Finite Group Databasebeta

← #19145044

Subgroups — #19145044

Order 5504.

656 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 141 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
2C2×#13063349C212yesmaximal, complemented
3#14583448C211yesmaximal, characteristic, complemented
4#127×D43C211yesmaximal, characteristic, complemented
5#14583289C211yesmaximal, characteristic, complemented
6#14583288C211yesmaximal, characteristic, complemented
7#14583286C211yesmaximal, characteristic, complemented
8#14583274C212yesmaximal, complemented
9#14583270C212yesmaximal, complemented
10#14582851C211yesmaximal, characteristic, complemented
11C43×#496C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic
13C2×#10621900C2211yescharacteristic
14C2×D4×D43—22no—
15C2×D4×D43C2212yes—
16#13063352—28no—
17#13063349—28no—
18C2×#10621873C2212yescomplemented
19C2×#10621883C2212yescomplemented
20C2×#10621884C2212yescomplemented
21C2×D344C2212yescomplemented
22C2×#10621882C2212yescomplemented
23C2×#10621882C2212yescomplemented
24C2×#10621872C2212yes—
25#13063323C2211yescharacteristic, complemented
26#13063322C2211yescharacteristic
27#13063321—22no—
28#13063321C2212yes—
29#13063321C2211yescharacteristic, complemented
30#13063313C2211yescharacteristic, complemented
31#13063298—22no—
32(C22⋊D43)⋊C4—22no—
33C42×D43C2211yescharacteristic
34#13063236C2211yescharacteristic, complemented
35C8×Dic43C2212yescomplemented
36C2×SD16×C43C2212yescomplemented
37C2×D8×C43C2212yescomplemented
38#127×C43C2211yescharacteristic
39#124×C43C2211yescharacteristic, complemented
40#97×C43C2211yescharacteristic, complemented
41C23×D43—22no—
42C2×Q8×C43C2311yescharacteristic
43C2×D4×C43—22no—
44C2×D4×C43C2311yescharacteristic
45C2×D4×C43C2312yes—
46C2×C22⋊D43—22no—
47C2×C22⋊D43—22no—
48C2×C22⋊D43—24no—
49C2×C22⋊D43—21no—
50C22×Dic43—21no—
51#10621902—24no—
52#10621900—24no—
53D4×D43—24no—
54D4×D43—24no—
55D4×D43—48no—
56C2×D172—22no—
57C2×D172—21no—
58C2×D172C2311yescharacteristic
59C2×D172C2312yes—
60C2×C4×D43—21no—
61C2×C4×D43D412yes—
62C2×C4×D43C2311yescharacteristic
63C2×Dic86C2311yescharacteristic
64SD16×C43—24no—
65D8×C43—24no—
66C2×C8×C43C2312yes—
67C22⋊C4×C43—22no—
68C42×C43C2311yescharacteristic
69#10621884—24no—
70#10621883—24no—
71#10621882—24no—
72#10621882—24no—
73(C2×D43)⋊C4—22no—
74Dic43⋊C4—22no—
75C4×Dic43D412yes—
76C4×Dic43C2311yescharacteristic
77C2×C43⋊C8C2312yes—
78D344—24no—
79#10621873—24no—
80#10621872D418yescomplemented
81C23×C43—21no—
82C23×C43—22no—
83C22×D43—21no—
84C22×D43—22no—
85C22×D43—48no—
86C22×D43—44no—
87C22×D43C2×D411yescharacteristic
88Q8×C43—22no—
89D4×C43—22no—
90D4×C43—22no—
91D4×C43—22no—
92D4×C43—44no—
93C2×C4×C43—21no—
94C2×C4×C43C2×D412yes—
95C2×C4×C43C2411yescharacteristic
96C22⋊D43—42no—
97C22⋊D43—44no—
98C22⋊D43—48no—
99C22⋊D43—44no—
100C2×Dic43—21no—
101C2×Dic43—42no—
102C2×Dic43C2×D411yescharacteristic
103C2×Dic43C2×D412yes—
104D172—22no—
105D172—22no—
106D172—22no—
107D172—44no—
108D172—42no—
109C4×D43—24no—
110C4×D43—42no—
111C4×D43C2×D414yes—
112Dic86—22no—
113C8×C43C2×D414yescomplemented
114C43⋊C8C2×D414yescomplemented
115C22×C43—42no—
116C22×C43—41no—
117C22×C43—44no—
118C22×C43—42no—
119C22×C43C22×D411yescharacteristic
120C2×D43—22no—
121C2×D43—42no—
122C2×D43—41no—
123C2×D43—44no—
124C2×D43—42no—
125C2×D43—88no—
126C2×D43#12712yes—
127C4×C43—22no—
128C4×C43—41no—
129C4×C43C22×D412yes—
130Dic43—41no—
131Dic43#12712yes—
132Dic43AGL(1,ℤ/8)14yescomplemented
133#3151—431nomaximal, Sylow
134C2×C43—82no—
135C2×C43—81no—
136C2×C43C2×#12711yescharacteristic
137C2×C43C2×AGL(1,ℤ/8)12yes—
138D43—22no—
139D43—81no—
140D43—82no—
141C2×AGL(1,ℤ/8)—432no—
142C2×AGL(1,ℤ/8)—432no—
143#532—431no—
144C2×#127—431no—
145#496—431no—
146#496—431no—
147#496—431no—
148#496D4311yescharacteristic, complemented
149#493—432no—
150#492—432no—
151C4×M16—431no—
152C43#315111yescharacteristic, complemented, Sylow
153C2×#41—431no—
154C2×#41—431no—
155C22×D4—432no—
156C22×D4—862no—
157AGL(1,ℤ/8)—868no—
158AGL(1,ℤ/8)—868no—
159C2×SD16—432no—
160C2×SD16—432no—
161C2×SD16—432no—
162C2×SD16C2×D4312yescomplemented
163C2×D8—432no—
164C2×D8—432no—
165C2×D8—432no—
166C2×D8C2×D4312yescomplemented
167C2×M16—432no—
168C4⋊Q8—431no—
169#127—432no—
170#127—431no—
171#127—431no—
172#127—862no—
173#127C2×D4311yescharacteristic
174#124—431no—
175#124C2×D4311yescharacteristic, complemented
176#121—862no—
177C4×D4—862no—
178C2×C42—431no—
179#97—431no—
180#97C2×D4311yescharacteristic, complemented
181C4×C8—432no—
182C24—862no—
183#41—864no—
184#41—864no—
185C2×Q8—431no—
186C2×Q8C22×D4311yescharacteristic
187C2×D4—22no—
188C2×D4—431no—
189C2×D4—432no—
190C2×D4—861no—
191C2×D4—864no—
192C2×D4—864no—
193C2×D4—862no—
194C2×D4—864no—
195C2×D4—862no—
196C2×D4—861no—
197C2×D4—862no—
198C2×D4—1728no—
199C2×D4C22×D4311yescharacteristic
200C2×D4C22×D4312yes—
201C22×C4—431no—
202C22×C4—432no—
203C22×C4—861no—
204C22×C4—861no—
205SD16—24no—
206SD16—864no—
207SD16—864no—
208SD16—864no—
209D8—24no—
210D8—864no—
211D8—864no—
212D8—864no—
213M16—438no—
214C2×C8—432no—
215C2×C8C22×D4312yes—
216C4⋊C4—862no—
217C22⋊C4—22no—
218C22⋊C4—862no—
219C42—432no—
220C42—431no—
221C42C22×D4311yescharacteristic
222C23—21no—
223C23—22no—
224C23—431no—
225C23—861no—
226C23—862no—
227C23—1724no—
228C23—1728no—
229Q8—22no—
230Q8—862no—
231D4—22no—
232D4—22no—
233D4—22no—
234D4—44no—
235D4—862no—
236D4—862no—
237D4—862no—
238D4—1724no—
239D4—1722no—
240D4—1724no—
241D4—1728no—
242D4—1724no—
243D4—1722no—
244C2×C4—21no—
245C2×C4—432no—
246C2×C4—431no—
247C2×C4—434no—
248C2×C4—864no—
249C2×C4—861no—
250C2×C4—1722no—
251C2×C4—1722no—
252C2×C4D4×D4312yes—
253C2×C4C23×D4311yescharacteristic
254C8—434no—
255C8D4×D4314yescomplemented
256C22—44no—
257C22—42no—
258C22—41no—
259C22—42no—
260C22—432no—
261C22—862no—
262C22—3448no—
263C22—1724no—
264C22—1722no—
265C22—1721no—
266C22—1722no—
267C22C2×D4×D4311yescharacteristic
268C4—22no—
269C4—41no—
270C4—434no—
271C4—432no—
272C4—1721no—
273C4C2×D4×D4312yes—
274C2—82no—
275C2—81no—
276C2—862no—
277C2—3442no—
278C2—3441no—
279C2#127×D4311yescharacteristic
280C2AGL(1,ℤ/8)×D4312yes—
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#496C2
socleC22×C43C22×D4
hypercenter#496D43
hypocenterC43#3151
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#13063352C2semidirect
2. C2×#13063349C2semidirect
3. #14583448C2semidirect
4. #127×D43C2semidirect
5. #14583289C2semidirect
6. #14583288C2semidirect
7. #14583286C2semidirect
8. #14583274C2semidirect
9. #14583270C2semidirect
10. #14582851C2semidirect
11. C43×#496C2semidirect
18. C2×#10621873C22semidirect
19. C2×#10621883C22semidirect
20. C2×#10621884C22semidirect
21. C2×D344C22semidirect
22. C2×#10621882C22semidirect
23. C2×#10621882C22semidirect
25. #13063323C22semidirect
29. #13063321C22semidirect
30. #13063313C22semidirect
34. #13063236C22semidirect
35. C8×Dic43C22semidirect
36. C2×SD16×C43C22semidirect
37. C2×D8×C43C22semidirect
39. #124×C43C22semidirect
40. #97×C43C22semidirect
80. #10621872D4semidirect
113. C8×C43C2×D4semidirect
114. C43⋊C8C2×D4semidirect
132. Dic43AGL(1,ℤ/8)semidirect
148. #496D43semidirect
152. C43#3151semidirect
162. C2×SD16C2×D43semidirect
166. C2×D8C2×D43semidirect
175. #124C2×D43semidirect
180. #97C2×D43semidirect
255. C8D4×D43semidirect