Finite Group Databasebeta

← #19145612

Subgroups — #19145612

Order 5504.

490 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 115 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#127×D43C211yesmaximal, characteristic, complemented
2#14583431C211yesmaximal, characteristic, complemented
3#14583287C212yesmaximal, complemented
4#14583262C212yesmaximal, complemented
5#14583100C211yesmaximal, characteristic, complemented
6#14583096C211yesmaximal, characteristic, complemented
7#14583094C211yesmaximal, characteristic, complemented
8#14583051C212yesmaximal, complemented
9#14583031C212yesmaximal, complemented
10#14582955C211yesmaximal, characteristic, complemented
11C43×#459C211yesmaximal, characteristic, complemented
12C2×D4×D43—21no—
13C2×D4×D43—21no—
14C2×D4×D43C2212yes—
15C2×#10621873C2212yescomplemented
16C2×#10621883C2212yescomplemented
17C2×#10621882C2212yescomplemented
18#13063322C2211yescharacteristic
19#13063321—21no—
20#13063321—21no—
21#13063321C2212yes—
22#13063318—21no—
23#13063316C2211yescharacteristic, complemented
24#13063312C2211yescharacteristic, complemented
25#13063307—21no—
26#13063305C2211yescharacteristic
27#13063296C2211yescharacteristic
28C4×Dic86C2211yescharacteristic, complemented
29C4×C22⋊D43—21no—
30#13063284—21no—
31C42×D43C2211yescharacteristic
32C4⋊(C43⋊C8)C2211yescharacteristic, complemented
33#13063247C2212yescomplemented
34#13063246C2212yescomplemented
35#13063245C2212yescomplemented
36(C2×D43)⋊C8C2212yes—
37#13063235C2212yescomplemented
38C2×D8×C43C2212yescomplemented
39#127×C43C2211yescharacteristic
40C4×D4×C43C2211yescharacteristic, complemented
41C4⋊C8×C43C2211yescharacteristic, complemented
42#102×C43C2212yescomplemented
43C23×D43—22no—
44C2×D4×C43—21no—
45C2×D4×C43—21no—
46C2×D4×C43C2312yes—
47C2×D4×C43C2311yescharacteristic
48C22×C4×C43—21no—
49C2×C22⋊D43—22no—
50C2×C22⋊D43—22no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—21no—
53D4×D43—42no—
54D4×D43—42no—
55D4×D43—44no—
56D4×D43—44no—
57C2×D172—21no—
58C2×D172—21no—
59C2×D172C2312yes—
60C2×C4×D43D411yescharacteristic
61C2×C4×D43D411yescharacteristic
62C2×C4×D43C2311yescharacteristic
63C2×Dic86C2311yescharacteristic
64D8×C43—42no—
65C2×C8×C43C2312yes—
66C4⋊C4×C43C2311yescharacteristic
67C22⋊C4×C43—21no—
68C42×C43C2311yescharacteristic
69C22⋊Dic43—21no—
70C22⋊Dic43—21no—
71C22⋊Dic43—21no—
72#10621883—42no—
73#10621882—42no—
74(C2×D43)⋊C4—21no—
75C4⋊Dic43—21no—
76C4⋊Dic43—21no—
77C4⋊Dic43C2311yescharacteristic
78Dic43⋊C4—21no—
79Dic43⋊C4—21no—
80C4×Dic43—21no—
81C4×Dic43D411yescharacteristic
82C4×Dic43D411yescharacteristic
83C4×Dic43C2311yescharacteristic
84C2×C43⋊C8C2312yes—
85#10621873—42no—
86C23×C43—21no—
87C23×C43—22no—
88C22×D43—22no—
89C22×D43—44no—
90C22×D43—44no—
91C22×D43—44no—
92C22×D43C2×D411yescharacteristic
93D4×C43—21no—
94D4×C43—22no—
95D4×C43—21no—
96D4×C43—22no—
97D4×C43—42no—
98D4×C43—42no—
99C2×C4×C43—21no—
100C2×C4×C43—42no—
101C2×C4×C43C2×D411yescharacteristic
102C2×C4×C43C2×D411yescharacteristic
103C2×C4×C43C2411yescharacteristic
104C22⋊D43—44no—
105C22⋊D43—44no—
106C22⋊D43—44no—
107C22⋊D43—42no—
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43C2×D411yescharacteristic
111C2×Dic43C2×D411yescharacteristic
112C2×Dic43C2×D411yescharacteristic
113D172—22no—
114D172—22no—
115D172—42no—
116D172—42no—
117C4×D43—22no—
118C4×D43—22no—
119C4×D43—21no—
120C4×D43—21no—
121Dic86—21no—
122Dic86—21no—
123C8×C43—22no—
124C43⋊C8—22no—
125C22×C43—42no—
126C22×C43—41no—
127C22×C43—42no—
128C22×C43—42no—
129C22×C43—41no—
130C22×C43—41no—
131C22×C43C22×D411yescharacteristic
132C2×D43—21no—
133C2×D43—21no—
134C2×D43—42no—
135C2×D43—42no—
136C2×D43—42no—
137C2×D43—88no—
138C2×D43AGL(1,ℤ/8)12yes—
139C4×C43—21no—
140C4×C43—41no—
141C4×C43AGL(1,ℤ/8)12yes—
142C4×C43H(5,𝔽2)11yescharacteristic
143C4×C43H(5,𝔽2)11yescharacteristic
144Dic43—21no—
145Dic43—21no—
146Dic43—21no—
147Dic43—41no—
148Dic43—41no—
149#3217—431nomaximal, Sylow
150C2×C43—82no—
151C2×C43—81no—
152C2×C43#53511yescharacteristic
153C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
154C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
155D43—22no—
156D43—82no—
157C2×#127—431no—
158#529—431no—
159#496—432no—
160#490—432no—
161#460—431no—
162#460—431no—
163#459—431no—
164#459D4311yescharacteristic, complemented
165#450—432no—
166#447—432no—
167#432—431no—
168C43#321711yescharacteristic, complemented, Sylow
169C22×D4—432no—
170C22×D4—861no—
171C22×D4—861no—
172C2×SD16—432no—
173C2×SD16—432no—
174C2×D8—432no—
175C2×D8C2×D4312yescomplemented
176#127—432no—
177#127—431no—
178#127—861no—
179#127—861no—
180#127C2×D4311yescharacteristic
181#126—861no—
182#125—431no—
183#124—431no—
184#123—861no—
185C22⋊Q8—431no—
186#121—431no—
187C4×Q8—431no—
188C4×D4—861no—
189C4×D4C2×D4311yescharacteristic, complemented
190#117—861no—
191C2×C42—431no—
192C4⋊C8—431no—
193C4⋊C8C2×D4311yescharacteristic, complemented
194#102—432no—
195#102—432no—
196#102—432no—
197#102C2×D4312yescomplemented
198C22⋊C8—432no—
199#97—432no—
200C24—862no—
201C2×Q8—431no—
202C2×D4—21no—
203C2×D4—21no—
204C2×D4—432no—
205C2×D4—862no—
206C2×D4—862no—
207C2×D4—862no—
208C2×D4—861no—
209C2×D4—861no—
210C2×D4—861no—
211C2×D4—1722no—
212C2×D4—1722no—
213C2×D4—1724no—
214C2×D4—1724no—
215C2×D4C22×D4312yes—
216C2×D4C22×D4311yescharacteristic
217C22×C4—21no—
218C22×C4—431no—
219C22×C4—431no—
220C22×C4—431no—
221SD16—1722no—
222SD16—1722no—
223D8—42no—
224D8—1722no—
225C2×C8—432no—
226C2×C8C22×D4312yes—
227C4⋊C4—431no—
228C4⋊C4—861no—
229C4⋊C4—861no—
230C4⋊C4—861no—
231C4⋊C4—861no—
232C4⋊C4C22×D4311yescharacteristic
233C22⋊C4—21no—
234C22⋊C4—861no—
235C22⋊C4—861no—
236C22⋊C4—861no—
237C22⋊C4—861no—
238C42—431no—
239C42—431no—
240C42—431no—
241C42—861no—
242C42C22×D4311yescharacteristic
243C23—21no—
244C23—22no—
245C23—431no—
246C23—862no—
247C23—1724no—
248C23—1724no—
249C23—1724no—
250Q8—861no—
251Q8—861no—
252D4—21no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—42no—
257D4—42no—
258D4—862no—
259D4—862no—
260D4—1722no—
261D4—1724no—
262D4—1724no—
263D4—1724no—
264D4—1722no—
265D4—1722no—
266C2×C4—21no—
267C2×C4—42no—
268C2×C4—431no—
269C2×C4—431no—
270C2×C4—431no—
271C2×C4—862no—
272C2×C4—862no—
273C2×C4—861no—
274C2×C4—861no—
275C2×C4—861no—
276C2×C4—861no—
277C2×C4D4×D4311yescharacteristic
278C2×C4D4×D4311yescharacteristic
279C2×C4C23×D4311yescharacteristic
280C8—22no—
281C8—862no—
282C22—42no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—432no—
289C22—861no—
290C22—861no—
291C22—3448no—
292C22—1722no—
293C22—1722no—
294C22—1722no—
295C22C2×D4×D4311yescharacteristic
296C4—21no—
297C4—41no—
298C4—861no—
299C4—861no—
300C4—861no—
301C4—1721no—
302C4—1721no—
303C4#1306334912yes—
304C4#1306337011yescharacteristic
305C4#1306337111yescharacteristic
306C2—82no—
307C2—81no—
308C2—862no—
309C2—3442no—
310C2#1458346511yescharacteristic
311C2AGL(1,ℤ/8)×D4311yescharacteristic
312C2C2×#1306334911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#459C2
socleC22×C43C22×D4
hypercenter#459D43
hypocenterC43#3217
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #127×D43C2semidirect
2. #14583431C2semidirect
3. #14583287C2semidirect
4. #14583262C2semidirect
5. #14583100C2semidirect
6. #14583096C2semidirect
7. #14583094C2semidirect
8. #14583051C2semidirect
9. #14583031C2semidirect
10. #14582955C2semidirect
11. C43×#459C2semidirect
15. C2×#10621873C22semidirect
16. C2×#10621883C22semidirect
17. C2×#10621882C22semidirect
23. #13063316C22semidirect
24. #13063312C22semidirect
28. C4×Dic86C22semidirect
32. C4⋊(C43⋊C8)C22semidirect
33. #13063247C22semidirect
34. #13063246C22semidirect
35. #13063245C22semidirect
37. #13063235C22semidirect
38. C2×D8×C43C22semidirect
40. C4×D4×C43C22semidirect
41. C4⋊C8×C43C22semidirect
42. #102×C43C22semidirect
164. #459D43semidirect
168. C43#3217semidirect
175. C2×D8C2×D43semidirect
189. C4×D4C2×D43semidirect
193. C4⋊C8C2×D43semidirect
197. #102C2×D43semidirect