Finite Group Databasebeta

← #19144968

Subgroups — #19144968

Order 5504.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#14583455C211yesmaximal, characteristic, complemented
2#127×D43C211yesmaximal, characteristic
3#14583265C211yesmaximal, characteristic, complemented
4#14583264C211yesmaximal, characteristic, complemented
5#14583263C211yesmaximal, characteristic, complemented
6#14583244C214yesmaximal, complemented
7#14582902C214yesmaximal, complemented
8#14582851C211yesmaximal, characteristic, complemented
9C43×#490C211yesmaximal, characteristic, complemented
10C2×D4×D43—22no—
11C2×D4×D43C2212yes—
12C2×#10621872C2212yes—
13#13063324C2212yescomplemented
14#13063322C2211yescharacteristic
15#13063321—22no—
16#13063321C2212yes—
17#13063317C2211yescharacteristic, complemented
18#13063303—22no—
19#13063290—22no—
20#13063283C2212yes—
21C42×D43C2211yescharacteristic
22#13063247C2214yescomplemented
23#13063246C2214yescomplemented
24#13063245C2214yescomplemented
25#13063236C2211yescharacteristic, complemented
26C8×Dic43C2212yescomplemented
27#127×C43C2211yescharacteristic
28#125×C43C2211yescharacteristic, complemented
29#102×C43C2214yescomplemented
30#97×C43C2211yescharacteristic, complemented
31C23×D43—22no—
32C2×D4×C43—22no—
33C2×D4×C43C2312yes—
34C2×C22⋊D43—22no—
35C2×C22⋊D43—24no—
36D4×D43—28no—
37D4×D43—48no—
38C2×D172—22no—
39C2×D172C2312yes—
40C2×C4×D43D412yes—
41C2×C4×D43C2311yescharacteristic
42C2×Dic86—22no—
43C2×C8×C43C2312yes—
44C4⋊C4×C43—22no—
45C4⋊C4×C43C2312yes—
46C42×C43C2311yescharacteristic
47(C2×D43)⋊C4—22no—
48C4⋊Dic43C2312yes—
49Dic43⋊C4—22no—
50Dic43⋊C4—22no—
51C4×Dic43—22no—
52C4×Dic43D412yes—
53C4×Dic43C2311yescharacteristic
54C2×C43⋊C8C2312yes—
55#10621872—24no—
56C23×C43—22no—
57C22×D43—22no—
58C22×D43—48no—
59C22×D43—44no—
60C22×D43C2×D411yescharacteristic
61D4×C43—24no—
62D4×C43—44no—
63C2×C4×C43—22no—
64C2×C4×C43C2×D412yes—
65C2×C4×C43C2411yescharacteristic
66C22⋊D43—44no—
67C22⋊D43—48no—
68C2×Dic43—22no—
69C2×Dic43C2×D411yescharacteristic
70C2×Dic43C2×D412yes—
71D172—24no—
72D172—44no—
73C4×D43—24no—
74C4×D43#4114yes—
75Dic86—44no—
76C8×C43—22no—
77C43⋊C8—22no—
78C22×C43—42no—
79C22×C43—44no—
80C22×C43C22×D411yescharacteristic
81C2×D43—22no—
82C2×D43—42no—
83C2×D43—44no—
84C2×D43—88no—
85C2×D43#12412yes—
86C4×C43—22no—
87C4×C43—42no—
88C4×C43C2×#4112yes—
89Dic43—42no—
90Dic43#12412yes—
91Dic43AGL(1,ℤ/8)14yes—
92#3138—431nomaximal, Sylow
93C2×C43—82no—
94C2×C43C2×#12411yescharacteristic
95C2×C43C2×AGL(1,ℤ/8)12yes—
96D43—22no—
97D43—82no—
98#533—431no—
99C2×#127—431no—
100#490—431no—
101#490—431no—
102#490—431no—
103#490D4311yescharacteristic, complemented
104#486—434no—
105#418—434no—
106C4×M16—431no—
107C43#313811yescharacteristic, complemented, Sylow
108C22×D4—432no—
109C22×D4—862no—
110C2×M16—432no—
111C4⋊Q8—432no—
112#127—432no—
113#127—431no—
114#127—862no—
115#127C2×D4311yescharacteristic
116#125—431no—
117#125C2×D4311yescharacteristic, complemented
118C22⋊Q8—862no—
119C4×Q8—862no—
120#117—432no—
121C2×C42—431no—
122#102—434no—
123#102—434no—
124#102—434no—
125#102C2×D4314yescomplemented
126#97—431no—
127#97C2×D4311yescharacteristic, complemented
128C4×C8—432no—
129C24—862no—
130C2×Q8—862no—
131C2×D4—22no—
132C2×D4—432no—
133C2×D4—868no—
134C2×D4—864no—
135C2×D4—862no—
136C2×D4—862no—
137C2×D4—1728no—
138C2×D4C22×D4312yes—
139C22×C4—431no—
140C22×C4—432no—
141M16—864no—
142C2×C8—432no—
143C2×C8C22×D4312yes—
144C4⋊C4—22no—
145C4⋊C4—432no—
146C4⋊C4—862no—
147C4⋊C4—862no—
148C4⋊C4C22×D4312yes—
149C22⋊C4—862no—
150C42—432no—
151C42—431no—
152C42—862no—
153C42C22×D4311yescharacteristic
154C23—22no—
155C23—431no—
156C23—862no—
157C23—1724no—
158C23—1728no—
159Q8—1724no—
160D4—24no—
161D4—44no—
162D4—864no—
163D4—1724no—
164D4—1724no—
165D4—1728no—
166C2×C4—22no—
167C2×C4—431no—
168C2×C4—432no—
169C2×C4—434no—
170C2×C4—864no—
171C2×C4—862no—
172C2×C4D4×D4312yes—
173C2×C4C23×D4311yescharacteristic
174C8—22no—
175C8—862no—
176C22—42no—
177C22—44no—
178C22—432no—
179C22—862no—
180C22—3448no—
181C22—1722no—
182C22—1724no—
183C22C2×D4×D4311yescharacteristic
184C4—22no—
185C4—42no—
186C4—432no—
187C4—434no—
188C4—1722no—
189C4#41×D4312yes—
190C2—82no—
191C2—862no—
192C2—3442no—
193C2#124×D4311yescharacteristic
194C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3138
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583455C2semidirect
3. #14583265C2semidirect
4. #14583264C2semidirect
5. #14583263C2semidirect
6. #14583244C2semidirect
7. #14582902C2semidirect
8. #14582851C2semidirect
9. C43×#490C2semidirect
13. #13063324C22semidirect
17. #13063317C22semidirect
22. #13063247C22semidirect
23. #13063246C22semidirect
24. #13063245C22semidirect
25. #13063236C22semidirect
26. C8×Dic43C22semidirect
28. #125×C43C22semidirect
29. #102×C43C22semidirect
30. #97×C43C22semidirect
103. #490D43semidirect
107. C43#3138semidirect
117. #125C2×D43semidirect
125. #102C2×D43semidirect
127. #97C2×D43semidirect