Finite Group Databasebeta

← #19146618

Subgroups — #19146618

Order 5504.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583589C211yesmaximal, characteristic, complemented
2D4×D172C211yesmaximal, characteristic
3#14583264C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583200C211yesmaximal, characteristic, complemented
7#14583145C211yesmaximal, characteristic, complemented
8#14583128C211yesmaximal, characteristic, complemented
9#14583100C211yesmaximal, characteristic, complemented
10#14583052C211yesmaximal, characteristic, complemented
11#14583052C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14582905C211yesmaximal, characteristic, complemented
14C2×#13063247C211yesmaximal, characteristic, complemented
15C43×#435C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C2×D4×D43—21no—
19C2×#10621873C2211yescharacteristic
20C2×#10621873C2211yescharacteristic, complemented
21C2×#10621873C2211yescharacteristic, complemented
22#13063322C2211yescharacteristic
23#13063318—21no—
24#13063317C2211yescharacteristic, complemented
25#13063315—21no—
26#13063306—21no—
27#13063304C2211yescharacteristic, complemented
28#13063304C2211yescharacteristic, complemented
29#13063300—21no—
30#13063299C2211yescharacteristic
31#13063299C2211yescharacteristic
32#13063295—21no—
33#13063295—21no—
34C4×Dic86C2211yescharacteristic, complemented
35C4×D172C2211yescharacteristic
36#13063284C2211yescharacteristic, complemented
37#13063281—21no—
38C2×C4⋊Dic43C2211yescharacteristic, complemented
39#13063259C2211yescharacteristic, complemented
40#13063259C2211yescharacteristic, complemented
41#13063257C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
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—
66C22×Dic43—21no—
67D4×D43—44no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—22no—
73C2×D172—22no—
74C2×D172—41no—
75C2×D172—41no—
76C2×D172C2311yescharacteristic
77C2×D172C2311yescharacteristic
78C2×D172C2311yescharacteristic
79C2×C4×D43—21no—
80C2×Dic86C2311yescharacteristic
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43C2311yescharacteristic
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C2×C8×C43C2311yescharacteristic
87C4⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C22⋊C4×C43D411yescharacteristic
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106Dic43⋊C4—21no—
107C4×Dic43—21no—
108C4×Dic43—21no—
109#10621873—22no—
110#10621873—41no—
111#10621873—41no—
112C23×C43C2×D411yescharacteristic
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—42no—
118C22×D43—42no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—81no—
122C22×D43—81no—
123D4×C43—22no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2411yescharacteristic
133C22⋊D43—42no—
134C22⋊D43—42no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—42no—
141D172—21no—
142D172—21no—
143D172—21no—
144D172—21no—
145D172—21no—
146D172—42no—
147D172—42no—
148D172—42no—
149D172—81no—
150D172#4112yes—
151C4×D43—42no—
152Dic86—21no—
153Dic86—21no—
154C8×C43—21no—
155C8×C43—21no—
156C8×C43—21no—
157C8×C43—21no—
158C22×C43—21no—
159C22×C43—21no—
160C22×C43—21no—
161C22×C43—21no—
162C22×C43—21no—
163C22×C43AGL(1,ℤ/8)12yes—
164C22×C43C22×D411yescharacteristic
165C2×D43—22no—
166C2×D43—41no—
167C2×D43—41no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—84no—
175C2×D43—84no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43C2×#4111yescharacteristic
181C4×C43H(5,𝔽2)11yescharacteristic
182Dic43—41no—
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187#3310—431nomaximal, Sylow
188C2×C43—22no—
189C2×C43—41no—
190C2×C43#54611yescharacteristic
191C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C43#57711yescharacteristic
193D43—42no—
194D43—81no—
195D43—81no—
196#552—431no—
197D42—431no—
198#490—431no—
199#482—431no—
200#480—431no—
201#478—431no—
202#468—431no—
203#465—431no—
204#460—431no—
205#450—431no—
206#450—431no—
207#440—431no—
208#435D4311yescharacteristic, complemented
209#418—431no—
210C2×#102—431no—
211C43#331011yescharacteristic, complemented, Sylow
212C22×D4—431no—
213C22×D4—431no—
214C22×D4—861no—
215C2×SD16—431no—
216C2×SD16—431no—
217C2×SD16—431no—
218C2×M16C2×D4311yescharacteristic, complemented
219C22×C8C2×D4311yescharacteristic, complemented
220#127—431no—
221#126—861no—
222#125—431no—
223#125—861no—
224#123—861no—
225C22⋊Q8—431no—
226C22⋊Q8—431no—
227#121—431no—
228#121—431no—
229#121—861no—
230#120—861no—
231#120—861no—
232C4×Q8—431no—
233C4×D4—431no—
234C4×D4C2×D4311yescharacteristic
235#117—431no—
236#117—861no—
237C2×C4⋊C4—431no—
238#107—431no—
239#107—431no—
240#106—431no—
241C4⋊C8C2×D4311yescharacteristic, complemented
242#103—431no—
243#102—431no—
244#102—431no—
245#102—431no—
246#102—431no—
247#102—431no—
248#102—431no—
249#102—431no—
250#102—431no—
251#102—431no—
252C22⋊C8C2×D4311yescharacteristic, complemented
253C22⋊C8C2×D4311yescharacteristic, complemented
254#97C2×D4311yescharacteristic, complemented
255C24—861no—
256C24—861no—
257C2×Q8—431no—
258C2×D4—431no—
259C2×D4—431no—
260C2×D4—431no—
261C2×D4—862no—
262C2×D4—862no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—861no—
266C2×D4—861no—
267C2×D4—861no—
268C2×D4—861no—
269C2×D4—1721no—
270C2×D4—1721no—
271C2×D4—1724no—
272C2×D4D17211yescharacteristic
273C22×C4—861no—
274C22×C4—861no—
275C22×C4C22×D4311yescharacteristic
276C22×C4C22×D4311yescharacteristic
277SD16—862no—
278SD16—1721no—
279SD16—1721no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D4311yescharacteristic
283C2×C8C22×D4311yescharacteristic
284C2×C8C22×D4311yescharacteristic
285C2×C8C22×D4311yescharacteristic
286C4⋊C4—431no—
287C4⋊C4—431no—
288C4⋊C4—431no—
289C4⋊C4—431no—
290C4⋊C4—861no—
291C4⋊C4—861no—
292C4⋊C4—861no—
293C4⋊C4—861no—
294C4⋊C4—861no—
295C4⋊C4—861no—
296C4⋊C4D17211yescharacteristic
297C22⋊C4—861no—
298C22⋊C4—861no—
299C22⋊C4—861no—
300C22⋊C4—861no—
301C22⋊C4—861no—
302C22⋊C4—861no—
303C22⋊C4D17211yescharacteristic
304C22⋊C4D17211yescharacteristic
305C42—861no—
306C42—861no—
307C42C22×D4311yescharacteristic
308C23—861no—
309C23—861no—
310C23—861no—
311C23—3441no—
312C23—3441no—
313C23—1722no—
314C23—1722no—
315C23—1722no—
316C23—1722no—
317C23C2×D17211yescharacteristic
318C23C2×D17211yescharacteristic
319Q8—861no—
320Q8—861no—
321D4—22no—
322D4—432no—
323D4—861no—
324D4—861no—
325D4—861no—
326D4—861no—
327D4—861no—
328D4—3441no—
329D4—1722no—
330D4—1722no—
331D4—1722no—
332D4—1722no—
333D4—1722no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—1722no—
344C2×C4—1722no—
345C2×C4C2×D17211yescharacteristic
346C2×C4C2×D17211yescharacteristic
347C2×C4C2×D17211yescharacteristic
348C2×C4C2×D17211yescharacteristic
349C2×C4C23×D4311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—862no—
360C22—3444no—
361C22—3444no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22#1306335312yes—
371C22C22×D17211yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—1721no—
377C4—1721no—
378C4—1721no—
379C4—1721no—
380C4—1721no—
381C4#41×D4311yescharacteristic
382C4#1306337011yescharacteristic
383C2—22no—
384C2—41no—
385C2—3441no—
386C2—3441no—
387C2—1722no—
388C2#1458354411yescharacteristic
389C2C2×#1306335311yescharacteristic
390C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#435C2
socleC22×C43C22×D4
hypercenter#435D43
hypocenterC43#3310
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. #14583589C2semidirect
3. #14583264C2semidirect
4. #14583224C2semidirect
5. #14583213C2semidirect
6. #14583200C2semidirect
7. #14583145C2semidirect
8. #14583128C2semidirect
9. #14583100C2semidirect
10. #14583052C2semidirect
11. #14583052C2semidirect
12. #14583001C2semidirect
13. #14582905C2semidirect
14. C2×#13063247C2semidirect
15. C43×#435C2semidirect
20. C2×#10621873C22semidirect
21. C2×#10621873C22semidirect
24. #13063317C22semidirect
27. #13063304C22semidirect
28. #13063304C22semidirect
34. C4×Dic86C22semidirect
36. #13063284C22semidirect
38. C2×C4⋊Dic43C22semidirect
39. #13063259C22semidirect
40. #13063259C22semidirect
41. #13063257C22semidirect
42. #13063250C22semidirect
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
208. #435D43semidirect
211. C43#3310semidirect
218. C2×M16C2×D43semidirect
219. C22×C8C2×D43semidirect
241. C4⋊C8C2×D43semidirect
252. C22⋊C8C2×D43semidirect
253. C22⋊C8C2×D43semidirect
254. #97C2×D43semidirect