Finite Group Databasebeta

← #19144839

Subgroups — #19144839

Order 5504.

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

normal subgroups only

This group has 418 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#14583504C211yesmaximal, characteristic, complemented
2#14583373C211yesmaximal, characteristic, complemented
3#14583224C212yesmaximal, complemented
4#14583200C212yesmaximal, complemented
5#14583095C212yesmaximal, complemented
6#14583035C212yesmaximal, complemented
7#14583012C212yesmaximal, complemented
8C4×D344C212yesmaximal, complemented
9C43×#433C211yesmaximal, characteristic, complemented
10C22×D172C2211yescharacteristic
11C2×D344C2212yes—
12C2×D344C2212yes—
13#13063322C2211yescharacteristic, complemented
14#13063317C2211yescharacteristic, complemented
15#13063310—22no—
16#13063299C2212yes—
17#13063298—22no—
18C4×D172C2212yes—
19C4×D172C2212yes—
20C4×D172C2212yescomplemented
21#13063287—22no—
22#13063284C2211yescharacteristic
23C22⋊C4×D43—22no—
24#13063259C2212yescomplemented
25#13063257C2212yescomplemented
26#13063247C2212yes—
27#13063247C2212yes—
28#13063247C2212yescomplemented
29#13063247C2212yescomplemented
30#117×C43C2211yescharacteristic
31C4⋊C8×C43C2212yescomplemented
32C22⋊C8×C43C2212yes—
33#97×C43C2211yescharacteristic, complemented
34C4×C8×C43C2211yescharacteristic, complemented
35C23×D43—21no—
36C22×C4×C43C2311yescharacteristic
37C2×C22⋊D43—22no—
38C2×D172—21no—
39C2×D172—24no—
40C2×D172—22no—
41C2×D172C2312yes—
42C2×D172C2312yes—
43C2×C4×D43—22no—
44C2×C4×D43—22no—
45C2×C4×D43—22no—
46C2×C8×C43C2312yes—
47C2×C8×C43C2312yes—
48C4⋊C4×C43D412yes—
49C22⋊C4×C43D412yes—
50C42×C43C2311yescharacteristic
51C42×C43C2311yescharacteristic
52C22⋊Dic43—21no—
53(C2×D43)⋊C4—22no—
54(C2×D43)⋊C4—22no—
55(C2×D43)⋊C4—22no—
56(C2×D43)⋊C4—22no—
57C4⋊Dic43C2312yes—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60C4×Dic43—21no—
61D344—24no—
62D344—24no—
63C23×C43C2×D411yescharacteristic
64C22×D43—22no—
65C22×D43—24no—
66C22×D43—22no—
67C22×D43—82no—
68C2×C4×C43—22no—
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D412yes—
71C2×C4×C43C2×D412yes—
72C2×C4×C43C2411yescharacteristic
73C22⋊D43—82no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76D172—24no—
77D172—22no—
78D172—22no—
79D172—22no—
80D172—82no—
81D172#4114yes—
82C4×D43—82no—
83C4×D43—82no—
84C4×D43—82no—
85C8×C43—22no—
86C8×C43—22no—
87C22×C43—21no—
88C22×C43—22no—
89C22×C43C22×D411yescharacteristic
90C2×D43—24no—
91C2×D43—42no—
92C2×D43—42no—
93C2×D43—42no—
94C2×D43—42no—
95C2×D43—42no—
96C2×D43—84no—
97C4×C43—21no—
98C4×C43—22no—
99C4×C43—22no—
100C4×C43C2×#4112yes—
101Dic43—42no—
102Dic43—42no—
103#3122—431nomaximal, Sylow
104C2×C43—41no—
105C2×C43#52511yescharacteristic
106C2×C43#57612yes—
107D43—44no—
108D43—82no—
109#540—431no—
110#518—431no—
111#482—432no—
112#478—432no—
113#459—432no—
114#447—432no—
115#442—432no—
116C4×D8—432no—
117#433D4311yescharacteristic, complemented
118C43#312211yescharacteristic, complemented, Sylow
119C22×D4—431no—
120C2×D8—432no—
121C2×D8—432no—
122#127—431no—
123#125—431no—
124#123—862no—
125#121—432no—
126#121—862no—
127C4×D4—432no—
128C4×D4—432no—
129C4×D4—432no—
130C4×D4—862no—
131#117—431no—
132#117C2×D4311yescharacteristic
133C2×C22⋊C4—862no—
134#107—432no—
135#106—432no—
136C4⋊C8C2×D4312yescomplemented
137#102—432no—
138#102—432no—
139#102—432no—
140#102—432no—
141C22⋊C8C2×D4312yes—
142#97C2×D4311yescharacteristic, complemented
143C4×C8C2×D4311yescharacteristic, complemented
144C24—861no—
145C2×D4—432no—
146C2×D4—432no—
147C2×D4—864no—
148C2×D4—862no—
149C2×D4—861no—
150C2×D4—862no—
151C22×C4—862no—
152C22×C4—862no—
153C22×C4—862no—
154C22×C4C22×D4311yescharacteristic
155D8—864no—
156D8—864no—
157C2×C8C22×D4312yes—
158C2×C8C22×D4312yes—
159C4⋊C4—432no—
160C4⋊C4—432no—
161C4⋊C4—862no—
162C4⋊C4D17212yes—
163C22⋊C4—861no—
164C22⋊C4—862no—
165C22⋊C4—862no—
166C22⋊C4—862no—
167C22⋊C4—862no—
168C22⋊C4D17212yes—
169C42—861no—
170C42C22×D4311yescharacteristic
171C42C22×D4311yescharacteristic
172C23—864no—
173C23—862no—
174C23—862no—
175C23—3442no—
176C23C2×D17211yescharacteristic
177D4—434no—
178D4—864no—
179D4—862no—
180D4—862no—
181D4—862no—
182D4—3442no—
183D4—3442no—
184C2×C4—22no—
185C2×C4—862no—
186C2×C4—862no—
187C2×C4—3442no—
188C2×C4—3442no—
189C2×C4—3442no—
190C2×C4C2×D17211yescharacteristic
191C2×C4C2×D17212yes—
192C2×C4C2×D17212yes—
193C2×C4C23×D4311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—864no—
199C22—3444no—
200C22—1722no—
201C22—1722no—
202C22—1722no—
203C22—1722no—
204C22—1722no—
205C22C22×D17211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—1722no—
210C4—1722no—
211C4#41×D4312yes—
212C2—41no—
213C2—3442no—
214C2—1724no—
215C2#1458341111yescharacteristic
216C2#1458370412yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3122
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583504C2semidirect
2. #14583373C2semidirect
3. #14583224C2semidirect
4. #14583200C2semidirect
5. #14583095C2semidirect
6. #14583035C2semidirect
7. #14583012C2semidirect
8. C4×D344C2semidirect
9. C43×#433C2semidirect
13. #13063322C22semidirect
14. #13063317C22semidirect
20. C4×D172C22semidirect
24. #13063259C22semidirect
25. #13063257C22semidirect
28. #13063247C22semidirect
29. #13063247C22semidirect
31. C4⋊C8×C43C22semidirect
33. #97×C43C22semidirect
34. C4×C8×C43C22semidirect
117. #433D43semidirect
118. C43#3122semidirect
136. C4⋊C8C2×D43semidirect
142. #97C2×D43semidirect
143. C4×C8C2×D43semidirect