Finite Group Databasebeta

← #19144072

Subgroups — #19144072

Order 5504.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#13063352C212yesmaximal, complemented
2#127×D43C211yesmaximal, characteristic, complemented
3C4×#10621902C211yesmaximal, characteristic, complemented
4#14583099C211yesmaximal, characteristic, complemented
5#14583097C212yesmaximal, complemented
6#14583095C211yesmaximal, characteristic, complemented
7#14583093C212yesmaximal, complemented
8#14583091C211yesmaximal, characteristic, complemented
9#14582921C211yesmaximal, characteristic, complemented
10#14582902C212yesmaximal, complemented
11C43×#460C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×D4×D43—21no—
14C2×D4×D43—21no—
15C2×D4×D43C2212yes—
16#13063352—28no—
17C2×#10621884C2212yescomplemented
18C2×D344C2212yescomplemented
19C2×#10621882C2212yescomplemented
20C2×#10621872C2212yes—
21#13063322C2211yescharacteristic
22#13063321—21no—
23#13063321—21no—
24#13063321C2212yes—
25Q8×Dic43C2211yescharacteristic, complemented
26C4×D172—21no—
27C4×D172C2211yescharacteristic, complemented
28#13063287—21no—
29#13063287C2211yescharacteristic, complemented
30#13063283—21no—
31#13063283C2211yescharacteristic
32C42×D43—21no—
33C42×D43C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35Dic43⋊C8C2212yescomplemented
36#13063247C2212yescomplemented
37#13063246C2212yescomplemented
38#13063245C2212yescomplemented
39C2×SD16×C43C2212yescomplemented
40#127×C43C2211yescharacteristic
41C4×Q8×C43C2211yescharacteristic, complemented
42C4⋊C8×C43C2211yescharacteristic, complemented
43#102×C43C2212yescomplemented
44C23×D43—22no—
45C2×Q8×C43C2311yescharacteristic
46C2×D4×C43—21no—
47C2×D4×C43—21no—
48C2×D4×C43C2312yes—
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52#10621902—22no—
53#10621902D414yescomplemented
54D4×D43—24no—
55D4×D43—24no—
56D4×D43—44no—
57D4×D43—44no—
58C2×D172—21no—
59C2×D172—21no—
60C2×D172—21no—
61C2×D172C2312yes—
62C2×D172C2311yescharacteristic
63C2×C4×D43—21no—
64C2×C4×D43—21no—
65C2×C4×D43—21no—
66C2×C4×D43D411yescharacteristic
67C2×C4×D43D411yescharacteristic
68C2×C4×D43C2311yescharacteristic
69SD16×C43—24no—
70C2×C8×C43C2312yes—
71C4⋊C4×C43—21no—
72C4⋊C4×C43C2311yescharacteristic
73C42×C43—21no—
74C42×C43C2311yescharacteristic
75#10621884—24no—
76#10621882—24no—
77(C2×D43)⋊C4—21no—
78(C2×D43)⋊C4—21no—
79(C2×D43)⋊C4—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43C2311yescharacteristic
82C4×Dic43—21no—
83C4×Dic43—21no—
84C4×Dic43D411yescharacteristic
85C4×Dic43D411yescharacteristic
86C4×Dic43C2311yescharacteristic
87C2×C43⋊C8C2312yes—
88D344—24no—
89#10621872—24no—
90C23×C43—22no—
91C22×D43—21no—
92C22×D43—22no—
93C22×D43—44no—
94C22×D43—44no—
95C22×D43—44no—
96C22×D43C2×D411yescharacteristic
97Q8×C43—21no—
98Q8×C43C2×D412yescomplemented
99D4×C43—22no—
100D4×C43—22no—
101D4×C43—42no—
102D4×C43—42no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2×D411yescharacteristic
107C2×C4×C43C2411yescharacteristic
108C22⋊D43—44no—
109C22⋊D43—44no—
110C22⋊D43—44no—
111C2×Dic43—21no—
112C2×Dic43C2×D411yescharacteristic
113C2×Dic43C2×D411yescharacteristic
114C2×Dic43C2×D411yescharacteristic
115D172—24no—
116D172—22no—
117D172—21no—
118D172—22no—
119D172—42no—
120D172—42no—
121D172C2×D412yescomplemented
122C4×D43—22no—
123C4×D43—24no—
124C4×D43—22no—
125C4×D43—42no—
126C4×D43—42no—
127C4×D43C2×D412yes—
128C4×D43#4112yes—
129C8×C43—22no—
130C43⋊C8—22no—
131C22×C43—42no—
132C22×C43—42no—
133C22×C43—42no—
134C22×C43C22×D411yescharacteristic
135C2×D43—21no—
136C2×D43—21no—
137C2×D43—22no—
138C2×D43—41no—
139C2×D43—41no—
140C2×D43—42no—
141C2×D43—42no—
142C2×D43—42no—
143C2×D43—88no—
144C2×D43#12112yes—
145C4×C43—22no—
146C4×C43—21no—
147C4×C43—41no—
148C4×C43AGL(1,ℤ/8)12yescomplemented
149C4×C43C22×D411yescharacteristic
150C4×C43C2×#4111yescharacteristic
151Dic43—21no—
152Dic43—41no—
153Dic43#12112yes—
154Dic43AGL(1,ℤ/8)12yescomplemented
155#3038—431nomaximal, Sylow
156C2×C43—82no—
157C2×C43C2×#12111yescharacteristic
158C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
159C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
160D43—22no—
161D43—42no—
162D43—82no—
163C2×AGL(1,ℤ/8)—432no—
164C2×#127—431no—
165C4×#41—431no—
166#460—432no—
167#460—431no—
168#460D4311yescharacteristic, complemented
169#459—431no—
170#459—431no—
171#459—432no—
172#423—431no—
173#418—432no—
174C43#303811yescharacteristic, complemented, Sylow
175C2×#41—431no—
176C22×D4—432no—
177C22×D4—861no—
178C22×D4—861no—
179AGL(1,ℤ/8)—868no—
180C2×SD16—432no—
181C2×SD16C2×D4312yescomplemented
182C2×D8—432no—
183C2×D8—432no—
184C2×M16—432no—
185#127—432no—
186#127—431no—
187#127—861no—
188#127—861no—
189#127C2×D4311yescharacteristic
190C4×Q8—431no—
191C4×Q8C2×D4311yescharacteristic, complemented
192C4×D4—431no—
193C4×D4—431no—
194C4×D4—861no—
195C4×D4—861no—
196#117—431no—
197#117—861no—
198C2×C42—431no—
199C2×C42—861no—
200C4⋊C8—432no—
201C4⋊C8—431no—
202C4⋊C8C2×D4311yescharacteristic, complemented
203#102—432no—
204#102—432no—
205#102—432no—
206#102C2×D4312yescomplemented
207C24—862no—
208#41—434no—
209#41—862no—
210C2×Q8C22×D4311yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—431no—
214C2×D4—432no—
215C2×D4—861no—
216C2×D4—864no—
217C2×D4—864no—
218C2×D4—862no—
219C2×D4—862no—
220C2×D4—862no—
221C2×D4—861no—
222C2×D4—861no—
223C2×D4—1724no—
224C2×D4—1724no—
225C2×D4C22×D4312yes—
226C22×C4—431no—
227C22×C4—431no—
228C22×C4—431no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232SD16—24no—
233SD16—864no—
234D8—864no—
235D8—864no—
236M16—864no—
237C2×C8—432no—
238C2×C8C22×D4312yes—
239C4⋊C4—21no—
240C4⋊C4—431no—
241C4⋊C4—861no—
242C4⋊C4C22×D4311yescharacteristic
243C22⋊C4—861no—
244C22⋊C4—861no—
245C22⋊C4—861no—
246C42—21no—
247C42—431no—
248C42—431no—
249C42—431no—
250C42—861no—
251C42—861no—
252C42C22×D4311yescharacteristic
253C23—22no—
254C23—431no—
255C23—861no—
256C23—862no—
257C23—1724no—
258C23—1724no—
259C23—1724no—
260Q8—21no—
261Q8D4×D4312yescomplemented
262D4—22no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—432no—
267D4—864no—
268D4—862no—
269D4—861no—
270D4—862no—
271D4—1722no—
272D4—1724no—
273D4—1724no—
274D4—1724no—
275D4—1722no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—431no—
279C2×C4—431no—
280C2×C4—432no—
281C2×C4—432no—
282C2×C4—431no—
283C2×C4—862no—
284C2×C4—864no—
285C2×C4—862no—
286C2×C4—861no—
287C2×C4—1722no—
288C2×C4—1722no—
289C2×C4D4×D4311yescharacteristic
290C2×C4D4×D4311yescharacteristic
291C2×C4C23×D4311yescharacteristic
292C8—22no—
293C8—862no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—432no—
298C22—861no—
299C22—861no—
300C22—862no—
301C22—3448no—
302C22—1722no—
303C22—1722no—
304C22—1722no—
305C22—1721no—
306C22—1721no—
307C22C2×D4×D4311yescharacteristic
308C4—22no—
309C4—21no—
310C4—41no—
311C4—432no—
312C4—432no—
313C4—861no—
314C4—1721no—
315C4#1306335212yescomplemented
316C4C2×D4×D4311yescharacteristic
317C4#41×D4311yescharacteristic
318C2—82no—
319C2—862no—
320C2—3442no—
321C2—1722no—
322C2#121×D4311yescharacteristic
323C2AGL(1,ℤ/8)×D4311yescharacteristic
324C2C2×#1306335211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3038
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#13063352C2semidirect
2. #127×D43C2semidirect
3. C4×#10621902C2semidirect
4. #14583099C2semidirect
5. #14583097C2semidirect
6. #14583095C2semidirect
7. #14583093C2semidirect
8. #14583091C2semidirect
9. #14582921C2semidirect
10. #14582902C2semidirect
11. C43×#460C2semidirect
17. C2×#10621884C22semidirect
18. C2×D344C22semidirect
19. C2×#10621882C22semidirect
25. Q8×Dic43C22semidirect
27. C4×D172C22semidirect
29. #13063287C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. Dic43⋊C8C22semidirect
36. #13063247C22semidirect
37. #13063246C22semidirect
38. #13063245C22semidirect
39. C2×SD16×C43C22semidirect
41. C4×Q8×C43C22semidirect
42. C4⋊C8×C43C22semidirect
43. #102×C43C22semidirect
53. #10621902D4semidirect
98. Q8×C43C2×D4semidirect
121. D172C2×D4semidirect
148. C4×C43AGL(1,ℤ/8)semidirect
154. Dic43AGL(1,ℤ/8)semidirect
168. #460D43semidirect
174. C43#3038semidirect
181. C2×SD16C2×D43semidirect
191. C4×Q8C2×D43semidirect
202. C4⋊C8C2×D43semidirect
206. #102C2×D43semidirect
261. Q8D4×D43semidirect
315. C4#13063352semidirect