Finite Group Databasebeta

← #19143998

Subgroups — #19143998

Order 5504.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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#14583735C211yesmaximal, characteristic, complemented
2#14583468C212yesmaximal, complemented
3#14583463C211yesmaximal, characteristic, complemented
4#14583087C218yesmaximal, complemented
5#14582872C212yesmaximal, complemented
6C43×#410C211yesmaximal, characteristic, complemented
7#13063373—21no—
8#13063372—22no—
9#13063371—22no—
10#13063370—21no—
11#13063370C2214yes—
12C2×#10621898—22no—
13C2×#10621898C2212yes—
14#41×D43—24no—
15C22×D172C2211yescharacteristic, complemented
16#13063322—22no—
17#13063321—21no—
18#13063314—21no—
19#13063313—22no—
20#13063300—24no—
21#13063299—22no—
22#13063295C2218yescomplemented
23#13063293C2214yescomplemented
24#13063284C2211yescharacteristic, complemented
25#13063239C2218yescomplemented
26C2×#41×C43C2211yescharacteristic
27#117×C43C2212yescomplemented
28#99×C43C2214yescomplemented
29C23×D43C2312yes—
30#41×C43—22no—
31#41×C43—22no—
32C2×Q8×C43D411yescharacteristic, complemented
33C2×D4×C43D411yescharacteristic, complemented
34C2×D4×C43C2312yes—
35C22×C4×C43D412yescomplemented
36C22×C4×C43C2311yescharacteristic
37C2×C22⋊D43—24no—
38C2×C22⋊D43—24no—
39C2×C22⋊D43C2314yes—
40#10621902—24no—
41Q8×D43—24no—
42#10621900—24no—
43#10621900—28no—
44D4×D43—24no—
45D4×D43—28no—
46#10621898—24no—
47#10621898—24no—
48#10621898—22no—
49#10621898—22no—
50#10621898—24no—
51#10621898—22no—
52#10621898—22no—
53C2×D172—22no—
54C2×D172—21no—
55C2×D172—22no—
56C2×D172—22no—
57C2×D172—21no—
58C2×D172—28no—
59C2×D172D412yescomplemented
60C2×C4×D43—24no—
61C2×C4×D43D414yescomplemented
62C2×Dic86—22no—
63C2×Dic86D412yescomplemented
64C4⋊C4×C43—22no—
65C22⋊C4×C43C2314yes—
66C42×C43—22no—
67C22⋊Dic43C2312yes—
68(C2×D43)⋊C4—24no—
69(C2×D43)⋊C4—28no—
70C4⋊Dic43—21no—
71C4×Dic43—21no—
72C23×C43C2×D412yes—
73C23×C43C2411yescharacteristic
74C22×D43—24no—
75C22×D43—24no—
76C22×D43—22no—
77C22×D43—82no—
78C22×D43C2×D414yes—
79Q8×C43—22no—
80D4×C43—24no—
81D4×C43—22no—
82C2×C4×C43—22no—
83C2×C4×C43—22no—
84C2×C4×C43—24no—
85C2×C4×C43C2×D412yes—
86C2×C4×C43C2×D411yescharacteristic
87C2×C4×C43C2×D411yescharacteristic
88C2×C4×C43C2×D412yes—
89C2×C4×C43C2×D412yes—
90C22⋊D43—28no—
91C22⋊D43—24no—
92C22⋊D43—24no—
93C22⋊D43—84no—
94C2×Dic43—24no—
95C2×Dic43—22no—
96C2×Dic43C2×D414yes—
97D172—24no—
98D172—22no—
99D172—22no—
100D172—41no—
101D172—42no—
102D172—41no—
103D172—88no—
104C4×D43—28no—
105C4×D43—24no—
106C4×D43—24no—
107Dic86—24no—
108Dic86—22no—
109Dic86—22no—
110C22×C43—22no—
111C22×C43—41no—
112C22×C43—42no—
113C22×C43C22×D412yes—
114C22×C43C22×D411yescharacteristic
115C2×D43—24no—
116C2×D43—44no—
117C2×D43—48no—
118C2×D43—44no—
119C2×D43—42no—
120C2×D43—84no—
121C4×C43—22no—
122C4×C43—44no—
123C4×C43#12011yescharacteristic
124C4×C43#12012yes—
125C4×C43#12011yescharacteristic
126Dic43—24no—
127Dic43—42no—
128#3027—431nomaximal, Sylow
129C2×C43—21no—
130C2×C43—22no—
131C2×C43—42no—
132C2×C43C2×#12011yescharacteristic
133D43—44no—
134D43—82no—
135#585—431no—
136#535—431no—
137#535—432no—
138B(4,𝔽2)—438no—
139#410—432no—
140#410D4311yescharacteristic, complemented
141C43#302711yescharacteristic, complemented, Sylow
1422−1+4—862no—
1432−1+4—861no—
144H(5,𝔽2)—434no—
145H(5,𝔽2)—862no—
146H(5,𝔽2)—861no—
147C2×#41—432no—
148C2×#41—864no—
149C2×#41—862no—
150C2×#41C2×D4311yescharacteristic
151C22×D4—431no—
152#127—862no—
153#127—861no—
154#124—862no—
155#124—861no—
156#121—864no—
157#121—862no—
158#120—434no—
159#120—438no—
160#117—431no—
161#117C2×D4312yescomplemented
162#99—438no—
163#99C2×D4314yescomplemented
164C24—432no—
165#41—22no—
166#41—22no—
167#41—864no—
168#41—864no—
169#41—868no—
170#41—864no—
171#41—864no—
172#41—862no—
173#41—862no—
174#41—864no—
175#41—862no—
176#41—862no—
177C2×Q8—432no—
178C2×Q8—862no—
179C2×Q8—864no—
180C2×Q8D17211yescharacteristic, complemented
181C2×D4—434no—
182C2×D4—432no—
183C2×D4—862no—
184C2×D4—868no—
185C2×D4—868no—
186C2×D4—864no—
187C2×D4—864no—
188C2×D4—864no—
189C2×D4—861no—
190C2×D4—861no—
191C2×D4—862no—
192C2×D4—862no—
193C2×D4D17211yescharacteristic, complemented
194C2×D4C22×D4312yes—
195C22×C4—434no—
196C22×C4—864no—
197C22×C4D17212yescomplemented
198C22×C4C22×D4311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—861no—
201C22⋊C4—432no—
202C22⋊C4—868no—
203C22⋊C4—864no—
204C22⋊C4C22×D4314yes—
205C42—22no—
206C42—861no—
207C23—434no—
208C23—864no—
209C23—864no—
210C23—862no—
211C23—3442no—
212C23C2×D17212yes—
213C23C23×D4311yescharacteristic
214Q8—22no—
215Q8—864no—
216Q8—862no—
217Q8—862no—
218D4—24no—
219D4—22no—
220D4—864no—
221D4—868no—
222D4—864no—
223D4—864no—
224D4—862no—
225D4—862no—
226D4—3448no—
227D4—3444no—
228D4—1721no—
229D4—1721no—
230D4—1722no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—434no—
235C2×C4—868no—
236C2×C4—864no—
237C2×C4—864no—
238C2×C4—864no—
239C2×C4—862no—
240C2×C4C2×D17212yes—
241C2×C4C2×D17211yescharacteristic
242C2×C4C2×D17211yescharacteristic
243C2×C4D4×D4312yes—
244C2×C4D4×D4312yes—
245C22—22no—
246C22—41no—
247C22—42no—
248C22—864no—
249C22—3444no—
250C22—1728no—
251C22—1724no—
252C22—1724no—
253C22—1722no—
254C22C2×D4×D4312yes—
255C22C22×D17211yescharacteristic
256C4—22no—
257C4—44no—
258C4—864no—
259C4—1722no—
260C4#1306329511yescharacteristic
261C4#1306329511yescharacteristic
262C4#1306329512yes—
263C2—22no—
264C2—21no—
265C2—42no—
266C2—3442no—
267C2—1724no—
268C2C2×#1306329511yescharacteristic
subgroupG/H
centerC2C2×#13063295
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC43×#410C2
socleC2×C43C2×#120
hypercenter#410D43
hypocenterC43#3027
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14583735C2semidirect
2. #14583468C2semidirect
3. #14583463C2semidirect
4. #14583087C2semidirect
5. #14582872C2semidirect
6. C43×#410C2semidirect
15. C22×D172C22semidirect
22. #13063295C22semidirect
23. #13063293C22semidirect
24. #13063284C22semidirect
25. #13063239C22semidirect
27. #117×C43C22semidirect
28. #99×C43C22semidirect
32. C2×Q8×C43D4semidirect
33. C2×D4×C43D4semidirect
35. C22×C4×C43D4semidirect
59. C2×D172D4semidirect
61. C2×C4×D43D4semidirect
63. C2×Dic86D4semidirect
140. #410D43semidirect
141. C43#3027semidirect
161. #117C2×D43semidirect
163. #99C2×D43semidirect
180. C2×Q8D172semidirect
193. C2×D4D172semidirect
197. C22×C4D172semidirect