Finite Group Databasebeta

← #19143948

Subgroups — #19143948

Order 5504.

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

normal subgroups only

This group has 724 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#14583699C212yesmaximal, complemented
3#14583445C211yesmaximal, characteristic, complemented
4#14583084C212yesmaximal, complemented
5#14583079C212yesmaximal, complemented
6#14583074C212yesmaximal, complemented
7#14583069C212yesmaximal, complemented
8C2×#13063251C212yesmaximal, complemented
9C43×#413C211yesmaximal, characteristic, complemented
10#13063373C2212yes—
11#13063372—22no—
12#13063371—22no—
13#13063370—22no—
14#13063370C2212yes—
15C2×#10621898—22no—
16C2×#10621898C2212yes—
17C2×#10621898C2211yescharacteristic, complemented
18#41×D43—24no—
19#13063358—22no—
20#13063358C2214yescomplemented
21#13063353—22no—
22#13063353C2214yescomplemented
23#13063347—24no—
24#13063323C2211yescharacteristic, complemented
25#13063321C2211yescharacteristic, complemented
26#13063314C2211yescharacteristic, complemented
27#13063312C2211yescharacteristic, complemented
28#13063297—22no—
29C4×C22⋊D43—22no—
30C2×C4×Dic43C2211yescharacteristic, complemented
31#13063251C2214yescomplemented
32#13063251C2214yescomplemented
33C2×#41×C43C2211yescharacteristic
34C2×M16×C43C2212yescomplemented
35#101×C43C2212yescomplemented
36#100×C43C2212yescomplemented
37#41×C43—22no—
38#41×C43—22no—
39C2×Q8×C43C2311yescharacteristic
40C2×D4×C43D412yes—
41C2×D4×C43C2311yescharacteristic
42C22×C4×C43D412yes—
43C22×C4×C43C2311yescharacteristic
44C2×C22⋊D43—24no—
45C2×C22⋊D43—22no—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—21no—
48C22×Dic43—21no—
49#10621902—24no—
50Q8×D43—24no—
51#10621900—28no—
52#10621900—24no—
53D4×D43—28no—
54D4×D43—24no—
55#10621898—24no—
56#10621898—24no—
57#10621898—22no—
58#10621898—24no—
59#10621898—22no—
60#10621898—22no—
61#10621898—22no—
62#10621898D414yescomplemented
63#10621898C2314yes—
64C2×D172—22no—
65C2×D172D412yescomplemented
66C2×D172C2311yescharacteristic
67C2×C4×D43—24no—
68C2×C4×D43—22no—
69C2×C4×D43—21no—
70C2×Dic86—22no—
71C2×Dic86D412yescomplemented
72C2×Dic86C2311yescharacteristic
73M16×C43—22no—
74M16×C43C2314yes—
75C2×C8×C43—22no—
76C22⋊Dic43—22no—
77(C2×D43)⋊C4—22no—
78Dic43⋊C4—22no—
79C4×Dic43—21no—
80C4×Dic43C2311yescharacteristic
81C4×Dic43C2311yescharacteristic
82Dic172—24no—
83D344—24no—
84#10621873—24no—
85#10621873—24no—
86C23×C43C2×D412yes—
87C23×C43C2×D411yescharacteristic
88C22×D43—24no—
89C22×D43—22no—
90C22×D43—21no—
91Q8×C43—22no—
92D4×C43—24no—
93D4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—22no—
96C2×C4×C43C2×D412yes—
97C2×C4×C43C2×D411yescharacteristic
98C2×C4×C43C2×D412yes—
99C2×C4×C43C2×D412yes—
100C2×C4×C43C2411yescharacteristic
101C22⋊D43—28no—
102C22⋊D43—24no—
103C22⋊D43—24no—
104C22⋊D43—44no—
105C22⋊D43—42no—
106C2×Dic43—24no—
107C2×Dic43—22no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—42no—
112D172—24no—
113D172—22no—
114D172—22no—
115D172C2×D414yes—
116C4×D43—28no—
117C4×D43—24no—
118C4×D43—24no—
119C4×D43—41no—
120C4×D43—41no—
121Dic86—24no—
122Dic86—22no—
123Dic86—22no—
124Dic86C2×D414yes—
125C8×C43—24no—
126C22×C43—22no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43#12012yes—
130C22×C43C22×D411yescharacteristic
131C2×D43—24no—
132C2×D43—42no—
133C2×D43—41no—
134C2×D43—82no—
135C2×D43—84no—
136C4×C43—22no—
137C4×C43#12011yescharacteristic
138C4×C43#12011yescharacteristic
139C4×C43C22×D412yes—
140Dic43—22no—
141Dic43—24no—
142Dic43—41no—
143Dic43—41no—
144#3018—431nomaximal, Sylow
145C2×C43—21no—
146C2×C43—22no—
147C2×C43—42no—
148C2×C43C2×#12011yescharacteristic
149D43—44no—
150D43—81no—
151#585—431no—
152#575—432no—
153#532—431no—
154#456—432no—
155#455—432no—
156#454—432no—
157#453—432no—
158C2×#104—432no—
159#413D4311yescharacteristic, complemented
160C43#301811yescharacteristic, complemented, Sylow
1612−1+4—432no—
1622−1+4—862no—
163H(5,𝔽2)—432no—
164H(5,𝔽2)—862no—
165H(5,𝔽2)—862no—
166C2×#41—432no—
167C2×#41—431no—
168C2×#41—864no—
169C2×#41—862no—
170C2×#41C2×D4311yescharacteristic
171#137—434no—
172#137—862no—
173AGL(1,ℤ/8)—434no—
174AGL(1,ℤ/8)—862no—
175#135—864no—
176C2×M16C2×D4312yescomplemented
177C4⋊Q8—431no—
178#127—431no—
179#124—431no—
180#124—431no—
181#121—862no—
182C4×D4—862no—
183C2×C42—431no—
184#104—434no—
185#104—434no—
186#101C2×D4312yescomplemented
187#100C2×D4312yescomplemented
188#41—22no—
189#41—22no—
190#41—434no—
191#41—434no—
192#41—864no—
193#41—864no—
194#41—864no—
195#41—868no—
196#41—864no—
197#41—862no—
198#41—864no—
199#41—862no—
200#41—862no—
201#41—862no—
202C2×Q8—432no—
203C2×Q8—431no—
204C2×Q8—862no—
205C2×Q8—864no—
206C2×Q8C22×D4311yescharacteristic
207C2×D4—432no—
208C2×D4—431no—
209C2×D4—862no—
210C2×D4—864no—
211C2×D4—868no—
212C2×D4—862no—
213C2×D4—864no—
214C2×D4—862no—
215C2×D4—861no—
216C2×D4D17212yes—
217C2×D4C22×D4311yescharacteristic
218C22×C4—864no—
219C22×C4—862no—
220C22×C4—861no—
221C22×C4—861no—
222C22×C4D17212yes—
223C22×C4C22×D4311yescharacteristic
224Q16—864no—
225SD16—864no—
226SD16—864no—
227D8—864no—
228M16—22no—
229M16C22×D4314yes—
230C2×C8—22no—
231C4⋊C4—862no—
232C22⋊C4—862no—
233C22⋊C4—862no—
234C42—431no—
235C42—431no—
236C42—861no—
237C23—864no—
238C23—862no—
239C23—861no—
240C23C2×D17212yes—
241C23C2×D17211yescharacteristic
242Q8—22no—
243Q8—434no—
244Q8—864no—
245Q8—862no—
246Q8—862no—
247D4—24no—
248D4—22no—
249D4—434no—
250D4—864no—
251D4—868no—
252D4—864no—
253D4—864no—
254D4—862no—
255D4—862no—
256D4—1724no—
257D4—1722no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—868no—
261C2×C4—864no—
262C2×C4—862no—
263C2×C4—861no—
264C2×C4—864no—
265C2×C4—864no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—1722no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4C2×D17212yes—
272C2×C4C2×D17211yescharacteristic
273C2×C4D4×D4312yes—
274C2×C4D4×D4312yes—
275C2×C4C23×D4311yescharacteristic
276C8—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—864no—
281C22—3442no—
282C22—3444no—
283C22—1722no—
284C22—1721no—
285C22#1306329512yes—
286C22C22×D17211yescharacteristic
287C4—22no—
288C4—862no—
289C4—864no—
290C4—1721no—
291C4—1721no—
292C4#1306329511yescharacteristic
293C4#1306329511yescharacteristic
294C4C2×D4×D4312yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—3441no—
299C2—1724no—
300C2C2×#1306329511yescharacteristic
subgroupG/H
centerC4#13063295
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#413C2
socleC2×C43C2×#120
hypercenter#413D43
hypocenterC43#3018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #14583735C2semidirect
2. #14583699C2semidirect
3. #14583445C2semidirect
4. #14583084C2semidirect
5. #14583079C2semidirect
6. #14583074C2semidirect
7. #14583069C2semidirect
8. C2×#13063251C2semidirect
9. C43×#413C2semidirect
17. C2×#10621898C22semidirect
20. #13063358C22semidirect
22. #13063353C22semidirect
24. #13063323C22semidirect
25. #13063321C22semidirect
26. #13063314C22semidirect
27. #13063312C22semidirect
30. C2×C4×Dic43C22semidirect
31. #13063251C22semidirect
32. #13063251C22semidirect
34. C2×M16×C43C22semidirect
35. #101×C43C22semidirect
36. #100×C43C22semidirect
62. #10621898D4semidirect
65. C2×D172D4semidirect
71. C2×Dic86D4semidirect
159. #413D43semidirect
160. C43#3018semidirect
176. C2×M16C2×D43semidirect
186. #101C2×D43semidirect
187. #100C2×D43semidirect