Finite Group Databasebeta

← #19146562

Subgroups — #19146562

Order 5504.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583549C211yesmaximal, characteristic, complemented
2#14583540C211yesmaximal, characteristic, complemented
3#14583260C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583188C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583116C211yesmaximal, characteristic, complemented
9#14583043C211yesmaximal, characteristic, complemented
10#14583032C211yesmaximal, characteristic, complemented
11#14583008C211yesmaximal, characteristic, complemented
12#14582970C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#465C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900—21no—
18C22×D172C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621872C2211yescharacteristic, complemented
22#13063324C2211yescharacteristic, complemented
23#13063314C2211yescharacteristic
24#13063310—21no—
25#13063307—21no—
26#13063306—21no—
27#13063302—21no—
28#13063300—21no—
29#13063300C2211yescharacteristic
30#13063296C2211yescharacteristic, complemented
31#13063295—21no—
32D4×Dic43C2211yescharacteristic, complemented
33#13063287C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35C2×C4⋊Dic43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic, complemented
37C22⋊C4×D43—21no—
38#13063256C2211yescharacteristic, complemented
39#13063256C2211yescharacteristic, complemented
40Dic43⋊C8C2211yescharacteristic, complemented
41#13063249C2211yescharacteristic, complemented
42#13063249C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68#10621902—22no—
69#10621902—41no—
70#10621900—44no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172—22no—
75C2×D172—41no—
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43C2311yescharacteristic
82C2×Dic86—21no—
83SD16×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43D411yescharacteristic
95#10621882—22no—
96#10621882—41no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4D411yescharacteristic
102C4⋊Dic43—21no—
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107Dic43⋊C4D411yescharacteristic
108C4×Dic43C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111#10621872—41no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—81no—
119C22×D43C2×D411yescharacteristic
120Q8×C43—21no—
121Q8×C43—21no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—42no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—22no—
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—42no—
137C2×Dic43—42no—
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140C2×Dic43C2×D411yescharacteristic
141D172—21no—
142D172—21no—
143D172—21no—
144D172—42no—
145D172—42no—
146D172—81no—
147D172#4112yescomplemented
148C4×D43—21no—
149C4×D43—21no—
150C4×D43—42no—
151C4×D43—42no—
152C4×D43—81no—
153Dic86—42no—
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43AGL(1,ℤ/8)12yes—
164C22×C43C22×D411yescharacteristic
165C2×D43—22no—
166C2×D43—21no—
167C2×D43—21no—
168C2×D43—21no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—84no—
175C4×C43—21no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43C2×#4111yescharacteristic
180C4×C43H(5,𝔽2)11yescharacteristic
181Dic43—21no—
182Dic43—21no—
183Dic43—21no—
184Dic43—41no—
185Dic43—41no—
186#3306—431nomaximal, Sylow
187C2×C43—22no—
188C2×C43—81no—
189C2×C43#54611yescharacteristic
190C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C43#57711yescharacteristic
192D43—41no—
193D43—42no—
194D43—81no—
195#547—431no—
196#546—431no—
197#489—431no—
198#483—431no—
199#481—431no—
200#476—431no—
201#469—431no—
202#465D4311yescharacteristic, complemented
203#463—431no—
204#449—431no—
205#447—431no—
206#442—431no—
207#435—431no—
208#417—431no—
209C2×#102—431no—
210C43#330611yescharacteristic, complemented, Sylow
211C2×#41—431no—
212C2×#41—861no—
213C22×D4—431no—
214C2×SD16C2×D4311yescharacteristic, complemented
215C2×D8—431no—
216C2×D8—431no—
217C2×M16—431no—
218C22×C8C2×D4311yescharacteristic
219C4⋊Q8—431no—
220#124—431no—
221#123—861no—
222#123—861no—
223#123—861no—
224C22⋊Q8—861no—
225C22⋊Q8C2×D4311yescharacteristic
226#121—431no—
227#121—431no—
228#121—861no—
229#121C2×D4311yescharacteristic
230#120—861no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C22⋊C4—861no—
237#106—431no—
238#106—431no—
239#106C2×D4311yescharacteristic, complemented
240C4⋊C8—431no—
241#103—431no—
242#103—431no—
243#103C2×D4311yescharacteristic, complemented
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102C2×D4311yescharacteristic, complemented
251C22⋊C8—431no—
252C22⋊C8—431no—
253#97—431no—
254C24—861no—
255#41—862no—
256#41—1721no—
257#41—1724no—
258C2×Q8—861no—
259C2×Q8C22×D4311yescharacteristic
260C2×D4—21no—
261C2×D4—431no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—862no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4C22×D4311yescharacteristic
271C22×C4—431no—
272C22×C4—861no—
273C22×C4—861no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4C22×D4311yescharacteristic
278SD16—41no—
279D8—862no—
280D8—1721no—
281M16—1721no—
282C2×C8—41no—
283C2×C8—431no—
284C2×C8—431no—
285C2×C8C22×D4311yescharacteristic
286C2×C8C22×D4311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4C22×D4311yescharacteristic
295C4⋊C4C22×D4311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—431no—
299C22⋊C4—431no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C42—431no—
307C23—21no—
308C23—431no—
309C23—861no—
310C23—861no—
311C23—3441no—
312C23—1722no—
313C23—1722no—
314C23D4×D4311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—1722no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—432no—
322D4—862no—
323D4—861no—
324D4—861no—
325D4—861no—
326D4—3441no—
327D4—1722no—
328D4—1722no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—431no—
336C2×C4—431no—
337C2×C4—431no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—3441no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4—1722no—
347C2×C4D4×D4311yescharacteristic
348C2×C4C23×D4311yescharacteristic
349C8—21no—
350C8—21no—
351C8—861no—
352C8—861no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22—862no—
362C22—3444no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22#1306335212yes—
369C22C2×D4×D4311yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—861no—
375C4—861no—
376C4—861no—
377C4—1721no—
378C4—1721no—
379C4#41×D4311yescharacteristic
380C4#1306337011yescharacteristic
381C2—22no—
382C2—81no—
383C2—3441no—
384C2—1721no—
385C2—1722no—
386C2#1458353811yescharacteristic
387C2C2×#1306335211yescharacteristic
388C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#465C2
socleC22×C43C22×D4
hypercenter#465D43
hypocenterC43#3306
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #14583549C2semidirect
2. #14583540C2semidirect
3. #14583260C2semidirect
4. #14583227C2semidirect
5. #14583219C2semidirect
6. #14583188C2semidirect
7. #14583151C2semidirect
8. #14583116C2semidirect
9. #14583043C2semidirect
10. #14583032C2semidirect
11. #14583008C2semidirect
12. #14582970C2semidirect
13. #14582899C2semidirect
14. C2×#13063247C2semidirect
15. C43×#465C2semidirect
21. C2×#10621872C22semidirect
22. #13063324C22semidirect
30. #13063296C22semidirect
32. D4×Dic43C22semidirect
36. C4⋊C4×D43C22semidirect
38. #13063256C22semidirect
39. #13063256C22semidirect
40. Dic43⋊C8C22semidirect
41. #13063249C22semidirect
42. #13063249C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063235C22semidirect
52. C2×SD16×C43C22semidirect
56. #106×C43C22semidirect
57. #103×C43C22semidirect
58. #102×C43C22semidirect
147. D172#41semidirect
202. #465D43semidirect
210. C43#3306semidirect
214. C2×SD16C2×D43semidirect
239. #106C2×D43semidirect
243. #103C2×D43semidirect
250. #102C2×D43semidirect