Finite Group Databasebeta

← #19144847

Subgroups — #19144847

Order 5504.

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

normal subgroups only

This group has 394 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#14583511C211yesmaximal, characteristic, complemented
2#14583240C212yesmaximal, complemented
3#14583199C212yesmaximal, complemented
4#14583104C212yesmaximal, complemented
5#14583050C212yesmaximal
6#14582999C212yesmaximal, complemented
7C4×#10621883C212yesmaximal, complemented
8#14582960C211yesmaximal, characteristic, complemented
9C43×#518C211yesmaximal, characteristic
10C2×#10621883C2212yes—
11C2×#10621883C2212yes—
12#13063325C2211yescharacteristic, complemented
13#13063318—22no—
14#13063317C2211yescharacteristic, complemented
15#13063315—22no—
16#13063304C2212yes—
17C4×Dic86C2212yescomplemented
18#13063258C2212yescomplemented
19#13063256C2212yescomplemented
20C4⋊(C43⋊C8)C2212yescomplemented
21#13063248C2212yescomplemented
22#13063248C2212yescomplemented
23#13063246C2212yes—
24#13063246C2212yes—
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×Dic86C2312yes—
43C4⋊C4×C43D412yes—
44C4⋊C4×C43C2312yes—
45C22⋊C4×C43—22no—
46C22⋊C4×C43—22no—
47C22⋊C4×C43—21no—
48C22⋊C4×C43D412yes—
49C42×C43—21no—
50C42×C43C2311yescharacteristic
51C42×C43C2311yescharacteristic
52C22⋊Dic43—22no—
53#10621883—24no—
54#10621883—24no—
55C4⋊Dic43—22no—
56C4⋊Dic43C2312yes—
57Dic43⋊C4—22no—
58Dic43⋊C4—22no—
59Dic43⋊C4—22no—
60C4×Dic43—22no—
61C2×C43⋊C8C2312yes—
62C2×C43⋊C8C2312yes—
63C23×C43—24no—
64C23×C43—22no—
65C23×C43—82no—
66C23×C43C2×D411yescharacteristic
67D4×C43—24no—
68D4×C43—22no—
69D4×C43#4114yes—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—82no—
73C2×C4×C43—82no—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2×D411yescharacteristic
76C2×C4×C43C2×D412yes—
77C2×C4×C43C2411yescharacteristic
78C2×Dic43—22no—
79C2×Dic43—22no—
80Dic86—22no—
81Dic86—22no—
82C43⋊C8—22no—
83C43⋊C8—22no—
84C22×C43—21no—
85C22×C43—24no—
86C22×C43—22no—
87C22×C43—42no—
88C22×C43—42no—
89C22×C43—84no—
90C22×C43C22×D411yescharacteristic
91C4×C43—21no—
92C4×C43—22no—
93C4×C43—22no—
94C4×C43—42no—
95C4×C43C2×#4112yes—
96Dic43—42no—
97Dic43—42no—
98#3123—431nomaximal, Sylow
99C2×C43—41no—
100C2×C43—44no—
101C2×C43#52511yescharacteristic
102C2×C43#57712yes—
103#541—431no—
104#518D4311yescharacteristic
105#485—432no—
106#478—432no—
107#461—432no—
108#450—432no—
109#440—432no—
110C4×SD16—432no—
111#433—431no—
112C43#312311yescharacteristic, complemented, Sylow
113C22×D4C2×D4311yescharacteristic
114C2×SD16—432no—
115C2×SD16—432no—
116C4⋊Q8—431no—
117#126—862no—
118#125—431no—
119#125—862no—
120C22⋊Q8—432no—
121C4×Q8—432no—
122C4×D4—22no—
123C4×D4C2×D4312yes—
124C4×D4C2×D4312yes—
125#117C2×D4311yescharacteristic
126#117C2×D4311yescharacteristic
127C2×C22⋊C4—22no—
128#107—432no—
129#106—432no—
130C4⋊C8—432no—
131#103—432no—
132#103—432no—
133#102—432no—
134#102—432no—
135C22⋊C8—432no—
136#97—431no—
137C4×C8—431no—
138C24—21no—
139C2×Q8—432no—
140C2×D4—24no—
141C2×D4—21no—
142C2×D4C22×D4312yes—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4C22×D4311yescharacteristic
146SD16—864no—
147SD16—864no—
148C2×C8—432no—
149C2×C8—432no—
150C4⋊C4—432no—
151C4⋊C4—862no—
152C4⋊C4—862no—
153C4⋊C4—862no—
154C4⋊C4—862no—
155C4⋊C4C22⋊D4312yes—
156C4⋊C4C22×D4312yes—
157C22⋊C4—21no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—862no—
161C22⋊C4C22⋊D4312yes—
162C42—21no—
163C42—862no—
164C42C22×D4311yescharacteristic
165C42C22×D4311yescharacteristic
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D4311yescharacteristic
170Q8—862no—
171Q8—862no—
172D4—24no—
173D4—22no—
174D4#1062189814yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—862no—
180C2×C4—862no—
181C2×C4C2×C22⋊D4311yescharacteristic
182C2×C4C2×C22⋊D4312yes—
183C2×C4C2×C22⋊D4312yes—
184C2×C4C23×D4311yescharacteristic
185C8—862no—
186C8—862no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D4311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—1722no—
199C4—1722no—
200C4C2×#1062189812yes—
201C2—41no—
202C2—44no—
203C2#1458341011yescharacteristic
204C2#1458371012yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#518C2
socleC22×C43C22×D4
hypercenter#518D43
hypocenterC43#3123
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. #14583511C2semidirect
2. #14583240C2semidirect
3. #14583199C2semidirect
4. #14583104C2semidirect
6. #14582999C2semidirect
7. C4×#10621883C2semidirect
8. #14582960C2semidirect
12. #13063325C22semidirect
14. #13063317C22semidirect
17. C4×Dic86C22semidirect
18. #13063258C22semidirect
19. #13063256C22semidirect
20. C4⋊(C43⋊C8)C22semidirect
21. #13063248C22semidirect
22. #13063248C22semidirect
26. #13063236C22semidirect
27. C4×C43⋊C8C22semidirect
112. C43#3123semidirect