Finite Group Databasebeta

← #19145641

Subgroups — #19145641

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583502C211yesmaximal, characteristic, complemented
2#14583466C211yesmaximal, characteristic, complemented
3#14583287C211yesmaximal, characteristic, complemented
4#14583274C211yesmaximal, characteristic, complemented
5#14583262C211yesmaximal, characteristic, complemented
6#14583252C211yesmaximal, characteristic, complemented
7#14583113C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583093C211yesmaximal, characteristic, complemented
10#14583092C211yesmaximal, characteristic, complemented
11#14583046C211yesmaximal, characteristic, complemented
12#14583042C211yesmaximal, characteristic, complemented
13#14583033C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#447C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621873C2211yescharacteristic, complemented
18C2×#10621883C2211yescharacteristic, complemented
19C2×D344C2211yescharacteristic, complemented
20C2×#10621882C2211yescharacteristic
21C2×#10621882C2211yescharacteristic
22C2×#10621882C2211yescharacteristic, complemented
23#13063321C2211yescharacteristic
24#13063321C2211yescharacteristic
25#13063321C2211yescharacteristic, complemented
26#13063316C2211yescharacteristic, complemented
27#13063312C2211yescharacteristic
28#13063312C2211yescharacteristic
29#13063309—21no—
30#13063307—21no—
31#13063299C2211yescharacteristic
32#13063297—21no—
33#13063296—21no—
34#13063296—21no—
35#13063296—21no—
36#13063294—21no—
37#13063294—21no—
38D4×Dic43C2211yescharacteristic, complemented
39#13063287C2211yescharacteristic, complemented
40#13063284C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic, complemented
42Dic43⋊C8C2211yescharacteristic, complemented
43#13063250C2211yescharacteristic, complemented
44#13063248C2211yescharacteristic, complemented
45#13063247C2211yescharacteristic, complemented
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic, complemented
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic, complemented
51C8×Dic43C2211yescharacteristic, complemented
52C22×D4×C43C2211yescharacteristic
53C2×D8×C43C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C24×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C2×D4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43—21no—
72C2×C22⋊D43—21no—
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C2×C22⋊D43—21no—
76C22×Dic43—21no—
77#10621898—41no—
78#10621898—41no—
79C2×D172C2311yescharacteristic
80C2×D172C2311yescharacteristic
81C2×C4×D43—21no—
82C2×C4×D43—21no—
83C2×Dic86C2311yescharacteristic
84D8×C43—41no—
85D8×C43—41no—
86C2×C8×C43C2311yescharacteristic
87C2×C8×C43C2311yescharacteristic
88C4⋊C4×C43C2311yescharacteristic
89C22⋊C4×C43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43—21no—
95C22⋊Dic43D411yescharacteristic
96C22⋊Dic43D411yescharacteristic
97#10621883—41no—
98#10621882—41no—
99#10621882—41no—
100#10621882—41no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103C4⋊Dic43—21no—
104C4⋊Dic43D411yescharacteristic
105C4⋊Dic43D411yescharacteristic
106C4⋊Dic43C2311yescharacteristic
107Dic43⋊C4—21no—
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112D344—41no—
113#10621873—41no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—42no—
118C23×C43—81no—
119C23×C43—81no—
120C23×C43C2×D411yescharacteristic
121C22×D43—21no—
122C22×D43—21no—
123D4×C43—21no—
124D4×C43—21no—
125D4×C43—21no—
126D4×C43—21no—
127D4×C43—21no—
128D4×C43—21no—
129D4×C43—42no—
130D4×C43—81no—
131C2×C4×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2411yescharacteristic
136C22⋊D43—42no—
137C22⋊D43—81no—
138C22⋊D43—81no—
139C22⋊D43—81no—
140C22⋊D43—81no—
141C22⋊D43—81no—
142C22⋊D43—81no—
143C22⋊D43—81no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—81no—
147C2×Dic43C2×D411yescharacteristic
148C2×Dic43C2×D411yescharacteristic
149C2×Dic43C2×D411yescharacteristic
150C2×Dic43C2×D411yescharacteristic
151D172—21no—
152D172—21no—
153D172—21no—
154D172—21no—
155C4×D43—42no—
156C4×D43—81no—
157Dic86—21no—
158Dic86—21no—
159C8×C43—21no—
160C8×C43—21no—
161C43⋊C8—21no—
162C43⋊C8—21no—
163C22×C43—21no—
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—84no—
176C22×C43C22×D411yescharacteristic
177C2×D43—41no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C4×C43—21no—
184C4×C43—41no—
185C4×C43H(5,𝔽2)11yescharacteristic
186C4×C43H(5,𝔽2)11yescharacteristic
187Dic43—21no—
188Dic43—21no—
189Dic43—21no—
190Dic43—21no—
191Dic43—41no—
192Dic43—41no—
193#3220—431nomaximal, Sylow
194C2×C43—41no—
195C2×C43—81no—
196C2×C43—81no—
197C2×C43—81no—
198C2×C43#53511yescharacteristic
199C2×C43#57611yescharacteristic
200C2×C43#57611yescharacteristic
201D43—81no—
202D43—81no—
203#540—431no—
204#535—431no—
205#496—431no—
206#493—431no—
207#490—431no—
208#488—431no—
209#463—431no—
210#463—431no—
211#459—431no—
212#459—431no—
213#449—431no—
214#449—431no—
215#447—431no—
216#447D4311yescharacteristic, complemented
217#433—431no—
218C43#322011yescharacteristic, complemented, Sylow
219C2×#41—431no—
220C22×D4C2×D4311yescharacteristic
221C2×SD16—431no—
222C2×SD16—431no—
223C2×D8—431no—
224C2×D8—431no—
225C2×D8—431no—
226C2×D8—431no—
227C2×D8C2×D4311yescharacteristic
228C2×D8C2×D4311yescharacteristic
229#127—431no—
230#127—431no—
231#127—431no—
232#125—431no—
233#124—431no—
234#124—431no—
235#123—861no—
236#123—861no—
237#121—431no—
238#121—861no—
239#121—861no—
240#121—861no—
241#121—861no—
242#121C2×D4311yescharacteristic
243#120—861no—
244#120—861no—
245C4×D4—431no—
246C4×D4—431no—
247#117—431no—
248C4⋊C8—431no—
249C4⋊C8—431no—
250#103—431no—
251#103—431no—
252#102—431no—
253#102—431no—
254#102—431no—
255#102—431no—
256#102C2×D4311yescharacteristic
257#102C2×D4311yescharacteristic
258C22⋊C8—431no—
259C22⋊C8C2×D4311yescharacteristic
260#97—431no—
261C4×C8—431no—
262C24—21no—
263#41—1721no—
264#41—1721no—
265C2×Q8—431no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—431no—
271C2×D4—431no—
272C2×D4—861no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4—861no—
279C2×D4—861no—
280C2×D4C22×D4311yescharacteristic
281C2×D4C22×D4311yescharacteristic
282C2×D4C22×D4311yescharacteristic
283C22×C4—861no—
284C22×C4—861no—
285C22×C4—861no—
286C22×C4C22×D4311yescharacteristic
287SD16—1721no—
288SD16—1721no—
289D8—41no—
290D8—41no—
291D8—1721no—
292D8—1721no—
293D8—1721no—
294D8—1721no—
295C2×C8—431no—
296C2×C8—431no—
297C2×C8C22×D4311yescharacteristic
298C2×C8C22×D4311yescharacteristic
299C4⋊C4—431no—
300C4⋊C4—431no—
301C4⋊C4—431no—
302C4⋊C4—861no—
303C4⋊C4—861no—
304C4⋊C4C22×D4311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—431no—
307C22⋊C4—431no—
308C22⋊C4—861no—
309C22⋊C4—861no—
310C22⋊C4—861no—
311C22⋊C4—861no—
312C22⋊C4—861no—
313C22⋊C4—861no—
314C22⋊C4—861no—
315C42—431no—
316C42—431no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—861no—
324C23—861no—
325C23D4×D4311yescharacteristic
326Q8—861no—
327Q8—861no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—861no—
337D4—861no—
338D4—861no—
339D4—861no—
340D4—3441no—
341D4—3441no—
342D4—3441no—
343D4—3441no—
344D4—3441no—
345D4—3441no—
346D4—3441no—
347D4—1722no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—431no—
352C2×C4—431no—
353C2×C4—431no—
354C2×C4—431no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—3441no—
358C2×C4—3441no—
359C2×C4—1722no—
360C2×C4D4×D4311yescharacteristic
361C2×C4C23×D4311yescharacteristic
362C8—21no—
363C8—21no—
364C8—861no—
365C8—861no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—84no—
379C22—1721no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22—1721no—
385C22C2×D4×D4311yescharacteristic
386C4—21no—
387C4—41no—
388C4—861no—
389C4—861no—
390C4—861no—
391C4—861no—
392C4—1721no—
393C4—1721no—
394C4#1306337011yescharacteristic
395C4#1306337011yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—81no—
400C2—3441no—
401C2—3441no—
402C2#1458346411yescharacteristic
403C2#1458370011yescharacteristic
404C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#447C2
socleC22×C43C22×D4
hypercenter#447D43
hypocenterC43#3220
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #14583502C2semidirect
2. #14583466C2semidirect
3. #14583287C2semidirect
4. #14583274C2semidirect
5. #14583262C2semidirect
6. #14583252C2semidirect
7. #14583113C2semidirect
8. #14583112C2semidirect
9. #14583093C2semidirect
10. #14583092C2semidirect
11. #14583046C2semidirect
12. #14583042C2semidirect
13. #14583033C2semidirect
14. #14582957C2semidirect
15. C43×#447C2semidirect
17. C2×#10621873C22semidirect
18. C2×#10621883C22semidirect
19. C2×D344C22semidirect
22. C2×#10621882C22semidirect
25. #13063321C22semidirect
26. #13063316C22semidirect
38. D4×Dic43C22semidirect
39. #13063287C22semidirect
41. Dic43⋊C8C22semidirect
42. Dic43⋊C8C22semidirect
43. #13063250C22semidirect
44. #13063248C22semidirect
45. #13063247C22semidirect
48. #13063245C22semidirect
50. #13063235C22semidirect
51. C8×Dic43C22semidirect
216. #447D43semidirect
218. C43#3220semidirect