Finite Group Databasebeta

← #19144521

Subgroups — #19144521

Order 5504.

458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 129 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#14583411C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
3#14583236C212yesmaximal, complemented
4#14583231C212yesmaximal, complemented
5#14583219C212yesmaximal, complemented
6#14583214C212yesmaximal, complemented
7#14582942C211yesmaximal, characteristic, complemented
8#14582901C211yesmaximal, characteristic, complemented
9#14582898C211yesmaximal, characteristic, complemented
10#14582862C211yesmaximal, characteristic, complemented
11C43×#428C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×C4×D43—21no—
14C22×C4×D43C2211yescharacteristic
15C2×#10621877C2211yescharacteristic
16#13063309—21no—
17#13063305C2211yescharacteristic
18#13063305C2211yescharacteristic
19#13063300C2211yescharacteristic
20#13063300C2211yescharacteristic
21#13063295—21no—
22C4×D172—21no—
23C4×D172—21no—
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4—21no—
26C4⋊C4×D43—21no—
27C4⋊C4×D43—21no—
28C4⋊C4×D43C2212yes—
29C4⋊C4×D43C2212yes—
30#13063258C2212yescomplemented
31#13063256C2212yescomplemented
32#13063250C2212yescomplemented
33#13063248C2212yescomplemented
34#13063247C2212yescomplemented
35#13063245C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37(C2×D43)⋊C8C2212yes—
38C2×M16×C43C2211yescharacteristic
39#117×C43C2211yescharacteristic
40C2×C4⋊C4×C43C2211yescharacteristic
41#107×C43C2212yescomplemented
42#106×C43C2212yescomplemented
43C23×D43D411yescharacteristic
44C22×C4×C43—21no—
45C22×C4×C43C2311yescharacteristic
46C2×C22⋊D43—21no—
47C22×Dic43—21no—
48C22×Dic43D411yescharacteristic
49#10621898—22no—
50#10621898—22no—
51C2×D172—21no—
52C2×D172—21no—
53C2×D172C2311yescharacteristic
54C2×C4×D43—22no—
55C2×C4×D43—22no—
56C2×C4×D43—21no—
57C2×C4×D43—22no—
58C2×C4×D43—22no—
59C2×C4×D43—44no—
60C2×C4×D43D411yescharacteristic
61C2×C4×D43D411yescharacteristic
62C2×C4×D43C2311yescharacteristic
63C2×C4×D43C2311yescharacteristic
64C2×Dic86C2311yescharacteristic
65M16×C43—22no—
66C2×C8×C43C2312yes—
67C4⋊C4×C43—21no—
68C4⋊C4×C43C2311yescharacteristic
69C4⋊C4×C43C2312yes—
70C4⋊C4×C43C2311yescharacteristic
71C22⋊C4×C43—21no—
72C42×C43—21no—
73(C2×D43)⋊C4—21no—
74(C2×D43)⋊C4—21no—
75(C2×D43)⋊C4—21no—
76(C2×D43)⋊C4—21no—
77C4⋊Dic43—21no—
78C4⋊Dic43—21no—
79C4⋊Dic43—21no—
80C4⋊Dic43C2312yes—
81Dic43⋊C4—22no—
82Dic43⋊C4—22no—
83#10621877—22no—
84C2×C43⋊C8C2312yes—
85C23×C43C2×D411yescharacteristic
86C22×D43—22no—
87C22×D43—22no—
88C22×D43—22no—
89C22×D43—21no—
90C22×D43C2×D411yescharacteristic
91C22×D43C2×D411yescharacteristic
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—42no—
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43#4112yes—
98C2×C4×C43#4112yes—
99C2×C4×C43C2411yescharacteristic
100C22⋊D43—42no—
101C2×Dic43—22no—
102C2×Dic43—22no—
103C2×Dic43—21no—
104C2×Dic43—42no—
105C2×Dic43C2×D411yescharacteristic
106C2×Dic43C2×D411yescharacteristic
107D172—21no—
108D172—21no—
109D172—42no—
110D172—42no—
111C4×D43—22no—
112C4×D43—22no—
113C4×D43—21no—
114C4×D43—21no—
115C4×D43—21no—
116C4×D43—21no—
117C4×D43—44no—
118C4×D43—44no—
119C4×D43—42no—
120Dic86—21no—
121Dic86—21no—
122C8×C43—22no—
123C43⋊C8—22no—
124C22×C43—21no—
125C22×C43—21no—
126C22×C43#12312yes—
127C22×C43C22×D411yescharacteristic
128C2×D43—28no—
129C2×D43—21no—
130C2×D43—21no—
131C2×D43—21no—
132C2×D43—21no—
133C2×D43—41no—
134C2×D43—41no—
135C2×D43—41no—
136C2×D43AGL(1,ℤ/8)12yes—
137C2×D43#13712yes—
138C4×C43—42no—
139C4×C43—41no—
140C4×C43—41no—
141C4×C43#12312yes—
142C4×C43C2×#4111yescharacteristic
143C4×C43C2×#4111yescharacteristic
144Dic43—21no—
145Dic43—21no—
146Dic43—41no—
147Dic43—42no—
148#3092—431nomaximal, Sylow
149C2×C43—22no—
150C2×C43C2×#12311yescharacteristic
151C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
152C2×C43C2×#13711yescharacteristic
153D43—22no—
154D43—22no—
155D43—81no—
156#525—431no—
157C22×C4⋊C4—431no—
158#484—432no—
159#483—432no—
160#481—432no—
161#480—432no—
162#428—431no—
163#428D4311yescharacteristic, complemented
164#417—431no—
165#417—431no—
166#407—431no—
167C43#309211yescharacteristic, complemented, Sylow
168C2×#41—431no—
169C23×C4—431no—
170C23×C4—861no—
171C2×M16—431no—
172C2×M16C2×D4311yescharacteristic
173#123—861no—
174C22⋊Q8—431no—
175C22⋊Q8—431no—
176#121—431no—
177#121—431no—
178#120—861no—
179C4×D4—861no—
180C4×D4—861no—
181#117C2×D4311yescharacteristic
182C2×C4⋊C4—431no—
183C2×C4⋊C4—432no—
184C2×C4⋊C4—432no—
185C2×C4⋊C4—861no—
186C2×C4⋊C4—861no—
187C2×C4⋊C4—861no—
188C2×C4⋊C4C2×D4311yescharacteristic
189#107—432no—
190#107C2×D4312yescomplemented
191#106—432no—
192#106C2×D4312yescomplemented
193#103—432no—
194#103—432no—
195#102—432no—
196#102—432no—
197C22⋊C8—432no—
198C22⋊C8—432no—
199C24—431no—
200#41—862no—
201#41—862no—
202C2×Q8—431no—
203C2×D4—431no—
204C2×D4—861no—
205C2×D4—861no—
206C2×D4—861no—
207C22×C4—21no—
208C22×C4—431no—
209C22×C4—431no—
210C22×C4—431no—
211C22×C4—431no—
212C22×C4—431no—
213C22×C4—862no—
214C22×C4—862no—
215C22×C4—862no—
216C22×C4—862no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4—1724no—
220C22×C4C22×D4311yescharacteristic
221M16—22no—
222M16—862no—
223C2×C8—432no—
224C2×C8C22×D4312yes—
225C4⋊C4—21no—
226C4⋊C4—432no—
227C4⋊C4—862no—
228C4⋊C4—862no—
229C4⋊C4—861no—
230C4⋊C4—861no—
231C4⋊C4—861no—
232C4⋊C4C22×D4312yes—
233C4⋊C4C22×D4311yescharacteristic
234C4⋊C4C22×D4311yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C22⋊C4—861no—
239C22⋊C4—861no—
240C42—21no—
241C23—431no—
242C23—431no—
243C23—862no—
244C23—862no—
245C23—862no—
246C23—861no—
247C23D4×D4311yescharacteristic
248Q8—861no—
249Q8—861no—
250D4—861no—
251D4—861no—
252D4—1722no—
253D4—1722no—
254D4—1722no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—42no—
259C2×C4—431no—
260C2×C4—431no—
261C2×C4—862no—
262C2×C4—862no—
263C2×C4—862no—
264C2×C4—861no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—861no—
268C2×C4—861no—
269C2×C4—862no—
270C2×C4—1724no—
271C2×C4—1724no—
272C2×C4—1722no—
273C2×C4—1722no—
274C2×C4#1062189812yes—
275C2×C4D4×D4311yescharacteristic
276C2×C4#1062190212yes—
277C2×C4C23×D4311yescharacteristic
278C8—22no—
279C8—862no—
280C22—21no—
281C22—21no—
282C22—432no—
283C22—432no—
284C22—868no—
285C22—861no—
286C22—861no—
287C22—861no—
288C22—861no—
289C22—1721no—
290C22—1721no—
291C22—1721no—
292C22#1306331012yes—
293C22C2×D4×D4311yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—861no—
298C4—861no—
299C4—1721no—
300C4—1722no—
301C4#1306331012yes—
302C4C2×#1062189811yescharacteristic
303C4C2×#1062190211yescharacteristic
304C2—22no—
305C2—862no—
306C2—862no—
307C2—3441no—
308C2C2×#1306331011yescharacteristic
309C2AGL(1,ℤ/8)×D4311yescharacteristic
310C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3092
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D43C2semidirect
3. #14583236C2semidirect
4. #14583231C2semidirect
5. #14583219C2semidirect
6. #14583214C2semidirect
7. #14582942C2semidirect
8. #14582901C2semidirect
9. #14582898C2semidirect
10. #14582862C2semidirect
11. C43×#428C2semidirect
30. #13063258C22semidirect
31. #13063256C22semidirect
32. #13063250C22semidirect
33. #13063248C22semidirect
34. #13063247C22semidirect
35. #13063245C22semidirect
41. #107×C43C22semidirect
42. #106×C43C22semidirect
163. #428D43semidirect
167. C43#3092semidirect
190. #107C2×D43semidirect
192. #106C2×D43semidirect