Finite Group Databasebeta

← #19146741

Subgroups — #19146741

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#14583599C211yesmaximal, characteristic, complemented
2D4×D172C211yesmaximal, characteristic, complemented
3#14583264C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583199C211yesmaximal, characteristic, complemented
7#14583151C211yesmaximal, characteristic, complemented
8#14583134C211yesmaximal, characteristic, complemented
9#14583094C211yesmaximal, characteristic, complemented
10#14583031C211yesmaximal, characteristic, complemented
11#14583031C211yesmaximal, characteristic, complemented
12#14582972C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic, complemented
14#102×D43C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C22×D172—21no—
17C2×D4×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×#10621882C2211yescharacteristic, complemented
20C2×#10621882C2211yescharacteristic, complemented
21C2×#10621872C2211yescharacteristic, complemented
22C2×C8×D43C2211yescharacteristic, complemented
23#13063322C2211yescharacteristic
24#13063318—21no—
25#13063317C2211yescharacteristic, complemented
26#13063308—21no—
27#13063300C2211yescharacteristic
28#13063300C2211yescharacteristic
29#13063299—21no—
30#13063298—21no—
31#13063296C2211yescharacteristic, complemented
32#13063296C2211yescharacteristic, complemented
33#13063295—21no—
34#13063295—21no—
35C4×D172C2211yescharacteristic
36C4×C22⋊D43—21no—
37#13063283C2211yescharacteristic, complemented
38C4⋊C4×D43C2211yescharacteristic, complemented
39#13063258C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063247C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic, complemented
44#13063247C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49#13063245C2211yescharacteristic, complemented
50(C2×D43)⋊C8C2211yescharacteristic, complemented
51(C2×D43)⋊C8C2211yescharacteristic, complemented
52C2×D8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic, complemented
55#106×C43C2211yescharacteristic, complemented
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic, complemented
58#97×C43C2211yescharacteristic, complemented
59C23×D43—21no—
60C23×D43—21no—
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43—21no—
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—
73C2×D172—21no—
74C2×D172—21no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—44no—
78C2×D172D411yescharacteristic
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43C2311yescharacteristic
83C2×C4×D43C2311yescharacteristic
84D8×C43—22no—
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C42×C43C2311yescharacteristic
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94#10621882—41no—
95#10621882—41no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4D411yescharacteristic
100(C2×D43)⋊C4D411yescharacteristic
101C4⋊Dic43D411yescharacteristic
102C4⋊Dic43C2311yescharacteristic
103C4⋊Dic43C2311yescharacteristic
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
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#4112yes—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—42no—
131C2×C4×C43—81no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2411yescharacteristic
135C22⋊D43—42no—
136C22⋊D43—42no—
137C22⋊D43—42no—
138C22⋊D43—81no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—22no—
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—42no—
149D172—42no—
150D172—42no—
151D172—81no—
152C4×D43—21no—
153C4×D43—21no—
154C4×D43—21no—
155C4×D43—21no—
156C4×D43—81no—
157C8×C43—21no—
158C8×C43—21no—
159C43⋊C8—21no—
160C43⋊C8—21no—
161C22×C43—22no—
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—21no—
171C2×D43—21no—
172C2×D43—21no—
173C2×D43—41no—
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—42no—
194C2×C43—81no—
195C2×C43#54611yescharacteristic
196C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C43#57611yescharacteristic
198D43—22no—
199D43—41no—
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#442D4311yescharacteristic, complemented
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×D8C2×D4311yescharacteristic
224C2×M16—431no—
225C22×C8—431no—
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—861no—
240C4×D4C2×D4311yescharacteristic
241C4×D4C2×D4311yescharacteristic, complemented
242#117—431no—
243C2×C4⋊C4—431no—
244#107—431no—
245#106—431no—
246#106C2×D4311yescharacteristic, complemented
247C4⋊C8—431no—
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#102C2×D4311yescharacteristic
257#102C2×D4311yescharacteristic, complemented
258C22⋊C8—431no—
259C22⋊C8—431no—
260#97C2×D4311yescharacteristic, complemented
261C24—861no—
262C24—861no—
263C2×D4—431no—
264C2×D4—431no—
265C2×D4—431no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—861no—
270C2×D4—862no—
271C2×D4—862no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—1724no—
277C2×D4—1721no—
278C2×D4—1721no—
279C2×D4C22×D4311yescharacteristic
280C2×D4C22×D4311yescharacteristic
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—861no—
286D8—22no—
287D8—1721no—
288D8—1721no—
289M16—1721no—
290C2×C8—431no—
291C2×C8—431no—
292C2×C8—1721no—
293C2×C8C22×D4311yescharacteristic
294C2×C8C22×D4311yescharacteristic
295C4⋊C4—431no—
296C4⋊C4—431no—
297C4⋊C4—431no—
298C4⋊C4—861no—
299C4⋊C4—861no—
300C4⋊C4—861no—
301C4⋊C4C22×D4311yescharacteristic
302C4⋊C4C22×D4311yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—431no—
306C22⋊C4—431no—
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—862no—
330D4—861no—
331D4—861no—
332D4—861no—
333D4—861no—
334D4—3441no—
335D4—3441no—
336D4—1722no—
337D4—1722no—
338D4—1722no—
339D4—1722no—
340D4—1722no—
341D4—1722no—
342D4#1062189812yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4—431no—
348C2×C4—431no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—3441no—
356C2×C4D4×D4311yescharacteristic
357C2×C4D4×D4311yescharacteristic
358C2×C4C23×D4311yescharacteristic
359C8—21no—
360C8—21no—
361C8—861no—
362C8—861no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—432no—
370C22—861no—
371C22—861no—
372C22—861no—
373C22—861no—
374C22—861no—
375C22—3444no—
376C22—3444no—
377C22—1721no—
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—
392C4C2×#1062189811yescharacteristic
393C4#1306337111yescharacteristic
394C2—42no—
395C2—81no—
396C2—862no—
397C2—3441no—
398C2—3441no—
399C2—1721no—
400C2#1458354511yescharacteristic
401C2AGL(1,ℤ/8)×D4311yescharacteristic
402C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14583599C2semidirect
2. D4×D172C2semidirect
3. #14583264C2semidirect
4. #14583225C2semidirect
5. #14583219C2semidirect
6. #14583199C2semidirect
7. #14583151C2semidirect
8. #14583134C2semidirect
9. #14583094C2semidirect
10. #14583031C2semidirect
11. #14583031C2semidirect
12. #14582972C2semidirect
13. #14582902C2semidirect
14. #102×D43C2semidirect
15. C43×#442C2semidirect
19. C2×#10621882C22semidirect
20. C2×#10621882C22semidirect
21. C2×#10621872C22semidirect
22. C2×C8×D43C22semidirect
25. #13063317C22semidirect
31. #13063296C22semidirect
32. #13063296C22semidirect
37. #13063283C22semidirect
38. C4⋊C4×D43C22semidirect
39. #13063258C22semidirect
40. #13063256C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063247C22semidirect
43. #13063247C22semidirect
44. #13063247C22semidirect
45. #13063247C22semidirect
48. #13063245C22semidirect
49. #13063245C22semidirect
50. (C2×D43)⋊C8C22semidirect
51. (C2×D43)⋊C8C22semidirect
54. C4×D4×C43C22semidirect
55. #106×C43C22semidirect
57. #102×C43C22semidirect
58. #97×C43C22semidirect
213. #442D43semidirect
217. C43#3318semidirect
241. C4×D4C2×D43semidirect
246. #106C2×D43semidirect
257. #102C2×D43semidirect
260. #97C2×D43semidirect