Finite Group Databasebeta

← #19146833

Subgroups — #19146833

Order 5504.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583612C211yesmaximal, characteristic, complemented
2D4×C22⋊D43C211yesmaximal, characteristic, complemented
3#14583244C211yesmaximal, characteristic, complemented
4#14583223C211yesmaximal, characteristic, complemented
5#14583222C211yesmaximal, characteristic, complemented
6#14583187C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583151C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14583033C211yesmaximal, characteristic, complemented
12#14582979C211yesmaximal, characteristic, complemented
13#14582975C211yesmaximal, characteristic, complemented
14#14582902C211yesmaximal, characteristic, complemented
15C43×#418C211yesmaximal, characteristic, complemented
16C22×C22⋊D43—21no—
17C2×D4×D43C2211yescharacteristic
18C2×D344C2211yescharacteristic, complemented
19C2×#10621882C2211yescharacteristic
20C2×#10621882C2211yescharacteristic, complemented
21C2×#10621872C2211yescharacteristic, complemented
22#13063324C2211yescharacteristic, complemented
23#13063321C2211yescharacteristic
24#13063313—21no—
25#13063311—21no—
26#13063300C2211yescharacteristic, complemented
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic, complemented
29#13063298—21no—
30#13063297—21no—
31#13063296C2211yescharacteristic
32#13063294—21no—
33#13063293—21no—
34D4×Dic43C2211yescharacteristic
35#13063287C2211yescharacteristic, complemented
36C4×C22⋊D43C2211yescharacteristic
37#13063283C2211yescharacteristic, complemented
38#13063282—21no—
39#13063258C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063246C2211yescharacteristic
46#13063246C2211yescharacteristic, complemented
47#13063245C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic, complemented
54#117×C43C2211yescharacteristic, complemented
55#102×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic, complemented
59C24×C43—21no—
60C23×D43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—22no—
63C2×D4×C43—41no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—44no—
74C2×C22⋊D43D411yescharacteristic
75C22×Dic43—21no—
76D4×D43—22no—
77D4×D43—41no—
78C2×D172—21no—
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×Dic86—21no—
84M16×C43—41no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C42×C43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43D411yescharacteristic
94#10621882—22no—
95#10621882—41no—
96(C2×D43)⋊C4—21no—
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⋊Dic43C2311yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110D344—41no—
111#10621872—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—42no—
115C23×C43—42no—
116C23×C43—81no—
117C23×C43C2×D411yescharacteristic
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—81no—
123C22×D43C2×D411yescharacteristic
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—42no—
128D4×C43#4112yes—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—22no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C22⋊D43—42no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—42no—
145C2×Dic43C2×D411yescharacteristic
146C2×Dic43C2×D411yescharacteristic
147C2×Dic43C2×D411yescharacteristic
148D172—21no—
149D172—21no—
150D172—21no—
151D172—21no—
152D172—81no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—42no—
156Dic86—81no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—22no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—84no—
171C22×C43C22×D411yescharacteristic
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—21no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—84no—
182C4×C43—21no—
183C4×C43—41no—
184C4×C43—41no—
185C4×C43C2×#4111yescharacteristic
186C4×C43H(5,𝔽2)11yescharacteristic
187Dic43—21no—
188Dic43—21no—
189Dic43—41no—
190Dic43—41no—
191Dic43AGL(1,ℤ/8)12yes—
192#3325—431nomaximal, Sylow
193C2×C43—42no—
194C2×C43—41no—
195C2×C43—81no—
196C2×C43#54611yescharacteristic
197C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C43#57611yescharacteristic
199D43—41no—
200D43—81no—
201D43—81no—
202#555—431no—
203D42—431no—
204#486—431no—
205#482—431no—
206#482—431no—
207#476—431no—
208#469—431no—
209#469—431no—
210#459—431no—
211#447—431no—
212#447—431no—
213C4×D8—431no—
214#436—431no—
215#418—431no—
216#418D4311yescharacteristic, complemented
217C43#332511yescharacteristic, complemented, Sylow
218C22×D4—431no—
219C22×D4—861no—
220C22×D4C2×D4311yescharacteristic
221C2×D8—431no—
222C2×D8—431no—
223C2×D8—431no—
224C2×M16—431no—
225C2×M16C2×D4311yescharacteristic, complemented
226C4⋊Q8—431no—
227#127—431no—
228#124—861no—
229#124—861no—
230#121—431no—
231#121—431no—
232#121—431no—
233#121—431no—
234#121—861no—
235#121—861no—
236#120—861no—
237#120—861no—
238C4×D4—431no—
239C4×D4—431no—
240C4×D4—431no—
241#117—431no—
242#117—861no—
243#117C2×D4311yescharacteristic, complemented
244#107—431no—
245#106—431no—
246#106—431no—
247C4⋊C8—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252#102—431no—
253#102—431no—
254#102C2×D4311yescharacteristic
255#102C2×D4311yescharacteristic
256#102C2×D4311yescharacteristic, complemented
257#102C2×D4311yescharacteristic, complemented
258C22⋊C8—431no—
259C22⋊C8—431no—
260C4×C8—431no—
261C24—21no—
262C24—861no—
263C2×Q8—861no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—431no—
268C2×D4—431no—
269C2×D4—431no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—862no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—1721no—
279C2×D4—1724no—
280C2×D4C22×D4311yescharacteristic
281C2×D4C22×D4311yescharacteristic
282C22×C4—431no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4C22×D4311yescharacteristic
286D8—862no—
287D8—1721no—
288D8—1721no—
289M16—41no—
290M16—1721no—
291C2×C8—431no—
292C2×C8—431no—
293C2×C8C22×D4311yescharacteristic
294C2×C8C22×D4311yescharacteristic
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—431no—
298C4⋊C4—861no—
299C4⋊C4C22×D4311yescharacteristic
300C4⋊C4C22×D4311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—431no—
303C22⋊C4—431no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C42—21no—
312C42—431no—
313C42—861no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—431no—
320C23—861no—
321C23—861no—
322C23—3441no—
323C23—1722no—
324C23—1722no—
325C23D4×D4311yescharacteristic
326Q8—3441no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—862no—
332D4—861no—
333D4—861no—
334D4—861no—
335D4—861no—
336D4—3441no—
337D4—3441no—
338D4—3441no—
339D4—1722no—
340D4—1722no—
341D4—1722no—
342D4—1722no—
343D4#1062189812yes—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—431no—
349C2×C4—431no—
350C2×C4—431no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—1722no—
356C2×C4—1722no—
357C2×C4D4×D4311yescharacteristic
358C2×C4C23×D4311yescharacteristic
359C8—21no—
360C8—21no—
361C8—861no—
362C8—861no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—84no—
373C22—861no—
374C22—861no—
375C22—861no—
376C22—3444no—
377C22—1721no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22C2×D4×D4311yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—432no—
388C4—861no—
389C4—861no—
390C4—1721no—
391C4—1721no—
392C4C2×#1062189811yescharacteristic
393C4#1306337011yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—3441no—
398C2—3441no—
399C2—1721no—
400C2#1458353911yescharacteristic
401C2AGL(1,ℤ/8)×D4311yescharacteristic
402C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#418C2
socleC22×C43C22×D4
hypercenter#418D43
hypocenterC43#3325
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #14583612C2semidirect
2. D4×C22⋊D43C2semidirect
3. #14583244C2semidirect
4. #14583223C2semidirect
5. #14583222C2semidirect
6. #14583187C2semidirect
7. #14583152C2semidirect
8. #14583151C2semidirect
9. #14583093C2semidirect
10. #14583034C2semidirect
11. #14583033C2semidirect
12. #14582979C2semidirect
13. #14582975C2semidirect
14. #14582902C2semidirect
15. C43×#418C2semidirect
18. C2×D344C22semidirect
20. C2×#10621882C22semidirect
21. C2×#10621872C22semidirect
22. #13063324C22semidirect
26. #13063300C22semidirect
28. #13063299C22semidirect
35. #13063287C22semidirect
37. #13063283C22semidirect
39. #13063258C22semidirect
40. #13063257C22semidirect
41. #13063256C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
46. #13063246C22semidirect
47. #13063245C22semidirect
48. #13063245C22semidirect
49. C22⋊(C43⋊C8)C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. C8×Dic43C22semidirect
53. C2×M16×C43C22semidirect
54. #117×C43C22semidirect
57. #102×C43C22semidirect
58. #102×C43C22semidirect
216. #418D43semidirect
217. C43#3325semidirect
225. C2×M16C2×D43semidirect
243. #117C2×D43semidirect
256. #102C2×D43semidirect
257. #102C2×D43semidirect