Finite Group Databasebeta

← #19145580

Subgroups — #19145580

Order 5504.

444 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583446C211yesmaximal, characteristic, complemented
2#124×D43C211yesmaximal, characteristic, complemented
3#14583287C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic, complemented
5#14583260C211yesmaximal, characteristic, complemented
6#14583257C211yesmaximal, characteristic, complemented
7#14583115C211yesmaximal, characteristic, complemented
8#14583114C211yesmaximal, characteristic, complemented
9#14583111C211yesmaximal, characteristic, complemented
10#14583039C211yesmaximal, characteristic, complemented
11#14583036C211yesmaximal, characteristic, complemented
12#14583034C211yesmaximal, characteristic, complemented
13#14583031C211yesmaximal, characteristic, complemented
14#14582955C211yesmaximal, characteristic, complemented
15C43×#463C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×Q8×D43C2211yescharacteristic
18C2×D4×D43C2211yescharacteristic
19C2×#10621873C2211yescharacteristic, complemented
20C2×#10621883C2211yescharacteristic, complemented
21C2×#10621884C2211yescharacteristic, complemented
22C2×D344C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063324C2211yescharacteristic, complemented
26#13063321C2211yescharacteristic, complemented
27#13063314C2211yescharacteristic
28#13063313C2211yescharacteristic
29#13063312C2211yescharacteristic
30#13063311—21no—
31#13063311—21no—
32#13063311—21no—
33#13063300C2211yescharacteristic
34#13063298—21no—
35#13063296C2211yescharacteristic
36C4×D172C2211yescharacteristic, complemented
37C4×C22⋊D43—21no—
38C22⋊C4×D43—21no—
39C22⋊C4×D43—21no—
40C42×D43C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic, complemented
42#13063250C2211yescharacteristic, complemented
43#13063249C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51#13063235C2211yescharacteristic, complemented
52C2×SD16×C43C2211yescharacteristic, complemented
53C2×D8×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#103×C43C2211yescharacteristic, complemented
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43—21no—
68Q8×D43—41no—
69Q8×D43—41no—
70D4×D43—41no—
71D4×D43—41no—
72#10621898—44no—
73C2×D172—21no—
74C2×D172C2311yescharacteristic
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43D411yescharacteristic
79C2×C4×D43D411yescharacteristic
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—21no—
82C2×Dic86—21no—
83C2×Dic86C2311yescharacteristic
84SD16×C43—41no—
85D8×C43—41no—
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊C4×C43—21no—
91C22⋊C4×C43—21no—
92C42×C43C2311yescharacteristic
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43—21no—
96#10621884—41no—
97#10621883—41no—
98#10621882—41no—
99#10621882—41no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104(C2×D43)⋊C4—21no—
105(C2×D43)⋊C4—21no—
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108C4×Dic43D411yescharacteristic
109C4×Dic43D411yescharacteristic
110C4×Dic43C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112C2×C43⋊C8C2311yescharacteristic
113D344—41no—
114#10621873—41no—
115C23×C43—21no—
116C23×C43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—42no—
120C22×D43—42no—
121C22×D43—42no—
122C22×D43C2×D411yescharacteristic
123Q8×C43—21no—
124Q8×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43—42no—
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
143C2×Dic43C2×D411yescharacteristic
144D172—21no—
145D172—21no—
146D172—21no—
147D172—21no—
148D172—42no—
149C4×D43—22no—
150C4×D43—21no—
151C4×D43—21no—
152C4×D43—41no—
153C4×D43—42no—
154C4×D43—42no—
155Dic86—21no—
156Dic86—21no—
157Dic86—42no—
158Dic86—42no—
159C8×C43—21no—
160C8×C43—21no—
161C43⋊C8—21no—
162C43⋊C8—21no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43C22×D411yescharacteristic
170C2×D43—21no—
171C2×D43—21no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43—41no—
178C2×D43—84no—
179C2×D43AGL(1,ℤ/8)12yes—
180C4×C43—21no—
181C4×C43—21no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43H(5,𝔽2)11yescharacteristic
185C4×C43H(5,𝔽2)11yescharacteristic
186Dic43—21no—
187Dic43—21no—
188Dic43—21no—
189Dic43—41no—
190Dic43—41no—
191#3213—431nomaximal, Sylow
192C2×C43—81no—
193C2×C43—81no—
194C2×C43#53511yescharacteristic
195C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C43#57511yescharacteristic
197D43—22no—
198D43—81no—
199D43—81no—
200#532—431no—
201C2×#124—431no—
202#496—431no—
203#496—431no—
204#489—431no—
205#489—431no—
206#463—431no—
207#463—431no—
208#463—431no—
209#463D4311yescharacteristic, complemented
210#448—431no—
211#448—431no—
212#447—431no—
213#447—431no—
214#432—431no—
215C43#321311yescharacteristic, complemented, Sylow
216C2×#41—861no—
217C22×Q8—431no—
218C22×D4—431no—
219C2×SD16—431no—
220C2×SD16—431no—
221C2×SD16—431no—
222C2×SD16C2×D4311yescharacteristic, complemented
223C2×D8—431no—
224C2×D8—431no—
225C2×D8—431no—
226C2×D8C2×D4311yescharacteristic
227C4⋊Q8—431no—
228#127—431no—
229#124—431no—
230#124—431no—
231#124—431no—
232#124—861no—
233#124—861no—
234#124—861no—
235#124C2×D4311yescharacteristic
236#121—431no—
237#121—431no—
238#121—861no—
239C4×D4—431no—
240C4×D4—861no—
241C4×D4C2×D4311yescharacteristic, complemented
242C2×C22⋊C4—861no—
243C2×C22⋊C4—861no—
244C2×C42—431no—
245C4⋊C8—431no—
246C4⋊C8C2×D4311yescharacteristic, complemented
247#103—431no—
248#103—431no—
249#103—431no—
250#103C2×D4311yescharacteristic, complemented
251#102—431no—
252#102—431no—
253#102—431no—
254#102C2×D4311yescharacteristic
255C22⋊C8—431no—
256C22⋊C8—431no—
257#97—431no—
258#97—431no—
259C24—861no—
260#41—1724no—
261C2×Q8—431no—
262C2×Q8—861no—
263C2×Q8—861no—
264C2×Q8—1721no—
265C2×Q8—1721no—
266C2×Q8C22×D4311yescharacteristic
267C2×D4—431no—
268C2×D4—431no—
269C2×D4—861no—
270C2×D4—861no—
271C2×D4—861no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—1721no—
275C2×D4—1721no—
276C2×D4C22×D4311yescharacteristic
277C2×D4C22×D4311yescharacteristic
278C22×C4—21no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—861no—
283C22×C4—861no—
284SD16—41no—
285SD16—1721no—
286SD16—1721no—
287SD16—1721no—
288D8—41no—
289D8—1721no—
290D8—1721no—
291D8—1721no—
292C2×C8—431no—
293C2×C8—431no—
294C2×C8C22×D4311yescharacteristic
295C2×C8C22×D4311yescharacteristic
296C4⋊C4—431no—
297C4⋊C4—861no—
298C4⋊C4C22×D4311yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—861no—
303C22⋊C4—861no—
304C22⋊C4—861no—
305C22⋊C4—861no—
306C22⋊C4—861no—
307C22⋊C4—861no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C42—431no—
312C42—431no—
313C42—431no—
314C42C22×D4311yescharacteristic
315C23—21no—
316C23—21no—
317C23—431no—
318C23—861no—
319C23—861no—
320C23—1722no—
321C23—1722no—
322C23—1722no—
323Q8—21no—
324Q8—21no—
325Q8—861no—
326Q8—861no—
327Q8—1722no—
328Q8—1722no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—861no—
334D4—861no—
335D4—861no—
336D4—861no—
337D4—1722no—
338D4—1722no—
339D4—1722no—
340D4—1722no—
341D4—1722no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—431no—
346C2×C4—431no—
347C2×C4—431no—
348C2×C4—862no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—1721no—
354C2×C4—1722no—
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—3444no—
373C22—1721no—
374C22—1721no—
375C22—1721no—
376C22—1721no—
377C22—1721no—
378C22—1721no—
379C22C2×D4×D4311yescharacteristic
380C4—21no—
381C4—21no—
382C4—41no—
383C4—41no—
384C4—861no—
385C4—861no—
386C4—861no—
387C4—1721no—
388C4—1721no—
389C4#1306337011yescharacteristic
390C4#1306337111yescharacteristic
391C2—81no—
392C2—81no—
393C2—862no—
394C2—3441no—
395C2—3441no—
396C2#1458346511yescharacteristic
397C2AGL(1,ℤ/8)×D4311yescharacteristic
398C2#1458369611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#463C2
socleC22×C43C22×D4
hypercenter#463D43
hypocenterC43#3213
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #14583446C2semidirect
2. #124×D43C2semidirect
3. #14583287C2semidirect
4. #14583285C2semidirect
5. #14583260C2semidirect
6. #14583257C2semidirect
7. #14583115C2semidirect
8. #14583114C2semidirect
9. #14583111C2semidirect
10. #14583039C2semidirect
11. #14583036C2semidirect
12. #14583034C2semidirect
13. #14583031C2semidirect
14. #14582955C2semidirect
15. C43×#463C2semidirect
19. C2×#10621873C22semidirect
20. C2×#10621883C22semidirect
21. C2×#10621884C22semidirect
25. #13063324C22semidirect
26. #13063321C22semidirect
36. C4×D172C22semidirect
41. C4⋊(C43⋊C8)C22semidirect
42. #13063250C22semidirect
43. #13063249C22semidirect
44. #13063248C22semidirect
50. #13063235C22semidirect
51. #13063235C22semidirect
52. C2×SD16×C43C22semidirect
55. C4×D4×C43C22semidirect
56. C4⋊C8×C43C22semidirect
57. #103×C43C22semidirect
209. #463D43semidirect
215. C43#3213semidirect
222. C2×SD16C2×D43semidirect
241. C4×D4C2×D43semidirect
246. C4⋊C8C2×D43semidirect
250. #103C2×D43semidirect