Finite Group Databasebeta

← #19145670

Subgroups — #19145670

Order 5504.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#14583512C211yesmaximal, characteristic, complemented
2#14583467C211yesmaximal, characteristic
3#14583294C211yesmaximal, characteristic, complemented
4#14583272C211yesmaximal, characteristic, complemented
5#14583265C211yesmaximal, characteristic, complemented
6#14583124C212yesmaximal, complemented
7#14583098C212yesmaximal, complemented
8#14583064C212yesmaximal, complemented
9#14583051C212yesmaximal, complemented
10#14582958C211yesmaximal, characteristic, complemented
11C43×#488C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×D4×D43C2211yescharacteristic
14C2×#10621885C2212yescomplemented
15C2×#10621873C2212yes—
16C2×#10621873C2212yescomplemented
17C2×#10621883C2212yes—
18#13063325C2211yescharacteristic, complemented
19#13063322C2211yescharacteristic
20#13063321C2211yescharacteristic
21#13063320—22no—
22#13063316—22no—
23#13063314C2211yescharacteristic
24#13063305C2212yes—
25#13063298—22no—
26#13063295—22no—
27#13063290C2212yescomplemented
28#13063282C2211yescharacteristic
29Dic43⋊C8C2212yescomplemented
30#13063245C2212yes—
31#13063245C2212yescomplemented
32(C2×D43)⋊C8C2212yes—
33#13063236C2211yescharacteristic, complemented
34#125×C43C2211yescharacteristic, complemented
35#124×C43C2211yescharacteristic
36#103×C43C2212yescomplemented
37#102×C43C2212yes—
38C4×C8×C43C2211yescharacteristic, complemented
39C23×D43—21no—
40C2×Q8×C43C2311yescharacteristic
41C2×D4×C43C2311yescharacteristic
42C2×C22⋊D43—21no—
43C2×C22⋊D43—22no—
44#10621902—42no—
45D4×D43—42no—
46C2×D172—22no—
47C2×D172—21no—
48C2×D172C2311yescharacteristic
49C2×D172C2311yescharacteristic
50C2×C4×D43—21no—
51C2×C4×D43C2311yescharacteristic
52C2×Dic86C2312yes—
53C2×C8×C43C2312yes—
54C4⋊C4×C43—22no—
55C4⋊C4×C43C2312yes—
56C22⋊C4×C43—22no—
57C42×C43C2311yescharacteristic
58#10621885—42no—
59#10621883—42no—
60(C2×D43)⋊C4—22no—
61(C2×D43)⋊C4—22no—
62(C2×D43)⋊C4D412yes—
63C4⋊Dic43—22no—
64C4⋊Dic43—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4D412yes—
67C4×Dic43—22no—
68C4×Dic43C2311yescharacteristic
69C2×C43⋊C8C2312yes—
70#10621873—42no—
71#10621873—42no—
72C23×C43—21no—
73C22×D43—21no—
74C22×D43—21no—
75C22×D43—42no—
76C22×D43—82no—
77C22×D43C2×D411yescharacteristic
78Q8×C43—22no—
79D4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43C2×D412yes—
83C2×C4×C43C2411yescharacteristic
84C22⋊D43—42no—
85C22⋊D43—82no—
86C2×Dic43—22no—
87C2×Dic43C2×D412yes—
88C2×Dic43C2×D411yescharacteristic
89D172—22no—
90D172—22no—
91D172—42no—
92D172—82no—
93C4×D43—22no—
94C4×D43—42no—
95Dic86—22no—
96Dic86—22no—
97C8×C43—22no—
98C43⋊C8—22no—
99C22×C43—41no—
100C22×C43—42no—
101C22×C43C22×D411yescharacteristic
102C2×D43—21no—
103C2×D43—22no—
104C2×D43—41no—
105C2×D43—41no—
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—84no—
109C4×C43—22no—
110C4×C43—41no—
111C4×C43—42no—
112C4×C43H(5,𝔽2)12yes—
113Dic43—21no—
114Dic43—22no—
115Dic43—42no—
116#3222—431nomaximal, Sylow
117C2×C43—81no—
118C2×C43#53511yescharacteristic
119C2×C43#57712yes—
120D43—41no—
121D43—81no—
122D43—81no—
123#541—431no—
124#535—431no—
125#497—431no—
126#492—431no—
127#490—431no—
128#488D4311yescharacteristic, complemented
129#464—432no—
130#460—432no—
131#452—432no—
132#450—432no—
133#433—431no—
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—862no—
146#125C2×D4311yescharacteristic, complemented
147#124—431no—
148#124C2×D4311yescharacteristic
149C22⋊Q8—432no—
150#121—862no—
151#120—862no—
152C4×Q8—432no—
153#117—431no—
154C4⋊C8—432no—
155#103C2×D4312yescomplemented
156#102—432no—
157#102—432no—
158#102C2×D4312yes—
159C22⋊C8—432no—
160#97—431no—
161C4×C8C2×D4311yescharacteristic, complemented
162C24—861no—
163#41—1722no—
164C2×Q8—432no—
165C2×Q8C22×D4311yescharacteristic
166C2×D4—431no—
167C2×D4—431no—
168C2×D4—861no—
169C2×D4—862no—
170C2×D4—861no—
171C2×D4—862no—
172C2×D4—1722no—
173C2×D4C22×D4311yescharacteristic
174C22×C4—431no—
175C22×C4—861no—
176Q16—1722no—
177SD16—1722no—
178SD16—1722no—
179SD16—1722no—
180C2×C8—432no—
181C2×C8C22×D4312yes—
182C4⋊C4—22no—
183C4⋊C4—432no—
184C4⋊C4—862no—
185C4⋊C4—862no—
186C4⋊C4—862no—
187C4⋊C4C22×D4312yes—
188C22⋊C4—22no—
189C22⋊C4—432no—
190C22⋊C4—862no—
191C22⋊C4—862no—
192C42—431no—
193C42—862no—
194C42C22×D4311yescharacteristic
195C23—21no—
196C23—431no—
197C23—861no—
198C23—861no—
199C23—3442no—
200C23—1722no—
201Q8—22no—
202Q8—862no—
203Q8—862no—
204D4—22no—
205D4—862no—
206D4—862no—
207D4—3442no—
208D4—3442no—
209D4—1722no—
210D4—1722no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—432no—
214C2×C4—431no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—1722no—
218C2×C4D4×D4312yes—
219C2×C4C23×D4311yescharacteristic
220C8—22no—
221C8—862no—
222C22—42no—
223C22—41no—
224C22—862no—
225C22—861no—
226C22—3444no—
227C22—1722no—
228C22—1722no—
229C22—1721no—
230C22—1721no—
231C22C2×D4×D4311yescharacteristic
232C4—22no—
233C4—42no—
234C4—41no—
235C4—862no—
236C4—861no—
237C4—1722no—
238C4#1306337112yes—
239C2—81no—
240C2—3441no—
241C2—3441no—
242C2—1721no—
243C2#1458346711yescharacteristic
244C2#1458370612yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#488C2
socleC22×C43C22×D4
hypercenter#488D43
hypocenterC43#3222
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #14583512C2semidirect
3. #14583294C2semidirect
4. #14583272C2semidirect
5. #14583265C2semidirect
6. #14583124C2semidirect
7. #14583098C2semidirect
8. #14583064C2semidirect
9. #14583051C2semidirect
10. #14582958C2semidirect
11. C43×#488C2semidirect
14. C2×#10621885C22semidirect
16. C2×#10621873C22semidirect
18. #13063325C22semidirect
27. #13063290C22semidirect
29. Dic43⋊C8C22semidirect
31. #13063245C22semidirect
33. #13063236C22semidirect
34. #125×C43C22semidirect
36. #103×C43C22semidirect
38. C4×C8×C43C22semidirect
128. #488D43semidirect
134. C43#3222semidirect
146. #125C2×D43semidirect
155. #103C2×D43semidirect
161. C4×C8C2×D43semidirect