Finite Group Databasebeta

← #19143823

Subgroups — #19143823

Order 5504.

994 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C22×D4×D43C211yesmaximal, characteristic, complemented
2C2×#13063352C212yesmaximal, complemented
3#14583412C211yesmaximal, characteristic, complemented
4#14583049C211yesmaximal, characteristic, complemented
5#14583048C212yesmaximal, complemented
6#14583035C211yesmaximal, characteristic, complemented
7#14583034C212yesmaximal, complemented
8#14583033C211yesmaximal, characteristic, complemented
9#14582902C212yesmaximal, complemented
10#14582861C211yesmaximal, characteristic, complemented
11C43×#450C211yesmaximal, characteristic, complemented
12C24×D43—21no—
13C2×#10621902C2211yescharacteristic, complemented
14C22×D172C2211yescharacteristic
15C22×C22⋊D43—21no—
16C2×D4×D43—28no—
17C2×D4×D43—21no—
18C2×D4×D43—21no—
19C2×D4×D43C2212yes—
20C2×D4×D43C2212yes—
21C22×C4×D43C2211yescharacteristic
22#13063352—28no—
23C2×#10621884C2212yescomplemented
24C2×D344C2212yescomplemented
25C2×#10621882C2212yescomplemented
26C2×#10621872C2212yescomplemented
27#13063310—21no—
28#13063301C2211yescharacteristic, complemented
29#13063300C2211yescharacteristic, complemented
30#13063299C2211yescharacteristic, complemented
31#13063295—21no—
32#13063287—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283C2211yescharacteristic, complemented
35#13063247C2212yescomplemented
36#13063246C2212yescomplemented
37#13063245C2212yescomplemented
38C22⋊(C43⋊C8)C2211yescharacteristic, complemented
39(C2×D43)⋊C8C2212yescomplemented
40C22×D4×C43C2211yescharacteristic
41C2×SD16×C43C2212yescomplemented
42C22⋊Q8×C43C2211yescharacteristic, complemented
43#102×C43C2212yescomplemented
44C22⋊C8×C43C2211yescharacteristic, complemented
45C24×C43—21no—
46C23×D43—28no—
47C23×D43—21no—
48C23×D43—22no—
49C23×D43—22no—
50C23×D43—44no—
51C23×D43—44no—
52C23×D43D411yescharacteristic
53C2×Q8×C43C2311yescharacteristic, complemented
54C2×D4×C43—24no—
55C2×D4×C43—21no—
56C2×D4×C43C2312yes—
57C22×C4×C43C2311yescharacteristic
58C2×C22⋊D43—28no—
59C2×C22⋊D43—22no—
60C2×C22⋊D43—22no—
61C2×C22⋊D43—21no—
62C22×Dic43D411yescharacteristic
63#10621902—24no—
64D4×D43—28no—
65D4×D43—28no—
66D4×D43—24no—
67D4×D43—24no—
68D4×D43—24no—
69D4×D43D418yescomplemented
70C2×D172—21no—
71C2×D172—24no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172C2312yes—
75C2×D172C2311yescharacteristic, complemented
76C2×C4×D43—24no—
77C2×C4×D43—21no—
78C2×C4×D43D411yescharacteristic
79C2×C4×D43D411yescharacteristic
80C2×C4×D43C2311yescharacteristic
81C2×C4×D43C2311yescharacteristic
82SD16×C43—24no—
83C2×C8×C43C2312yescomplemented
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic, complemented
86C22⋊C4×C43—21no—
87#10621884—24no—
88#10621882—24no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43C2311yescharacteristic, complemented
94Dic43⋊C4—21no—
95C4×Dic43—21no—
96C2×C43⋊C8C2312yescomplemented
97D344—24no—
98#10621872—24no—
99C23×C43—24no—
100C23×C43—22no—
101C23×C43—42no—
102C23×C43—42no—
103C23×C43C2×D411yescharacteristic
104C22×D43—22no—
105C22×D43—22no—
106C22×D43—22no—
107C22×D43—24no—
108C22×D43—28no—
109C22×D43—22no—
110C22×D43—28no—
111C22×D43—21no—
112C22×D43—432no—
113C22×D43—44no—
114C22×D43—44no—
115C22×D43—44no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—44no—
119C22×D43C2×D411yescharacteristic
120C22×D43C2×D411yescharacteristic
121Q8×C43—22no—
122D4×C43—24no—
123D4×C43—22no—
124D4×C43C2×D414yes—
125C2×C4×C43—22no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—28no—
131C22⋊D43—28no—
132C22⋊D43—42no—
133C2×Dic43—22no—
134C2×Dic43—21no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—24no—
138D172—22no—
139D172—22no—
140D172—42no—
141D172—42no—
142D172C2×D414yes—
143C4×D43—22no—
144C4×D43—22no—
145C4×D43—22no—
146C4×D43—42no—
147C4×D43C2×D414yes—
148C8×C43—22no—
149C43⋊C8—22no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—24no—
153C22×C43—48no—
154C22×C43—42no—
155C22×C43—42no—
156C22×C43AGL(1,ℤ/8)12yescomplemented
157C22×C43C22×D411yescharacteristic
158C2×D43—28no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—24no—
164C2×D43—416no—
165C2×D43—416no—
166C2×D43—48no—
167C2×D43—42no—
168C2×D43—42no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43#12012yes—
173C2×D43AGL(1,ℤ/8)12yescomplemented
174C4×C43—21no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43C22×D412yes—
178Dic43—21no—
179Dic43—41no—
180Dic43#12012yes—
181#3003—431nomaximal, Sylow
182C2×C43—22no—
183C2×C43—44no—
184C2×C43C2×#12011yescharacteristic
185C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
187D43—22no—
188D43—22no—
189D43—44no—
190D43—81no—
191C23×D4—431no—
192C2×AGL(1,ℤ/8)—432no—
193#525—431no—
194#450—432no—
195#450—431no—
196#450D4311yescharacteristic, complemented
197#447—431no—
198#447—432no—
199#447—431no—
200#418—432no—
201#407—431no—
202C43#300311yescharacteristic, complemented, Sylow
203C25—861no—
204C2×#41—431no—
205C22×D4—432no—
206C22×D4—432no—
207C22×D4—431no—
208C22×D4—861no—
209C22×D4—861no—
210C22×D4—861no—
211C22×D4—868no—
212C22×D4C2×D4311yescharacteristic
213C23×C4—431no—
214AGL(1,ℤ/8)—868no—
215C2×SD16—432no—
216C2×SD16C2×D4312yescomplemented
217C2×D8—432no—
218C2×D8—432no—
219C2×M16—432no—
220#123—861no—
221C22⋊Q8—431no—
222C22⋊Q8C2×D4311yescharacteristic, complemented
223#121—431no—
224#121—431no—
225#120—861no—
226C4×D4—861no—
227C4×D4—861no—
228#117—431no—
229#102—432no—
230#102—432no—
231#102—432no—
232#102C2×D4312yescomplemented
233C22⋊C8—431no—
234C22⋊C8—432no—
235C22⋊C8C2×D4311yescharacteristic, complemented
236C24—21no—
237C24—431no—
238C24—862no—
239C24—862no—
240C24—868no—
241C24—861no—
242C24—1724no—
243C24—1724no—
244#41—864no—
245C2×Q8C22×D4311yescharacteristic, complemented
246C2×D4—24no—
247C2×D4—21no—
248C2×D4—438no—
249C2×D4—432no—
250C2×D4—431no—
251C2×D4—864no—
252C2×D4—861no—
253C2×D4—861no—
254C2×D4—864no—
255C2×D4—862no—
256C2×D4—862no—
257C2×D4—864no—
258C2×D4—868no—
259C2×D4—868no—
260C2×D4—868no—
261C2×D4—864no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4C22×D4312yes—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—431no—
269C22×C4—431no—
270C22×C4—864no—
271C22×C4—861no—
272C22×C4C22×D4311yescharacteristic
273SD16—24no—
274SD16—864no—
275D8—864no—
276D8—864no—
277M16—864no—
278C2×C8—432no—
279C2×C8C22×D4312yescomplemented
280C4⋊C4—21no—
281C4⋊C4—431no—
282C4⋊C4—861no—
283C4⋊C4C22×D4311yescharacteristic, complemented
284C22⋊C4—21no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C42—861no—
290C23—24no—
291C23—22no—
292C23—42no—
293C23—42no—
294C23—431no—
295C23—431no—
296C23—862no—
297C23—862no—
298C23—868no—
299C23—864no—
300C23—868no—
301C23—862no—
302C23—862no—
303C23—861no—
304C23—1722no—
305C23—1724no—
306C23—17232no—
307C23—1724no—
308C23—1724no—
309C23—1724no—
310C23—1722no—
311C23D4×D4311yescharacteristic
312Q8—22no—
313D4—24no—
314D4—22no—
315D4—434no—
316D4—864no—
317D4—868no—
318D4—868no—
319D4—862no—
320D4—862no—
321D4—1722no—
322D4—1722no—
323D4—1722no—
324D4D4×D4314yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—431no—
329C2×C4—434no—
330C2×C4—431no—
331C2×C4—862no—
332C2×C4—862no—
333C2×C4—862no—
334C2×C4—862no—
335C2×C4—861no—
336C2×C4—1722no—
337C2×C4D4×D4311yescharacteristic
338C2×C4C23×D4311yescharacteristic
339C8—22no—
340C8—862no—
341C22—21no—
342C22—21no—
343C22—24no—
344C22—48no—
345C22—42no—
346C22—42no—
347C22—432no—
348C22—432no—
349C22—868no—
350C22—861no—
351C22—861no—
352C22—861no—
353C22—861no—
354C22—864no—
355C22—1728no—
356C22—17216no—
357C22—17216no—
358C22—1721no—
359C22—1721no—
360C22—1721no—
361C22—1722no—
362C22—1722no—
363C22#1306335212yescomplemented
364C22C2×D4×D4311yescharacteristic
365C4—21no—
366C4—41no—
367C4—41no—
368C4—432no—
369C4—861no—
370C4—1721no—
371C4C2×D4×D4312yes—
372C2—22no—
373C2—44no—
374C2—862no—
375C2—862no—
376C2—3441no—
377C2—1724no—
378C2#120×D4311yescharacteristic
379C2AGL(1,ℤ/8)×D4311yescharacteristic
380C2C2×#1306335211yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3003
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×D4×D43C2semidirect
2. C2×#13063352C2semidirect
3. #14583412C2semidirect
4. #14583049C2semidirect
5. #14583048C2semidirect
6. #14583035C2semidirect
7. #14583034C2semidirect
8. #14583033C2semidirect
9. #14582902C2semidirect
10. #14582861C2semidirect
11. C43×#450C2semidirect
13. C2×#10621902C22semidirect
23. C2×#10621884C22semidirect
24. C2×D344C22semidirect
25. C2×#10621882C22semidirect
26. C2×#10621872C22semidirect
28. #13063301C22semidirect
29. #13063300C22semidirect
30. #13063299C22semidirect
34. #13063283C22semidirect
35. #13063247C22semidirect
36. #13063246C22semidirect
37. #13063245C22semidirect
38. C22⋊(C43⋊C8)C22semidirect
39. (C2×D43)⋊C8C22semidirect
41. C2×SD16×C43C22semidirect
42. C22⋊Q8×C43C22semidirect
43. #102×C43C22semidirect
44. C22⋊C8×C43C22semidirect
53. C2×Q8×C43C23semidirect
69. D4×D43D4semidirect
75. C2×D172C23semidirect
83. C2×C8×C43C23semidirect
85. C4⋊C4×C43C23semidirect
93. C4⋊Dic43C23semidirect
96. C2×C43⋊C8C23semidirect
156. C22×C43AGL(1,ℤ/8)semidirect
173. C2×D43AGL(1,ℤ/8)semidirect
196. #450D43semidirect
202. C43#3003semidirect
216. C2×SD16C2×D43semidirect
222. C22⋊Q8C2×D43semidirect
232. #102C2×D43semidirect
235. C22⋊C8C2×D43semidirect
245. C2×Q8C22×D43semidirect
279. C2×C8C22×D43semidirect
283. C4⋊C4C22×D43semidirect
363. C22#13063352semidirect