Finite Group Databasebeta

← #19144533

Subgroups — #19144533

Order 5504.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#13063296C211yesmaximal, characteristic
2#117×D43C211yesmaximal, characteristic, complemented
3#14583222C212yesmaximal, complemented
4#14583221C212yesmaximal, complemented
5#14583216C212yesmaximal, complemented
6#14583211C212yesmaximal, complemented
7#14582942C211yesmaximal, characteristic, complemented
8#14582941C211yesmaximal, characteristic, complemented
9#14582904C211yesmaximal, characteristic, complemented
10#14582862C211yesmaximal, characteristic, complemented
11C43×#418C211yesmaximal, characteristic, complemented
12C22×C22⋊D43—21no—
13C22×C4×D43C2211yescharacteristic
14C2×#10621877C2211yescharacteristic
15#13063296—21no—
16#13063296—21no—
17#13063296C2212yes—
18#13063296C2212yes—
19#13063284C2211yescharacteristic
20#13063283C2211yescharacteristic, complemented
21#13063283C2211yescharacteristic, complemented
22#13063282—21no—
23#13063281—21no—
24C2×C4⋊Dic43C2211yescharacteristic
25C4⋊C4×D43C2211yescharacteristic, complemented
26C4⋊C4×D43C2211yescharacteristic, complemented
27C2×C22⋊Dic43—21no—
28C22⋊C4×D43—21no—
29C42×D43—21no—
30#13063259C2212yescomplemented
31#13063258C2212yescomplemented
32#13063257C2212yescomplemented
33#13063256C2212yescomplemented
34#13063246C2212yescomplemented
35#13063246C2212yescomplemented
36(C2×D43)⋊C8C2212yescomplemented
37(C2×D43)⋊C8C2212yescomplemented
38C22×D4×C43C2211yescharacteristic
39C2×M16×C43C2211yescharacteristic
40#117×C43C2211yescharacteristic
41#102×C43C2212yescomplemented
42#102×C43C2212yescomplemented
43C24×C43—21no—
44C23×D43D411yescharacteristic
45C2×D4×C43—21no—
46C2×D4×C43—22no—
47C2×D4×C43—22no—
48C2×D4×C43C2312yes—
49C22×C4×C43C2311yescharacteristic
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—44no—
53C22×Dic43—21no—
54C22×Dic43D411yescharacteristic
55C2×C4×D43—22no—
56C2×C4×D43—22no—
57C2×C4×D43—21no—
58C2×C4×D43—21no—
59C2×C4×D43D411yescharacteristic
60C2×C4×D43D411yescharacteristic
61C2×C4×D43C2311yescharacteristic
62C2×C4×D43C2311yescharacteristic
63M16×C43—22no—
64C2×C8×C43C2312yes—
65C4⋊C4×C43C2311yescharacteristic
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C42×C43—21no—
69C22⋊Dic43—22no—
70C22⋊Dic43—22no—
71C22⋊Dic43—21no—
72(C2×D43)⋊C4—21no—
73(C2×D43)⋊C4—21no—
74C4⋊Dic43—21no—
75C4⋊Dic43C2311yescharacteristic
76C4⋊Dic43C2311yescharacteristic
77C4⋊Dic43C2312yes—
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80C4×Dic43—21no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83#10621877—22no—
84C2×C43⋊C8C2312yes—
85C23×C43—22no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43C2×D411yescharacteristic
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—41no—
93C22×D43C2×D411yescharacteristic
94C22×D43C2×D411yescharacteristic
95D4×C43—22no—
96D4×C43—22no—
97D4×C43—42no—
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43#4112yes—
102C2×C4×C43#4112yes—
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—44no—
105C22⋊D43—44no—
106C2×Dic43—22no—
107C2×Dic43—21no—
108C2×Dic43—21no—
109C2×Dic43—22no—
110C2×Dic43—42no—
111C2×Dic43C2×D411yescharacteristic
112C2×Dic43C2×D411yescharacteristic
113C4×D43—22no—
114C4×D43—22no—
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—21no—
118C4×D43—21no—
119C4×D43—42no—
120C4×D43—42no—
121C8×C43—22no—
122C43⋊C8—22no—
123C22×C43—21no—
124C22×C43—21no—
125C22×C43—42no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—84no—
129C22×C43#12312yes—
130C22×C43C22×D411yescharacteristic
131C2×D43—21no—
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—21no—
135C2×D43—21no—
136C2×D43—44no—
137C2×D43AGL(1,ℤ/8)12yes—
138C4×C43—41no—
139C4×C43—41no—
140C4×C43#12312yes—
141C4×C43C2×#4111yescharacteristic
142C4×C43C2×#4111yescharacteristic
143Dic43—21no—
144Dic43—21no—
145Dic43—41no—
146Dic43—42no—
147Dic43—41no—
148#3094—431nomaximal, Sylow
149C2×C43—22no—
150C2×C43—82no—
151C2×C43C2×#12311yescharacteristic
152C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
153C2×C43#57511yescharacteristic
154D43—22no—
155D43—41no—
156C2×#121—431no—
157C2×#117—431no—
158#482—432no—
159#482—432no—
160#481—432no—
161#480—432no—
162#428—431no—
163#428—431no—
164#418—431no—
165#418D4311yescharacteristic, complemented
166#407—431no—
167C43#309411yescharacteristic, complemented, Sylow
168C22×D4—861no—
169C22×D4C2×D4311yescharacteristic
170C23×C4—431no—
171C2×M16—431no—
172C2×M16C2×D4311yescharacteristic
173#121—432no—
174#121—432no—
175#121—861no—
176#121—861no—
177#117—431no—
178#117—431no—
179#117—431no—
180#117—861no—
181#117—861no—
182#117C2×D4311yescharacteristic
183C2×C4⋊C4—431no—
184C2×C4⋊C4—431no—
185C2×C4⋊C4—431no—
186C2×C22⋊C4—861no—
187C2×C22⋊C4—861no—
188C2×C42—861no—
189#107—432no—
190#107—432no—
191#106—432no—
192#106—432no—
193#102—432no—
194#102—432no—
195#102C2×D4312yescomplemented
196#102C2×D4312yescomplemented
197C22⋊C8—432no—
198C22⋊C8—432no—
199C24—21no—
200C24—431no—
201C2×D4—22no—
202C2×D4—21no—
203C2×D4—22no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—1724no—
207C2×D4C22×D4312yes—
208C22×C4—431no—
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—431no—
213C22×C4—861no—
214C22×C4—861no—
215C22×C4—862no—
216C22×C4—862no—
217C22×C4—861no—
218C22×C4C22×D4311yescharacteristic
219M16—22no—
220M16—862no—
221C2×C8—432no—
222C2×C8C22×D4312yes—
223C4⋊C4—431no—
224C4⋊C4—431no—
225C4⋊C4—432no—
226C4⋊C4—861no—
227C4⋊C4—861no—
228C4⋊C4—861no—
229C4⋊C4C22×D4311yescharacteristic
230C4⋊C4C22×D4311yescharacteristic
231C22⋊C4—21no—
232C22⋊C4—861no—
233C22⋊C4—861no—
234C22⋊C4—862no—
235C22⋊C4—862no—
236C22⋊C4—861no—
237C42—21no—
238C42—861no—
239C42—861no—
240C42—861no—
241C23—22no—
242C23—42no—
243C23—42no—
244C23—42no—
245C23—431no—
246C23—431no—
247C23—862no—
248C23—862no—
249C23—1721no—
250C23D4×D4311yescharacteristic
251D4—22no—
252D4—22no—
253D4—42no—
254D4—1724no—
255D4—1724no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—431no—
259C2×C4—431no—
260C2×C4—862no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—861no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—862no—
270C2×C4—1722no—
271C2×C4—1722no—
272C2×C4—1722no—
273C2×C4#1062189812yes—
274C2×C4D4×D4311yescharacteristic
275C2×C4#1062190012yes—
276C2×C4C23×D4311yescharacteristic
277C8—22no—
278C8—862no—
279C22—21no—
280C22—21no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—84no—
285C22—432no—
286C22—861no—
287C22—861no—
288C22—861no—
289C22—861no—
290C22—861no—
291C22—1724no—
292C22#1306330712yes—
293C22C2×D4×D4311yescharacteristic
294C4—41no—
295C4—41no—
296C4—861no—
297C4—861no—
298C4—1722no—
299C4—1721no—
300C4—1721no—
301C4#1306330712yes—
302C4C2×#1062190011yescharacteristic
303C4C2×#1062189811yescharacteristic
304C2—22no—
305C2—82no—
306C2—862no—
307C2—1721no—
308C2C2×#1306330711yescharacteristic
309C2AGL(1,ℤ/8)×D4311yescharacteristic
310C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#418C2
socleC22×C43C22×D4
hypercenter#418D43
hypocenterC43#3094
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #117×D43C2semidirect
3. #14583222C2semidirect
4. #14583221C2semidirect
5. #14583216C2semidirect
6. #14583211C2semidirect
7. #14582942C2semidirect
8. #14582941C2semidirect
9. #14582904C2semidirect
10. #14582862C2semidirect
11. C43×#418C2semidirect
20. #13063283C22semidirect
21. #13063283C22semidirect
25. C4⋊C4×D43C22semidirect
26. C4⋊C4×D43C22semidirect
30. #13063259C22semidirect
31. #13063258C22semidirect
32. #13063257C22semidirect
33. #13063256C22semidirect
34. #13063246C22semidirect
35. #13063246C22semidirect
36. (C2×D43)⋊C8C22semidirect
37. (C2×D43)⋊C8C22semidirect
41. #102×C43C22semidirect
42. #102×C43C22semidirect
165. #418D43semidirect
167. C43#3094semidirect
195. #102C2×D43semidirect
196. #102C2×D43semidirect