Finite Group Databasebeta

← #19146553

Subgroups — #19146553

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#14583552C211yesmaximal, characteristic, complemented
2#14583544C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic, complemented
4#14583231C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583045C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14582969C211yesmaximal, characteristic, complemented
13#14582897C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#476C211yesmaximal, characteristic, complemented
16C2×#10621902—21no—
17C2×#10621900C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic, complemented
20C2×D344C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621872C2211yescharacteristic, complemented
23C2×C8×D43C2211yescharacteristic
24#13063313C2211yescharacteristic
25#13063310—21no—
26#13063310—21no—
27#13063309—21no—
28#13063305C2211yescharacteristic
29#13063301—21no—
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063300C2211yescharacteristic, complemented
33#13063299—21no—
34#13063295—21no—
35C4×D172C2211yescharacteristic
36C4×D172C2211yescharacteristic, complemented
37C4⋊C4×D43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C4—21no—
40#13063256C2211yescharacteristic, complemented
41#13063250C2211yescharacteristic, complemented
42#13063248C2211yescharacteristic, complemented
43#13063248C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51#13063236C2211yescharacteristic, complemented
52C4⋊Q8×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#106×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C22×Dic43—21no—
66#10621902—44no—
67#10621900—22no—
68#10621900—41no—
69D4×D43—22no—
70D4×D43—41no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172D411yescharacteristic
75C2×D172C2311yescharacteristic
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×C4×D43C2311yescharacteristic
82C2×Dic86C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C4⋊C4×C43—21no—
86C4⋊C4×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C42×C43C2311yescharacteristic
91#10621882—22no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4D411yescharacteristic
100(C2×D43)⋊C4D411yescharacteristic
101C4⋊Dic43—21no—
102C4⋊Dic43D411yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108D344—41no—
109#10621873—41no—
110#10621872—41no—
111C8×D43—41no—
112C23×C43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—42no—
116C22×D43—42no—
117C22×D43—81no—
118C22×D43C2×D411yescharacteristic
119C22×D43C2×D411yescharacteristic
120Q8×C43—42no—
121D4×C43—21no—
122D4×C43#4112yescomplemented
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—81no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—42no—
131C22⋊D43—42no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137D172—22no—
138D172—21no—
139D172—21no—
140D172—21no—
141D172—21no—
142D172—42no—
143D172—42no—
144D172—81no—
145C4×D43—21no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—21no—
149C4×D43—42no—
150C4×D43—42no—
151C4×D43—42no—
152Dic86—21no—
153Dic86—21no—
154C8×C43—21no—
155C8×C43—21no—
156C43⋊C8—21no—
157C43⋊C8—21no—
158C22×C43—22no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—21no—
166C2×D43—21no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—84no—
174C2×D43AGL(1,ℤ/8)12yes—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43C2×#4111yescharacteristic
181C4×C43H(5,𝔽2)11yescharacteristic
182Dic43—21no—
183Dic43—21no—
184Dic43—41no—
185Dic43—41no—
186#3306—431nomaximal, Sylow
187C2×C43—42no—
188C2×C43#54611yescharacteristic
189C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C43#57711yescharacteristic
191D43—22no—
192D43—41no—
193D43—81no—
194D43—81no—
195#547—431no—
196#546—431no—
197#489—431no—
198#483—431no—
199#481—431no—
200#476D4311yescharacteristic, complemented
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—431no—
212C2×#41—861no—
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—861no—
222#123—861no—
223#123—861no—
224C22⋊Q8—431no—
225C22⋊Q8—861no—
226#121—431no—
227#121—431no—
228#121—431no—
229#121—861no—
230#120—861no—
231C4×D4—431no—
232C4×D4—431no—
233C4×D4C2×D4311yescharacteristic
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C22⋊C4—861no—
237#106—431no—
238#106C2×D4311yescharacteristic, complemented
239#106C2×D4311yescharacteristic, complemented
240C4⋊C8C2×D4311yescharacteristic, complemented
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#102C2×D4311yescharacteristic
250#102C2×D4311yescharacteristic
251C22⋊C8—431no—
252C22⋊C8—431no—
253#97—431no—
254C24—861no—
255#41—862no—
256#41—1721no—
257#41—1724no—
258C2×Q8—21no—
259C2×Q8—431no—
260C2×D4—431no—
261C2×D4—431no—
262C2×D4—431no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—862no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4C22×D4311yescharacteristic
271C22×C4—21no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—861no—
275C22×C4—861no—
276C22×C4—861no—
277C22×C4—861no—
278SD16—1721no—
279D8—862no—
280D8—1721no—
281M16—1721no—
282C2×C8—431no—
283C2×C8—431no—
284C2×C8—1721no—
285C2×C8C22×D4311yescharacteristic
286C2×C8C22×D4311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4C22×D4311yescharacteristic
294C4⋊C4C22×D4311yescharacteristic
295C4⋊C4C22×D4311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—431no—
298C22⋊C4—431no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C42C22×D4311yescharacteristic
307C23—21no—
308C23—431no—
309C23—431no—
310C23—861no—
311C23—861no—
312C23—3441no—
313C23—1722no—
314C23—1722no—
315Q8—42no—
316Q8—861no—
317Q8—861no—
318D4—21no—
319D4—862no—
320D4—861no—
321D4—861no—
322D4—861no—
323D4—861no—
324D4—3441no—
325D4—1722no—
326D4—1722no—
327D4—1722no—
328D4—1722no—
329D4#1062190212yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—81no—
334C2×C4—431no—
335C2×C4—431no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—1722no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4—1722no—
346C2×C4D4×D4311yescharacteristic
347C2×C4D4×D4311yescharacteristic
348C2×C4C23×D4311yescharacteristic
349C8—21no—
350C8—21no—
351C8—861no—
352C8—861no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—432no—
357C22—861no—
358C22—861no—
359C22—861no—
360C22—861no—
361C22—861no—
362C22—3444no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22C2×D4×D4311yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—861no—
376C4—861no—
377C4—1721no—
378C4—1721no—
379C4C2×#1062190211yescharacteristic
380C4#1306337111yescharacteristic
381C2—42no—
382C2—862no—
383C2—3441no—
384C2—3441no—
385C2—1721no—
386C2#1458354011yescharacteristic
387C2AGL(1,ℤ/8)×D4311yescharacteristic
388C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#476C2
socleC22×C43C22×D4
hypercenter#476D43
hypocenterC43#3306
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #14583552C2semidirect
2. #14583544C2semidirect
3. #14583261C2semidirect
4. #14583231C2semidirect
5. #14583219C2semidirect
6. #14583153C2semidirect
7. #14583129C2semidirect
8. #14583115C2semidirect
9. #14583045C2semidirect
10. #14583034C2semidirect
11. #14583009C2semidirect
12. #14582969C2semidirect
13. #14582897C2semidirect
14. #102×D43C2semidirect
15. C43×#476C2semidirect
19. C2×#10621873C22semidirect
22. C2×#10621872C22semidirect
32. #13063300C22semidirect
36. C4×D172C22semidirect
38. C4⋊C4×D43C22semidirect
40. #13063256C22semidirect
41. #13063250C22semidirect
42. #13063248C22semidirect
43. #13063248C22semidirect
48. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. #13063236C22semidirect
52. C4⋊Q8×C43C22semidirect
54. #106×C43C22semidirect
55. #106×C43C22semidirect
56. C4⋊C8×C43C22semidirect
122. D4×C43#41semidirect
200. #476D43semidirect
210. C43#3306semidirect
219. C4⋊Q8C2×D43semidirect
238. #106C2×D43semidirect
239. #106C2×D43semidirect
240. C4⋊C8C2×D43semidirect
329. D4#10621902semidirect