Finite Group Databasebeta

← #19145431

Subgroups — #19145431

Order 5504.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#14583409C212yesmaximal, complemented
2#14583243C212yesmaximal, complemented
3#14583222C212yesmaximal, complemented
4#14583157C211yesmaximal, characteristic, complemented
5#14583143C212yesmaximal, complemented
6#14583062C212yesmaximal, complemented
7#14583041C212yesmaximal, complemented
8#14582862C211yesmaximal, characteristic, complemented
9C43×#469C211yesmaximal, characteristic, complemented
10C2×#10621900C2212yes—
11C22×C4×D43C2211yescharacteristic
12C2×Dic172C2211yescharacteristic, complemented
13C2×#10621883C2212yescomplemented
14C2×#10621877C2211yescharacteristic
15#13063307—22no—
16#13063305C2212yes—
17#13063304C2212yes—
18#13063296C2212yes—
19#13063293—22no—
20D4×Dic43—22no—
21(C22⋊D43)⋊C4—22no—
22#13063283C2212yes—
23#13063258C2212yescomplemented
24#13063257C2211yescharacteristic, complemented
25#13063250C2212yescomplemented
26#13063248C2212yescomplemented
27#13063246C2212yescomplemented
28(C2×D43)⋊C8C2212yes—
29(C2×D43)⋊C8C2212yes—
30C2×D8×C43C2211yescharacteristic, complemented
31C2×M16×C43C2211yescharacteristic
32#121×C43C2212yes—
33#106×C43C2211yescharacteristic, complemented
34#102×C43C2212yescomplemented
35C23×D43D411yescharacteristic
36C2×D4×C43—22no—
37C2×D4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—22no—
40C2×C22⋊D43—22no—
41C22×Dic43—22no—
42C22×Dic43D411yescharacteristic
43#10621900—42no—
44#10621900—42no—
45C2×C4×D43—41no—
46C2×C4×D43—41no—
47C2×C4×D43D412yes—
48C2×C4×D43C2312yes—
49C2×Dic86C2312yes—
50D8×C43—41no—
51M16×C43—41no—
52C2×C8×C43C2311yescharacteristic
53C2×C8×C43C2311yescharacteristic
54C4⋊C4×C43C2312yes—
55C22⋊C4×C43—22no—
56C22⋊Dic43—22no—
57C22⋊Dic43—22no—
58#10621883—42no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61C4⋊Dic43—22no—
62C4⋊Dic43C2312yes—
63Dic43⋊C4—22no—
64C4×Dic43—22no—
65#10621877—41no—
66C2×C43⋊C8C2312yes—
67Dic172—41no—
68C23×C43—22no—
69C23×C43C2×D411yescharacteristic
70C22×D43—41no—
71C22×D43—42no—
72C22×D43C2×D412yes—
73D4×C43—22no—
74D4×C43—22no—
75D4×C43—44no—
76C2×C4×C43—21no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C22⋊D43—44no—
82C22⋊D43—44no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—41no—
86C2×Dic43—44no—
87C2×Dic43C2×D412yes—
88C4×D43—22no—
89C4×D43—22no—
90C4×D43—42no—
91Dic86—22no—
92Dic86—22no—
93C8×C43—21no—
94C8×C43—21no—
95C43⋊C8—22no—
96C22×C43—21no—
97C22×C43—22no—
98C22×C43—42no—
99C22×C43—42no—
100C22×C43—42no—
101C22×C43C22×D411yescharacteristic
102C2×D43—22no—
103C2×D43—22no—
104C2×D43—22no—
105C2×D43—44no—
106C4×C43—21no—
107C4×C43—42no—
108C4×C43H(5,𝔽2)11yescharacteristic
109C4×C43H(5,𝔽2)11yescharacteristic
110Dic43—22no—
111Dic43—42no—
112Dic43—42no—
113#3197—431nomaximal, Sylow
114C2×C43—41no—
115C2×C43—82no—
116C2×C43#53411yescharacteristic
117C2×C43#57512yes—
118D43—42no—
119#525—432no—
120#485—432no—
121#482—432no—
122#470—431no—
123#469D4311yescharacteristic, complemented
124#468—432no—
125#452—432no—
126#449—432no—
127#407—431no—
128C43#319711yescharacteristic, complemented, Sylow
129C2×#41—432no—
130C23×C4—431no—
131C2×Q16—431no—
132C2×SD16—432no—
133C2×D8C2×D4311yescharacteristic, complemented
134C2×M16—431no—
135C2×M16C2×D4311yescharacteristic
136#123—862no—
137C22⋊Q8—432no—
138C22⋊Q8—432no—
139#121—432no—
140#121C2×D4312yes—
141#120—862no—
142C4×D4—862no—
143C4×D4—862no—
144#117—432no—
145#107—432no—
146#106—431no—
147#106C2×D4311yescharacteristic, complemented
148#103—432no—
149#103—432no—
150#102—432no—
151#102C2×D4312yescomplemented
152C22⋊C8—432no—
153C22⋊C8—432no—
154C24—431no—
155#41—1722no—
156#41—1722no—
157C2×Q8—432no—
158C2×D4—22no—
159C2×D4—862no—
160C2×D4—862no—
161C2×D4C22×D4312yes—
162C22×C4—431no—
163C22×C4—432no—
164C22×C4—432no—
165C22×C4—862no—
166C22×C4—1721no—
167C22×C4—1721no—
168C22×C4C22×D4311yescharacteristic
169Q16—1721no—
170SD16—1722no—
171D8—41no—
172M16—41no—
173M16—1721no—
174C2×C8—432no—
175C2×C8C22×D4311yescharacteristic
176C2×C8C22×D4311yescharacteristic
177C4⋊C4—432no—
178C4⋊C4—862no—
179C4⋊C4—862no—
180C4⋊C4C22×D4312yes—
181C22⋊C4—22no—
182C22⋊C4—862no—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C42—862no—
187C23—22no—
188C23—432no—
189C23—1721no—
190C23—1722no—
191C23D4×D4311yescharacteristic
192Q8—862no—
193Q8—862no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—1724no—
198D4—1724no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—432no—
203C2×C4—862no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—1722no—
208C2×C4—1721no—
209C2×C4—1724no—
210C2×C4D4×D4311yescharacteristic
211C2×C4C23×D4311yescharacteristic
212C8—21no—
213C8—21no—
214C8—862no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—862no—
221C22—862no—
222C22—862no—
223C22—1724no—
224C22C2×D4×D4311yescharacteristic
225C4—21no—
226C4—42no—
227C4—862no—
228C4—1722no—
229C4—1722no—
230C4#1306337011yescharacteristic
231C4#1306337111yescharacteristic
232C2—41no—
233C2—82no—
234C2—1722no—
235C2#1458345711yescharacteristic
236C2#1458369512yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#469C2
socleC22×C43C22×D4
hypercenter#469D43
hypocenterC43#3197
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14583409C2semidirect
2. #14583243C2semidirect
3. #14583222C2semidirect
4. #14583157C2semidirect
5. #14583143C2semidirect
6. #14583062C2semidirect
7. #14583041C2semidirect
8. #14582862C2semidirect
9. C43×#469C2semidirect
12. C2×Dic172C22semidirect
13. C2×#10621883C22semidirect
23. #13063258C22semidirect
24. #13063257C22semidirect
25. #13063250C22semidirect
26. #13063248C22semidirect
27. #13063246C22semidirect
30. C2×D8×C43C22semidirect
33. #106×C43C22semidirect
34. #102×C43C22semidirect
123. #469D43semidirect
128. C43#3197semidirect
133. C2×D8C2×D43semidirect
147. #106C2×D43semidirect
151. #102C2×D43semidirect