Finite Group Databasebeta

← #19146395

Subgroups — #19146395

Order 5504.

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

normal subgroups only

This group has 476 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#14583704C212yesmaximal, complemented
2#14583701C212yesmaximal, complemented
3#14583276C211yesmaximal, characteristic, complemented
4#14583170C212yesmaximal, complemented
5#14583169C212yesmaximal, complemented
6#14583068C214yesmaximal, complemented
7#14583017C211yesmaximal, characteristic, complemented
8C43×#443C211yesmaximal, characteristic, complemented
9#13063371C2214yescomplemented
10#13063353—24no—
11#13063353C2214yescomplemented
12#13063352—24no—
13#13063350C2214yescomplemented
14#13063348—22no—
15#13063347—22no—
16#13063347C2211yescharacteristic
17C2×D344—22no—
18C2×D344C2212yescomplemented
19C2×D344C2212yescomplemented
20D8×D43—22no—
21#13063331C2212yescomplemented
22#13063322C2212yescomplemented
23#13063261C2211yescharacteristic, complemented
24#13063253C2212yescomplemented
25#13063241C2214yescomplemented
26#135×C43C2211yescharacteristic
27#131×C43C2212yescomplemented
28#108×C43C2211yescharacteristic, complemented
29#104×C43C2212yescomplemented
30C4×C8×C43C2211yescharacteristic, complemented
31#41×C43C2312yes—
32#10621902—24no—
33D4×D43—24no—
34D4×D43—44no—
35#10621898—24no—
36#10621898C2312yes—
37C2×D172—24no—
38C2×D172—42no—
39C2×D172C2314yes—
40Q16×C43D411yescharacteristic, complemented
41SD16×C43D412yescomplemented
42D8×C43D411yescharacteristic, complemented
43M16×C43—22no—
44M16×C43C2312yes—
45C2×C8×C43—22no—
46C2×C8×C43C2311yescharacteristic
47C2×C8×C43C2311yescharacteristic
48C42×C43C2311yescharacteristic
49#10621884—24no—
50#10621882—24no—
51#10621877C2312yes—
52Dic172D411yescharacteristic, complemented
53D344—24no—
54D344—22no—
55D344—22no—
56D344—22no—
57D344—22no—
58D344D411yescharacteristic, complemented
59#10621873—24no—
60#10621873D412yescomplemented
61#10621872—22no—
62C8×D43—22no—
63C22×D43—24no—
64C22×D43—44no—
65Q8×C43C2×D412yes—
66D4×C43—22no—
67D4×C43C2×D412yes—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43C2411yescharacteristic
71C22⋊D43—22no—
72C22⋊D43—44no—
73D172—24no—
74D172—24no—
75D172—44no—
76D172—84no—
77D172C2×D412yes—
78C4×D43—22no—
79C4×D43—44no—
80Dic86C2×D412yes—
81C8×C43—22no—
82C8×C43C2×D411yescharacteristic
83C8×C43C2×D411yescharacteristic
84C8×C43C2×D411yescharacteristic
85C8×C43C2×D411yescharacteristic
86C43⋊C8—22no—
87C22×C43—22no—
88C22×C43H(5,𝔽2)11yescharacteristic
89C2×D43—22no—
90C2×D43—44no—
91C2×D43—84no—
92C2×D43—164no—
93C4×C43—22no—
94C4×C43—22no—
95C4×C43C22×D411yescharacteristic
96C4×C43C22×D411yescharacteristic
97Dic43—22no—
98#3292—431nomaximal, Sylow
99C2×C43—21no—
100C2×C43—42no—
101C2×C43D4211yescharacteristic
102D43—42no—
103D43—84no—
104#576—432no—
105#576—432no—
106#493—431no—
107#472—432no—
108#472—432no—
109#453—434no—
110#443—431no—
111#443D4311yescharacteristic, complemented
112C43#329211yescharacteristic, complemented, Sylow
113H(5,𝔽2)—434no—
114AGL(1,ℤ/8)—434no—
115AGL(1,ℤ/8)—434no—
116AGL(1,ℤ/8)—864no—
117AGL(1,ℤ/8)—864no—
118#135—431no—
119#135—862no—
120#135—862no—
121#135C2×D4311yescharacteristic
122C2×D8—432no—
123C2×D8—432no—
124C2×D8—862no—
125C2×D8—862no—
126#131—432no—
127#131C2×D4312yescomplemented
128#127—432no—
129#108—431no—
130#108C2×D4311yescharacteristic, complemented
131#104—432no—
132#104C2×D4312yescomplemented
133#100—434no—
134C4×C8C2×D4311yescharacteristic, complemented
135#41—432no—
136#41—864no—
137#41—864no—
138#41C22×D4312yes—
139C2×D4—434no—
140C2×D4—864no—
141C2×D4—864no—
142C2×D4—1722no—
143C2×D4—1724no—
144Q16—431no—
145Q16D17211yescharacteristic, complemented
146SD16—432no—
147SD16—864no—
148SD16—864no—
149SD16D17212yescomplemented
150D8—431no—
151D8—864no—
152D8—864no—
153D8—862no—
154D8—862no—
155D8—862no—
156D8—862no—
157D8D17211yescharacteristic, complemented
158M16—22no—
159M16—432no—
160M16—862no—
161M16C22×D4312yes—
162C2×C8—22no—
163C2×C8—862no—
164C2×C8C22×D4311yescharacteristic
165C2×C8C22×D4311yescharacteristic
166C42C22×D4311yescharacteristic
167C23—864no—
168C23—1724no—
169Q8—432no—
170Q8C2×D17212yes—
171D4—22no—
172D4—432no—
173D4—862no—
174D4—864no—
175D4—864no—
176D4—3444no—
177D4—1724no—
178D4—1724no—
179D4C2×D17212yes—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—862no—
183C2×C4—1724no—
184C2×C4C23×D4311yescharacteristic
185C8—22no—
186C8—862no—
187C8C2×D17211yescharacteristic
188C8C2×D17211yescharacteristic
189C8D4×D4311yescharacteristic
190C8D4×D4311yescharacteristic
191C22—22no—
192C22—862no—
193C22—3444no—
194C22—1724no—
195C22—6884no—
196C22#1306337111yescharacteristic
197C4—22no—
198C4—22no—
199C4—862no—
200C4C2×D4×D4311yescharacteristic
201C4C22×D17211yescharacteristic
202C2—21no—
203C2—42no—
204C2—3444no—
205C2—1722no—
206C2D4×D17211yescharacteristic
subgroupG/H
centerC2D4×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#443C2
socleC2×C43D42
hypercenter#443D43
hypocenterC43#3292
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #14583704C2semidirect
2. #14583701C2semidirect
3. #14583276C2semidirect
4. #14583170C2semidirect
5. #14583169C2semidirect
6. #14583068C2semidirect
7. #14583017C2semidirect
8. C43×#443C2semidirect
9. #13063371C22semidirect
11. #13063353C22semidirect
13. #13063350C22semidirect
18. C2×D344C22semidirect
19. C2×D344C22semidirect
21. #13063331C22semidirect
22. #13063322C22semidirect
23. #13063261C22semidirect
24. #13063253C22semidirect
25. #13063241C22semidirect
27. #131×C43C22semidirect
28. #108×C43C22semidirect
29. #104×C43C22semidirect
30. C4×C8×C43C22semidirect
40. Q16×C43D4semidirect
41. SD16×C43D4semidirect
42. D8×C43D4semidirect
52. Dic172D4semidirect
58. D344D4semidirect
60. #10621873D4semidirect
111. #443D43semidirect
112. C43#3292semidirect
127. #131C2×D43semidirect
130. #108C2×D43semidirect
132. #104C2×D43semidirect
134. C4×C8C2×D43semidirect
145. Q16D172semidirect
149. SD16D172semidirect
157. D8D172semidirect