2×D412yes—
100C22×C43—22no—
101C22×C43—22no—
102C22×C43—22no—
103C22×C43C22×D411yescharacteristic
104C2×D43—24no—
105C2×D43—42no—
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—42no—
109C2×D43—42no—
110C2×D43—88no—
111C4×C43—22no—
112C4×C43—21no—
113C4×C43—21no—
114C4×C43C22×D411yescharacteristic
115C4×C43H(5,𝔽2)11yescharacteristic
116Dic43—42no—
117Dic43—42no—
118#3273—431nomaximal, Sylow
119C2×C43—42no—
120C2×C43D4211yescharacteristic
121C2×C43#57511yescharacteristic
122C2×C43#57611yescharacteristic
123D43—44no—
124D43—82no—
125C2×AGL(1,ℤ/8)—432no—
126#546—432no—
127#495—431no—
128#468—432no—
129#463—432no—
130#452—432no—
131#447—432no—
132C4×D8—431no—
133#436D4311yescharacteristic, complemented
134C43#327311yescharacteristic, complemented, Sylow
135C2×#41—432no—
136C22×D4—432no—
137AGL(1,ℤ/8)—868no—
138C2×Q16—431no—
139C2×SD16—432no—
140C2×SD16—432no—
141C2×D8—431no—
142C2×D8—432no—
143C2×D8—431no—
144C2×M16C2×D4312yescomplemented
145#124—432no—
146#123—862no—
147C22⋊Q8—432no—
148#121—432no—
149#121—862no—
150#120—862no—
151C4×D4—432no—
152C4×D4C2×D4311yescharacteristic
153C2×C22⋊C4—862no—
154#107—431no—
155C4⋊C8C2×D4311yescharacteristic, complemented
156#103—432no—
157#102—432no—
158#102—432no—
159C22⋊C8C2×D4312yescomplemented
160C4×C8C2×D4311yescharacteristic, complemented
161C24—862no—
162#41—864no—
163#41—1722no—
164C2×Q8—432no—
165C2×D4—432no—
166C2×D4—432no—
167C2×D4—864no—
168C2×D4—862no—
169C2×D4—862no—
170C2×D4—862no—
171C2×D4—1722no—
172C2×D4D17211yescharacteristic
173C22×C4—862no—
174C22×C4—862no—
175C22×C4C22×D4312yes—
176Q16—1721no—
177SD16—864no—
178SD16—864no—
179D8—434no—
180D8—864no—
181D8—1721no—
182M16—24no—
183C2×C8C22×D4311yescharacteristic
184C2×C8C22×D4312yes—
185C2×C8C22×D4311yescharacteristic
186C4⋊C4—432no—
187C4⋊C4—862no—
188C4⋊C4D17211yescharacteristic
189C22⋊C4—862no—
190C22⋊C4—862no—
191C22⋊C4—862no—
192C22⋊C4—862no—
193C22⋊C4—862no—
194C22⋊C4D17212yes—
195C42C22×D4311yescharacteristic
196C23—862no—
197C23—862no—
198C23—3442no—
199C23—1724no—
200C23—1724no—
201C23C2×D17212yes—
202Q8—862no—
203Q8—862no—
204D4—41no—
205D4—434no—
206D4—862no—
207D4—862no—
208D4—862no—
209D4—3442no—
210D4—1724no—
211D4—1724no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—3442no—
217C2×C4—1724no—
218C2×C4C2×D17211yescharacteristic
219C2×C4C2×D17211yescharacteristic
220C2×C4C2×D17212yes—
221C2×C4C23×D4311yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D4312yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—864no—
229C22—3448no—
230C22—1722no—
231C22—1722no—
232C22—1722no—
233C22—1722no—
234C22—1722no—
235C22C22×D17211yescharacteristic
236C4—21no—
237C4—21no—
238C4—22no—
239C4—1722no—
240C4—1722no—
241C4C2×D4×D4311yescharacteristic
242C4#1306337111yescharacteristic
243C2—42no—
244C2—3442no—
245C2—1724no—
246C2D4×D17211yescharacteristic
247C2#1458369911yescharacteristic
248C2#1458370411yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#436C2
socleC22×C43C22×D4
hypercenter#436D43
hypocenterC43#3273
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#13063353C2semidirect
2. #14583545C2semidirect
3. #14583283C2semidirect
4. #14583145C2semidirect
5. #14583115C2semidirect
6. #14583063C2semidirect
7. #14583035C2semidirect
8. C4×D344C2semidirect
9. C43×#436C2semidirect
11. C22×D172C22semidirect
13. C2×Dic172C22semidirect
14. C2×#10621873C22semidirect
15. C2×#10621873C22semidirect
19. #13063313C22semidirect
21. #13063304C22semidirect
25. C4×D172C22semidirect
27. #13063259C22semidirect
28. #13063250C22semidirect
29. #13063247C22semidirect
30. #13063247C22semidirect
31. C2×M16×C43C22semidirect
33. C4⋊C8×C43C22semidirect
34. C22⋊C8×C43C22semidirect
35. C4×C8×C43C22semidirect
68. D344D4semidirect
133. #436D43semidirect
134. C43#3273semidirect
144. C2×M16C2×D43semidirect
155. C4⋊C8C2×D43semidirect
159. C22⋊C8C2×D43semidirect
160. C4×C8C2×D43semidirect