Finite Group Databasebeta

← #19144070

Subgroups — #19144070

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×#13063349C212yesmaximal, complemented
2#127×D43C211yesmaximal, characteristic, complemented
3C4×#10621900C211yesmaximal, characteristic, complemented
4#14583100C211yesmaximal, characteristic, complemented
5#14583098C212yesmaximal, complemented
6#14583096C211yesmaximal, characteristic, complemented
7#14583094C211yesmaximal, characteristic, complemented
8#14583092C212yesmaximal, complemented
9#14582921C211yesmaximal, characteristic, complemented
10#14582902C212yesmaximal, complemented
11C43×#459C211yesmaximal, characteristic, complemented
12C2×#10621900C2211yescharacteristic
13C2×D4×D43—21no—
14C2×D4×D43—21no—
15C2×D4×D43C2212yes—
16#13063349—28no—
17C2×#10621873C2212yescomplemented
18C2×#10621883C2212yescomplemented
19C2×#10621882C2212yescomplemented
20C2×#10621872C2212yes—
21#13063322C2211yescharacteristic
22#13063321—21no—
23#13063321—21no—
24#13063321C2212yes—
25C4×Dic86C2211yescharacteristic, complemented
26#13063290C2211yescharacteristic, complemented
27D4×Dic43C2211yescharacteristic, complemented
28C4×C22⋊D43—21no—
29(C22⋊D43)⋊C4—21no—
30#13063283C2211yescharacteristic
31#13063281—21no—
32C2×C4×Dic43—21no—
33C42×D43C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35Dic43⋊C8C2212yescomplemented
36#13063247C2212yescomplemented
37#13063246C2212yescomplemented
38#13063245C2212yescomplemented
39C2×D8×C43C2212yescomplemented
40#127×C43C2211yescharacteristic
41C4×D4×C43C2211yescharacteristic, complemented
42C4⋊C8×C43C2211yescharacteristic, complemented
43#102×C43C2212yescomplemented
44C23×D43—22no—
45C2×D4×C43—21no—
46C2×D4×C43—21no—
47C2×D4×C43C2312yes—
48C2×D4×C43C2311yescharacteristic
49C22×C4×C43—21no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—22no—
53C2×C22⋊D43—21no—
54C22×Dic43—21no—
55C22×Dic43—21no—
56#10621900—22no—
57#10621900D414yescomplemented
58D4×D43—24no—
59D4×D43—24no—
60D4×D43—44no—
61D4×D43—44no—
62C2×D172—21no—
63C2×D172—21no—
64C2×D172C2312yes—
65C2×C4×D43D411yescharacteristic
66C2×C4×D43D411yescharacteristic
67C2×C4×D43C2311yescharacteristic
68C2×Dic86C2311yescharacteristic
69D8×C43—24no—
70C2×C8×C43C2312yes—
71C4⋊C4×C43C2311yescharacteristic
72C22⋊C4×C43—21no—
73C42×C43C2311yescharacteristic
74C22⋊Dic43—21no—
75#10621883—24no—
76#10621882—24no—
77(C2×D43)⋊C4—21no—
78C4⋊Dic43C2311yescharacteristic
79Dic43⋊C4—21no—
80Dic43⋊C4—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83C4×Dic43—21no—
84C4×Dic43D411yescharacteristic
85C4×Dic43D411yescharacteristic
86C4×Dic43C2311yescharacteristic
87C2×C43⋊C8C2312yes—
88#10621873—24no—
89#10621872—24no—
90C23×C43—21no—
91C23×C43—22no—
92C22×D43—22no—
93C22×D43—44no—
94C22×D43—44no—
95C22×D43—44no—
96C22×D43C2×D411yescharacteristic
97D4×C43—22no—
98D4×C43—21no—
99D4×C43—22no—
100D4×C43—42no—
101D4×C43—42no—
102D4×C43C2×D412yescomplemented
103C2×C4×C43—21no—
104C2×C4×C43—42no—
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43C2×D411yescharacteristic
107C2×C4×C43C2411yescharacteristic
108C22⋊D43—24no—
109C22⋊D43—44no—
110C22⋊D43—44no—
111C22⋊D43—44no—
112C2×Dic43—21no—
113C2×Dic43—24no—
114C2×Dic43—21no—
115C2×Dic43—42no—
116C2×Dic43C2×D411yescharacteristic
117C2×Dic43C2×D411yescharacteristic
118C2×Dic43C2×D411yescharacteristic
119D172—22no—
120D172—22no—
121D172—42no—
122D172—42no—
123C4×D43—22no—
124C4×D43—22no—
125C4×D43C2×D412yes—
126C4×D43#4112yes—
127Dic86—21no—
128Dic86C2×D412yescomplemented
129C8×C43—22no—
130C43⋊C8—22no—
131C22×C43—22no—
132C22×C43—41no—
133C22×C43—41no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43—42no—
137C22×C43C22×D411yescharacteristic
138C2×D43—21no—
139C2×D43—21no—
140C2×D43—42no—
141C2×D43—42no—
142C2×D43—42no—
143C2×D43—88no—
144C2×D43#12112yes—
145C4×C43—21no—
146C4×C43—41no—
147C4×C43AGL(1,ℤ/8)12yescomplemented
148C4×C43C22×D411yescharacteristic
149C4×C43C2×#4111yescharacteristic
150Dic43—22no—
151Dic43—21no—
152Dic43—41no—
153Dic43#12112yes—
154Dic43AGL(1,ℤ/8)12yescomplemented
155#3038—431nomaximal, Sylow
156C2×C43—42no—
157C2×C43—82no—
158C2×C43C2×#12111yescharacteristic
159C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
160C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
161D43—22no—
162D43—82no—
163C2×AGL(1,ℤ/8)—432no—
164C2×#127—431no—
165C4×#41—431no—
166#460—431no—
167#460—431no—
168#460—432no—
169#459—432no—
170#459—431no—
171#459D4311yescharacteristic, complemented
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×SD16—432no—
182C2×D8—432no—
183C2×D8C2×D4312yescomplemented
184C2×M16—432no—
185#127—432no—
186#127—431no—
187#127—861no—
188#127—861no—
189#127C2×D4311yescharacteristic
190C4×Q8—431no—
191C4×Q8—431no—
192C4×D4—431no—
193C4×D4—861no—
194C4×D4—861no—
195C4×D4C2×D4311yescharacteristic, complemented
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×Q8—431no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—432no—
214C2×D4—864no—
215C2×D4—864no—
216C2×D4—862no—
217C2×D4—862no—
218C2×D4—862no—
219C2×D4—861no—
220C2×D4—861no—
221C2×D4—861no—
222C2×D4—1724no—
223C2×D4—1724no—
224C2×D4C22×D4312yes—
225C2×D4C22×D4311yescharacteristic
226C22×C4—21no—
227C22×C4—431no—
228C22×C4—431no—
229C22×C4—431no—
230C22×C4—861no—
231C22×C4—861no—
232SD16—864no—
233SD16—864no—
234D8—24no—
235D8—864no—
236M16—864no—
237C2×C8—432no—
238C2×C8C22×D4312yes—
239C4⋊C4—431no—
240C4⋊C4—861no—
241C4⋊C4—861no—
242C4⋊C4C22×D4311yescharacteristic
243C22⋊C4—21no—
244C22⋊C4—861no—
245C22⋊C4—861no—
246C42—431no—
247C42—431no—
248C42—431no—
249C42—861no—
250C42—861no—
251C42—861no—
252C42C22×D4311yescharacteristic
253C23—21no—
254C23—22no—
255C23—431no—
256C23—862no—
257C23—1724no—
258C23—1724no—
259C23—1724no—
260Q8—432no—
261Q8—861no—
262D4—22no—
263D4—21no—
264D4—22no—
265D4—42no—
266D4—42no—
267D4—864no—
268D4—862no—
269D4—862no—
270D4—1722no—
271D4—1724no—
272D4—1724no—
273D4—1724no—
274D4—1722no—
275D4D4×D4312yescomplemented
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—431no—
279C2×C4—431no—
280C2×C4—432no—
281C2×C4—432no—
282C2×C4—431no—
283C2×C4—862no—
284C2×C4—864no—
285C2×C4—861no—
286C2×C4—862no—
287C2×C4—861no—
288C2×C4—1722no—
289C2×C4D4×D4311yescharacteristic
290C2×C4D4×D4311yescharacteristic
291C2×C4C23×D4311yescharacteristic
292C8—22no—
293C8—862no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—432no—
301C22—861no—
302C22—861no—
303C22—3448no—
304C22—1722no—
305C22—1722no—
306C22—1722no—
307C22C2×D4×D4311yescharacteristic
308C4—21no—
309C4—41no—
310C4—432no—
311C4—432no—
312C4—862no—
313C4—861no—
314C4—1721no—
315C4#1306334912yescomplemented
316C4C2×D4×D4311yescharacteristic
317C4#41×D4311yescharacteristic
318C2—42no—
319C2—82no—
320C2—862no—
321C2—3442no—
322C2#121×D4311yescharacteristic
323C2AGL(1,ℤ/8)×D4311yescharacteristic
324C2C2×#1306334911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3038
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#13063349C2semidirect
2. #127×D43C2semidirect
3. C4×#10621900C2semidirect
4. #14583100C2semidirect
5. #14583098C2semidirect
6. #14583096C2semidirect
7. #14583094C2semidirect
8. #14583092C2semidirect
9. #14582921C2semidirect
10. #14582902C2semidirect
11. C43×#459C2semidirect
17. C2×#10621873C22semidirect
18. C2×#10621883C22semidirect
19. C2×#10621882C22semidirect
25. C4×Dic86C22semidirect
26. #13063290C22semidirect
27. D4×Dic43C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. Dic43⋊C8C22semidirect
36. #13063247C22semidirect
37. #13063246C22semidirect
38. #13063245C22semidirect
39. C2×D8×C43C22semidirect
41. C4×D4×C43C22semidirect
42. C4⋊C8×C43C22semidirect
43. #102×C43C22semidirect
57. #10621900D4semidirect
102. D4×C43C2×D4semidirect
128. Dic86C2×D4semidirect
147. C4×C43AGL(1,ℤ/8)semidirect
154. Dic43AGL(1,ℤ/8)semidirect
171. #459D43semidirect
174. C43#3038semidirect
183. C2×D8C2×D43semidirect
195. C4×D4C2×D43semidirect
202. C4⋊C8C2×D43semidirect
206. #102C2×D43semidirect
275. D4D4×D43semidirect
315. C4#13063349semidirect