Finite Group Databasebeta

← #19144838

Subgroups — #19144838

Order 5504.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583504C211yesmaximal, characteristic, complemented
2#14583223C212yesmaximal, complemented
3#14583199C212yesmaximal, complemented
4#14583094C212yesmaximal, complemented
5#14583033C212yesmaximal, complemented
6#14583009C212yesmaximal, complemented
7C4×#10621882C212yesmaximal, complemented
8#14582960C211yesmaximal, characteristic, complemented
9C43×#518C211yesmaximal, characteristic, complemented
10C2×#10621882C2212yes—
11C2×#10621882C2212yes—
12#13063322C2211yescharacteristic, complemented
13#13063317C2211yescharacteristic, complemented
14#13063310—22no—
15#13063299C2212yes—
16#13063298—22no—
17C4×D172C2212yescomplemented
18#13063258C2212yescomplemented
19#13063256C2212yescomplemented
20C4⋊(C43⋊C8)C2212yescomplemented
21#13063246C2212yes—
22#13063246C2212yes—
23#13063245C2212yescomplemented
24#13063245C2212yescomplemented
25C22⋊(C43⋊C8)C2212yes—
26#13063236C2211yescharacteristic, complemented
27C4×C43⋊C8C2211yescharacteristic, complemented
28C22×D4×C43C2211yescharacteristic
29C4×D4×C43—22no—
30C4×D4×C43C2212yes—
31C4×D4×C43C2212yes—
32#117×C43C2211yescharacteristic
33#117×C43C2211yescharacteristic
34C2×C22⋊C4×C43—22no—
35C24×C43—21no—
36C2×D4×C43—24no—
37C2×D4×C43—21no—
38C2×D4×C43C2312yes—
39C22×C4×C43—22no—
40C22×C4×C43—22no—
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—22no—
43C2×D172—22no—
44C2×D172C2312yes—
45C2×C4×D43—22no—
46C4⋊C4×C43D412yes—
47C4⋊C4×C43C2312yes—
48C22⋊C4×C43—22no—
49C22⋊C4×C43—22no—
50C22⋊C4×C43—21no—
51C22⋊C4×C43D412yes—
52C42×C43—21no—
53C42×C43C2311yescharacteristic
54C42×C43C2311yescharacteristic
55#10621882—24no—
56#10621882—24no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59C4⋊Dic43C2312yes—
60Dic43⋊C4—22no—
61C2×C43⋊C8C2312yes—
62C2×C43⋊C8C2312yes—
63C23×C43—24no—
64C23×C43—22no—
65C23×C43—82no—
66C23×C43C2×D411yescharacteristic
67C22×D43—22no—
68D4×C43—24no—
69D4×C43—22no—
70D4×C43#4114yes—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—82no—
74C2×C4×C43—82no—
75C2×C4×C43C2×D412yes—
76C2×C4×C43C2×D411yescharacteristic
77C2×C4×C43C2×D412yes—
78C2×C4×C43C2411yescharacteristic
79C22⋊D43—82no—
80C2×Dic43—22no—
81D172—22no—
82D172—22no—
83D172—82no—
84C4×D43—82no—
85C43⋊C8—22no—
86C43⋊C8—22no—
87C22×C43—21no—
88C22×C43—24no—
89C22×C43—22no—
90C22×C43—42no—
91C22×C43—42no—
92C22×C43—84no—
93C22×C43C22×D411yescharacteristic
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—42no—
97C4×C43—21no—
98C4×C43—22no—
99C4×C43—22no—
100C4×C43—42no—
101C4×C43C2×#4112yes—
102Dic43—42no—
103#3122—431nomaximal, Sylow
104C2×C43—41no—
105C2×C43—44no—
106C2×C43#52511yescharacteristic
107C2×C43#57612yes—
108D43—82no—
109#540—431no—
110#518D4311yescharacteristic, complemented
111#482—432no—
112#478—432no—
113#459—432no—
114#447—432no—
115#442—432no—
116C4×D8—432no—
117#433—431no—
118C43#312211yescharacteristic, complemented, Sylow
119C22×D4C2×D4311yescharacteristic
120C2×D8—432no—
121C2×D8—432no—
122#127—431no—
123#125—431no—
124#123—862no—
125#121—432no—
126#121—862no—
127C4×D4—22no—
128C4×D4—432no—
129C4×D4C2×D4312yes—
130C4×D4C2×D4312yes—
131#117C2×D4311yescharacteristic
132#117C2×D4311yescharacteristic
133C2×C22⋊C4—22no—
134#107—432no—
135#106—432no—
136C4⋊C8—432no—
137#102—432no—
138#102—432no—
139#102—432no—
140#102—432no—
141C22⋊C8—432no—
142#97—431no—
143C4×C8—431no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—432no—
148C2×D4—862no—
149C2×D4—862no—
150C2×D4C22×D4312yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—862no—
154C22×C4C22×D4311yescharacteristic
155D8—864no—
156D8—864no—
157C2×C8—432no—
158C2×C8—432no—
159C4⋊C4—432no—
160C4⋊C4—862no—
161C4⋊C4C22⋊D4312yes—
162C4⋊C4C22×D4312yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—862no—
167C22⋊C4—862no—
168C22⋊C4C22⋊D4312yes—
169C42—21no—
170C42C22×D4311yescharacteristic
171C42C22×D4311yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—862no—
176C23C2×C22⋊D4311yescharacteristic
177D4—24no—
178D4—22no—
179D4—862no—
180D4—862no—
181D4—3442no—
182D4—3442no—
183D4#1062189814yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—862no—
189C2×C4—3442no—
190C2×C4C2×C22⋊D4311yescharacteristic
191C2×C4C2×C22⋊D4312yes—
192C2×C4C2×C22⋊D4312yes—
193C2×C4C23×D4311yescharacteristic
194C8—862no—
195C8—862no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—1722no—
203C22—1722no—
204C22—1722no—
205C22C22×C22⋊D4311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1722no—
211C4C2×#1062189812yes—
212C2—41no—
213C2—44no—
214C2—3442no—
215C2#1458341011yescharacteristic
216C2#1458370212yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#518C2
socleC22×C43C22×D4
hypercenter#518D43
hypocenterC43#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14583504C2semidirect
2. #14583223C2semidirect
3. #14583199C2semidirect
4. #14583094C2semidirect
5. #14583033C2semidirect
6. #14583009C2semidirect
7. C4×#10621882C2semidirect
8. #14582960C2semidirect
9. C43×#518C2semidirect
12. #13063322C22semidirect
13. #13063317C22semidirect
17. C4×D172C22semidirect
18. #13063258C22semidirect
19. #13063256C22semidirect
20. C4⋊(C43⋊C8)C22semidirect
23. #13063245C22semidirect
24. #13063245C22semidirect
26. #13063236C22semidirect
27. C4×C43⋊C8C22semidirect
110. #518D43semidirect
118. C43#3122semidirect