Finite Group Databasebeta

← #19146735

Subgroups — #19146735

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#14583602C211yesmaximal, characteristic, complemented
2#14583534C211yesmaximal, characteristic, complemented
3#14583222C211yesmaximal, characteristic, complemented
4#14583216C211yesmaximal, characteristic, complemented
5#14583196C211yesmaximal, characteristic, complemented
6#14583151C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583091C211yesmaximal, characteristic, complemented
9#14583034C211yesmaximal, characteristic, complemented
10#14583034C211yesmaximal, characteristic, complemented
11#14583012C211yesmaximal, characteristic, complemented
12#14582972C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#490C211yesmaximal, characteristic, complemented
16C2×D4×D43—21no—
17C2×D4×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×#10621882C2211yescharacteristic, complemented
21C2×#10621882C2211yescharacteristic, complemented
22C2×#10621872C2211yescharacteristic, complemented
23C2×C8×D43C2211yescharacteristic, complemented
24#13063320—21no—
25#13063310—21no—
26#13063300—21no—
27#13063300C2211yescharacteristic, complemented
28#13063300C2211yescharacteristic, complemented
29#13063296—21no—
30#13063296C2211yescharacteristic
31#13063296C2211yescharacteristic
32#13063293—21no—
33#13063293—21no—
34C4×D172C2211yescharacteristic
35C4×D172C2211yescharacteristic
36C4×D172C2211yescharacteristic, complemented
37#13063287—21no—
38#13063283C2211yescharacteristic, complemented
39C4⋊C4×D43C2211yescharacteristic, complemented
40#13063258C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43C4⋊(C43⋊C8)C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic, complemented
47#13063246C2211yescharacteristic, complemented
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52#127×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic, complemented
54#102×C43C2211yescharacteristic, complemented
55#102×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic, complemented
58#97×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68C2×C22⋊D43—21no—
69D4×D43—22no—
70D4×D43—22no—
71D4×D43—41no—
72D4×D43—41no—
73D4×D43—44no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172D411yescharacteristic
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×C4×D43—21no—
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×C4×D43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43C2311yescharacteristic
89C4⋊C4×C43C2311yescharacteristic
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93#10621882—41no—
94#10621882—41no—
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)⋊C4D411yescharacteristic
101(C2×D43)⋊C4D411yescharacteristic
102C4⋊Dic43D411yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109D344—22no—
110#10621872—41no—
111C8×D43—41no—
112C23×C43—21no—
113C23×C43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—42no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—81no—
121C22×D43—81no—
122C22×D43C2×D411yescharacteristic
123C22×D43C2×D411yescharacteristic
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—42no—
129D4×C43—81no—
130C2×C4×C43—21no—
131C2×C4×C43—21no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—42no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—42no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—22no—
144D172—21no—
145D172—21no—
146D172—21no—
147D172—42no—
148D172—81no—
149D172#4112yes—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—42no—
155C4×D43—81no—
156C4×D43—81no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43C22×D411yescharacteristic
168C2×D43—21no—
169C2×D43—21no—
170C2×D43—22no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—21no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—84no—
180C2×D43—84no—
181C2×D43AGL(1,ℤ/8)12yes—
182C4×C43—21no—
183C4×C43—21no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43C2×#4111yescharacteristic
187C4×C43H(5,𝔽2)11yescharacteristic
188Dic43—21no—
189Dic43—21no—
190Dic43—41no—
191Dic43—41no—
192#3318—431nomaximal, Sylow
193C2×C43—81no—
194C2×C43—81no—
195C2×C43#54611yescharacteristic
196C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C43#57611yescharacteristic
198D43—22no—
199D43—41no—
200D43—42no—
201D43—81no—
202#553—431no—
203D42—431no—
204#490D4311yescharacteristic, complemented
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#435—431no—
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×M16—431no—
225C22×C8—431no—
226#127C2×D4311yescharacteristic
227#126—861no—
228#125C2×D4311yescharacteristic, complemented
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—431no—
241C4×D4—861no—
242#117—431no—
243C2×C4⋊C4—431no—
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, complemented
255#102C2×D4311yescharacteristic, complemented
256#102C2×D4311yescharacteristic, complemented
257#102C2×D4311yescharacteristic, complemented
258C22⋊C8—431no—
259C22⋊C8—431no—
260#97C2×D4311yescharacteristic, complemented
261C24—861no—
262C24—861no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—431no—
266C2×D4—431no—
267C2×D4—431no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—862no—
273C2×D4—862no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—1721no—
277C2×D4—1721no—
278C2×D4—1724no—
279C2×D4C22×D4311yescharacteristic
280C2×D4C22×D4311yescharacteristic
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286D8—862no—
287D8—1721no—
288D8—1721no—
289M16—1721no—
290C2×C8—431no—
291C2×C8—431no—
292C2×C8—1721no—
293C2×C8C22×D4311yescharacteristic
294C2×C8C22×D4311yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—431no—
298C4⋊C4—431no—
299C4⋊C4—431no—
300C4⋊C4—861no—
301C4⋊C4C22×D4311yescharacteristic
302C4⋊C4C22×D4311yescharacteristic
303C22⋊C4—431no—
304C22⋊C4—431no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C42—861no—
313C42C22×D4311yescharacteristic
314C23—21no—
315C23—21no—
316C23—431no—
317C23—431no—
318C23—861no—
319C23—861no—
320C23—3441no—
321C23—3441no—
322C23—1722no—
323C23—1722no—
324C23—1722no—
325C23—1722no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—432no—
333D4—862no—
334D4—861no—
335D4—861no—
336D4—861no—
337D4—3441no—
338D4—1722no—
339D4—1722no—
340D4—1722no—
341D4—1722no—
342D4—1722no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—431no—
346C2×C4—431no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—3441no—
354C2×C4—3441no—
355C2×C4—1722no—
356C2×C4D4×D4311yescharacteristic
357C2×C4D4×D4311yescharacteristic
358C2×C4C23×D4311yescharacteristic
359C8—21no—
360C8—21no—
361C8—861no—
362C8—861no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—432no—
370C22—861no—
371C22—861no—
372C22—861no—
373C22—861no—
374C22—861no—
375C22—862no—
376C22—3444no—
377C22—3444no—
378C22—1721no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22C2×D4×D4311yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—861no—
389C4—861no—
390C4—1721no—
391C4—1721no—
392C4#41×D4311yescharacteristic
393C4#1306337111yescharacteristic
394C2—81no—
395C2—81no—
396C2—862no—
397C2—3441no—
398C2—1721no—
399C2—1722no—
400C2#1458354211yescharacteristic
401C2AGL(1,ℤ/8)×D4311yescharacteristic
402C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#490C2
socleC22×C43C22×D4
hypercenter#490D43
hypocenterC43#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #14583602C2semidirect
2. #14583534C2semidirect
3. #14583222C2semidirect
4. #14583216C2semidirect
5. #14583196C2semidirect
6. #14583151C2semidirect
7. #14583134C2semidirect
8. #14583091C2semidirect
9. #14583034C2semidirect
10. #14583034C2semidirect
11. #14583012C2semidirect
12. #14582972C2semidirect
13. #14582902C2semidirect
14. #102×D43C2semidirect
15. C43×#490C2semidirect
20. C2×#10621882C22semidirect
21. C2×#10621882C22semidirect
22. C2×#10621872C22semidirect
23. C2×C8×D43C22semidirect
27. #13063300C22semidirect
28. #13063300C22semidirect
36. C4×D172C22semidirect
38. #13063283C22semidirect
39. C4⋊C4×D43C22semidirect
40. #13063258C22semidirect
41. #13063257C22semidirect
42. #13063256C22semidirect
43. C4⋊(C43⋊C8)C22semidirect
45. #13063247C22semidirect
46. #13063246C22semidirect
47. #13063246C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
53. #125×C43C22semidirect
54. #102×C43C22semidirect
55. #102×C43C22semidirect
56. #102×C43C22semidirect
57. #102×C43C22semidirect
58. #97×C43C22semidirect
204. #490D43semidirect
217. C43#3318semidirect
228. #125C2×D43semidirect
254. #102C2×D43semidirect
255. #102C2×D43semidirect
256. #102C2×D43semidirect
257. #102C2×D43semidirect
260. #97C2×D43semidirect