Finite Group Databasebeta

← #19145438

Subgroups — #19145438

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#14583412C212yesmaximal, complemented
2#14583238C212yesmaximal, complemented
3#14583225C212yesmaximal, complemented
4#14583152C211yesmaximal, characteristic, complemented
5#14583147C212yesmaximal, complemented
6#14583060C212yesmaximal, complemented
7#14583047C212yesmaximal, complemented
8#14582862C211yesmaximal, characteristic, complemented
9C43×#470C211yesmaximal, characteristic, complemented
10C2×#10621902C2212yes—
11C22×C4×D43C2211yescharacteristic
12C2×#10621884C2212yescomplemented
13C2×D344C2211yescharacteristic, complemented
14C2×#10621877C2211yescharacteristic
15#13063310—22no—
16#13063301C2212yes—
17#13063300C2212yes—
18#13063299C2212yes—
19#13063295—22no—
20#13063287—22no—
21(C22⋊D43)⋊C4—22no—
22#13063283C2212yes—
23#13063258C2212yescomplemented
24#13063257C2211yescharacteristic, complemented
25#13063249C2212yescomplemented
26#13063247C2212yescomplemented
27#13063245C2212yescomplemented
28(C2×D43)⋊C8C2212yes—
29(C2×D43)⋊C8C2212yes—
30C2×Q16×C43C2211yescharacteristic, complemented
31C2×M16×C43C2211yescharacteristic
32C22⋊Q8×C43C2212yes—
33#106×C43C2211yescharacteristic, complemented
34#103×C43C2212yescomplemented
35C23×D43D411yescharacteristic
36C2×Q8×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C2×C22⋊D43—22no—
39C22×Dic43D411yescharacteristic
40#10621902—42no—
41#10621902—42no—
42C2×D172—22no—
43C2×D172—22no—
44C2×D172C2312yes—
45C2×C4×D43—22no—
46C2×C4×D43—41no—
47C2×C4×D43—41no—
48C2×C4×D43D412yes—
49C2×C4×D43C2312yes—
50Q16×C43—41no—
51M16×C43—41no—
52C2×C8×C43C2311yescharacteristic
53C2×C8×C43C2311yescharacteristic
54C4⋊C4×C43—22no—
55C4⋊C4×C43C2312yes—
56C22⋊C4×C43—22no—
57#10621884—42no—
58(C2×D43)⋊C4—22no—
59(C2×D43)⋊C4—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62C4⋊Dic43C2312yes—
63Dic43⋊C4—22no—
64C4×Dic43—22no—
65#10621877—41no—
66C2×C43⋊C8C2312yes—
67D344—41no—
68C23×C43C2×D411yescharacteristic
69C22×D43—22no—
70C22×D43—41no—
71C22×D43—42no—
72C22×D43C2×D412yes—
73Q8×C43—22no—
74Q8×C43—22no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2411yescharacteristic
81C22⋊D43—44no—
82C2×Dic43—22no—
83C2×Dic43—41no—
84C2×Dic43C2×D412yes—
85D172—22no—
86D172—22no—
87D172—44no—
88D172—44no—
89C4×D43—22no—
90C4×D43—22no—
91C4×D43—42no—
92C4×D43—44no—
93C8×C43—21no—
94C8×C43—21no—
95C43⋊C8—22no—
96C22×C43—21no—
97C22×C43—22no—
98C22×C43C22×D411yescharacteristic
99C2×D43—22no—
100C2×D43—22no—
101C2×D43—22no—
102C2×D43—44no—
103C2×D43—42no—
104C2×D43—42no—
105C2×D43—42no—
106C4×C43—21no—
107C4×C43—42no—
108C4×C43—42no—
109C4×C43H(5,𝔽2)11yescharacteristic
110C4×C43H(5,𝔽2)11yescharacteristic
111Dic43—22no—
112Dic43—42no—
113#3197—431nomaximal, Sylow
114C2×C43—41no—
115C2×C43#53411yescharacteristic
116C2×C43#57512yes—
117D43—42no—
118D43—82no—
119#525—432no—
120#485—432no—
121#482—432no—
122#470D4311yescharacteristic, complemented
123#469—431no—
124#468—432no—
125#452—432no—
126#449—432no—
127#407—431no—
128C43#319711yescharacteristic, complemented, Sylow
129C2×#41—432no—
130C23×C4—431no—
131C2×Q16C2×D4311yescharacteristic, complemented
132C2×SD16—432no—
133C2×D8—431no—
134C2×M16—431no—
135C2×M16C2×D4311yescharacteristic
136#123—862no—
137C22⋊Q8—432no—
138C22⋊Q8C2×D4312yes—
139#121—432no—
140#121—432no—
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#103C2×D4312yescomplemented
150#102—432no—
151#102—432no—
152C22⋊C8—432no—
153C22⋊C8—432no—
154C24—431no—
155#41—1722no—
156#41—1722no—
157C2×Q8C22×D4312yes—
158C2×D4—432no—
159C2×D4—862no—
160C2×D4—862no—
161C2×D4—862no—
162C22×C4—431no—
163C22×C4—432no—
164C22×C4—432no—
165C22×C4—862no—
166C22×C4—1721no—
167C22×C4—1721no—
168C22×C4C22×D4311yescharacteristic
169Q16—41no—
170SD16—1722no—
171D8—1721no—
172M16—41no—
173M16—1721no—
174C2×C8—432no—
175C2×C8C22×D4311yescharacteristic
176C2×C8C22×D4311yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—432no—
179C4⋊C4—862no—
180C4⋊C4C22×D4312yes—
181C22⋊C4—22no—
182C22⋊C4—862no—
183C22⋊C4—862no—
184C22⋊C4—862no—
185C22⋊C4—862no—
186C42—862no—
187C23—432no—
188C23—862no—
189C23—1721no—
190C23—1722no—
191C23D4×D4311yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—862no—
195D4—862no—
196D4—1724no—
197D4—1724no—
198D4—1724no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—432no—
204C2×C4—862no—
205C2×C4—862no—
206C2×C4—862no—
207C2×C4—1722no—
208C2×C4—1724no—
209C2×C4—1721no—
210C2×C4D4×D4311yescharacteristic
211C2×C4C23×D4311yescharacteristic
212C8—21no—
213C8—21no—
214C8—862no—
215C22—22no—
216C22—21no—
217C22—862no—
218C22—862no—
219C22—862no—
220C22—1724no—
221C22—1722no—
222C22—1722no—
223C22—1722no—
224C22C2×D4×D4311yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—862no—
229C4—1722no—
230C4#1306337011yescharacteristic
231C4#1306337111yescharacteristic
232C2—41no—
233C2—3442no—
234C2—1722no—
235C2#1458345711yescharacteristic
236C2#1458369812yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#470C2
socleC22×C43C22×D4
hypercenter#470D43
hypocenterC43#3197
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #14583412C2semidirect
2. #14583238C2semidirect
3. #14583225C2semidirect
4. #14583152C2semidirect
5. #14583147C2semidirect
6. #14583060C2semidirect
7. #14583047C2semidirect
8. #14582862C2semidirect
9. C43×#470C2semidirect
12. C2×#10621884C22semidirect
13. C2×D344C22semidirect
23. #13063258C22semidirect
24. #13063257C22semidirect
25. #13063249C22semidirect
26. #13063247C22semidirect
27. #13063245C22semidirect
30. C2×Q16×C43C22semidirect
33. #106×C43C22semidirect
34. #103×C43C22semidirect
122. #470D43semidirect
128. C43#3197semidirect
131. C2×Q16C2×D43semidirect
147. #106C2×D43semidirect
149. #103C2×D43semidirect