Finite Group Databasebeta

← #19143966

Subgroups — #19143966

Order 5504.

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

normal subgroups only

This group has 736 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
2C2×#13063351C212yesmaximal, complemented
3#14583071C214yesmaximal, complemented
4#14583066C214yesmaximal, complemented
5#14582917C212yesmaximal, complemented
6#14582883C211yesmaximal, characteristic, complemented
7C43×#535C211yesmaximal, characteristic, complemented
8#13063373C2212yescomplemented
9#13063372—22no—
10#13063371—22no—
11#13063370—22no—
12#13063370C2212yescomplemented
13C2×#10621898—22no—
14C2×#10621898C2212yes—
15#41×D43—24no—
16#13063351—24no—
17#13063351C2218yescomplemented
18C2×#10621883—22no—
19C2×#10621882—22no—
20C2×#10621877C2212yescomplemented
21#13063253C2218yescomplemented
22#13063244C2212yescomplemented
23#13063242C2212yescomplemented
24C2×#41×C43C2211yescharacteristic
25C22×D4×C43C2211yescharacteristic, complemented
26#127×C43C2212yescomplemented
27#124×C43C2212yescomplemented
28#121×C43—22no—
29#120×C43—22no—
30#117×C43C2211yescharacteristic, complemented
31C24×C43—21no—
32#41×C43—22no—
33#41×C43—22no—
34C2×Q8×C43C2311yescharacteristic
35C2×D4×C43—21no—
36C2×D4×C43—24no—
37C2×D4×C43—22no—
38C2×D4×C43—22no—
39C2×D4×C43D412yes—
40C2×D4×C43C2312yes—
41C2×D4×C43C2311yescharacteristic
42C22×C4×C43D412yes—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—24no—
45C2×C22⋊D43—22no—
46#10621902—24no—
47Q8×D43—24no—
48#10621900—28no—
49#10621900—24no—
50D4×D43—28no—
51D4×D43—24no—
52#10621898—24no—
53#10621898—24no—
54#10621898—22no—
55#10621898—24no—
56#10621898—22no—
57#10621898D414yescomplemented
58#10621898C2314yes—
59C2×D172—22no—
60C2×D172D412yescomplemented
61C2×C4×D43—24no—
62C2×C4×D43—22no—
63C2×Dic86—22no—
64C2×Dic86D412yescomplemented
65C4⋊C4×C43—21no—
66C22⋊C4×C43—24no—
67C22⋊C4×C43—21no—
68C42×C43C2312yes—
69#10621883—28no—
70#10621882—28no—
71#10621877—22no—
72#10621877C2314yes—
73C2×C43⋊C8—22no—
74C23×C43—22no—
75C23×C43—42no—
76C23×C43—82no—
77C23×C43C2×D412yes—
78C23×C43C2×D411yescharacteristic
79C22×D43—24no—
80C22×D43—22no—
81Q8×C43—22no—
82D4×C43—24no—
83D4×C43—22no—
84D4×C43—24no—
85D4×C43—41no—
86D4×C43—41no—
87D4×C43—84no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43C2×D412yes—
92C2×C4×C43C2×D412yes—
93C2×C4×C43C2×D412yes—
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2411yescharacteristic
96C22⋊D43—28no—
97C22⋊D43—24no—
98C22⋊D43—24no—
99C2×Dic43—24no—
100C2×Dic43—22no—
101D172—24no—
102D172—22no—
103D172C2×D414yes—
104C4×D43—28no—
105C4×D43—24no—
106C4×D43—24no—
107Dic86—24no—
108Dic86—22no—
109Dic86C2×D414yes—
110C43⋊C8—24no—
111C22×C43—22no—
112C22×C43—41no—
113C22×C43—42no—
114C22×C43—44no—
115C22×C43—42no—
116C22×C43—84no—
117C22×C43#12012yes—
118C22×C43C22×D411yescharacteristic
119C2×D43—24no—
120C2×D43—82no—
121C2×D43—84no—
122C4×C43—22no—
123C4×C43—42no—
124C4×C43#12011yescharacteristic
125C4×C43#12011yescharacteristic
126C4×C43C22×D412yes—
127Dic43—24no—
128#3021—431nomaximal, Sylow
129C2×C43—21no—
130C2×C43—22no—
131C2×C43—42no—
132C2×C43—82no—
133C2×C43C2×#12011yescharacteristic
134D43—44no—
135#585—431no—
136C2×AGL(1,ℤ/8)—432no—
137#535D4311yescharacteristic, complemented
138#454—434no—
139#453—434no—
140#421—432no—
141#413—431no—
142C43#302111yescharacteristic, complemented, Sylow
1432−1+4—432no—
1442−1+4—862no—
145H(5,𝔽2)—432no—
146H(5,𝔽2)—862no—
147H(5,𝔽2)—862no—
148C2×#41—432no—
149C2×#41—864no—
150C2×#41—862no—
151C2×#41C2×D4311yescharacteristic
152C22×D4C2×D4311yescharacteristic, complemented
153AGL(1,ℤ/8)—438no—
154AGL(1,ℤ/8)—864no—
155C2×SD16—862no—
156C2×D8—862no—
157C2×M16—432no—
158#127C2×D4312yescomplemented
159#124C2×D4312yescomplemented
160#121—22no—
161#120—22no—
162#117C2×D4311yescharacteristic, complemented
163#104—438no—
164#101—432no—
165#100—432no—
166C24—21no—
167#41—22no—
168#41—22no—
169#41—434no—
170#41—434no—
171#41—864no—
172#41—864no—
173#41—864no—
174#41—868no—
175#41—864no—
176#41—862no—
177#41—862no—
178#41—864no—
179C2×Q8—432no—
180C2×Q8—862no—
181C2×Q8—864no—
182C2×Q8C22×D4311yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—432no—
188C2×D4—862no—
189C2×D4—864no—
190C2×D4—868no—
191C2×D4—862no—
192C2×D4—864no—
193C2×D4C22⋊D4312yes—
194C2×D4C22×D4312yes—
195C2×D4C22×D4311yescharacteristic
196C22×C4—864no—
197C22×C4—862no—
198C22×C4C22⋊D4312yes—
199C22×C4C22×D4311yescharacteristic
200SD16—868no—
201D8—868no—
202M16—434no—
203M16—862no—
204C2×C8—862no—
205C4⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—24no—
208C42C22×D4312yes—
209C23—22no—
210C23—42no—
211C23—82no—
212C23—864no—
213C23—862no—
214C23C2×C22⋊D4312yes—
215C23C2×C22⋊D4311yescharacteristic
216Q8—22no—
217Q8—434no—
218Q8—864no—
219Q8—862no—
220D4—24no—
221D4—22no—
222D4—24no—
223D4—41no—
224D4—41no—
225D4—84no—
226D4—434no—
227D4—864no—
228D4—868no—
229D4—864no—
230D4—864no—
231D4—862no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—868no—
236C2×C4—864no—
237C2×C4—862no—
238C2×C4—864no—
239C2×C4—864no—
240C2×C4D4×D4312yes—
241C2×C4D4×D4312yes—
242C2×C4C2×C22⋊D4312yes—
243C2×C4C2×C22⋊D4311yescharacteristic
244C2×C4C23×D4311yescharacteristic
245C8—864no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—44no—
250C22—42no—
251C22—84no—
252C22—864no—
253C22—3442no—
254C22—3444no—
255C22#1306329312yes—
256C22C22×C22⋊D4311yescharacteristic
257C4—22no—
258C4—42no—
259C4—864no—
260C4#1306329311yescharacteristic
261C4#1306329311yescharacteristic
262C4C2×D4×D4312yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—1724no—
268C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#535C2
socleC2×C43C2×#120
hypercenter#535D43
hypocenterC43#3021
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #14583735C2semidirect
2. C2×#13063351C2semidirect
3. #14583071C2semidirect
4. #14583066C2semidirect
5. #14582917C2semidirect
6. #14582883C2semidirect
7. C43×#535C2semidirect
8. #13063373C22semidirect
12. #13063370C22semidirect
17. #13063351C22semidirect
20. C2×#10621877C22semidirect
21. #13063253C22semidirect
22. #13063244C22semidirect
23. #13063242C22semidirect
25. C22×D4×C43C22semidirect
26. #127×C43C22semidirect
27. #124×C43C22semidirect
30. #117×C43C22semidirect
57. #10621898D4semidirect
60. C2×D172D4semidirect
64. C2×Dic86D4semidirect
137. #535D43semidirect
142. C43#3021semidirect
152. C22×D4C2×D43semidirect
158. #127C2×D43semidirect
159. #124C2×D43semidirect
162. #117C2×D43semidirect