Finite Group Databasebeta

← #19146550

Subgroups — #19146550

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#14583545C211yesmaximal, characteristic, complemented
2#14583261C211yesmaximal, characteristic, complemented
3#14583229C211yesmaximal, characteristic, complemented
4#14583217C211yesmaximal, characteristic, complemented
5#14583186C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583126C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583032C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14C2×#13063245C211yesmaximal, characteristic, complemented
15C43×#547C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×#10621883C2211yescharacteristic, complemented
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×#10621877C2211yescharacteristic, complemented
22C22×C43⋊C8C2211yescharacteristic
23#13063313C2211yescharacteristic
24#13063310—21no—
25#13063304C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063298—21no—
28#13063293—21no—
29C4×D172C2211yescharacteristic
30C22⋊C4×D43—21no—
31#13063256C2211yescharacteristic, complemented
32#13063256C2211yescharacteristic, complemented
33#13063256C2211yescharacteristic, complemented
34C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#13063248C2211yescharacteristic, complemented
36#13063248C2211yescharacteristic, complemented
37#13063248C2211yescharacteristic, complemented
38#13063246C2211yescharacteristic, complemented
39#13063245C2211yescharacteristic
40#13063245C2211yescharacteristic
41#13063245C2211yescharacteristic
42#13063245C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47#13063236C2211yescharacteristic, complemented
48C2×#41×C43—21no—
49C4⋊Q8×C43C2211yescharacteristic, complemented
50#123×C43—21no—
51#123×C43—21no—
52C22⋊Q8×C43—21no—
53#121×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic, complemented
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic, complemented
57C2×C4⋊C4×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60#41×C43—44no—
61C2×Q8×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43D411yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2311yescharacteristic
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73#10621898—22no—
74#10621898—41no—
75C2×D172—21no—
76C2×D172—22no—
77C2×D172—41no—
78C2×D172C2311yescharacteristic
79C2×D172C2311yescharacteristic
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×Dic86C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43D411yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C22⋊C4×C43—21no—
93C22⋊C4×C43D411yescharacteristic
94C22⋊C4×C43D411yescharacteristic
95C42×C43C2311yescharacteristic
96C22⋊Dic43—21no—
97#10621883—41no—
98#10621882—22no—
99#10621882—41no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106#10621877—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C23×C43C2×D411yescharacteristic
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—81no—
120Q8×C43—42no—
121D4×C43—22no—
122D4×C43—21no—
123D4×C43—21no—
124D4×C43—42no—
125D4×C43—42no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—42no—
134C2×C4×C43—42no—
135C2×C4×C43—42no—
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2×D411yescharacteristic
138C2×C4×C43C2×D411yescharacteristic
139C2×C4×C43C2×D411yescharacteristic
140C2×C4×C43C2411yescharacteristic
141C22⋊D43—42no—
142C22⋊D43—81no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—42no—
149D172#4112yescomplemented
150C4×D43—42no—
151C4×D43—81no—
152Dic86—21no—
153Dic86—21no—
154C43⋊C8—21no—
155C43⋊C8—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43AGL(1,ℤ/8)12yes—
167C22×C43C22×D411yescharacteristic
168C2×D43—22no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—84no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43C2×#4111yescharacteristic
183C4×C43H(5,𝔽2)11yescharacteristic
184Dic43—41no—
185Dic43—41no—
186#3306—431nomaximal, Sylow
187C2×C43—22no—
188C2×C43—41no—
189C2×C43—81no—
190C2×C43#54611yescharacteristic
191C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C43#57711yescharacteristic
193D43—42no—
194D43—81no—
195#547D4311yescharacteristic, complemented
196#546—431no—
197#489—431no—
198#483—431no—
199#481—431no—
200#476—431no—
201#469—431no—
202#465—431no—
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—21no—
212C2×#41—431no—
213C22×D4—431no—
214C2×SD16—431no—
215C2×D8—431no—
216C2×D8—431no—
217C2×M16—431no—
218C22×C8—431no—
219C4⋊Q8C2×D4311yescharacteristic, complemented
220#124—431no—
221#123—21no—
222#123—21no—
223#123—861no—
224C22⋊Q8—21no—
225C22⋊Q8—431no—
226#121—431no—
227#121—861no—
228#121C2×D4311yescharacteristic
229#121C2×D4311yescharacteristic, complemented
230#120—861no—
231C4×D4—431no—
232C4×D4C2×D4311yescharacteristic
233C4×D4C2×D4311yescharacteristic, complemented
234C2×C4⋊C4C2×D4311yescharacteristic
235C2×C4⋊C4C2×D4311yescharacteristic, complemented
236C2×C22⋊C4—861no—
237#106—431no—
238#106—431no—
239#106—431no—
240C4⋊C8—431no—
241#103—431no—
242#103—431no—
243#103—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251C22⋊C8—431no—
252C22⋊C8—431no—
253#97—431no—
254C24—861no—
255#41—44no—
256#41—862no—
257#41—1721no—
258C2×Q8—21no—
259C2×Q8—431no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—431no—
263C2×D4—431no—
264C2×D4—862no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—1721no—
269C2×D4C22⋊D4311yescharacteristic
270C2×D4C22×D4311yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4C22×D4311yescharacteristic
277C22×C4C22×D4311yescharacteristic
278SD16—1721no—
279D8—862no—
280D8—1721no—
281M16—1721no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8—431no—
285C2×C8—431no—
286C2×C8—1721no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—431no—
291C4⋊C4—861no—
292C4⋊C4C22⋊D4311yescharacteristic
293C4⋊C4C22×D4311yescharacteristic
294C4⋊C4C22×D4311yescharacteristic
295C4⋊C4C22×D4311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4C22⋊D4311yescharacteristic
305C22⋊C4C22⋊D4311yescharacteristic
306C42C22×D4311yescharacteristic
307C23—21no—
308C23—861no—
309C23—861no—
310C23—3441no—
311C23—1722no—
312C23—1722no—
313C23C2×C22⋊D4311yescharacteristic
314C23C2×C22⋊D4311yescharacteristic
315Q8—42no—
316Q8—861no—
317Q8—861no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—432no—
324D4—861no—
325D4—861no—
326D4—861no—
327D4—3441no—
328D4—1722no—
329D4—1722no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—3441no—
343C2×C4—1722no—
344C2×C4C2×C22⋊D4311yescharacteristic
345C2×C4C2×C22⋊D4311yescharacteristic
346C2×C4C2×C22⋊D4311yescharacteristic
347C2×C4C2×C22⋊D4311yescharacteristic
348C2×C4C23×D4311yescharacteristic
349C8—861no—
350C8—861no—
351C8—861no—
352C8—861no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—862no—
362C22—3444no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22#1306335112yes—
369C22C22×C22⋊D4311yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—1721no—
378C4—1721no—
379C4#41×D4311yescharacteristic
380C4#1306337111yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—3441no—
385C2—1722no—
386C2#1458353711yescharacteristic
387C2C2×#1306335111yescharacteristic
388C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#547C2
socleC22×C43C22×D4
hypercenter#547D43
hypocenterC43#3306
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14583545C2semidirect
2. #14583261C2semidirect
3. #14583229C2semidirect
4. #14583217C2semidirect
5. #14583186C2semidirect
6. #14583150C2semidirect
7. #14583126C2semidirect
8. #14583114C2semidirect
9. #14583042C2semidirect
10. #14583032C2semidirect
11. #14583009C2semidirect
12. #14582971C2semidirect
13. #14582898C2semidirect
14. C2×#13063245C2semidirect
15. C43×#547C2semidirect
18. C2×#10621883C22semidirect
21. C2×#10621877C22semidirect
31. #13063256C22semidirect
32. #13063256C22semidirect
33. #13063256C22semidirect
34. C4⋊(C43⋊C8)C22semidirect
35. #13063248C22semidirect
36. #13063248C22semidirect
37. #13063248C22semidirect
38. #13063246C22semidirect
46. C22⋊(C43⋊C8)C22semidirect
47. #13063236C22semidirect
49. C4⋊Q8×C43C22semidirect
54. #121×C43C22semidirect
56. C4×D4×C43C22semidirect
58. C2×C4⋊C4×C43C22semidirect
149. D172#41semidirect
195. #547D43semidirect
210. C43#3306semidirect
219. C4⋊Q8C2×D43semidirect
229. #121C2×D43semidirect
233. C4×D4C2×D43semidirect
235. C2×C4⋊C4C2×D43semidirect