Finite Group Databasebeta

← #19144842

Subgroups — #19144842

Order 5504.

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

normal subgroups only

This group has 394 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#14583373C211yesmaximal, characteristic
2#14583237C212yesmaximal, complemented
3#14583196C212yesmaximal, complemented
4#14583101C212yesmaximal, complemented
5#14583049C212yesmaximal
6#14582997C212yesmaximal, complemented
7C4×#10621884C212yesmaximal, complemented
8#14582960C211yesmaximal, characteristic, complemented
9C43×#541C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C2×#10621884C2212yes—
12C2×#10621884C2212yes—
13C4×D172C2212yes—
14C4×D172C2212yes—
15#13063287—22no—
16#13063284C2211yescharacteristic
17C22⋊C4×D43—22no—
18#13063258C2212yescomplemented
19#13063256C2212yescomplemented
20C4⋊(C43⋊C8)C2212yescomplemented
21#13063249C2212yescomplemented
22#13063249C2212yescomplemented
23#13063245C2212yes—
24#13063245C2212yes—
25C22⋊(C43⋊C8)C2212yes—
26#13063236C2211yescharacteristic, complemented
27C4×C43⋊C8C2211yescharacteristic, complemented
28C4⋊Q8×C43C2211yescharacteristic, complemented
29#126×C43—22no—
30#125×C43—22no—
31#125×C43C2211yescharacteristic, complemented
32C22⋊Q8×C43C2212yes—
33C4×Q8×C43C2212yescomplemented
34#117×C43C2211yescharacteristic
35C23×D43—21no—
36C2×Q8×C43C2312yes—
37C22×C4×C43C2311yescharacteristic
38C2×D172—21no—
39C2×D172—24no—
40C2×D172C2312yes—
41C2×C4×D43—22no—
42C2×C4×D43—22no—
43C4⋊C4×C43—22no—
44C4⋊C4×C43—22no—
45C4⋊C4×C43—22no—
46C4⋊C4×C43—22no—
47C4⋊C4×C43D412yes—
48C4⋊C4×C43C2312yes—
49C22⋊C4×C43—22no—
50C22⋊C4×C43D412yes—
51C42×C43—22no—
52C42×C43C2311yescharacteristic
53C42×C43C2311yescharacteristic
54C22⋊Dic43—21no—
55#10621884—24no—
56#10621884—24no—
57(C2×D43)⋊C4—22no—
58(C2×D43)⋊C4—22no—
59C4⋊Dic43C2312yes—
60C4×Dic43—21no—
61C2×C43⋊C8C2312yes—
62C2×C43⋊C8C2312yes—
63C23×C43C2×D411yescharacteristic
64C22×D43—22no—
65C22×D43—24no—
66C22×D43—82no—
67Q8×C43—22no—
68Q8×C43—22no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D412yes—
74C2×C4×C43C2×D412yes—
75C2×C4×C43C2411yescharacteristic
76C2×Dic43—22no—
77D172—24no—
78D172—22no—
79D172#4114yes—
80C4×D43—82no—
81C4×D43—82no—
82C43⋊C8—22no—
83C43⋊C8—22no—
84C22×C43—21no—
85C22×C43—22no—
86C22×C43C22×D411yescharacteristic
87C2×D43—24no—
88C2×D43—42no—
89C2×D43—42no—
90C2×D43—84no—
91C4×C43—21no—
92C4×C43—22no—
93C4×C43—22no—
94C4×C43—42no—
95C4×C43—42no—
96C4×C43C2×#4112yes—
97Dic43—42no—
98#3123—431nomaximal, Sylow
99C2×C43—41no—
100C2×C43#52511yescharacteristic
101C2×C43#57712yes—
102D43—44no—
103#541D4311yescharacteristic, complemented
104#518—431no—
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×D4—431no—
114C2×SD16—432no—
115C2×SD16—432no—
116C4⋊Q8C2×D4311yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D4311yescharacteristic, complemented
120C22⋊Q8C2×D4312yes—
121C4×Q8C2×D4312yescomplemented
122C4×D4—432no—
123C4×D4—432no—
124C4×D4—862no—
125#117—431no—
126#117C2×D4311yescharacteristic
127C2×C22⋊C4—862no—
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—861no—
139C2×Q8C22×D4312yes—
140C2×D4—432no—
141C2×D4—864no—
142C2×D4—861no—
143C22×C4—862no—
144C22×C4—862no—
145C22×C4C22×D4311yescharacteristic
146SD16—864no—
147SD16—864no—
148C2×C8—432no—
149C2×C8—432no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—432no—
155C4⋊C4C22⋊D4312yes—
156C4⋊C4C22×D4312yes—
157C22⋊C4—22no—
158C22⋊C4—861no—
159C22⋊C4—862no—
160C22⋊C4—862no—
161C22⋊C4C22⋊D4312yes—
162C42—22no—
163C42—861no—
164C42C22×D4311yescharacteristic
165C42C22×D4311yescharacteristic
166C23—864no—
167C23—862no—
168C23—3442no—
169C23C2×C22⋊D4311yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—434no—
173D4—864no—
174D4—862no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—862no—
179C2×C4—3442no—
180C2×C4—3442no—
181C2×C4C2×C22⋊D4312yes—
182C2×C4C2×C22⋊D4311yescharacteristic
183C2×C4C2×C22⋊D4312yes—
184C2×C4C23×D4311yescharacteristic
185C8—862no—
186C8—862no—
187C22—21no—
188C22—22no—
189C22—864no—
190C22—3444no—
191C22—1722no—
192C22—1722no—
193C22C22×C22⋊D4311yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—1722no—
200C4#41×D4312yes—
201C2—41no—
202C2—1724no—
203C2#1458340611yescharacteristic
204C2#1458370712yes—
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#541C2
socleC22×C43C22×D4
hypercenter#541D43
hypocenterC43#3123
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14583237C2semidirect
3. #14583196C2semidirect
4. #14583101C2semidirect
6. #14582997C2semidirect
7. C4×#10621884C2semidirect
8. #14582960C2semidirect
9. C43×#541C2semidirect
18. #13063258C22semidirect
19. #13063256C22semidirect
20. C4⋊(C43⋊C8)C22semidirect
21. #13063249C22semidirect
22. #13063249C22semidirect
26. #13063236C22semidirect
27. C4×C43⋊C8C22semidirect
28. C4⋊Q8×C43C22semidirect
31. #125×C43C22semidirect
33. C4×Q8×C43C22semidirect
103. #541D43semidirect
112. C43#3123semidirect
116. C4⋊Q8C2×D43semidirect
119. #125C2×D43semidirect
121. C4×Q8C2×D43semidirect