Finite Group Databasebeta

← #19146738

Subgroups — #19146738

Order 5504.

462 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#14583595C211yesmaximal, characteristic, complemented
2D4×D172C211yesmaximal, characteristic, complemented
3#14583264C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583218C211yesmaximal, characteristic, complemented
6#14583200C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583135C211yesmaximal, characteristic, complemented
9#14583095C211yesmaximal, characteristic, complemented
10#14583035C211yesmaximal, characteristic, complemented
11#14583035C211yesmaximal, characteristic, complemented
12#14583012C211yesmaximal, characteristic, complemented
13#14582905C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×D4×D43—21no—
19C2×D344C2211yescharacteristic
20C2×D344C2211yescharacteristic, complemented
21C2×D344C2211yescharacteristic, complemented
22#13063322C2211yescharacteristic
23#13063320—21no—
24#13063317C2211yescharacteristic, complemented
25#13063307—21no—
26#13063300—21no—
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063299C2211yescharacteristic, complemented
30#13063299C2211yescharacteristic, complemented
31#13063297—21no—
32#13063295—21no—
33#13063295—21no—
34C4×D172C2211yescharacteristic
35C4×D172C2211yescharacteristic, complemented
36(C22⋊D43)⋊C4—21no—
37#13063284C2211yescharacteristic, complemented
38C2×C4⋊Dic43C2211yescharacteristic, complemented
39#13063259C2211yescharacteristic, complemented
40#13063257C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic, complemented
47#13063247C2211yescharacteristic, complemented
48#13063247C2211yescharacteristic, complemented
49#13063247C2211yescharacteristic, complemented
50#13063247C2211yescharacteristic, complemented
51#13063247C2211yescharacteristic, complemented
52C2×M16×C43C2211yescharacteristic, complemented
53C22×C8×C43C2211yescharacteristic, complemented
54C4×D4×C43C2211yescharacteristic
55C4⋊C8×C43C2211yescharacteristic, complemented
56C22⋊C8×C43C2211yescharacteristic, complemented
57C22⋊C8×C43C2211yescharacteristic, complemented
58#97×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43—21no—
61C2×D4×C43D411yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C22×Dic43—21no—
69D4×D43—44no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—21no—
73C2×D172—21no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172C2311yescharacteristic
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×D172C2311yescharacteristic
82C2×C4×D43—21no—
83C2×C4×D43—21no—
84M16×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C2×C8×C43C2311yescharacteristic
89C2×C8×C43C2311yescharacteristic
90C4⋊C4×C43D411yescharacteristic
91C22⋊C4×C43D411yescharacteristic
92C22⋊C4×C43D411yescharacteristic
93C42×C43C2311yescharacteristic
94C22⋊Dic43—21no—
95(C2×D43)⋊C4—21no—
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—
101C4⋊Dic43—21no—
102C4⋊Dic43C2311yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105C4⋊Dic43C2311yescharacteristic
106Dic43⋊C4—21no—
107Dic43⋊C4—21no—
108C4×Dic43—21no—
109D344—22no—
110D344—41no—
111D344—41no—
112C23×C43C2×D411yescharacteristic
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—42no—
122C22×D43—81no—
123C22×D43—81no—
124D4×C43—22no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—42no—
135C22⋊D43—42no—
136C22⋊D43—42no—
137C22⋊D43—81no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—81no—
143D172—21no—
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—21no—
149D172—21no—
150D172—42no—
151D172—42no—
152D172—42no—
153D172—81no—
154D172#4112yes—
155C4×D43—42no—
156C4×D43—81no—
157C8×C43—21no—
158C8×C43—21no—
159C8×C43—21no—
160C8×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
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—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—84no—
181C2×D43—84no—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—21no—
185C4×C43—21no—
186C4×C43C2×#4111yescharacteristic
187C4×C43H(5,𝔽2)11yescharacteristic
188Dic43—41no—
189Dic43—41no—
190Dic43—41no—
191Dic43—41no—
192#3318—431nomaximal, Sylow
193C2×C43—22no—
194C2×C43—41no—
195C2×C43#54611yescharacteristic
196C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C43#57611yescharacteristic
198D43—42no—
199D43—81no—
200D43—81no—
201D43—81no—
202#553—431no—
203D42—431no—
204#490—431no—
205#482—431no—
206#481—431no—
207#478—431no—
208#469—431no—
209#466—431no—
210#459—431no—
211#447—431no—
212#447—431no—
213#442—431no—
214#435D4311yescharacteristic, complemented
215#418—431no—
216C2×#102—431no—
217C43#331811yescharacteristic, complemented, Sylow
218C22×D4—431no—
219C22×D4—431no—
220C22×D4—861no—
221C2×D8—431no—
222C2×D8—431no—
223C2×D8—431no—
224C2×M16C2×D4311yescharacteristic, complemented
225C22×C8C2×D4311yescharacteristic, complemented
226#127—431no—
227#126—861no—
228#125—431no—
229#123—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—861no—
241C4×D4C2×D4311yescharacteristic
242#117—431no—
243C2×C4⋊C4—431no—
244#107—431no—
245#106—431no—
246#106—431no—
247C4⋊C8C2×D4311yescharacteristic, complemented
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252#102—431no—
253#102—431no—
254#102—431no—
255#102—431no—
256#102—431no—
257#102—431no—
258C22⋊C8C2×D4311yescharacteristic, complemented
259C22⋊C8C2×D4311yescharacteristic, complemented
260#97C2×D4311yescharacteristic, complemented
261C24—861no—
262C24—861no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—431no—
267C2×D4—862no—
268C2×D4—862no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4—1724no—
280C2×D4D17211yescharacteristic
281C22×C4—861no—
282C22×C4—861no—
283C22×C4—861no—
284C22×C4C22×D4311yescharacteristic
285C22×C4C22×D4311yescharacteristic
286D8—862no—
287D8—1721no—
288D8—1721no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D4311yescharacteristic
292C2×C8C22×D4311yescharacteristic
293C2×C8C22×D4311yescharacteristic
294C2×C8C22×D4311yescharacteristic
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—431no—
298C4⋊C4—431no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4D17211yescharacteristic
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4D17211yescharacteristic
311C22⋊C4D17211yescharacteristic
312C42—861no—
313C42C22×D4311yescharacteristic
314C23—861no—
315C23—861no—
316C23—861no—
317C23—861no—
318C23—3441no—
319C23—3441no—
320C23—1722no—
321C23—1722no—
322C23—1722no—
323C23—1722no—
324C23C2×D17211yescharacteristic
325C23C2×D17211yescharacteristic
326D4—22no—
327D4—432no—
328D4—861no—
329D4—861no—
330D4—861no—
331D4—861no—
332D4—861no—
333D4—861no—
334D4—861no—
335D4—3441no—
336D4—3441no—
337D4—1722no—
338D4—1722no—
339D4—1722no—
340D4—1722no—
341D4—1722no—
342D4—1722no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—3441no—
352C2×C4—3441no—
353C2×C4—1722no—
354C2×C4C2×D17211yescharacteristic
355C2×C4C2×D17211yescharacteristic
356C2×C4C2×D17211yescharacteristic
357C2×C4C2×D17211yescharacteristic
358C2×C4C23×D4311yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—862no—
369C22—3444no—
370C22—3444no—
371C22—1721no—
372C22—1721no—
373C22—1721no—
374C22—1721no—
375C22—1721no—
376C22—1721no—
377C22—1721no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22#1306335312yes—
383C22C22×D17211yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—1721no—
389C4—1721no—
390C4—1721no—
391C4—1721no—
392C4#41×D4311yescharacteristic
393C4#1306337011yescharacteristic
394C2—22no—
395C2—41no—
396C2—3441no—
397C2—3441no—
398C2—3441no—
399C2—1722no—
400C2#1458354411yescharacteristic
401C2C2×#1306335311yescharacteristic
402C2#1458370411yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #14583595C2semidirect
2. D4×D172C2semidirect
3. #14583264C2semidirect
4. #14583224C2semidirect
5. #14583218C2semidirect
6. #14583200C2semidirect
7. #14583152C2semidirect
8. #14583135C2semidirect
9. #14583095C2semidirect
10. #14583035C2semidirect
11. #14583035C2semidirect
12. #14583012C2semidirect
13. #14582905C2semidirect
14. C2×#13063247C2semidirect
15. C43×#435C2semidirect
20. C2×D344C22semidirect
21. C2×D344C22semidirect
24. #13063317C22semidirect
29. #13063299C22semidirect
30. #13063299C22semidirect
35. C4×D172C22semidirect
37. #13063284C22semidirect
38. C2×C4⋊Dic43C22semidirect
39. #13063259C22semidirect
40. #13063257C22semidirect
41. #13063257C22semidirect
45. #13063247C22semidirect
46. #13063247C22semidirect
47. #13063247C22semidirect
48. #13063247C22semidirect
49. #13063247C22semidirect
50. #13063247C22semidirect
51. #13063247C22semidirect
52. C2×M16×C43C22semidirect
53. C22×C8×C43C22semidirect
55. C4⋊C8×C43C22semidirect
56. C22⋊C8×C43C22semidirect
57. C22⋊C8×C43C22semidirect
58. #97×C43C22semidirect
214. #435D43semidirect
217. C43#3318semidirect
224. C2×M16C2×D43semidirect
225. C22×C8C2×D43semidirect
247. C4⋊C8C2×D43semidirect
258. C22⋊C8C2×D43semidirect
259. C22⋊C8C2×D43semidirect
260. #97C2×D43semidirect