Finite Group Databasebeta

← #19145669

Subgroups — #19145669

Order 5504.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#14583468C211yesmaximal, characteristic
3#14583293C211yesmaximal, characteristic, complemented
4#14583272C211yesmaximal, characteristic, complemented
5#14583264C211yesmaximal, characteristic, complemented
6#14583254C211yesmaximal, characteristic, complemented
7#14583122C212yesmaximal, complemented
8#14583100C212yesmaximal, complemented
9#14583063C212yesmaximal, complemented
10#14583052C212yesmaximal, complemented
11C43×#433C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×D172C2211yescharacteristic
14C2×Dic172C2212yescomplemented
15C2×#10621873C2212yes—
16C2×#10621873C2212yes—
17C2×#10621873C2212yescomplemented
18#13063325C2211yescharacteristic, complemented
19#13063322C2211yescharacteristic
20#13063322C2211yescharacteristic
21#13063318—22no—
22#13063317C2211yescharacteristic, complemented
23#13063315—22no—
24#13063313C2211yescharacteristic
25#13063313C2211yescharacteristic
26#13063304C2212yes—
27#13063300—22no—
28#13063295—22no—
29C4×Dic86C2212yescomplemented
30#13063250C2212yescomplemented
31#13063247C2212yes—
32#13063247C2212yes—
33#13063247C2212yescomplemented
34#117×C43C2211yescharacteristic
35C4⋊C8×C43C2212yescomplemented
36C22⋊C8×C43C2212yes—
37#97×C43C2211yescharacteristic, complemented
38C4×C8×C43C2211yescharacteristic, complemented
39C23×D43—21no—
40C22×C4×C43C2311yescharacteristic
41C2×C22⋊D43—21no—
42#10621898—42no—
43C2×D172—21no—
44C2×D172—22no—
45C2×D172—22no—
46C2×D172—42no—
47C2×D172C2311yescharacteristic
48C2×D172C2311yescharacteristic
49C2×D172C2311yescharacteristic
50C2×C4×D43—21no—
51C2×Dic86C2311yescharacteristic
52C2×Dic86C2312yes—
53C2×C8×C43C2312yes—
54C2×C8×C43C2312yes—
55C4⋊C4×C43D412yes—
56C22⋊C4×C43D412yes—
57C42×C43C2311yescharacteristic
58C42×C43C2311yescharacteristic
59C22⋊Dic43—22no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62C4⋊Dic43—22no—
63C4⋊Dic43C2312yes—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—22no—
67C4×Dic43—22no—
68Dic172—42no—
69#10621873—42no—
70#10621873—42no—
71#10621873—42no—
72C23×C43C2×D411yescharacteristic
73C22×D43—21no—
74C22×D43—21no—
75C22×D43—21no—
76C22×D43—42no—
77C22×D43—82no—
78C2×C4×C43—22no—
79C2×C4×C43C2×D412yes—
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2411yescharacteristic
83C22⋊D43—42no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—21no—
87D172—22no—
88D172—22no—
89D172—22no—
90D172—42no—
91D172—82no—
92D172—82no—
93C4×D43—42no—
94Dic86—22no—
95Dic86—22no—
96Dic86—22no—
97C8×C43—22no—
98C8×C43—22no—
99C22×C43—21no—
100C22×C43—22no—
101C22×C43C22×D411yescharacteristic
102C2×D43—41no—
103C2×D43—41no—
104C2×D43—41no—
105C2×D43—42no—
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—84no—
109C4×C43—21no—
110C4×C43—22no—
111C4×C43—22no—
112C4×C43H(5,𝔽2)12yes—
113Dic43—41no—
114Dic43—42no—
115Dic43—42no—
116#3222—431nomaximal, Sylow
117C2×C43—41no—
118C2×C43#53511yescharacteristic
119C2×C43#57712yes—
120D43—81no—
121D43—81no—
122D43—81no—
123#541—431no—
124#535—431no—
125#497—431no—
126#492—431no—
127#490—431no—
128#488—431no—
129#464—432no—
130#460—432no—
131#452—432no—
132#450—432no—
133#433D4311yescharacteristic, complemented
134C43#322211yescharacteristic, complemented, Sylow
135C2×#41—431no—
136C22×D4—431no—
137C2×Q16—432no—
138C2×SD16—432no—
139C2×SD16—432no—
140C2×SD16—432no—
141C4⋊Q8—431no—
142#127—431no—
143#127—431no—
144#126—862no—
145#125—431no—
146#125—862no—
147#124—431no—
148#124—431no—
149C22⋊Q8—432no—
150#121—862no—
151#120—862no—
152C4×Q8—432no—
153#117C2×D4311yescharacteristic
154C4⋊C8C2×D4312yescomplemented
155#103—432no—
156#102—432no—
157#102—432no—
158#102—432no—
159C22⋊C8C2×D4312yes—
160#97C2×D4311yescharacteristic, complemented
161C4×C8C2×D4311yescharacteristic, complemented
162C24—861no—
163#41—1722no—
164C2×Q8—431no—
165C2×Q8—432no—
166C2×D4—431no—
167C2×D4—431no—
168C2×D4—431no—
169C2×D4—861no—
170C2×D4—862no—
171C2×D4—862no—
172C2×D4—861no—
173C2×D4—1722no—
174C22×C4—861no—
175C22×C4C22×D4311yescharacteristic
176Q16—1722no—
177SD16—1722no—
178SD16—1722no—
179SD16—1722no—
180C2×C8C22×D4312yes—
181C2×C8C22×D4312yes—
182C4⋊C4—432no—
183C4⋊C4—862no—
184C4⋊C4—862no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4D17212yes—
188C22⋊C4—862no—
189C22⋊C4—862no—
190C22⋊C4—862no—
191C22⋊C4D17212yes—
192C42—862no—
193C42C22×D4311yescharacteristic
194C42C22×D4311yescharacteristic
195C23—861no—
196C23—861no—
197C23—861no—
198C23—3442no—
199C23—1722no—
200C23C2×D17211yescharacteristic
201Q8—862no—
202Q8—862no—
203Q8—862no—
204D4—862no—
205D4—862no—
206D4—862no—
207D4—3442no—
208D4—3442no—
209D4—1722no—
210D4—1722no—
211C2×C4—22no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—861no—
215C2×C4—1722no—
216C2×C4C2×D17212yes—
217C2×C4C2×D17212yes—
218C2×C4C2×D17211yescharacteristic
219C2×C4C23×D4311yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—3444no—
225C22—1722no—
226C22—1722no—
227C22—1722no—
228C22—1721no—
229C22—1721no—
230C22—1721no—
231C22C22×D17211yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—1722no—
236C4—1721no—
237C4—1722no—
238C4#1306337112yes—
239C2—41no—
240C2—3441no—
241C2—3441no—
242C2—3441no—
243C2#1458346811yescharacteristic
244C2#1458371112yes—
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3222
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. #14583511C2semidirect
3. #14583293C2semidirect
4. #14583272C2semidirect
5. #14583264C2semidirect
6. #14583254C2semidirect
7. #14583122C2semidirect
8. #14583100C2semidirect
9. #14583063C2semidirect
10. #14583052C2semidirect
11. C43×#433C2semidirect
14. C2×Dic172C22semidirect
17. C2×#10621873C22semidirect
18. #13063325C22semidirect
22. #13063317C22semidirect
29. C4×Dic86C22semidirect
30. #13063250C22semidirect
33. #13063247C22semidirect
35. C4⋊C8×C43C22semidirect
37. #97×C43C22semidirect
38. C4×C8×C43C22semidirect
133. #433D43semidirect
134. C43#3222semidirect
154. C4⋊C8C2×D43semidirect
160. #97C2×D43semidirect
161. C4×C8C2×D43semidirect