Finite Group Databasebeta

← #19144691

Subgroups — #19144691

Order 5504.

444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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#14583451C211yesmaximal, characteristic, complemented
2C2×#13063287C211yesmaximal, characteristic
3#14583234C211yesmaximal, characteristic, complemented
4#14583178C212yesmaximal, complemented
5#14583103C212yesmaximal, complemented
6#14583052C211yesmaximal, characteristic
7#14583049C211yesmaximal, characteristic
8#14583002C212yesmaximal, complemented
9#14582998C212yesmaximal, complemented
10#14582953C211yesmaximal, characteristic, complemented
11C43×#484C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C4×D43—21no—
14C2×#10621873C2212yes—
15C2×#10621884C2212yes—
16#13063324C2211yescharacteristic, complemented
17#13063323C2211yescharacteristic, complemented
18#13063315—21no—
19#13063304C2211yescharacteristic
20#13063302—21no—
21Q8×Dic43C2211yescharacteristic, complemented
22#13063290—21no—
23#13063290C2211yescharacteristic, complemented
24#13063287—21no—
25#13063287—21no—
26#13063287C2212yes—
27#13063287C2212yes—
28#13063281—21no—
29C2×(C2×D43)⋊C4—21no—
30C2×C4×Dic43C2211yescharacteristic
31#13063258C2212yescomplemented
32Dic43⋊C8C2212yescomplemented
33#13063248C2212yescomplemented
34#13063247C2212yes—
35#13063245C2212yes—
36C22⋊(C43⋊C8)C2211yescharacteristic
37#13063235C2212yescomplemented
38C22⋊Q8×C43C2211yescharacteristic
39C2×C4⋊C4×C43C2211yescharacteristic
40#107×C43C2212yescomplemented
41#103×C43C2212yescomplemented
42C22⋊C8×C43C2211yescharacteristic
43C23×D43—21no—
44C2×Q8×C43C2311yescharacteristic
45C22×C4×C43—21no—
46C22×C4×C43C2311yescharacteristic
47C22×Dic43D411yescharacteristic
48C22×Dic43D411yescharacteristic
49C2×D172—21no—
50C2×D172—24no—
51C2×D172C2312yes—
52C2×C4×D43—22no—
53C2×C4×D43—22no—
54C2×C4×D43—44no—
55C2×Dic86—21no—
56C2×Dic86C2311yescharacteristic
57C2×C8×C43C2312yes—
58C4⋊C4×C43—21no—
59C4⋊C4×C43—21no—
60C4⋊C4×C43C2312yes—
61C4⋊C4×C43C2311yescharacteristic
62C22⋊C4×C43—21no—
63C22⋊Dic43—21no—
64#10621884—24no—
65(C2×D43)⋊C4—22no—
66(C2×D43)⋊C4—22no—
67C4⋊Dic43—21no—
68C4⋊Dic43C2311yescharacteristic
69Dic43⋊C4—21no—
70Dic43⋊C4—21no—
71Dic43⋊C4—21no—
72Dic43⋊C4—21no—
73Dic43⋊C4—21no—
74C4×Dic43—21no—
75C4×Dic43—21no—
76C4×Dic43D411yescharacteristic
77C4×Dic43D411yescharacteristic
78C4×Dic43C2311yescharacteristic
79C4×Dic43C2311yescharacteristic
80C2×C43⋊C8C2312yes—
81#10621873—24no—
82C23×C43C2×D411yescharacteristic
83C22×D43—24no—
84C22×D43—22no—
85C22×D43—42no—
86C22×D43—42no—
87Q8×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43—21no—
90C2×C4×C43—21no—
91C2×C4×C43—22no—
92C2×C4×C43—42no—
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2411yescharacteristic
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—21no—
98C2×Dic43—21no—
99C2×Dic43C2×D411yescharacteristic
100C2×Dic43C2×D411yescharacteristic
101C2×Dic43C2×D411yescharacteristic
102C2×Dic43C2×D411yescharacteristic
103D172—24no—
104D172—22no—
105D172#4114yes—
106C4×D43—44no—
107C4×D43—44no—
108Dic86—22no—
109Dic86—42no—
110C8×C43—22no—
111C43⋊C8—22no—
112C22×C43—21no—
113C22×C43—21no—
114C22×C43#13712yes—
115C22×C43C22×D411yescharacteristic
116C2×D43—24no—
117C2×D43—48no—
118C2×D43—42no—
119C2×D43—42no—
120C4×C43—21no—
121C4×C43—41no—
122C4×C43—41no—
123C4×C43—42no—
124C4×C43C2×#4112yes—
125Dic43—21no—
126Dic43—21no—
127Dic43—21no—
128Dic43—41no—
129Dic43—41no—
130Dic43AGL(1,ℤ/8)12yes—
131#3110—431nomaximal, Sylow
132C2×C43—22no—
133C2×C43#52511yescharacteristic
134C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
135C2×C43C2×#13711yescharacteristic
136D43—44no—
137#533—431no—
138C2×C4×D4—431no—
139#484—431no—
140#484D4311yescharacteristic, complemented
141#474—432no—
142#461—432no—
143#450—431no—
144#450—431no—
145#440—432no—
146#440—432no—
147#432—431no—
148C43#311011yescharacteristic, complemented, Sylow
149C22×D4—431no—
150C23×C4—861no—
151C2×SD16—432no—
152C2×SD16—432no—
153C4⋊Q8—431no—
154C4⋊Q8—431no—
155#125—861no—
156C22⋊Q8—431no—
157C22⋊Q8—861no—
158C22⋊Q8C2×D4311yescharacteristic
159C4×Q8—431no—
160C4×Q8—431no—
161C4×Q8—861no—
162C4×D4—432no—
163C4×D4—432no—
164C4×D4—861no—
165C4×D4—861no—
166#117—861no—
167C2×C4⋊C4C2×D4311yescharacteristic
168C2×C22⋊C4—861no—
169C2×C42—431no—
170#107—432no—
171#107C2×D4312yescomplemented
172C4⋊C8—432no—
173#103—432no—
174#103C2×D4312yescomplemented
175#102—432no—
176#102—432no—
177C22⋊C8—431no—
178C22⋊C8C2×D4311yescharacteristic
179#97—432no—
180C24—861no—
181C2×Q8—431no—
182C2×Q8—861no—
183C2×Q8C22×D4311yescharacteristic
184C2×D4—432no—
185C2×D4—864no—
186C2×D4—861no—
187C22×C4—21no—
188C22×C4—431no—
189C22×C4—431no—
190C22×C4—862no—
191C22×C4—862no—
192C22×C4—1724no—
193C22×C4C22×D4311yescharacteristic
194SD16—864no—
195SD16—864no—
196C2×C8—432no—
197C2×C8C22×D4312yes—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—431no—
201C4⋊C4—861no—
202C4⋊C4—861no—
203C4⋊C4—861no—
204C4⋊C4—861no—
205C4⋊C4—861no—
206C4⋊C4—861no—
207C4⋊C4C22×D4311yescharacteristic
208C4⋊C4C22×D4312yes—
209C22⋊C4—21no—
210C22⋊C4—862no—
211C22⋊C4—862no—
212C22⋊C4—861no—
213C42—431no—
214C42—431no—
215C42—431no—
216C42—431no—
217C42—861no—
218C42—861no—
219C23—864no—
220C23—862no—
221C23—1722no—
222C23—1722no—
223C23D4×D4311yescharacteristic
224Q8—22no—
225Q8—862no—
226Q8—1722no—
227D4—434no—
228D4—864no—
229D4—862no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—431no—
236C2×C4—431no—
237C2×C4—431no—
238C2×C4—431no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—861no—
242C2×C4—861no—
243C2×C4—1724no—
244C2×C4—1724no—
245C2×C4D4×D4311yescharacteristic
246C2×C4C23×D4311yescharacteristic
247C8—22no—
248C8—862no—
249C22—21no—
250C22—21no—
251C22—864no—
252C22—1728no—
253C22—1722no—
254C22—1722no—
255C22#1306335712yes—
256C22C2×D4×D4311yescharacteristic
257C4—21no—
258C4—41no—
259C4—42no—
260C4—41no—
261C4—432no—
262C4—861no—
263C4—861no—
264C4—861no—
265C4—1721no—
266C4—1721no—
267C4#41×D4312yes—
268C2—22no—
269C2—1724no—
270C2#1458340711yescharacteristic
271C2AGL(1,ℤ/8)×D4311yescharacteristic
272C2C2×#1306335711yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#484C2
socleC22×C43C22×D4
hypercenter#484D43
hypocenterC43#3110
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #14583451C2semidirect
3. #14583234C2semidirect
4. #14583178C2semidirect
5. #14583103C2semidirect
8. #14583002C2semidirect
9. #14582998C2semidirect
10. #14582953C2semidirect
11. C43×#484C2semidirect
16. #13063324C22semidirect
17. #13063323C22semidirect
21. Q8×Dic43C22semidirect
23. #13063290C22semidirect
31. #13063258C22semidirect
32. Dic43⋊C8C22semidirect
33. #13063248C22semidirect
37. #13063235C22semidirect
40. #107×C43C22semidirect
41. #103×C43C22semidirect
140. #484D43semidirect
148. C43#3110semidirect
171. #107C2×D43semidirect
174. #103C2×D43semidirect