Finite Group Databasebeta

← #19143943

Subgroups — #19143943

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#14583697C212yesmaximal, complemented
3#14583081C212yesmaximal, complemented
4#14583076C212yesmaximal, complemented
5#14583071C212yesmaximal, complemented
6#14583066C212yesmaximal, complemented
7C2×#13063253C212yesmaximal, complemented
8#14582883C211yesmaximal, characteristic, complemented
9C43×#532C211yesmaximal, characteristic, complemented
10#13063373C2212yes—
11#13063372—22no—
12#13063371—22no—
13#13063370—22no—
14#13063370C2212yes—
15C2×#10621898—22no—
16C2×#10621898C2212yes—
17#41×D43—24no—
18#13063356C2214yescomplemented
19#13063355—22no—
20#13063351C2214yescomplemented
21#13063350—22no—
22#13063345—24no—
23C2×#10621877C2212yescomplemented
24#13063253C2214yescomplemented
25#13063253C2214yescomplemented
26#13063244C2212yescomplemented
27#13063242C2212yescomplemented
28C2×#41×C43C2211yescharacteristic
29C2×#41×C43C2211yescharacteristic, complemented
30C4⋊Q8×C43C2211yescharacteristic, complemented
31#127×C43C2211yescharacteristic, complemented
32#124×C43C2211yescharacteristic, complemented
33#124×C43C2211yescharacteristic, complemented
34#121×C43—22no—
35C4×D4×C43—22no—
36C2×C42×C43C2211yescharacteristic, complemented
37#41×C43—22no—
38#41×C43—22no—
39#41×C43—22no—
40#41×C43—22no—
41C2×Q8×C43C2311yescharacteristic
42C2×Q8×C43C2311yescharacteristic
43C2×D4×C43—22no—
44C2×D4×C43—21no—
45C2×D4×C43D412yes—
46C2×D4×C43C2311yescharacteristic
47C2×D4×C43C2311yescharacteristic
48C22×C4×C43—21no—
49C22×C4×C43—21no—
50C22×C4×C43D412yes—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—24no—
53C2×C22⋊D43—22no—
54#10621902—24no—
55Q8×D43—24no—
56#10621900—28no—
57#10621900—24no—
58D4×D43—28no—
59D4×D43—24no—
60#10621898—24no—
61#10621898—24no—
62#10621898—22no—
63#10621898—24no—
64#10621898—22no—
65#10621898D414yescomplemented
66#10621898C2314yes—
67C2×D172—22no—
68C2×D172D412yescomplemented
69C2×C4×D43—24no—
70C2×C4×D43—22no—
71C2×Dic86—22no—
72C2×Dic86D412yescomplemented
73C4⋊C4×C43—22no—
74C22⋊C4×C43—22no—
75C22⋊C4×C43—22no—
76C42×C43—21no—
77C42×C43C2311yescharacteristic
78C42×C43C2311yescharacteristic
79#10621885—24no—
80#10621884—24no—
81#10621883—24no—
82#10621882—24no—
83#10621877—22no—
84#10621877C2314yes—
85C2×C43⋊C8—22no—
86C23×C43—21no—
87C23×C43C2×D412yes—
88C23×C43C2×D411yescharacteristic
89C22×D43—24no—
90C22×D43—22no—
91Q8×C43—22no—
92Q8×C43—22no—
93D4×C43—24no—
94D4×C43—22no—
95D4×C43—22no—
96D4×C43—44no—
97D4×C43—42no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—42no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43C2×D412yes—
107C2×C4×C43C2×D412yes—
108C2×C4×C43C2×D412yes—
109C2×C4×C43C2×D411yescharacteristic
110C2×C4×C43C2411yescharacteristic
111C22⋊D43—28no—
112C22⋊D43—24no—
113C22⋊D43—24no—
114C2×Dic43—24no—
115C2×Dic43—22no—
116D172—24no—
117D172—22no—
118D172C2×D414yes—
119C4×D43—28no—
120C4×D43—24no—
121C4×D43—24no—
122Dic86—24no—
123Dic86—22no—
124Dic86C2×D414yes—
125C43⋊C8—24no—
126C22×C43—22no—
127C22×C43—41no—
128C22×C43—42no—
129C22×C43—42no—
130C22×C43—41no—
131C22×C43#12012yes—
132C22×C43C22×D411yescharacteristic
133C2×D43—24no—
134C2×D43—82no—
135C2×D43—84no—
136C4×C43—22no—
137C4×C43—22no—
138C4×C43—41no—
139C4×C43—41no—
140C4×C43#12011yescharacteristic
141C4×C43#12011yescharacteristic
142C4×C43C22×D412yes—
143Dic43—24no—
144#3018—431nomaximal, Sylow
145C2×C43—21no—
146C2×C43—22no—
147C2×C43—42no—
148C2×C43—81no—
149C2×C43C2×#12011yescharacteristic
150D43—44no—
151#585—431no—
152#575—432no—
153#532D4311yescharacteristic, complemented
154#456—432no—
155#455—432no—
156#454—432no—
157#453—432no—
158C2×#104—432no—
159#413—431no—
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—864no—
168C2×#41—862no—
169C2×#41C2×D4311yescharacteristic
170C2×#41C2×D4311yescharacteristic, complemented
171#137—434no—
172#137—862no—
173AGL(1,ℤ/8)—434no—
174AGL(1,ℤ/8)—862no—
175#135—864no—
176C2×M16—432no—
177C4⋊Q8C2×D4311yescharacteristic, complemented
178#127C2×D4311yescharacteristic, complemented
179#124C2×D4311yescharacteristic, complemented
180#124C2×D4311yescharacteristic, complemented
181#121—22no—
182C4×D4—22no—
183C2×C42C2×D4311yescharacteristic, complemented
184#104—434no—
185#104—434no—
186#101—432no—
187#100—432no—
188#41—22no—
189#41—22no—
190#41—22no—
191#41—22no—
192#41—434no—
193#41—434no—
194#41—864no—
195#41—864no—
196#41—864no—
197#41—868no—
198#41—864no—
199#41—862no—
200#41—862no—
201#41—864no—
202C2×Q8—432no—
203C2×Q8—862no—
204C2×Q8—864no—
205C2×Q8C22×D4311yescharacteristic
206C2×Q8C22×D4311yescharacteristic
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—432no—
210C2×D4—862no—
211C2×D4—864no—
212C2×D4—868no—
213C2×D4—862no—
214C2×D4—864no—
215C2×D4C22⋊D4312yes—
216C2×D4C22×D4311yescharacteristic
217C2×D4C22×D4311yescharacteristic
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—864no—
221C22×C4—862no—
222C22×C4C22⋊D4312yes—
223C22×C4C22×D4311yescharacteristic
224Q16—864no—
225SD16—864no—
226SD16—864no—
227D8—864no—
228M16—434no—
229M16—862no—
230C2×C8—862no—
231C4⋊C4—22no—
232C22⋊C4—22no—
233C22⋊C4—22no—
234C42—21no—
235C42C22×D4311yescharacteristic
236C42C22×D4311yescharacteristic
237C23—21no—
238C23—864no—
239C23—862no—
240C23C2×C22⋊D4312yes—
241C23C2×C22⋊D4311yescharacteristic
242Q8—22no—
243Q8—22no—
244Q8—434no—
245Q8—864no—
246Q8—862no—
247D4—24no—
248D4—22no—
249D4—22no—
250D4—44no—
251D4—42no—
252D4—434no—
253D4—864no—
254D4—868no—
255D4—864no—
256D4—864no—
257D4—862no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—868no—
267C2×C4—864no—
268C2×C4—862no—
269C2×C4—864no—
270C2×C4—864no—
271C2×C4D4×D4312yes—
272C2×C4D4×D4312yes—
273C2×C4C2×C22⋊D4312yes—
274C2×C4C2×C22⋊D4311yescharacteristic
275C2×C4C23×D4311yescharacteristic
276C8—864no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—42no—
281C22—41no—
282C22—864no—
283C22—3442no—
284C22—3444no—
285C22#1306329312yes—
286C22C22×C22⋊D4311yescharacteristic
287C4—22no—
288C4—22no—
289C4—41no—
290C4—41no—
291C4—864no—
292C4#1306329311yescharacteristic
293C4#1306329311yescharacteristic
294C4C2×D4×D4312yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—81no—
299C2—1724no—
300C2C2×#1306329311yescharacteristic
subgroupG/H
centerC4#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#532C2
socleC2×C43C2×#120
hypercenter#532D43
hypocenterC43#3018
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14583735C2semidirect
2. #14583697C2semidirect
3. #14583081C2semidirect
4. #14583076C2semidirect
5. #14583071C2semidirect
6. #14583066C2semidirect
7. C2×#13063253C2semidirect
8. #14582883C2semidirect
9. C43×#532C2semidirect
18. #13063356C22semidirect
20. #13063351C22semidirect
23. C2×#10621877C22semidirect
24. #13063253C22semidirect
25. #13063253C22semidirect
26. #13063244C22semidirect
27. #13063242C22semidirect
29. C2×#41×C43C22semidirect
30. C4⋊Q8×C43C22semidirect
31. #127×C43C22semidirect
32. #124×C43C22semidirect
33. #124×C43C22semidirect
36. C2×C42×C43C22semidirect
65. #10621898D4semidirect
68. C2×D172D4semidirect
72. C2×Dic86D4semidirect
153. #532D43semidirect
160. C43#3018semidirect
170. C2×#41C2×D43semidirect
177. C4⋊Q8C2×D43semidirect
178. #127C2×D43semidirect
179. #124C2×D43semidirect
180. #124C2×D43semidirect
183. C2×C42C2×D43semidirect